TSTP Solution File: SYO040^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO040^1 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue Mar 29 00:50:27 EDT 2022
% Result : Timeout 286.54s 286.92s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYO040^1 : TPTP v7.5.0. Released v4.0.0.
% 0.11/0.11 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.32 % Computer : n013.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % RAMPerCPU : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % DateTime : Fri Mar 11 06:45:07 EST 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.11/0.34 Python 2.7.5
% 6.87/7.10 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 6.87/7.10 FOF formula (<kernel.Constant object at 0x1999710>, <kernel.DependentProduct object at 0x2ae9e9adf560>) of role type named f
% 6.87/7.10 Using role type
% 6.87/7.10 Declaring f:(Prop->Prop)
% 6.87/7.10 FOF formula (<kernel.Constant object at 0x19994d0>, <kernel.DependentProduct object at 0x2ae9e9adf638>) of role type named h
% 6.87/7.10 Using role type
% 6.87/7.10 Declaring h:(Prop->fofType)
% 6.87/7.10 FOF formula (<kernel.Constant object at 0x199dd40>, <kernel.Sort object at 0x2ae9e9ad8638>) of role type named x
% 6.87/7.10 Using role type
% 6.87/7.10 Declaring x:Prop
% 6.87/7.10 FOF formula (not (((eq fofType) (h (f (f (f x))))) (h (f x)))) of role axiom named 2
% 6.87/7.10 A new axiom: (not (((eq fofType) (h (f (f (f x))))) (h (f x))))
% 6.87/7.10 Parameter fofType_DUMMY:fofType.
% 6.87/7.10 We need to prove []
% 6.87/7.10 Parameter f:(Prop->Prop).
% 6.87/7.10 Parameter fofType:Type.
% 6.87/7.10 Parameter h:(Prop->fofType).
% 6.87/7.10 Parameter x:Prop.
% 6.87/7.10 Axiom 2:(not (((eq fofType) (h (f (f (f x))))) (h (f x)))).
% 6.87/7.10 There are no conjectures!
% 6.87/7.10 Adding conjecture False, to look for Unsatisfiability
% 6.87/7.10 Trying to prove False
% 6.87/7.10 Found eq_ref000:=(eq_ref00 P):((P (h (f (f (f x)))))->(P (h (f (f (f x))))))
% 6.87/7.10 Found (eq_ref00 P) as proof of (P0 (h (f (f (f x)))))
% 6.87/7.10 Found ((eq_ref0 (h (f (f (f x))))) P) as proof of (P0 (h (f (f (f x)))))
% 6.87/7.10 Found (((eq_ref fofType) (h (f (f (f x))))) P) as proof of (P0 (h (f (f (f x)))))
% 6.87/7.10 Found (((eq_ref fofType) (h (f (f (f x))))) P) as proof of (P0 (h (f (f (f x)))))
% 6.87/7.10 Found eq_ref000:=(eq_ref00 P):((P (h (f (f (f x)))))->(P (h (f (f (f x))))))
% 6.87/7.10 Found (eq_ref00 P) as proof of (P0 (h (f (f (f x)))))
% 6.87/7.10 Found ((eq_ref0 (h (f (f (f x))))) P) as proof of (P0 (h (f (f (f x)))))
% 6.87/7.10 Found (((eq_ref fofType) (h (f (f (f x))))) P) as proof of (P0 (h (f (f (f x)))))
% 6.87/7.10 Found (((eq_ref fofType) (h (f (f (f x))))) P) as proof of (P0 (h (f (f (f x)))))
% 6.87/7.10 Found eq_ref000:=(eq_ref00 P):((P (h (f (f (f x)))))->(P (h (f (f (f x))))))
% 6.87/7.10 Found (eq_ref00 P) as proof of (P0 (h (f (f (f x)))))
% 6.87/7.10 Found ((eq_ref0 (h (f (f (f x))))) P) as proof of (P0 (h (f (f (f x)))))
% 6.87/7.10 Found (((eq_ref fofType) (h (f (f (f x))))) P) as proof of (P0 (h (f (f (f x)))))
% 6.87/7.10 Found (((eq_ref fofType) (h (f (f (f x))))) P) as proof of (P0 (h (f (f (f x)))))
% 6.87/7.10 Found eq_ref00:=(eq_ref0 (h (f (f (f x))))):(((eq fofType) (h (f (f (f x))))) (h (f (f (f x)))))
% 6.87/7.10 Found (eq_ref0 (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 6.87/7.10 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 6.87/7.10 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 6.87/7.10 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 6.87/7.10 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 6.87/7.10 Found (eq_ref0 b) as proof of (((eq fofType) b) (h (f x)))
% 6.87/7.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f x)))
% 6.87/7.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f x)))
% 6.87/7.10 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f x)))
% 6.87/7.10 Found eq_ref000:=(eq_ref00 P):((P (h (f x)))->(P (h (f x))))
% 6.87/7.10 Found (eq_ref00 P) as proof of (P0 (h (f x)))
% 6.87/7.10 Found ((eq_ref0 (h (f x))) P) as proof of (P0 (h (f x)))
% 6.87/7.10 Found (((eq_ref fofType) (h (f x))) P) as proof of (P0 (h (f x)))
% 6.87/7.10 Found (((eq_ref fofType) (h (f x))) P) as proof of (P0 (h (f x)))
% 6.87/7.10 Found eq_ref000:=(eq_ref00 P):((P (h (f x)))->(P (h (f x))))
% 6.87/7.10 Found (eq_ref00 P) as proof of (P0 (h (f x)))
% 6.87/7.10 Found ((eq_ref0 (h (f x))) P) as proof of (P0 (h (f x)))
% 6.87/7.10 Found (((eq_ref fofType) (h (f x))) P) as proof of (P0 (h (f x)))
% 6.87/7.10 Found (((eq_ref fofType) (h (f x))) P) as proof of (P0 (h (f x)))
% 6.87/7.10 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 6.87/7.10 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 6.87/7.10 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 6.87/7.10 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 6.87/7.10 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 6.87/7.10 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 6.87/7.10 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 6.87/7.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 6.87/7.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 21.65/21.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 21.65/21.84 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 21.65/21.84 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 21.65/21.84 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 21.65/21.84 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 21.65/21.84 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 21.65/21.84 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 21.65/21.84 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 21.65/21.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 21.65/21.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 21.65/21.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 21.65/21.84 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 21.65/21.84 Found (eq_ref0 b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 21.65/21.84 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 21.65/21.84 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 21.65/21.84 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 21.65/21.84 Found eq_ref00:=(eq_ref0 (h (f x))):(((eq fofType) (h (f x))) (h (f x)))
% 21.65/21.84 Found (eq_ref0 (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 21.65/21.84 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 21.65/21.84 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 21.65/21.84 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 21.65/21.84 Found eq_ref000:=(eq_ref00 P):((P (f (f (f x))))->(P (f (f (f x)))))
% 21.65/21.84 Found (eq_ref00 P) as proof of (P0 (P (f (f (f x)))))
% 21.65/21.84 Found ((eq_ref0 (f (f (f x)))) P) as proof of (P0 (P (f (f (f x)))))
% 21.65/21.84 Found (((eq_ref Prop) (f (f (f x)))) P) as proof of (P0 (P (f (f (f x)))))
% 21.65/21.84 Found (((eq_ref Prop) (f (f (f x)))) P) as proof of (P0 (P (f (f (f x)))))
% 21.65/21.84 Found eq_ref000:=(eq_ref00 P):((P (f (f (f x))))->(P (f (f (f x)))))
% 21.65/21.84 Found (eq_ref00 P) as proof of (P0 (P (f (f (f x)))))
% 21.65/21.84 Found ((eq_ref0 (f (f (f x)))) P) as proof of (P0 (P (f (f (f x)))))
% 21.65/21.84 Found (((eq_ref Prop) (f (f (f x)))) P) as proof of (P0 (P (f (f (f x)))))
% 21.65/21.84 Found (((eq_ref Prop) (f (f (f x)))) P) as proof of (P0 (P (f (f (f x)))))
% 21.65/21.84 Found eq_ref000:=(eq_ref00 P):((P (f (f (f x))))->(P (f (f (f x)))))
% 21.65/21.84 Found (eq_ref00 P) as proof of (P0 (P (f (f (f x)))))
% 21.65/21.84 Found ((eq_ref0 (f (f (f x)))) P) as proof of (P0 (P (f (f (f x)))))
% 21.65/21.84 Found (((eq_ref Prop) (f (f (f x)))) P) as proof of (P0 (P (f (f (f x)))))
% 21.65/21.84 Found (((eq_ref Prop) (f (f (f x)))) P) as proof of (P0 (P (f (f (f x)))))
% 21.65/21.84 Found eq_ref000:=(eq_ref00 P):((P (f (f (f x))))->(P (f (f (f x)))))
% 21.65/21.84 Found (eq_ref00 P) as proof of (P0 (P (f (f (f x)))))
% 21.65/21.84 Found ((eq_ref0 (f (f (f x)))) P) as proof of (P0 (P (f (f (f x)))))
% 21.65/21.84 Found (((eq_ref Prop) (f (f (f x)))) P) as proof of (P0 (P (f (f (f x)))))
% 21.65/21.84 Found (((eq_ref Prop) (f (f (f x)))) P) as proof of (P0 (P (f (f (f x)))))
% 21.65/21.84 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 21.65/21.84 Found (eq_ref00 P) as proof of (P0 (f x))
% 21.65/21.84 Found ((eq_ref0 (f x)) P) as proof of (P0 (f x))
% 21.65/21.84 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 21.65/21.84 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 21.65/21.84 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 21.65/21.84 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 21.65/21.84 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 21.65/21.84 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 21.65/21.84 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 21.65/21.84 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 21.65/21.84 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 21.65/21.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 21.65/21.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 21.65/21.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 21.65/21.84 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 21.65/21.84 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 21.65/21.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 21.65/21.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 21.65/21.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 21.65/21.84 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 21.65/21.84 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 29.40/29.61 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 29.40/29.61 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 29.40/29.61 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 29.40/29.61 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 29.40/29.61 Found (eq_ref00 P) as proof of (P0 (f x))
% 29.40/29.61 Found ((eq_ref0 (f x)) P) as proof of (P0 (f x))
% 29.40/29.61 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 29.40/29.61 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 29.40/29.61 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 29.40/29.61 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 29.40/29.61 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 29.40/29.61 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 29.40/29.61 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 29.40/29.61 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 29.40/29.61 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 29.40/29.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 29.40/29.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 29.40/29.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 29.40/29.61 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 29.40/29.61 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 29.40/29.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 29.40/29.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 29.40/29.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 29.40/29.61 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 29.40/29.61 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 29.40/29.61 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 29.40/29.61 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 29.40/29.61 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 29.40/29.61 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 29.40/29.61 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 29.40/29.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 29.40/29.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 29.40/29.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 29.40/29.61 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 29.40/29.61 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 29.40/29.61 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 29.40/29.61 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 29.40/29.61 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 29.40/29.61 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 29.40/29.61 Found (eq_ref00 P) as proof of (P0 ((P (f x))->(P (f x))))
% 29.40/29.61 Found ((eq_ref0 (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 29.40/29.61 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 29.40/29.61 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 29.40/29.61 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 29.40/29.61 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 29.40/29.61 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 29.40/29.61 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 29.40/29.61 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 29.40/29.61 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 29.40/29.61 Found (eq_ref00 P) as proof of (P0 ((P (f x))->(P (f x))))
% 29.40/29.61 Found ((eq_ref0 (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 29.40/29.61 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 29.40/29.61 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 29.40/29.61 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 29.40/29.61 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 29.40/29.61 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 29.40/29.61 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 29.40/29.61 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 29.40/29.61 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 29.40/29.61 Found (eq_ref00 P) as proof of (P0 (f x))
% 29.40/29.61 Found ((eq_ref0 (f x)) P) as proof of (P0 (f x))
% 29.40/29.61 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 29.40/29.61 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 29.40/29.61 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 29.40/29.61 Found (eq_ref00 P) as proof of (P0 x)
% 29.40/29.61 Found ((eq_ref0 (f x)) P) as proof of (P0 x)
% 29.40/29.61 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 29.40/29.61 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 29.40/29.61 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 29.40/29.61 Found (eq_ref00 P) as proof of (P0 x)
% 29.40/29.61 Found ((eq_ref0 (f x)) P) as proof of (P0 x)
% 29.40/29.61 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 32.95/33.16 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 32.95/33.16 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 32.95/33.16 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 32.95/33.16 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 32.95/33.16 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 32.95/33.16 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 32.95/33.16 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 32.95/33.16 Found (eq_ref00 P) as proof of (P0 (f x))
% 32.95/33.16 Found ((eq_ref0 (f x)) P) as proof of (P0 (f x))
% 32.95/33.16 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 32.95/33.16 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 32.95/33.16 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 32.95/33.16 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 32.95/33.16 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 32.95/33.16 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 32.95/33.16 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 32.95/33.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 32.95/33.16 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 32.95/33.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 32.95/33.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 32.95/33.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 32.95/33.16 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 32.95/33.16 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 32.95/33.16 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 32.95/33.16 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 32.95/33.16 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 32.95/33.16 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 32.95/33.16 Found (eq_ref00 P) as proof of (P0 ((P (f x))->(P (f x))))
% 32.95/33.16 Found ((eq_ref0 (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 32.95/33.16 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 32.95/33.16 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 32.95/33.16 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 32.95/33.16 Found (eq_ref00 P) as proof of (P0 (f x))
% 32.95/33.16 Found ((eq_ref0 (f x)) P) as proof of (P0 (f x))
% 32.95/33.16 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 32.95/33.16 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 32.95/33.16 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 32.95/33.16 Found (eq_ref00 P) as proof of (P0 ((P (f x))->(P (f x))))
% 32.95/33.16 Found ((eq_ref0 (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 32.95/33.16 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 32.95/33.16 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 32.95/33.16 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 32.95/33.16 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 32.95/33.16 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 32.95/33.16 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 32.95/33.16 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 32.95/33.16 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 32.95/33.16 Found (eq_ref00 P) as proof of (P0 x)
% 32.95/33.16 Found ((eq_ref0 (f x)) P) as proof of (P0 x)
% 32.95/33.16 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 32.95/33.16 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 32.95/33.16 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 32.95/33.16 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 32.95/33.16 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 32.95/33.16 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 32.95/33.16 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 32.95/33.16 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 32.95/33.16 Found (eq_ref00 P) as proof of (P0 x)
% 32.95/33.16 Found ((eq_ref0 (f x)) P) as proof of (P0 x)
% 32.95/33.16 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 32.95/33.16 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 32.95/33.16 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 32.95/33.16 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 32.95/33.16 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 32.95/33.16 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 32.95/33.16 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 32.95/33.16 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 32.95/33.16 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 32.95/33.16 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 32.95/33.16 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 32.95/33.16 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 32.95/33.16 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 32.95/33.16 Found (eq_ref00 P) as proof of (P0 (f x))
% 32.95/33.16 Found ((eq_ref0 (f x)) P) as proof of (P0 (f x))
