TSTP Solution File: SYO043^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO043^1 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue Mar 29 00:50:28 EDT 2022
% Result : Timeout 292.36s 292.76s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : SYO043^1 : TPTP v7.5.0. Released v4.0.0.
% 0.06/0.11 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.32 % Computer : n020.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 08:10:41 EST 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.33 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.11/0.33 Python 2.7.5
% 7.55/7.81 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 7.55/7.81 FOF formula (<kernel.Constant object at 0x2acdd55f8c68>, <kernel.DependentProduct object at 0x2acdd55f8fc8>) of role type named f
% 7.55/7.81 Using role type
% 7.55/7.81 Declaring f:(Prop->Prop)
% 7.55/7.81 FOF formula (<kernel.Constant object at 0x2acdd55f8680>, <kernel.DependentProduct object at 0x2acdd55f8c20>) of role type named q
% 7.55/7.81 Using role type
% 7.55/7.81 Declaring q:((Prop->Prop)->(Prop->Prop))
% 7.55/7.81 FOF formula (<kernel.Constant object at 0x2acdd55f87e8>, <kernel.Sort object at 0x2acdd55f1638>) of role type named x
% 7.55/7.81 Using role type
% 7.55/7.81 Declaring x:Prop
% 7.55/7.81 FOF formula ((and ((and ((q f) x)) (f (f x)))) (not (((eq Prop) (f ((q f) x))) (f x)))) of role axiom named 5
% 7.55/7.81 A new axiom: ((and ((and ((q f) x)) (f (f x)))) (not (((eq Prop) (f ((q f) x))) (f x))))
% 7.55/7.81 We need to prove []
% 7.55/7.81 Parameter f:(Prop->Prop).
% 7.55/7.81 Parameter q:((Prop->Prop)->(Prop->Prop)).
% 7.55/7.81 Parameter x:Prop.
% 7.55/7.81 Axiom 5:((and ((and ((q f) x)) (f (f x)))) (not (((eq Prop) (f ((q f) x))) (f x)))).
% 7.55/7.81 There are no conjectures!
% 7.55/7.81 Adding conjecture False, to look for Unsatisfiability
% 7.55/7.81 Trying to prove False
% 7.55/7.81 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 7.55/7.81 Found (eq_ref00 P) as proof of (P0 (f ((q f) x)))
% 7.55/7.81 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 7.55/7.81 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 7.55/7.81 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 7.55/7.81 Found eq_ref00:=(eq_ref0 (f ((q f) x))):(((eq Prop) (f ((q f) x))) (f ((q f) x)))
% 7.55/7.81 Found (eq_ref0 (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 7.55/7.81 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 7.55/7.81 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 7.55/7.81 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 7.55/7.81 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 7.55/7.81 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 7.55/7.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 7.55/7.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 7.55/7.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 7.55/7.81 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 7.55/7.81 Found (eq_ref00 P) as proof of (P0 (f ((q f) x)))
% 7.55/7.81 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 7.55/7.81 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 7.55/7.81 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 7.55/7.81 Found eq_ref00:=(eq_ref0 (f ((q f) x))):(((eq Prop) (f ((q f) x))) (f ((q f) x)))
% 7.55/7.81 Found (eq_ref0 (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 7.55/7.81 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 7.55/7.81 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 7.55/7.81 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 7.55/7.81 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 7.55/7.81 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 7.55/7.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 7.55/7.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 7.55/7.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 7.55/7.81 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 7.55/7.81 Found (eq_ref00 P) as proof of (P0 (P (f ((q f) x))))