% 32.95/33.16 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 56.19/56.39 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 56.19/56.39 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 56.19/56.39 Found (eq_ref0 (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 56.19/56.39 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 56.19/56.39 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 56.19/56.39 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 56.19/56.39 Found (eq_ref0 (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 56.19/56.39 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 56.19/56.39 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 56.19/56.39 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 56.19/56.39 Found (eq_ref0 (f x)) as proof of (P x)
% 56.19/56.39 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 56.19/56.39 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 56.19/56.39 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 56.19/56.39 Found (eq_ref0 (f x)) as proof of (P x)
% 56.19/56.39 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 56.19/56.39 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 56.19/56.39 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 56.19/56.39 Found (eq_ref0 (f x)) as proof of (P x)
% 56.19/56.39 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 56.19/56.39 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 56.19/56.39 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 56.19/56.39 Found (eq_ref0 (f x)) as proof of (P x)
% 56.19/56.39 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 56.19/56.39 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 56.19/56.39 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 56.19/56.39 Found (eq_ref0 (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 56.19/56.39 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 56.19/56.39 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 56.19/56.39 Found x0:(P (h (f (f (f x)))))
% 56.19/56.39 Instantiate: b:=(h (f (f (f x)))):fofType
% 56.19/56.39 Found x0 as proof of (P0 b)
% 56.19/56.39 Found eq_ref00:=(eq_ref0 (h (f x))):(((eq fofType) (h (f x))) (h (f x)))
% 56.19/56.39 Found (eq_ref0 (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 56.19/56.39 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 56.19/56.39 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 56.19/56.39 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 56.19/56.39 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 56.19/56.39 Found (eq_ref0 (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 56.19/56.39 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 56.19/56.39 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 56.19/56.39 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 56.19/56.39 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 56.19/56.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 56.19/56.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 56.19/56.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 56.19/56.39 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 56.19/56.39 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 56.19/56.39 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 56.19/56.39 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 56.19/56.39 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 56.19/56.39 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 56.19/56.39 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 56.19/56.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 56.19/56.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 56.19/56.39 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 56.19/56.39 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 56.19/56.39 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 56.19/56.39 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 56.19/56.39 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 56.19/56.39 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 56.19/56.39 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 56.19/56.39 Found (eq_ref00 P) as proof of (P0 x)
% 56.19/56.39 Found ((eq_ref0 x) P) as proof of (P0 x)
% 56.19/56.39 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 56.19/56.39 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 56.19/56.39 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 56.19/56.39 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 56.19/56.39 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 56.19/56.39 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 56.19/56.39 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 67.21/67.44 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 67.21/67.44 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 67.21/67.44 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 67.21/67.44 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 67.21/67.44 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 67.21/67.44 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 67.21/67.44 Found (eq_ref00 P) as proof of (P0 x)
% 67.21/67.44 Found ((eq_ref0 x) P) as proof of (P0 x)
% 67.21/67.44 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 67.21/67.44 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 67.21/67.44 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 67.21/67.44 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 67.21/67.44 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 67.21/67.44 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 67.21/67.44 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 67.21/67.44 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 67.21/67.44 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 67.21/67.44 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 67.21/67.44 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 67.21/67.44 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 67.21/67.44 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 67.21/67.44 Found (eq_ref00 P) as proof of (P0 x)
% 67.21/67.44 Found ((eq_ref0 x) P) as proof of (P0 x)
% 67.21/67.44 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 67.21/67.44 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 67.21/67.44 Found x0:(P (h (f (f (f x)))))
% 67.21/67.44 Instantiate: a:=(f (f (f x))):Prop
% 67.21/67.44 Found x0 as proof of (P0 (h a))
% 67.21/67.44 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 67.21/67.44 Found (eq_ref0 a) as proof of (((eq Prop) a) (f x))
% 67.21/67.44 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 67.21/67.44 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 67.21/67.44 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 67.21/67.44 Found eq_ref00:=(eq_ref0 (h (f (f (f x))))):(((eq fofType) (h (f (f (f x))))) (h (f (f (f x)))))
% 67.21/67.44 Found (eq_ref0 (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 67.21/67.44 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 67.21/67.44 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 67.21/67.44 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 67.21/67.44 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 67.21/67.44 Found (eq_ref0 b) as proof of (((eq fofType) b) (h (f x)))
% 67.21/67.44 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f x)))
% 67.21/67.44 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f x)))
% 67.21/67.44 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f x)))
% 67.21/67.44 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 67.21/67.44 Found (eq_ref0 b) as proof of (P b)
% 67.21/67.44 Found ((eq_ref fofType) b) as proof of (P b)
% 67.21/67.44 Found ((eq_ref fofType) b) as proof of (P b)
% 67.21/67.44 Found ((eq_ref fofType) b) as proof of (P b)
% 67.21/67.44 Found eq_ref00:=(eq_ref0 (h (f x))):(((eq fofType) (h (f x))) (h (f x)))
% 67.21/67.44 Found (eq_ref0 (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 67.21/67.44 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 67.21/67.44 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 67.21/67.44 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 67.21/67.44 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 67.21/67.44 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 67.21/67.44 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 67.21/67.44 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 67.21/67.44 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 67.21/67.44 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 67.21/67.44 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 67.21/67.44 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 67.21/67.44 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 67.21/67.44 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 67.21/67.44 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 67.21/67.44 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 67.21/67.44 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 67.21/67.44 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 67.21/67.44 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 67.21/67.44 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 67.21/67.44 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 67.21/67.44 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 72.13/72.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 72.13/72.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 72.13/72.31 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 72.13/72.31 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 72.13/72.31 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 72.13/72.31 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 72.13/72.31 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 72.13/72.31 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 72.13/72.31 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 72.13/72.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 72.13/72.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 72.13/72.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 72.13/72.31 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 72.13/72.31 Found (eq_ref00 P) as proof of (P0 x)
% 72.13/72.31 Found ((eq_ref0 x) P) as proof of (P0 x)
% 72.13/72.31 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 72.13/72.31 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 72.13/72.31 Found eq_ref000:=(eq_ref00 P):((P (f (f (f x))))->(P (f (f (f x)))))
% 72.13/72.31 Found (eq_ref00 P) as proof of (P0 (P (f (f (f x)))))
% 72.13/72.31 Found ((eq_ref0 (f (f (f x)))) P) as proof of (P0 (P (f (f (f x)))))
% 72.13/72.31 Found (((eq_ref Prop) (f (f (f x)))) P) as proof of (P0 (P (f (f (f x)))))
% 72.13/72.31 Found (((eq_ref Prop) (f (f (f x)))) P) as proof of (P0 (P (f (f (f x)))))
% 72.13/72.31 Found x0:(P (h (f x)))
% 72.13/72.31 Instantiate: b:=(h (f x)):fofType
% 72.13/72.31 Found x0 as proof of (P0 b)
% 72.13/72.31 Found eq_ref00:=(eq_ref0 (h (f (f (f x))))):(((eq fofType) (h (f (f (f x))))) (h (f (f (f x)))))
% 72.13/72.31 Found (eq_ref0 (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 72.13/72.31 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 72.13/72.31 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 72.13/72.31 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 72.13/72.31 Found eq_ref000:=(eq_ref00 P):((P (h (f (f (f x)))))->(P (h (f (f (f x))))))
% 72.13/72.31 Found (eq_ref00 P) as proof of (P0 (h (f (f (f x)))))
% 72.13/72.31 Found ((eq_ref0 (h (f (f (f x))))) P) as proof of (P0 (h (f (f (f x)))))
% 72.13/72.31 Found (((eq_ref fofType) (h (f (f (f x))))) P) as proof of (P0 (h (f (f (f x)))))
% 72.13/72.31 Found (((eq_ref fofType) (h (f (f (f x))))) P) as proof of (P0 (h (f (f (f x)))))
% 72.13/72.31 Found eq_ref00:=(eq_ref0 (h (f (f (f x))))):(((eq fofType) (h (f (f (f x))))) (h (f (f (f x)))))
% 72.13/72.31 Found (eq_ref0 (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 72.13/72.31 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 72.13/72.31 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 72.13/72.31 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 72.13/72.31 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 72.13/72.31 Found (eq_ref0 b) as proof of (((eq fofType) b) (h (f x)))
% 72.13/72.31 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f x)))
% 72.13/72.31 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f x)))
% 72.13/72.31 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f x)))
% 72.13/72.31 Found eq_ref000:=(eq_ref00 P):((P (f (f (f x))))->(P (f (f (f x)))))
% 72.13/72.31 Found (eq_ref00 P) as proof of (P0 (P (f (f (f x)))))
% 72.13/72.31 Found ((eq_ref0 (f (f (f x)))) P) as proof of (P0 (P (f (f (f x)))))
% 72.13/72.31 Found (((eq_ref Prop) (f (f (f x)))) P) as proof of (P0 (P (f (f (f x)))))
% 72.13/72.31 Found (((eq_ref Prop) (f (f (f x)))) P) as proof of (P0 (P (f (f (f x)))))
% 72.13/72.31 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 72.13/72.31 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 72.13/72.31 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 72.13/72.31 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 72.13/72.31 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 72.13/72.31 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 72.13/72.31 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 72.13/72.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 72.13/72.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 72.13/72.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 72.13/72.31 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 72.13/72.31 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 72.13/72.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 72.13/72.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 72.13/72.31 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 97.04/97.30 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 97.04/97.30 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 97.04/97.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 97.04/97.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 97.04/97.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 97.04/97.30 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 97.04/97.30 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 97.04/97.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 97.04/97.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 97.04/97.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 97.04/97.30 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 97.04/97.30 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 97.04/97.30 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 97.04/97.30 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 97.04/97.30 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 97.04/97.30 Found eq_ref000:=(eq_ref00 P):((P (f (f (f x))))->(P (f (f (f x)))))
% 97.04/97.30 Found (eq_ref00 P) as proof of (P0 (P (f (f (f x)))))
% 97.04/97.30 Found ((eq_ref0 (f (f (f x)))) P) as proof of (P0 (P (f (f (f x)))))
% 97.04/97.30 Found (((eq_ref Prop) (f (f (f x)))) P) as proof of (P0 (P (f (f (f x)))))
% 97.04/97.30 Found (((eq_ref Prop) (f (f (f x)))) P) as proof of (P0 (P (f (f (f x)))))
% 97.04/97.30 Found eq_ref000:=(eq_ref00 P):((P (f (f (f x))))->(P (f (f (f x)))))
% 97.04/97.30 Found (eq_ref00 P) as proof of (P0 (P (f (f (f x)))))
% 97.04/97.30 Found ((eq_ref0 (f (f (f x)))) P) as proof of (P0 (P (f (f (f x)))))
% 97.04/97.30 Found (((eq_ref Prop) (f (f (f x)))) P) as proof of (P0 (P (f (f (f x)))))
% 97.04/97.30 Found (((eq_ref Prop) (f (f (f x)))) P) as proof of (P0 (P (f (f (f x)))))
% 97.04/97.30 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 97.04/97.30 Found (eq_ref00 P) as proof of (P0 x)
% 97.04/97.30 Found ((eq_ref0 x) P) as proof of (P0 x)
% 97.04/97.30 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 97.04/97.30 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 97.04/97.30 Found eq_ref00:=(eq_ref0 (h (f (f (f x))))):(((eq fofType) (h (f (f (f x))))) (h (f (f (f x)))))
% 97.04/97.30 Found (eq_ref0 (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b0)
% 97.04/97.30 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b0)
% 97.04/97.30 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b0)
% 97.04/97.30 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b0)
% 97.04/97.30 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 97.04/97.30 Found (eq_ref0 b0) as proof of (((eq fofType) b0) (h (f x)))
% 97.04/97.30 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h (f x)))
% 97.04/97.30 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h (f x)))
% 97.04/97.30 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h (f x)))
% 97.04/97.30 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 97.04/97.30 Found (eq_ref00 P) as proof of (P0 x)
% 97.04/97.30 Found ((eq_ref0 x) P) as proof of (P0 x)
% 97.04/97.30 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 97.04/97.30 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 97.04/97.30 Found x0:(P (f (f (f x))))
% 97.04/97.30 Instantiate: b:=(f (f (f x))):Prop
% 97.04/97.30 Found x0 as proof of (P0 b)
% 97.04/97.30 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 97.04/97.30 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 97.04/97.30 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 97.04/97.30 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 97.04/97.30 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 97.04/97.30 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 97.04/97.30 Found (eq_ref00 P) as proof of (P0 x)
% 97.04/97.30 Found ((eq_ref0 x) P) as proof of (P0 x)
% 97.04/97.30 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 97.04/97.30 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 97.04/97.30 Found x0:(P (f (f (f x))))
% 97.04/97.30 Instantiate: b:=(f (f (f x))):Prop
% 97.04/97.30 Found x0 as proof of (P0 b)
% 97.04/97.30 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 97.04/97.30 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 97.04/97.30 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 97.04/97.30 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 97.04/97.30 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 97.04/97.30 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 97.04/97.30 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 97.04/97.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 97.04/97.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 97.04/97.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 97.04/97.30 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 97.04/97.30 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 97.04/97.30 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 106.27/106.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 106.27/106.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 106.27/106.48 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 106.27/106.48 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 106.27/106.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 106.27/106.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 106.27/106.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 106.27/106.48 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 106.27/106.48 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 106.27/106.48 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 106.27/106.48 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 106.27/106.48 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 106.27/106.48 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 106.27/106.48 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 106.27/106.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 106.27/106.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 106.27/106.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 106.27/106.48 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 106.27/106.48 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 106.27/106.48 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 106.27/106.48 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 106.27/106.48 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 106.27/106.48 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 106.27/106.48 Found (eq_ref00 P) as proof of (P0 x)
% 106.27/106.48 Found ((eq_ref0 x) P) as proof of (P0 x)
% 106.27/106.48 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 106.27/106.48 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 106.27/106.48 Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% 106.27/106.48 Found (eq_ref00 P) as proof of (P0 b)
% 106.27/106.48 Found ((eq_ref0 b) P) as proof of (P0 b)
% 106.27/106.48 Found (((eq_ref fofType) b) P) as proof of (P0 b)
% 106.27/106.48 Found (((eq_ref fofType) b) P) as proof of (P0 b)
% 106.27/106.48 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 106.27/106.48 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 106.27/106.48 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 106.27/106.48 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 106.27/106.48 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 106.27/106.48 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 106.27/106.48 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 106.27/106.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 106.27/106.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 106.27/106.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 106.27/106.48 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 106.27/106.48 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 106.27/106.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 106.27/106.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 106.27/106.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 106.27/106.48 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 106.27/106.48 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 106.27/106.48 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 106.27/106.48 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 106.27/106.48 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 106.27/106.48 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 106.27/106.48 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 106.27/106.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 106.27/106.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 106.27/106.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 106.27/106.48 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 106.27/106.48 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 106.27/106.48 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 106.27/106.48 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 106.27/106.48 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 106.27/106.48 Found eq_ref000:=(eq_ref00 P1):((P1 (h (f x)))->(P1 (h (f x))))
% 106.27/106.48 Found (eq_ref00 P1) as proof of (P2 (h (f x)))
% 106.27/106.48 Found ((eq_ref0 (h (f x))) P1) as proof of (P2 (h (f x)))
% 106.27/106.48 Found (((eq_ref fofType) (h (f x))) P1) as proof of (P2 (h (f x)))
% 106.27/106.48 Found (((eq_ref fofType) (h (f x))) P1) as proof of (P2 (h (f x)))
% 106.27/106.48 Found eq_ref000:=(eq_ref00 P1):((P1 (h (f x)))->(P1 (h (f x))))
% 106.27/106.48 Found (eq_ref00 P1) as proof of (P2 (h (f x)))
% 106.27/106.48 Found ((eq_ref0 (h (f x))) P1) as proof of (P2 (h (f x)))
% 106.27/106.48 Found (((eq_ref fofType) (h (f x))) P1) as proof of (P2 (h (f x)))
% 106.27/106.48 Found (((eq_ref fofType) (h (f x))) P1) as proof of (P2 (h (f x)))
% 106.27/106.48 Found eq_ref000:=(eq_ref00 P1):((P1 (h (f x)))->(P1 (h (f x))))
% 106.27/106.48 Found (eq_ref00 P1) as proof of (P2 (h (f x)))
% 106.27/106.48 Found ((eq_ref0 (h (f x))) P1) as proof of (P2 (h (f x)))
% 111.68/111.92 Found (((eq_ref fofType) (h (f x))) P1) as proof of (P2 (h (f x)))
% 111.68/111.92 Found (((eq_ref fofType) (h (f x))) P1) as proof of (P2 (h (f x)))
% 111.68/111.92 Found eq_ref000:=(eq_ref00 P1):((P1 (h (f x)))->(P1 (h (f x))))
% 111.68/111.92 Found (eq_ref00 P1) as proof of (P2 (h (f x)))
% 111.68/111.92 Found ((eq_ref0 (h (f x))) P1) as proof of (P2 (h (f x)))
% 111.68/111.92 Found (((eq_ref fofType) (h (f x))) P1) as proof of (P2 (h (f x)))
% 111.68/111.92 Found (((eq_ref fofType) (h (f x))) P1) as proof of (P2 (h (f x)))
% 111.68/111.92 Found x0:(P (f (f (f x))))
% 111.68/111.92 Instantiate: a:=(f (f x)):Prop
% 111.68/111.92 Found x0 as proof of (P0 a)
% 111.68/111.92 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 111.68/111.92 Found (eq_ref0 a) as proof of (((eq Prop) a) x)
% 111.68/111.92 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 111.68/111.92 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 111.68/111.92 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 111.68/111.92 Found x0:(P (f (f (f x))))
% 111.68/111.92 Instantiate: a:=(f (f x)):Prop
% 111.68/111.92 Found x0 as proof of (P0 (f a))
% 111.68/111.92 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 111.68/111.92 Found (eq_ref0 a) as proof of (((eq Prop) a) x)
% 111.68/111.92 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 111.68/111.92 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 111.68/111.92 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 111.68/111.92 Found x0:(P (f (f (f x))))
% 111.68/111.92 Instantiate: a:=(f (f x)):Prop
% 111.68/111.92 Found x0 as proof of (P0 (P (f a)))
% 111.68/111.92 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 111.68/111.92 Found (eq_ref0 a) as proof of (((eq Prop) a) x)
% 111.68/111.92 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 111.68/111.92 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 111.68/111.92 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 111.68/111.92 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 111.68/111.92 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 111.68/111.92 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 111.68/111.92 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 111.68/111.92 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 111.68/111.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 111.68/111.92 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 111.68/111.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 111.68/111.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 111.68/111.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 111.68/111.92 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 111.68/111.92 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 111.68/111.92 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 111.68/111.92 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 111.68/111.92 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 111.68/111.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 111.68/111.92 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 111.68/111.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 111.68/111.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 111.68/111.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 111.68/111.92 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 111.68/111.92 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 111.68/111.92 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 111.68/111.92 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 111.68/111.92 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 111.68/111.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 111.68/111.92 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 111.68/111.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 111.68/111.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 111.68/111.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 111.68/111.92 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 111.68/111.92 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 111.68/111.92 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 111.68/111.92 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 111.68/111.92 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 111.68/111.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 111.68/111.92 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 111.68/111.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 111.68/111.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 111.68/111.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 114.24/114.47 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 114.24/114.47 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 114.24/114.47 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 114.24/114.47 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 114.24/114.47 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 114.24/114.47 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 114.24/114.47 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 114.24/114.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 114.24/114.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 114.24/114.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 114.24/114.47 Found x0:(P (f (f (f x))))
% 114.24/114.47 Instantiate: a:=(f (f x)):Prop
% 114.24/114.47 Found x0 as proof of (P0 a)
% 114.24/114.47 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 114.24/114.47 Found (eq_ref0 a) as proof of (((eq Prop) a) x)
% 114.24/114.47 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 114.24/114.47 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 114.24/114.47 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 114.24/114.47 Found x0:(P (f (f (f x))))
% 114.24/114.47 Instantiate: a:=(f (f x)):Prop
% 114.24/114.47 Found x0 as proof of (P0 (f a))
% 114.24/114.47 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 114.24/114.47 Found (eq_ref0 a) as proof of (((eq Prop) a) x)
% 114.24/114.47 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 114.24/114.47 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 114.24/114.47 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 114.24/114.47 Found x0:(P (f (f (f x))))
% 114.24/114.47 Instantiate: a:=(f (f x)):Prop
% 114.24/114.47 Found x0 as proof of (P0 (P (f a)))
% 114.24/114.47 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 114.24/114.47 Found (eq_ref0 a) as proof of (((eq Prop) a) x)
% 114.24/114.47 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 114.24/114.47 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 114.24/114.47 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 114.24/114.47 Found x0:(P (h (f x)))
% 114.24/114.47 Instantiate: a:=(f x):Prop
% 114.24/114.47 Found x0 as proof of (P0 (h a))
% 114.24/114.47 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 114.24/114.47 Found (eq_ref0 a) as proof of (((eq Prop) a) (f (f (f x))))
% 114.24/114.47 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f (f x))))
% 114.24/114.47 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f (f x))))
% 114.24/114.47 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f (f x))))
% 114.24/114.47 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 114.24/114.47 Found (eq_ref0 b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 114.24/114.47 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 114.24/114.47 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 114.24/114.47 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 114.24/114.47 Found eq_ref00:=(eq_ref0 (h (f x))):(((eq fofType) (h (f x))) (h (f x)))
% 114.24/114.47 Found (eq_ref0 (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 114.24/114.47 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 114.24/114.47 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 114.24/114.47 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 114.24/114.47 Found eq_ref00:=(eq_ref0 (h (f x))):(((eq fofType) (h (f x))) (h (f x)))
% 114.24/114.47 Found (eq_ref0 (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 114.24/114.47 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 114.24/114.47 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 114.24/114.47 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 114.24/114.47 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 114.24/114.47 Found (eq_ref0 b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 114.24/114.47 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 114.24/114.47 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 114.24/114.47 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 114.24/114.47 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 114.24/114.47 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 114.24/114.47 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 114.24/114.47 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 114.24/114.47 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 114.24/114.47 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 114.24/114.47 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 114.24/114.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 114.24/114.47 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 125.41/125.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 125.41/125.67 Found eq_ref00:=(eq_ref0 (h (f x))):(((eq fofType) (h (f x))) (h (f x)))
% 125.41/125.67 Found (eq_ref0 (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 125.41/125.67 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 125.41/125.67 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 125.41/125.67 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 125.41/125.67 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 125.41/125.67 Found (eq_ref0 b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 125.41/125.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 125.41/125.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 125.41/125.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 125.41/125.67 Found eq_ref000:=(eq_ref00 P):((P (h (f x)))->(P (h (f x))))
% 125.41/125.67 Found (eq_ref00 P) as proof of (P0 (h (f x)))
% 125.41/125.67 Found ((eq_ref0 (h (f x))) P) as proof of (P0 (h (f x)))
% 125.41/125.67 Found (((eq_ref fofType) (h (f x))) P) as proof of (P0 (h (f x)))
% 125.41/125.67 Found (((eq_ref fofType) (h (f x))) P) as proof of (P0 (h (f x)))
% 125.41/125.67 Found eq_ref00:=(eq_ref0 (h (f x))):(((eq fofType) (h (f x))) (h (f x)))
% 125.41/125.67 Found (eq_ref0 (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 125.41/125.67 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 125.41/125.67 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 125.41/125.67 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 125.41/125.67 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 125.41/125.67 Found (eq_ref0 b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 125.41/125.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 125.41/125.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 125.41/125.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 125.41/125.67 Found eq_ref000:=(eq_ref00 P1):((P1 (f (f (f x))))->(P1 (f (f (f x)))))
% 125.41/125.67 Found (eq_ref00 P1) as proof of (P2 (P1 (f (f (f x)))))
% 125.41/125.67 Found ((eq_ref0 (f (f (f x)))) P1) as proof of (P2 (P1 (f (f (f x)))))
% 125.41/125.67 Found (((eq_ref Prop) (f (f (f x)))) P1) as proof of (P2 (P1 (f (f (f x)))))
% 125.41/125.67 Found (((eq_ref Prop) (f (f (f x)))) P1) as proof of (P2 (P1 (f (f (f x)))))
% 125.41/125.67 Found eq_ref000:=(eq_ref00 P1):((P1 (f (f (f x))))->(P1 (f (f (f x)))))
% 125.41/125.67 Found (eq_ref00 P1) as proof of (P2 (P1 (f (f (f x)))))
% 125.41/125.67 Found ((eq_ref0 (f (f (f x)))) P1) as proof of (P2 (P1 (f (f (f x)))))
% 125.41/125.67 Found (((eq_ref Prop) (f (f (f x)))) P1) as proof of (P2 (P1 (f (f (f x)))))
% 125.41/125.67 Found (((eq_ref Prop) (f (f (f x)))) P1) as proof of (P2 (P1 (f (f (f x)))))
% 125.41/125.67 Found eq_ref000:=(eq_ref00 P1):((P1 (f (f (f x))))->(P1 (f (f (f x)))))
% 125.41/125.67 Found (eq_ref00 P1) as proof of (P2 (P1 (f (f (f x)))))
% 125.41/125.67 Found ((eq_ref0 (f (f (f x)))) P1) as proof of (P2 (P1 (f (f (f x)))))
% 125.41/125.67 Found (((eq_ref Prop) (f (f (f x)))) P1) as proof of (P2 (P1 (f (f (f x)))))
% 125.41/125.67 Found (((eq_ref Prop) (f (f (f x)))) P1) as proof of (P2 (P1 (f (f (f x)))))
% 125.41/125.67 Found eq_ref000:=(eq_ref00 P1):((P1 (f (f (f x))))->(P1 (f (f (f x)))))
% 125.41/125.67 Found (eq_ref00 P1) as proof of (P2 (P1 (f (f (f x)))))
% 125.41/125.67 Found ((eq_ref0 (f (f (f x)))) P1) as proof of (P2 (P1 (f (f (f x)))))
% 125.41/125.67 Found (((eq_ref Prop) (f (f (f x)))) P1) as proof of (P2 (P1 (f (f (f x)))))
% 125.41/125.67 Found (((eq_ref Prop) (f (f (f x)))) P1) as proof of (P2 (P1 (f (f (f x)))))
% 125.41/125.67 Found eq_ref000:=(eq_ref00 P1):((P1 (f (f (f x))))->(P1 (f (f (f x)))))
% 125.41/125.67 Found (eq_ref00 P1) as proof of (P2 (P1 (f (f (f x)))))
% 125.41/125.67 Found ((eq_ref0 (f (f (f x)))) P1) as proof of (P2 (P1 (f (f (f x)))))
% 125.41/125.67 Found (((eq_ref Prop) (f (f (f x)))) P1) as proof of (P2 (P1 (f (f (f x)))))
% 125.41/125.67 Found (((eq_ref Prop) (f (f (f x)))) P1) as proof of (P2 (P1 (f (f (f x)))))
% 125.41/125.67 Found eq_ref000:=(eq_ref00 P1):((P1 (f (f (f x))))->(P1 (f (f (f x)))))
% 125.41/125.67 Found (eq_ref00 P1) as proof of (P2 (P1 (f (f (f x)))))
% 125.41/125.67 Found ((eq_ref0 (f (f (f x)))) P1) as proof of (P2 (P1 (f (f (f x)))))
% 125.41/125.67 Found (((eq_ref Prop) (f (f (f x)))) P1) as proof of (P2 (P1 (f (f (f x)))))
% 125.41/125.67 Found (((eq_ref Prop) (f (f (f x)))) P1) as proof of (P2 (P1 (f (f (f x)))))
% 125.41/125.67 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 125.41/125.67 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 125.41/125.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 125.41/125.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 138.27/138.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 138.27/138.51 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 138.27/138.51 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 138.27/138.51 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 138.27/138.51 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 138.27/138.51 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 138.27/138.51 Found eq_ref000:=(eq_ref00 P1):((P1 (f (f (f x))))->(P1 (f (f (f x)))))
% 138.27/138.51 Found (eq_ref00 P1) as proof of (P2 (P1 (f (f (f x)))))
% 138.27/138.51 Found ((eq_ref0 (f (f (f x)))) P1) as proof of (P2 (P1 (f (f (f x)))))
% 138.27/138.51 Found (((eq_ref Prop) (f (f (f x)))) P1) as proof of (P2 (P1 (f (f (f x)))))
% 138.27/138.51 Found (((eq_ref Prop) (f (f (f x)))) P1) as proof of (P2 (P1 (f (f (f x)))))
% 138.27/138.51 Found eq_ref000:=(eq_ref00 P1):((P1 (f (f (f x))))->(P1 (f (f (f x)))))
% 138.27/138.51 Found (eq_ref00 P1) as proof of (P2 (P1 (f (f (f x)))))
% 138.27/138.51 Found ((eq_ref0 (f (f (f x)))) P1) as proof of (P2 (P1 (f (f (f x)))))
% 138.27/138.51 Found (((eq_ref Prop) (f (f (f x)))) P1) as proof of (P2 (P1 (f (f (f x)))))
% 138.27/138.51 Found (((eq_ref Prop) (f (f (f x)))) P1) as proof of (P2 (P1 (f (f (f x)))))
% 138.27/138.51 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 138.27/138.51 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 138.27/138.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 138.27/138.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 138.27/138.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 138.27/138.51 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 138.27/138.51 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 138.27/138.51 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 138.27/138.51 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 138.27/138.51 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 138.27/138.51 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 138.27/138.51 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 138.27/138.51 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 138.27/138.51 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 138.27/138.51 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 138.27/138.51 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 138.27/138.51 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 138.27/138.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 138.27/138.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 138.27/138.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 138.27/138.51 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 138.27/138.51 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 138.27/138.51 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 138.27/138.51 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 138.27/138.51 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 138.27/138.51 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 138.27/138.51 Found (eq_ref0 b0) as proof of (((eq fofType) b0) (h (f (f (f x)))))
% 138.27/138.51 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h (f (f (f x)))))
% 138.27/138.51 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h (f (f (f x)))))
% 138.27/138.51 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h (f (f (f x)))))
% 138.27/138.51 Found eq_ref00:=(eq_ref0 (h (f x))):(((eq fofType) (h (f x))) (h (f x)))
% 138.27/138.51 Found (eq_ref0 (h (f x))) as proof of (((eq fofType) (h (f x))) b0)
% 138.27/138.51 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b0)
% 138.27/138.51 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b0)
% 138.27/138.51 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b0)
% 138.27/138.51 Found eq_ref000:=(eq_ref00 P):((P (h (f (f (f x)))))->(P (h (f (f (f x))))))
% 138.27/138.51 Found (eq_ref00 P) as proof of (P0 (h (f (f (f x)))))
% 138.27/138.51 Found ((eq_ref0 (h (f (f (f x))))) P) as proof of (P0 (h (f (f (f x)))))
% 138.27/138.51 Found (((eq_ref fofType) (h (f (f (f x))))) P) as proof of (P0 (h (f (f (f x)))))
% 138.27/138.51 Found (((eq_ref fofType) (h (f (f (f x))))) P) as proof of (P0 (h (f (f (f x)))))
% 138.27/138.51 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 138.27/138.51 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 138.27/138.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 138.27/138.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 138.27/138.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 138.27/138.51 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 138.27/138.51 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 150.27/150.52 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 150.27/150.52 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 150.27/150.52 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 150.27/150.52 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 150.27/150.52 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 150.27/150.52 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 150.27/150.52 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 150.27/150.52 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 150.27/150.52 Found x0:(P (f x))
% 150.27/150.52 Instantiate: b:=(f x):Prop
% 150.27/150.52 Found x0 as proof of (P0 b)
% 150.27/150.52 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 150.27/150.52 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 150.27/150.52 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 150.27/150.52 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 150.27/150.52 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 150.27/150.52 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 150.27/150.52 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 150.27/150.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 150.27/150.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 150.27/150.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 150.27/150.52 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 150.27/150.52 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 150.27/150.52 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 150.27/150.52 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 150.27/150.52 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 150.27/150.52 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 150.27/150.52 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 150.27/150.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 150.27/150.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 150.27/150.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 150.27/150.52 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 150.27/150.52 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 150.27/150.52 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 150.27/150.52 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 150.27/150.52 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 150.27/150.52 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 150.27/150.52 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b0)
% 150.27/150.52 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b0)
% 150.27/150.52 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b0)
% 150.27/150.52 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b0)
% 150.27/150.52 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 150.27/150.52 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x))
% 150.27/150.52 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x))
% 150.27/150.52 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x))
% 150.27/150.52 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x))
% 150.27/150.52 Found x0:(P (f x))
% 150.27/150.52 Instantiate: b:=(f x):Prop
% 150.27/150.52 Found x0 as proof of (P0 b)
% 150.27/150.52 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 150.27/150.52 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 150.27/150.52 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 150.27/150.52 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 150.27/150.52 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 150.27/150.52 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 150.27/150.52 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b0)
% 150.27/150.52 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b0)
% 150.27/150.52 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b0)
% 150.27/150.52 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b0)
% 150.27/150.52 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 150.27/150.52 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x))
% 150.27/150.52 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x))
% 150.27/150.52 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x))
% 150.27/150.52 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x))
% 150.27/150.52 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 150.27/150.52 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 173.87/174.16 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 173.87/174.16 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 173.87/174.16 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 173.87/174.16 Found eq_ref000:=(eq_ref00 P):((P (h (f x)))->(P (h (f x))))
% 173.87/174.16 Found (eq_ref00 P) as proof of (P0 (h (f x)))
% 173.87/174.16 Found ((eq_ref0 (h (f x))) P) as proof of (P0 (h (f x)))
% 173.87/174.16 Found (((eq_ref fofType) (h (f x))) P) as proof of (P0 (h (f x)))
% 173.87/174.16 Found (((eq_ref fofType) (h (f x))) P) as proof of (P0 (h (f x)))
% 173.87/174.16 Found x0:(P (f x))
% 173.87/174.16 Instantiate: b:=(f x):Prop
% 173.87/174.16 Found x0 as proof of (P0 b)
% 173.87/174.16 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 173.87/174.16 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 173.87/174.16 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 173.87/174.16 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 173.87/174.16 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 173.87/174.16 Found eq_ref000:=(eq_ref00 P):((P (h (f (f (f x)))))->(P (h (f (f (f x))))))
% 173.87/174.16 Found (eq_ref00 P) as proof of (P0 (h (f (f (f x)))))
% 173.87/174.16 Found ((eq_ref0 (h (f (f (f x))))) P) as proof of (P0 (h (f (f (f x)))))
% 173.87/174.16 Found (((eq_ref fofType) (h (f (f (f x))))) P) as proof of (P0 (h (f (f (f x)))))
% 173.87/174.16 Found (((eq_ref fofType) (h (f (f (f x))))) P) as proof of (P0 (h (f (f (f x)))))
% 173.87/174.16 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 173.87/174.16 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 173.87/174.16 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 173.87/174.16 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 173.87/174.16 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 173.87/174.16 Found eq_ref000:=(eq_ref00 P):((P (h (f (f (f x)))))->(P (h (f (f (f x))))))
% 173.87/174.16 Found (eq_ref00 P) as proof of (P0 (h (f (f (f x)))))
% 173.87/174.16 Found ((eq_ref0 (h (f (f (f x))))) P) as proof of (P0 (h (f (f (f x)))))
% 173.87/174.16 Found (((eq_ref fofType) (h (f (f (f x))))) P) as proof of (P0 (h (f (f (f x)))))
% 173.87/174.16 Found (((eq_ref fofType) (h (f (f (f x))))) P) as proof of (P0 (h (f (f (f x)))))
% 173.87/174.16 Found x0:(P (f x))
% 173.87/174.16 Instantiate: b:=(f x):Prop
% 173.87/174.16 Found x0 as proof of (P0 b)
% 173.87/174.16 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 173.87/174.16 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 173.87/174.16 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 173.87/174.16 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 173.87/174.16 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 173.87/174.16 Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% 173.87/174.16 Found (eq_ref00 P) as proof of (P0 b)
% 173.87/174.16 Found ((eq_ref0 b) P) as proof of (P0 b)
% 173.87/174.16 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 173.87/174.16 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 173.87/174.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 173.87/174.16 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 173.87/174.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 173.87/174.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 173.87/174.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 173.87/174.16 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 173.87/174.16 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 173.87/174.16 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 173.87/174.16 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 173.87/174.16 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 173.87/174.16 Found x0:(P (f (f x)))
% 173.87/174.16 Instantiate: b:=(f (f x)):Prop
% 173.87/174.16 Found x0 as proof of (P0 b)
% 173.87/174.16 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 173.87/174.16 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 173.87/174.16 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 173.87/174.16 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 173.87/174.16 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 173.87/174.16 Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% 173.87/174.16 Found (eq_ref00 P) as proof of (P0 b)
% 173.87/174.16 Found ((eq_ref0 b) P) as proof of (P0 b)
% 173.87/174.16 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 173.87/174.16 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 173.87/174.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 173.87/174.16 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 173.87/174.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 173.87/174.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 173.87/174.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 181.58/181.88 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 181.58/181.88 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 181.58/181.88 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 181.58/181.88 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 181.58/181.88 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 181.58/181.88 Found eq_ref00:=(eq_ref0 (h (f (f (f x))))):(((eq fofType) (h (f (f (f x))))) (h (f (f (f x)))))
% 181.58/181.88 Found (eq_ref0 (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 181.58/181.88 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 181.58/181.88 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 181.58/181.88 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 181.58/181.88 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 181.58/181.88 Found (eq_ref0 b) as proof of (((eq fofType) b) (h (f x)))
% 181.58/181.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f x)))
% 181.58/181.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f x)))
% 181.58/181.88 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f x)))
% 181.58/181.88 Found x0:(P (f (f x)))
% 181.58/181.88 Instantiate: b:=(f (f x)):Prop
% 181.58/181.88 Found x0 as proof of (P0 b)
% 181.58/181.88 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 181.58/181.88 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 181.58/181.88 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 181.58/181.88 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 181.58/181.88 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 181.58/181.88 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 181.58/181.88 Found (eq_ref00 P1) as proof of (P2 (f x))
% 181.58/181.88 Found ((eq_ref0 (f x)) P1) as proof of (P2 (f x))
% 181.58/181.88 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 181.58/181.88 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 181.58/181.88 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 181.58/181.88 Found (eq_ref00 P1) as proof of (P2 (f x))
% 181.58/181.88 Found ((eq_ref0 (f x)) P1) as proof of (P2 (f x))
% 181.58/181.88 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 181.58/181.88 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 181.58/181.88 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 181.58/181.88 Found (eq_ref00 P1) as proof of (P2 (f x))
% 181.58/181.88 Found ((eq_ref0 (f x)) P1) as proof of (P2 (f x))
% 181.58/181.88 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 181.58/181.88 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 181.58/181.88 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 181.58/181.88 Found (eq_ref00 P1) as proof of (P2 (f x))
% 181.58/181.88 Found ((eq_ref0 (f x)) P1) as proof of (P2 (f x))
% 181.58/181.88 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 181.58/181.88 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 181.58/181.88 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 181.58/181.88 Found (eq_ref00 P1) as proof of (P2 (f x))
% 181.58/181.88 Found ((eq_ref0 (f x)) P1) as proof of (P2 (f x))
% 181.58/181.88 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 181.58/181.88 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 181.58/181.88 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 181.58/181.88 Found (eq_ref00 P1) as proof of (P2 (f x))
% 181.58/181.88 Found ((eq_ref0 (f x)) P1) as proof of (P2 (f x))
% 181.58/181.88 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 181.58/181.88 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 181.58/181.88 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 181.58/181.88 Found (eq_ref00 P) as proof of (P0 (f x))
% 181.58/181.88 Found ((eq_ref0 (f x)) P) as proof of (P0 (f x))
% 181.58/181.88 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 181.58/181.88 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 181.58/181.88 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 181.58/181.88 Found (eq_ref00 P) as proof of (P0 (f x))
% 181.58/181.88 Found ((eq_ref0 (f x)) P) as proof of (P0 (f x))
% 181.58/181.88 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 181.58/181.88 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 181.58/181.88 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 181.58/181.88 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 181.58/181.88 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 181.58/181.88 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 181.58/181.88 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 181.58/181.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 181.58/181.88 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 181.58/181.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 181.58/181.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 181.58/181.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 183.85/184.17 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 183.85/184.17 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 183.85/184.17 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 183.85/184.17 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 183.85/184.17 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 183.85/184.17 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 183.85/184.17 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 183.85/184.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 183.85/184.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 183.85/184.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 183.85/184.17 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 183.85/184.17 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 183.85/184.17 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 183.85/184.17 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 183.85/184.17 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 183.85/184.17 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 183.85/184.17 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 183.85/184.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 183.85/184.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 183.85/184.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 183.85/184.17 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 183.85/184.17 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 183.85/184.17 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 183.85/184.17 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 183.85/184.17 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 183.85/184.17 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 183.85/184.17 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 183.85/184.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 183.85/184.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 183.85/184.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 183.85/184.17 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 183.85/184.17 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 183.85/184.17 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 183.85/184.17 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 183.85/184.17 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 183.85/184.17 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 183.85/184.17 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 183.85/184.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 183.85/184.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 183.85/184.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 183.85/184.17 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 183.85/184.17 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 183.85/184.17 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 183.85/184.17 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 183.85/184.17 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 183.85/184.17 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 183.85/184.17 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 183.85/184.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 183.85/184.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 183.85/184.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 183.85/184.17 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 183.85/184.17 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 183.85/184.17 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 183.85/184.17 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 183.85/184.17 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 183.85/184.17 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 183.85/184.17 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 183.85/184.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 183.85/184.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 183.85/184.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 183.85/184.17 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 183.85/184.17 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 183.85/184.17 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 183.85/184.17 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 183.85/184.17 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 183.85/184.17 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 183.85/184.17 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 183.85/184.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 188.78/189.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 188.78/189.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 188.78/189.12 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 188.78/189.12 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 188.78/189.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 188.78/189.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 188.78/189.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 188.78/189.12 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 188.78/189.12 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 188.78/189.12 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 188.78/189.12 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 188.78/189.12 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 188.78/189.12 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 188.78/189.12 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 188.78/189.12 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 188.78/189.12 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 188.78/189.12 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 188.78/189.12 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 188.78/189.12 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 188.78/189.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 188.78/189.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 188.78/189.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 188.78/189.12 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 188.78/189.12 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 188.78/189.12 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 188.78/189.12 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 188.78/189.12 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 188.78/189.12 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 188.78/189.12 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 188.78/189.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 188.78/189.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 188.78/189.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 188.78/189.12 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 188.78/189.12 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 188.78/189.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 188.78/189.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 188.78/189.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 188.78/189.12 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 188.78/189.12 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 188.78/189.12 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 188.78/189.12 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 188.78/189.12 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 188.78/189.12 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 188.78/189.12 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 188.78/189.12 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 188.78/189.12 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 188.78/189.12 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 188.78/189.12 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 188.78/189.12 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 188.78/189.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 188.78/189.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 188.78/189.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 188.78/189.12 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 188.78/189.12 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 188.78/189.12 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 188.78/189.12 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 188.78/189.12 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 188.78/189.12 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 188.78/189.12 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 188.78/189.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 188.78/189.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 188.78/189.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 188.78/189.12 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 188.78/189.12 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 188.78/189.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 188.78/189.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 188.78/189.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 188.78/189.12 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 195.39/195.73 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 195.39/195.73 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 195.39/195.73 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 195.39/195.73 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 195.39/195.73 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 195.39/195.73 Found (eq_ref00 P1) as proof of (P2 (f x))
% 195.39/195.73 Found ((eq_ref0 (f x)) P1) as proof of (P2 (f x))
% 195.39/195.73 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 195.39/195.73 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 195.39/195.73 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 195.39/195.73 Found (eq_ref00 P1) as proof of (P2 (f x))
% 195.39/195.73 Found ((eq_ref0 (f x)) P1) as proof of (P2 (f x))
% 195.39/195.73 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 195.39/195.73 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 195.39/195.73 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 195.39/195.73 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 195.39/195.73 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 195.39/195.73 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 195.39/195.73 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 195.39/195.73 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 195.39/195.73 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 195.39/195.73 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 195.39/195.73 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 195.39/195.73 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 195.39/195.73 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 195.39/195.73 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 195.39/195.73 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 195.39/195.73 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 195.39/195.73 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 195.39/195.73 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 195.39/195.73 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 195.39/195.73 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 195.39/195.73 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 195.39/195.73 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 195.39/195.73 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 195.39/195.73 Found (eq_ref00 P) as proof of (P0 (f x))
% 195.39/195.73 Found ((eq_ref0 (f x)) P) as proof of (P0 (f x))
% 195.39/195.73 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 195.39/195.73 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 195.39/195.73 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 195.39/195.73 Found (eq_ref00 P) as proof of (P0 (f x))
% 195.39/195.73 Found ((eq_ref0 (f x)) P) as proof of (P0 (f x))
% 195.39/195.73 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 195.39/195.73 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 195.39/195.73 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 195.39/195.73 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 195.39/195.73 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 195.39/195.73 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 195.39/195.73 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 195.39/195.73 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 195.39/195.73 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 195.39/195.73 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 195.39/195.73 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 195.39/195.73 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 195.39/195.73 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 195.39/195.73 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 195.39/195.73 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 195.39/195.73 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 195.39/195.73 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 195.39/195.73 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 195.39/195.73 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 195.39/195.73 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 195.39/195.73 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 195.39/195.73 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 195.39/195.73 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 195.39/195.73 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 195.39/195.73 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 195.39/195.73 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 195.39/195.73 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 195.39/195.73 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 198.79/199.16 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 198.79/199.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 198.79/199.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 198.79/199.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 198.79/199.16 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 198.79/199.16 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 198.79/199.16 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 198.79/199.16 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 198.79/199.16 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 198.79/199.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 198.79/199.16 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 198.79/199.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 198.79/199.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 198.79/199.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 198.79/199.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 198.79/199.16 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 198.79/199.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 198.79/199.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 198.79/199.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 198.79/199.16 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 198.79/199.16 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 198.79/199.16 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 198.79/199.16 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 198.79/199.16 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 198.79/199.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 198.79/199.16 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 198.79/199.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 198.79/199.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 198.79/199.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 198.79/199.16 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 198.79/199.16 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 198.79/199.16 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 198.79/199.16 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 198.79/199.16 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 198.79/199.16 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 198.79/199.16 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 198.79/199.16 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 198.79/199.16 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 198.79/199.16 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 198.79/199.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 198.79/199.16 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 198.79/199.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 198.79/199.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 198.79/199.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 198.79/199.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 198.79/199.16 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 198.79/199.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 198.79/199.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 198.79/199.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 198.79/199.16 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 198.79/199.16 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 198.79/199.16 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 198.79/199.16 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 198.79/199.16 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 198.79/199.16 Found eq_ref00:=(eq_ref0 (h (f x))):(((eq fofType) (h (f x))) (h (f x)))
% 198.79/199.16 Found (eq_ref0 (h (f x))) as proof of (((eq fofType) (h (f x))) b0)
% 198.79/199.16 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b0)
% 198.79/199.16 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b0)
% 198.79/199.16 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b0)
% 198.79/199.16 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 198.79/199.16 Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% 198.79/199.16 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% 198.79/199.16 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% 198.79/199.16 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% 198.79/199.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 198.79/199.16 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 198.79/199.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 198.79/199.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 212.26/212.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 212.26/212.58 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 212.26/212.58 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.26/212.58 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.26/212.58 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.26/212.58 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.26/212.58 Found eq_ref000:=(eq_ref00 P):((P (h (f x)))->(P (h (f x))))
% 212.26/212.58 Found (eq_ref00 P) as proof of (P0 (h (f x)))
% 212.26/212.58 Found ((eq_ref0 (h (f x))) P) as proof of (P0 (h (f x)))
% 212.26/212.58 Found (((eq_ref fofType) (h (f x))) P) as proof of (P0 (h (f x)))
% 212.26/212.58 Found (((eq_ref fofType) (h (f x))) P) as proof of (P0 (h (f x)))
% 212.26/212.58 Found eq_ref000:=(eq_ref00 P):((P (h (f x)))->(P (h (f x))))
% 212.26/212.58 Found (eq_ref00 P) as proof of (P0 (h (f x)))
% 212.26/212.58 Found ((eq_ref0 (h (f x))) P) as proof of (P0 (h (f x)))
% 212.26/212.58 Found (((eq_ref fofType) (h (f x))) P) as proof of (P0 (h (f x)))
% 212.26/212.58 Found (((eq_ref fofType) (h (f x))) P) as proof of (P0 (h (f x)))
% 212.26/212.58 Found x0:(P (f x))
% 212.26/212.58 Instantiate: a:=x:Prop
% 212.26/212.58 Found x0 as proof of (P0 (P (f a)))
% 212.26/212.58 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 212.26/212.58 Found (eq_ref0 a) as proof of (((eq Prop) a) (f (f x)))
% 212.26/212.58 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 212.26/212.58 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 212.26/212.58 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 212.26/212.58 Found x0:(P (f x))
% 212.26/212.58 Instantiate: a:=x:Prop
% 212.26/212.58 Found x0 as proof of (P0 a)
% 212.26/212.58 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 212.26/212.58 Found (eq_ref0 a) as proof of (((eq Prop) a) (f (f x)))
% 212.26/212.58 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 212.26/212.58 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 212.26/212.58 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 212.26/212.58 Found x0:(P (f x))
% 212.26/212.58 Instantiate: a:=x:Prop
% 212.26/212.58 Found x0 as proof of (P0 (P (f a)))
% 212.26/212.58 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 212.26/212.58 Found (eq_ref0 a) as proof of (((eq Prop) a) (f (f x)))
% 212.26/212.58 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 212.26/212.58 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 212.26/212.58 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 212.26/212.58 Found x0:(P (f x))
% 212.26/212.58 Instantiate: a:=x:Prop
% 212.26/212.58 Found x0 as proof of (P0 a)
% 212.26/212.58 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 212.26/212.58 Found (eq_ref0 a) as proof of (((eq Prop) a) (f (f x)))
% 212.26/212.58 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 212.26/212.58 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 212.26/212.58 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 212.26/212.58 Found x0:(P (f x))
% 212.26/212.58 Instantiate: a:=x:Prop
% 212.26/212.58 Found x0 as proof of (P0 (f a))
% 212.26/212.58 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 212.26/212.58 Found (eq_ref0 a) as proof of (((eq Prop) a) (f (f x)))
% 212.26/212.58 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 212.26/212.58 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 212.26/212.58 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 212.26/212.58 Found x0:(P (f x))
% 212.26/212.58 Instantiate: a:=x:Prop
% 212.26/212.58 Found x0 as proof of (P0 (f a))
% 212.26/212.58 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 212.26/212.58 Found (eq_ref0 a) as proof of (((eq Prop) a) (f (f x)))
% 212.26/212.58 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 212.26/212.58 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 212.26/212.58 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 212.26/212.58 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 212.26/212.58 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 212.26/212.58 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 212.26/212.58 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 212.26/212.58 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 212.26/212.58 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 212.26/212.58 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 212.26/212.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 212.26/212.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 212.26/212.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 212.26/212.58 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 212.26/212.58 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 212.26/212.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 212.26/212.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 212.26/212.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 217.07/217.37 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 217.07/217.37 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 217.07/217.37 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 217.07/217.37 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 217.07/217.37 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 217.07/217.37 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 217.07/217.37 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 217.07/217.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 217.07/217.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 217.07/217.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 217.07/217.37 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 217.07/217.37 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 217.07/217.37 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 217.07/217.37 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 217.07/217.37 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 217.07/217.37 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 217.07/217.37 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 217.07/217.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 217.07/217.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 217.07/217.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 217.07/217.37 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 217.07/217.37 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 217.07/217.37 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 217.07/217.37 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 217.07/217.37 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 217.07/217.37 Found x0:(P (f x))
% 217.07/217.37 Instantiate: a:=x:Prop
% 217.07/217.37 Found x0 as proof of (P0 (f a))
% 217.07/217.37 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 217.07/217.37 Found (eq_ref0 a) as proof of (((eq Prop) a) (f (f x)))
% 217.07/217.37 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 217.07/217.37 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 217.07/217.37 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 217.07/217.37 Found x0:(P (f x))
% 217.07/217.37 Instantiate: a:=x:Prop
% 217.07/217.37 Found x0 as proof of (P0 a)
% 217.07/217.37 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 217.07/217.37 Found (eq_ref0 a) as proof of (((eq Prop) a) (f (f x)))
% 217.07/217.37 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 217.07/217.37 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 217.07/217.37 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 217.07/217.37 Found x0:(P (f x))
% 217.07/217.37 Instantiate: a:=x:Prop
% 217.07/217.37 Found x0 as proof of (P0 a)
% 217.07/217.37 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 217.07/217.37 Found (eq_ref0 a) as proof of (((eq Prop) a) (f (f x)))
% 217.07/217.37 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 217.07/217.37 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 217.07/217.37 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 217.07/217.37 Found x0:(P (f x))
% 217.07/217.37 Instantiate: a:=x:Prop
% 217.07/217.37 Found x0 as proof of (P0 (P (f a)))
% 217.07/217.37 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 217.07/217.37 Found (eq_ref0 a) as proof of (((eq Prop) a) (f (f x)))
% 217.07/217.37 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 217.07/217.37 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 217.07/217.37 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 217.07/217.37 Found x0:(P (f x))
% 217.07/217.37 Instantiate: a:=x:Prop
% 217.07/217.37 Found x0 as proof of (P0 (P (f a)))
% 217.07/217.37 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 217.07/217.37 Found (eq_ref0 a) as proof of (((eq Prop) a) (f (f x)))
% 217.07/217.37 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 217.07/217.37 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 217.07/217.37 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 217.07/217.37 Found x0:(P (f x))
% 217.07/217.37 Instantiate: a:=x:Prop
% 217.07/217.37 Found x0 as proof of (P0 (f a))
% 217.07/217.37 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 217.07/217.37 Found (eq_ref0 a) as proof of (((eq Prop) a) (f (f x)))
% 217.07/217.37 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 217.07/217.37 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 217.07/217.37 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 217.07/217.37 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 217.07/217.37 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 217.07/217.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 217.07/217.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 217.07/217.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 217.07/217.37 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 217.07/217.37 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 222.67/222.99 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 222.67/222.99 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 222.67/222.99 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 222.67/222.99 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 222.67/222.99 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 222.67/222.99 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 222.67/222.99 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 222.67/222.99 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 222.67/222.99 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 222.67/222.99 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 222.67/222.99 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 222.67/222.99 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 222.67/222.99 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 222.67/222.99 Found eq_ref000:=(eq_ref00 P0):((P0 (h (f (f (f (f (f x)))))))->(P0 (h (f (f (f (f (f x))))))))
% 222.67/222.99 Found (eq_ref00 P0) as proof of (P1 (h (f (f (f (f (f x)))))))
% 222.67/222.99 Found ((eq_ref0 (h (f (f (f (f (f x))))))) P0) as proof of (P1 (h (f (f (f (f (f x)))))))
% 222.67/222.99 Found (((eq_ref fofType) (h (f (f (f (f (f x))))))) P0) as proof of (P1 (h (f (f (f (f (f x)))))))
% 222.67/222.99 Found (((eq_ref fofType) (h (f (f (f (f (f x))))))) P0) as proof of (P1 (h (f (f (f (f (f x)))))))
% 222.67/222.99 Found eq_ref000:=(eq_ref00 P0):((P0 (h (f (f (f (f (f x)))))))->(P0 (h (f (f (f (f (f x))))))))
% 222.67/222.99 Found (eq_ref00 P0) as proof of (P1 (h (f (f (f (f (f x)))))))
% 222.67/222.99 Found ((eq_ref0 (h (f (f (f (f (f x))))))) P0) as proof of (P1 (h (f (f (f (f (f x)))))))
% 222.67/222.99 Found (((eq_ref fofType) (h (f (f (f (f (f x))))))) P0) as proof of (P1 (h (f (f (f (f (f x)))))))
% 222.67/222.99 Found (((eq_ref fofType) (h (f (f (f (f (f x))))))) P0) as proof of (P1 (h (f (f (f (f (f x)))))))
% 222.67/222.99 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 222.67/222.99 Found (eq_ref00 P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 222.67/222.99 Found ((eq_ref0 (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 222.67/222.99 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 222.67/222.99 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 222.67/222.99 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 222.67/222.99 Found (eq_ref00 P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 222.67/222.99 Found ((eq_ref0 (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 222.67/222.99 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 222.67/222.99 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 222.67/222.99 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 222.67/222.99 Found (eq_ref00 P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 222.67/222.99 Found ((eq_ref0 (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 222.67/222.99 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 222.67/222.99 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 222.67/222.99 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 222.67/222.99 Found (eq_ref00 P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 222.67/222.99 Found ((eq_ref0 (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 222.67/222.99 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 222.67/222.99 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 222.67/222.99 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 222.67/222.99 Found (eq_ref00 P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 222.67/222.99 Found ((eq_ref0 (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 222.67/222.99 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 222.67/222.99 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 222.67/222.99 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 222.67/222.99 Found (eq_ref00 P1) as proof of (P2 (P1 (f x)))
% 222.67/222.99 Found ((eq_ref0 (f x)) P1) as proof of (P2 (P1 (f x)))
% 222.67/222.99 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 222.67/222.99 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 222.67/222.99 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 222.67/222.99 Found (eq_ref00 P1) as proof of (P2 (P1 (f x)))
% 222.67/222.99 Found ((eq_ref0 (f x)) P1) as proof of (P2 (P1 (f x)))
% 222.67/222.99 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 222.67/222.99 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 222.67/222.99 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 222.67/222.99 Found (eq_ref00 P1) as proof of (P2 (P1 (f x)))
% 222.67/222.99 Found ((eq_ref0 (f x)) P1) as proof of (P2 (P1 (f x)))
% 225.03/225.32 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 225.03/225.32 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 225.03/225.32 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 225.03/225.32 Found (eq_ref00 P1) as proof of (P2 (P1 (f x)))
% 225.03/225.32 Found ((eq_ref0 (f x)) P1) as proof of (P2 (P1 (f x)))
% 225.03/225.32 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 225.03/225.32 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 225.03/225.32 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 225.03/225.32 Found (eq_ref00 P1) as proof of (P2 (P1 (f x)))
% 225.03/225.32 Found ((eq_ref0 (f x)) P1) as proof of (P2 (P1 (f x)))
% 225.03/225.32 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 225.03/225.32 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 225.03/225.32 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 225.03/225.32 Found (eq_ref00 P1) as proof of (P2 (P1 (f x)))
% 225.03/225.32 Found ((eq_ref0 (f x)) P1) as proof of (P2 (P1 (f x)))
% 225.03/225.32 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 225.03/225.32 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 225.03/225.32 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 225.03/225.32 Found (eq_ref00 P1) as proof of (P2 (f x))
% 225.03/225.32 Found ((eq_ref0 (f x)) P1) as proof of (P2 (f x))
% 225.03/225.32 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 225.03/225.32 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 225.03/225.32 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 225.03/225.32 Found (eq_ref00 P1) as proof of (P2 x)
% 225.03/225.32 Found ((eq_ref0 (f x)) P1) as proof of (P2 x)
% 225.03/225.32 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 x)
% 225.03/225.32 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 x)
% 225.03/225.32 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 225.03/225.32 Found (eq_ref00 P1) as proof of (P2 (P1 (f x)))
% 225.03/225.32 Found ((eq_ref0 (f x)) P1) as proof of (P2 (P1 (f x)))
% 225.03/225.32 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 225.03/225.32 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 225.03/225.32 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 225.03/225.32 Found (eq_ref00 P1) as proof of (P2 (f x))
% 225.03/225.32 Found ((eq_ref0 (f x)) P1) as proof of (P2 (f x))
% 225.03/225.32 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 225.03/225.32 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 225.03/225.32 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 225.03/225.32 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 225.03/225.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 225.03/225.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 225.03/225.32 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 225.03/225.32 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 225.03/225.32 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 225.03/225.32 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 225.03/225.32 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 225.03/225.32 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 225.03/225.32 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 225.03/225.32 Found (eq_ref00 P1) as proof of (P2 x)
% 225.03/225.32 Found ((eq_ref0 (f x)) P1) as proof of (P2 x)
% 225.03/225.32 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 x)
% 225.03/225.32 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 x)
% 225.03/225.32 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 225.03/225.32 Found (eq_ref00 P1) as proof of (P2 x)
% 225.03/225.32 Found ((eq_ref0 (f x)) P1) as proof of (P2 x)
% 225.03/225.32 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 x)
% 225.03/225.32 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 x)
% 225.03/225.32 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 225.03/225.32 Found (eq_ref00 P1) as proof of (P2 (f x))
% 225.03/225.32 Found ((eq_ref0 (f x)) P1) as proof of (P2 (f x))
% 225.03/225.32 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 225.03/225.32 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 225.03/225.32 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 225.03/225.32 Found (eq_ref00 P1) as proof of (P2 (P1 (f x)))
% 225.03/225.32 Found ((eq_ref0 (f x)) P1) as proof of (P2 (P1 (f x)))
% 225.03/225.32 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 225.03/225.32 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 225.03/225.32 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 225.03/225.32 Found (eq_ref00 P1) as proof of (P2 (f x))
% 225.03/225.32 Found ((eq_ref0 (f x)) P1) as proof of (P2 (f x))
% 225.03/225.32 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 225.03/225.32 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 225.03/225.32 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 225.03/225.32 Found (eq_ref00 P1) as proof of (P2 x)
% 225.03/225.32 Found ((eq_ref0 (f x)) P1) as proof of (P2 x)
% 227.64/227.94 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 x)
% 227.64/227.94 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 x)
% 227.64/227.94 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 227.64/227.94 Found (eq_ref00 P1) as proof of (P2 (P1 (f x)))
% 227.64/227.94 Found ((eq_ref0 (f x)) P1) as proof of (P2 (P1 (f x)))
% 227.64/227.94 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 227.64/227.94 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 227.64/227.94 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 227.64/227.94 Found (eq_ref00 P1) as proof of (P2 (P1 (f x)))
% 227.64/227.94 Found ((eq_ref0 (f x)) P1) as proof of (P2 (P1 (f x)))
% 227.64/227.94 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 227.64/227.94 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 227.64/227.94 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 227.64/227.94 Found (eq_ref00 P1) as proof of (P2 (f x))
% 227.64/227.94 Found ((eq_ref0 (f x)) P1) as proof of (P2 (f x))
% 227.64/227.94 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 227.64/227.94 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 227.64/227.94 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 227.64/227.94 Found (eq_ref00 P1) as proof of (P2 x)
% 227.64/227.94 Found ((eq_ref0 (f x)) P1) as proof of (P2 x)
% 227.64/227.94 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 x)
% 227.64/227.94 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 x)
% 227.64/227.94 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 227.64/227.94 Found (eq_ref00 P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 227.64/227.94 Found ((eq_ref0 (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 227.64/227.94 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 227.64/227.94 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 227.64/227.94 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 227.64/227.94 Found (eq_ref00 P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 227.64/227.94 Found ((eq_ref0 (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 227.64/227.94 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 227.64/227.94 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 227.64/227.94 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 227.64/227.94 Found (eq_ref00 P1) as proof of (P2 (P1 (f x)))
% 227.64/227.94 Found ((eq_ref0 (f x)) P1) as proof of (P2 (P1 (f x)))
% 227.64/227.94 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 227.64/227.94 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 227.64/227.94 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 227.64/227.94 Found (eq_ref00 P1) as proof of (P2 (f x))
% 227.64/227.94 Found ((eq_ref0 (f x)) P1) as proof of (P2 (f x))
% 227.64/227.94 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 227.64/227.94 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 227.64/227.94 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 227.64/227.94 Found (eq_ref00 P1) as proof of (P2 (P1 (f x)))
% 227.64/227.94 Found ((eq_ref0 (f x)) P1) as proof of (P2 (P1 (f x)))
% 227.64/227.94 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 227.64/227.94 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 227.64/227.94 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 227.64/227.94 Found (eq_ref00 P1) as proof of (P2 x)
% 227.64/227.94 Found ((eq_ref0 (f x)) P1) as proof of (P2 x)
% 227.64/227.94 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 x)
% 227.64/227.94 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 x)
% 227.64/227.94 Found eq_ref000:=(eq_ref00 P0):((P0 (h (f (f (f (f (f x)))))))->(P0 (h (f (f (f (f (f x))))))))
% 227.64/227.94 Found (eq_ref00 P0) as proof of (P1 (h (f (f (f (f (f x)))))))
% 227.64/227.94 Found ((eq_ref0 (h (f (f (f (f (f x))))))) P0) as proof of (P1 (h (f (f (f (f (f x)))))))
% 227.64/227.94 Found (((eq_ref fofType) (h (f (f (f (f (f x))))))) P0) as proof of (P1 (h (f (f (f (f (f x)))))))
% 227.64/227.94 Found (((eq_ref fofType) (h (f (f (f (f (f x))))))) P0) as proof of (P1 (h (f (f (f (f (f x)))))))
% 227.64/227.94 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 227.64/227.94 Found (eq_ref00 P1) as proof of (P2 (P1 (f x)))
% 227.64/227.94 Found ((eq_ref0 (f x)) P1) as proof of (P2 (P1 (f x)))
% 227.64/227.94 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 227.64/227.94 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 227.64/227.94 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 227.64/227.94 Found (eq_ref00 P1) as proof of (P2 (f x))
% 227.64/227.94 Found ((eq_ref0 (f x)) P1) as proof of (P2 (f x))
% 227.64/227.94 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 227.64/227.94 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 227.64/227.94 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 227.64/227.94 Found (eq_ref00 P1) as proof of (P2 (P1 (f x)))
% 227.64/227.94 Found ((eq_ref0 (f x)) P1) as proof of (P2 (P1 (f x)))
% 227.64/227.94 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 231.74/232.09 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 231.74/232.09 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 231.74/232.09 Found (eq_ref00 P1) as proof of (P2 x)
% 231.74/232.09 Found ((eq_ref0 (f x)) P1) as proof of (P2 x)
% 231.74/232.09 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 x)
% 231.74/232.09 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 x)
% 231.74/232.09 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 231.74/232.09 Found (eq_ref00 P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 231.74/232.09 Found ((eq_ref0 (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 231.74/232.09 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 231.74/232.09 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 231.74/232.09 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 231.74/232.09 Found (eq_ref00 P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 231.74/232.09 Found ((eq_ref0 (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 231.74/232.09 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 231.74/232.09 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 231.74/232.09 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 231.74/232.09 Found (eq_ref00 P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 231.74/232.09 Found ((eq_ref0 (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 231.74/232.09 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 231.74/232.09 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 231.74/232.09 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 231.74/232.09 Found (eq_ref00 P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 231.74/232.09 Found ((eq_ref0 (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 231.74/232.09 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 231.74/232.09 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 231.74/232.09 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 231.74/232.09 Found (eq_ref00 P1) as proof of (P2 (P1 (f x)))
% 231.74/232.09 Found ((eq_ref0 (f x)) P1) as proof of (P2 (P1 (f x)))
% 231.74/232.09 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 231.74/232.09 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 231.74/232.09 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 231.74/232.09 Found (eq_ref00 P1) as proof of (P2 (f x))
% 231.74/232.09 Found ((eq_ref0 (f x)) P1) as proof of (P2 (f x))
% 231.74/232.09 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 231.74/232.09 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 231.74/232.09 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 231.74/232.09 Found (eq_ref00 P1) as proof of (P2 (f x))
% 231.74/232.09 Found ((eq_ref0 (f x)) P1) as proof of (P2 (f x))
% 231.74/232.09 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 231.74/232.09 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 231.74/232.09 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 231.74/232.09 Found (eq_ref00 P1) as proof of (P2 (P1 (f x)))
% 231.74/232.09 Found ((eq_ref0 (f x)) P1) as proof of (P2 (P1 (f x)))
% 231.74/232.09 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 231.74/232.09 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 231.74/232.09 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 231.74/232.09 Found (eq_ref00 P1) as proof of (P2 (f x))
% 231.74/232.09 Found ((eq_ref0 (f x)) P1) as proof of (P2 (f x))
% 231.74/232.09 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 231.74/232.09 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 231.74/232.09 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 231.74/232.09 Found (eq_ref00 P1) as proof of (P2 (P1 (f x)))
% 231.74/232.09 Found ((eq_ref0 (f x)) P1) as proof of (P2 (P1 (f x)))
% 231.74/232.09 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 231.74/232.09 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 231.74/232.09 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 231.74/232.09 Found (eq_ref00 P1) as proof of (P2 x)
% 231.74/232.09 Found ((eq_ref0 (f x)) P1) as proof of (P2 x)
% 231.74/232.09 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 x)
% 231.74/232.09 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 x)
% 231.74/232.09 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 231.74/232.09 Found (eq_ref00 P1) as proof of (P2 (P1 (f x)))
% 231.74/232.09 Found ((eq_ref0 (f x)) P1) as proof of (P2 (P1 (f x)))
% 231.74/232.09 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 231.74/232.09 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 231.74/232.09 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 231.74/232.09 Found (eq_ref00 P1) as proof of (P2 x)
% 231.74/232.09 Found ((eq_ref0 (f x)) P1) as proof of (P2 x)
% 231.74/232.09 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 x)
% 231.74/232.09 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 x)
% 231.74/232.09 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 238.53/238.85 Found (eq_ref00 P1) as proof of (P2 (P1 (f x)))
% 238.53/238.85 Found ((eq_ref0 (f x)) P1) as proof of (P2 (P1 (f x)))
% 238.53/238.85 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 238.53/238.85 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 238.53/238.85 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 238.53/238.85 Found (eq_ref00 P1) as proof of (P2 (P1 (f x)))
% 238.53/238.85 Found ((eq_ref0 (f x)) P1) as proof of (P2 (P1 (f x)))
% 238.53/238.85 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 238.53/238.85 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 238.53/238.85 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 238.53/238.85 Found (eq_ref00 P1) as proof of (P2 (P1 (f x)))
% 238.53/238.85 Found ((eq_ref0 (f x)) P1) as proof of (P2 (P1 (f x)))
% 238.53/238.85 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 238.53/238.85 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 238.53/238.85 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 238.53/238.85 Found (eq_ref00 P1) as proof of (P2 (f x))
% 238.53/238.85 Found ((eq_ref0 (f x)) P1) as proof of (P2 (f x))
% 238.53/238.85 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 238.53/238.85 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 238.53/238.85 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 238.53/238.85 Found (eq_ref00 P1) as proof of (P2 x)
% 238.53/238.85 Found ((eq_ref0 (f x)) P1) as proof of (P2 x)
% 238.53/238.85 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 x)
% 238.53/238.85 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 x)
% 238.53/238.85 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 238.53/238.85 Found (eq_ref00 P1) as proof of (P2 (P1 (f x)))
% 238.53/238.85 Found ((eq_ref0 (f x)) P1) as proof of (P2 (P1 (f x)))
% 238.53/238.85 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 238.53/238.85 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 238.53/238.85 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 238.53/238.85 Found (eq_ref00 P1) as proof of (P2 x)
% 238.53/238.85 Found ((eq_ref0 (f x)) P1) as proof of (P2 x)
% 238.53/238.85 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 x)
% 238.53/238.85 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 x)
% 238.53/238.85 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 238.53/238.85 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 238.53/238.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 238.53/238.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 238.53/238.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 238.53/238.85 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 238.53/238.85 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 238.53/238.85 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 238.53/238.85 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 238.53/238.85 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 238.53/238.85 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 238.53/238.85 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 238.53/238.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 238.53/238.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 238.53/238.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 238.53/238.85 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 238.53/238.85 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 238.53/238.85 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 238.53/238.85 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 238.53/238.85 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 238.53/238.85 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 238.53/238.85 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 238.53/238.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 238.53/238.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 238.53/238.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 238.53/238.85 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 238.53/238.85 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 238.53/238.85 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 238.53/238.85 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 238.53/238.85 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 238.53/238.85 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 238.53/238.85 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 238.53/238.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 238.53/238.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 238.53/238.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 238.53/238.85 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 238.53/238.85 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 238.53/238.85 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 242.22/242.58 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 242.22/242.58 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 242.22/242.58 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 242.22/242.58 Found (eq_ref00 P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 242.22/242.58 Found ((eq_ref0 (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 242.22/242.58 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 242.22/242.58 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 242.22/242.58 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 242.22/242.58 Found (eq_ref00 P1) as proof of (P2 (P1 (f x)))
% 242.22/242.58 Found ((eq_ref0 (f x)) P1) as proof of (P2 (P1 (f x)))
% 242.22/242.58 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 242.22/242.58 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 242.22/242.58 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 242.22/242.58 Found (eq_ref00 P1) as proof of (P2 (P1 (f x)))
% 242.22/242.58 Found ((eq_ref0 (f x)) P1) as proof of (P2 (P1 (f x)))
% 242.22/242.58 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 242.22/242.58 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 242.22/242.58 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 242.22/242.58 Found (eq_ref00 P1) as proof of (P2 x)
% 242.22/242.58 Found ((eq_ref0 (f x)) P1) as proof of (P2 x)
% 242.22/242.58 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 x)
% 242.22/242.58 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 x)
% 242.22/242.58 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 242.22/242.58 Found (eq_ref00 P1) as proof of (P2 (f x))
% 242.22/242.58 Found ((eq_ref0 (f x)) P1) as proof of (P2 (f x))
% 242.22/242.58 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 242.22/242.58 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 242.22/242.58 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 242.22/242.58 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 242.22/242.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 242.22/242.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 242.22/242.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 242.22/242.58 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 242.22/242.58 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 242.22/242.58 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 242.22/242.58 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 242.22/242.58 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 242.22/242.58 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 242.22/242.58 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 242.22/242.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 242.22/242.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 242.22/242.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 242.22/242.58 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 242.22/242.58 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 242.22/242.58 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 242.22/242.58 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 242.22/242.58 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 242.22/242.58 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 242.22/242.58 Found (eq_ref00 P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 242.22/242.58 Found ((eq_ref0 (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 242.22/242.58 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 242.22/242.58 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 242.22/242.58 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 242.22/242.58 Found (eq_ref00 P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 242.22/242.58 Found ((eq_ref0 (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 242.22/242.58 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 242.22/242.58 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 242.22/242.58 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 242.22/242.58 Found (eq_ref00 P1) as proof of (P2 (f x))
% 242.22/242.58 Found ((eq_ref0 (f x)) P1) as proof of (P2 (f x))
% 242.22/242.58 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 242.22/242.58 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 242.22/242.58 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 242.22/242.58 Found (eq_ref00 P1) as proof of (P2 (P1 (f x)))
% 242.22/242.58 Found ((eq_ref0 (f x)) P1) as proof of (P2 (P1 (f x)))
% 242.22/242.58 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 242.22/242.58 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 242.22/242.58 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 242.22/242.58 Found (eq_ref00 P1) as proof of (P2 (P1 (f x)))
% 242.22/242.58 Found ((eq_ref0 (f x)) P1) as proof of (P2 (P1 (f x)))
% 253.53/253.87 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 253.53/253.87 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 253.53/253.87 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 253.53/253.87 Found (eq_ref00 P1) as proof of (P2 x)
% 253.53/253.87 Found ((eq_ref0 (f x)) P1) as proof of (P2 x)
% 253.53/253.87 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 x)
% 253.53/253.87 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 x)
% 253.53/253.87 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 253.53/253.87 Found (eq_ref00 P1) as proof of (P2 (P1 (f x)))
% 253.53/253.87 Found ((eq_ref0 (f x)) P1) as proof of (P2 (P1 (f x)))
% 253.53/253.87 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 253.53/253.87 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 253.53/253.87 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 253.53/253.87 Found (eq_ref00 P1) as proof of (P2 (f x))
% 253.53/253.87 Found ((eq_ref0 (f x)) P1) as proof of (P2 (f x))
% 253.53/253.87 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 253.53/253.87 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (f x))
% 253.53/253.87 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 253.53/253.87 Found (eq_ref00 P1) as proof of (P2 x)
% 253.53/253.87 Found ((eq_ref0 (f x)) P1) as proof of (P2 x)
% 253.53/253.87 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 x)
% 253.53/253.87 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 x)
% 253.53/253.87 Found eq_ref000:=(eq_ref00 P1):((P1 (f x))->(P1 (f x)))
% 253.53/253.87 Found (eq_ref00 P1) as proof of (P2 (P1 (f x)))
% 253.53/253.87 Found ((eq_ref0 (f x)) P1) as proof of (P2 (P1 (f x)))
% 253.53/253.87 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 253.53/253.87 Found (((eq_ref Prop) (f x)) P1) as proof of (P2 (P1 (f x)))
% 253.53/253.87 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 253.53/253.87 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 253.53/253.87 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 253.53/253.87 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 253.53/253.87 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 253.53/253.87 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 253.53/253.87 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 253.53/253.87 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 253.53/253.87 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 253.53/253.87 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 253.53/253.87 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 253.53/253.87 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 253.53/253.87 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 253.53/253.87 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 253.53/253.87 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 253.53/253.87 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 253.53/253.87 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 253.53/253.87 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 253.53/253.87 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 253.53/253.87 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 253.53/253.87 Found x0:(P (f (f x)))
% 253.53/253.87 Instantiate: b:=(f (f x)):Prop
% 253.53/253.87 Found x0 as proof of (P0 b)
% 253.53/253.87 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 253.53/253.87 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 253.53/253.87 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 253.53/253.87 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 253.53/253.87 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 253.53/253.87 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 253.53/253.87 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 253.53/253.87 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 253.53/253.87 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 253.53/253.87 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 253.53/253.87 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 253.53/253.87 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 253.53/253.87 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 253.53/253.87 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 253.53/253.87 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 253.53/253.87 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 253.53/253.87 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 253.53/253.87 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 253.53/253.87 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 253.53/253.87 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 253.53/253.87 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 253.53/253.87 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 253.53/253.87 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 253.53/253.87 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 274.13/274.55 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 274.13/274.55 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 274.13/274.55 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 274.13/274.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 274.13/274.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 274.13/274.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 274.13/274.55 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 274.13/274.55 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 274.13/274.55 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 274.13/274.55 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 274.13/274.55 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 274.13/274.55 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 274.13/274.55 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 274.13/274.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 274.13/274.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 274.13/274.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 274.13/274.55 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 274.13/274.55 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 274.13/274.55 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 274.13/274.55 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 274.13/274.55 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 274.13/274.55 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 274.13/274.55 Found (eq_ref0 b) as proof of (P b)
% 274.13/274.55 Found ((eq_ref Prop) b) as proof of (P b)
% 274.13/274.55 Found ((eq_ref Prop) b) as proof of (P b)
% 274.13/274.55 Found ((eq_ref Prop) b) as proof of (P b)
% 274.13/274.55 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 274.13/274.55 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 274.13/274.55 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 274.13/274.55 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 274.13/274.55 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 274.13/274.55 Found x0:(P (f (f x)))
% 274.13/274.55 Instantiate: b:=(f (f x)):Prop
% 274.13/274.55 Found x0 as proof of (P0 b)
% 274.13/274.55 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 274.13/274.55 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 274.13/274.55 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 274.13/274.55 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 274.13/274.55 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 274.13/274.55 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 274.13/274.55 Found (eq_ref0 b) as proof of (P b)
% 274.13/274.55 Found ((eq_ref Prop) b) as proof of (P b)
% 274.13/274.55 Found ((eq_ref Prop) b) as proof of (P b)
% 274.13/274.55 Found ((eq_ref Prop) b) as proof of (P b)
% 274.13/274.55 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 274.13/274.55 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 274.13/274.55 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 274.13/274.55 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 274.13/274.55 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 274.13/274.55 Found eq_ref000:=(eq_ref00 P):((P (h (f x)))->(P (h (f x))))
% 274.13/274.55 Found (eq_ref00 P) as proof of (P0 (h (f x)))
% 274.13/274.55 Found ((eq_ref0 (h (f x))) P) as proof of (P0 (h (f x)))
% 274.13/274.55 Found (((eq_ref fofType) (h (f x))) P) as proof of (P0 (h (f x)))
% 274.13/274.55 Found (((eq_ref fofType) (h (f x))) P) as proof of (P0 (h (f x)))
% 274.13/274.55 Found eq_ref000:=(eq_ref00 P):((P (h (f x)))->(P (h (f x))))
% 274.13/274.55 Found (eq_ref00 P) as proof of (P0 (h (f x)))
% 274.13/274.55 Found ((eq_ref0 (h (f x))) P) as proof of (P0 (h (f x)))
% 274.13/274.55 Found (((eq_ref fofType) (h (f x))) P) as proof of (P0 (h (f x)))
% 274.13/274.55 Found (((eq_ref fofType) (h (f x))) P) as proof of (P0 (h (f x)))
% 274.13/274.55 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 274.13/274.55 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 274.13/274.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 274.13/274.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 274.13/274.55 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 274.13/274.55 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 274.13/274.55 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 274.13/274.55 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 274.13/274.55 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 274.13/274.55 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 274.13/274.55 Found eq_ref00:=(eq_ref0 (h (f (f (f (f (f x))))))):(((eq fofType) (h (f (f (f (f (f x))))))) (h (f (f (f (f (f x)))))))
% 278.29/278.64 Found (eq_ref0 (h (f (f (f (f (f x))))))) as proof of (((eq fofType) (h (f (f (f (f (f x))))))) b)
% 278.29/278.64 Found ((eq_ref fofType) (h (f (f (f (f (f x))))))) as proof of (((eq fofType) (h (f (f (f (f (f x))))))) b)
% 278.29/278.64 Found ((eq_ref fofType) (h (f (f (f (f (f x))))))) as proof of (((eq fofType) (h (f (f (f (f (f x))))))) b)
% 278.29/278.64 Found ((eq_ref fofType) (h (f (f (f (f (f x))))))) as proof of (((eq fofType) (h (f (f (f (f (f x))))))) b)
% 278.29/278.64 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 278.29/278.64 Found (eq_ref0 b) as proof of (((eq fofType) b) (h (f x)))
% 278.29/278.64 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f x)))
% 278.29/278.64 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f x)))
% 278.29/278.64 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f x)))
% 278.29/278.64 Found x0:(P (f (f (f x))))
% 278.29/278.64 Instantiate: b:=(f (f (f x))):Prop
% 278.29/278.64 Found x0 as proof of (P0 b)
% 278.29/278.64 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 278.29/278.64 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 278.29/278.64 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 278.29/278.64 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 278.29/278.64 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 278.29/278.64 Found eq_ref000:=(eq_ref00 P):((P (h (f x)))->(P (h (f x))))
% 278.29/278.64 Found (eq_ref00 P) as proof of (P0 (h (f x)))
% 278.29/278.64 Found ((eq_ref0 (h (f x))) P) as proof of (P0 (h (f x)))
% 278.29/278.64 Found (((eq_ref fofType) (h (f x))) P) as proof of (P0 (h (f x)))
% 278.29/278.64 Found (((eq_ref fofType) (h (f x))) P) as proof of (P0 (h (f x)))
% 278.29/278.64 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 278.29/278.64 Found (eq_ref0 (f x)) as proof of (P1 x)
% 278.29/278.64 Found ((eq_ref Prop) (f x)) as proof of (P1 x)
% 278.29/278.64 Found ((eq_ref Prop) (f x)) as proof of (P1 x)
% 278.29/278.64 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 278.29/278.64 Found (eq_ref0 (f x)) as proof of (P1 x)
% 278.29/278.64 Found ((eq_ref Prop) (f x)) as proof of (P1 x)
% 278.29/278.64 Found ((eq_ref Prop) (f x)) as proof of (P1 x)
% 278.29/278.64 Found eq_ref000:=(eq_ref00 P):((P (h (f x)))->(P (h (f x))))
% 278.29/278.64 Found (eq_ref00 P) as proof of (P0 (h (f x)))
% 278.29/278.64 Found ((eq_ref0 (h (f x))) P) as proof of (P0 (h (f x)))
% 278.29/278.64 Found (((eq_ref fofType) (h (f x))) P) as proof of (P0 (h (f x)))
% 278.29/278.64 Found (((eq_ref fofType) (h (f x))) P) as proof of (P0 (h (f x)))
% 278.29/278.64 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 278.29/278.64 Found (eq_ref0 (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 278.29/278.64 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 278.29/278.64 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 278.29/278.64 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 278.29/278.64 Found (eq_ref0 (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 278.29/278.64 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 278.29/278.64 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 278.29/278.64 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 278.29/278.64 Found (eq_ref0 (f x)) as proof of (P1 x)
% 278.29/278.64 Found ((eq_ref Prop) (f x)) as proof of (P1 x)
% 278.29/278.64 Found ((eq_ref Prop) (f x)) as proof of (P1 x)
% 278.29/278.64 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 278.29/278.64 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b0)
% 278.29/278.64 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 278.29/278.64 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 278.29/278.64 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 278.29/278.64 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 278.29/278.64 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f (f (f x))))
% 278.29/278.64 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f (f (f x))))
% 278.29/278.64 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f (f (f x))))
% 278.29/278.64 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f (f (f x))))
% 278.29/278.64 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 278.29/278.64 Found (eq_ref0 (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 278.29/278.64 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 278.29/278.64 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 278.29/278.64 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 278.29/278.64 Found (eq_ref0 (f x)) as proof of (P1 x)
% 278.29/278.64 Found ((eq_ref Prop) (f x)) as proof of (P1 x)
% 278.29/278.64 Found ((eq_ref Prop) (f x)) as proof of (P1 x)
% 278.29/278.64 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 278.29/278.64 Found (eq_ref0 (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 278.29/278.64 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 286.54/286.92 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 286.54/286.92 Found (eq_ref0 (f x)) as proof of (P1 x)
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (P1 x)
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (P1 x)
% 286.54/286.92 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 286.54/286.92 Found (eq_ref0 (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 286.54/286.92 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 286.54/286.92 Found (eq_ref0 (f x)) as proof of (P1 x)
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (P1 x)
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (P1 x)
% 286.54/286.92 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 286.54/286.92 Found (eq_ref0 (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 286.54/286.92 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 286.54/286.92 Found (eq_ref0 (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 286.54/286.92 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 286.54/286.92 Found (eq_ref0 (f x)) as proof of (P1 x)
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (P1 x)
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (P1 x)
% 286.54/286.92 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 286.54/286.92 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 286.54/286.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 286.54/286.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 286.54/286.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 286.54/286.92 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 286.54/286.92 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b0)
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 286.54/286.92 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 286.54/286.92 Found (eq_ref0 (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 286.54/286.92 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 286.54/286.92 Found (eq_ref0 (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 286.54/286.92 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 286.54/286.92 Found (eq_ref0 (f x)) as proof of (P1 x)
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (P1 x)
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (P1 x)
% 286.54/286.92 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 286.54/286.92 Found (eq_ref0 (f x)) as proof of (P1 x)
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (P1 x)
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (P1 x)
% 286.54/286.92 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 286.54/286.92 Found (eq_ref0 (f x)) as proof of (P1 x)
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (P1 x)
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (P1 x)
% 286.54/286.92 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 286.54/286.92 Found (eq_ref0 (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 286.54/286.92 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 286.54/286.92 Found (eq_ref0 (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 286.54/286.92 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 286.54/286.92 Found (eq_ref0 (f x)) as proof of (P1 x)
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (P1 x)
% 286.54/286.92 Found ((eq_ref Prop) (f x)) as proof of (P1 x)
% 286.54/286.92 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 286.54/286.92 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 286.54/286.92 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 293.33/293.74 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 293.33/293.74 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 293.33/293.74 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 293.33/293.74 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 293.33/293.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 293.33/293.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 293.33/293.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 293.33/293.74 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 293.33/293.74 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 293.33/293.74 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 293.33/293.74 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 293.33/293.74 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 293.33/293.74 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 293.33/293.74 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 293.33/293.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 293.33/293.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 293.33/293.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 293.33/293.74 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 293.33/293.74 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 293.33/293.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 293.33/293.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 293.33/293.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 293.33/293.74 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 293.33/293.74 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 293.33/293.74 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 293.33/293.74 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 293.33/293.74 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 293.33/293.74 Found x0:(P (f (f (f x))))
% 293.33/293.74 Instantiate: b:=(f (f (f x))):Prop
% 293.33/293.74 Found x0 as proof of (P0 b)
% 293.33/293.74 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 293.33/293.74 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 293.33/293.74 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 293.33/293.74 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 293.33/293.74 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 293.33/293.74 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 293.33/293.74 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 293.33/293.74 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 293.33/293.74 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 293.33/293.74 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 293.33/293.74 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 293.33/293.74 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 293.33/293.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 293.33/293.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 293.33/293.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 293.33/293.74 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 293.33/293.74 Found (eq_ref0 (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 293.33/293.74 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 293.33/293.74 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 293.33/293.74 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 293.33/293.74 Found (eq_ref0 (f x)) as proof of (P1 x)
% 293.33/293.74 Found ((eq_ref Prop) (f x)) as proof of (P1 x)
% 293.33/293.74 Found ((eq_ref Prop) (f x)) as proof of (P1 x)
% 293.33/293.74 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 293.33/293.74 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b0)
% 293.33/293.74 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 293.33/293.74 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 293.33/293.74 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 293.33/293.74 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 293.33/293.74 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f (f (f x))))
% 293.33/293.74 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f (f (f x))))
% 293.33/293.74 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f (f (f x))))
% 293.33/293.74 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f (f (f x))))
% 293.33/293.74 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 293.33/293.74 Found (eq_ref0 (f x)) as proof of (P1 x)
% 293.33/293.74 Found ((eq_ref Prop) (f x)) as proof of (P1 x)
% 293.33/293.74 Found ((eq_ref Prop) (f x)) as proof of (P1 x)
% 293.33/293.74 Found eq_ref000:=(eq_ref00 P0):((P0 (f (f (f x))))->(P0 (f (f (f x)))))
% 293.33/293.74 Found (eq_ref00 P0) as proof of (P1 (P0 (f (f (f x)))))
% 293.33/293.74 Found ((eq_ref0
%------------------------------------------------------------------------------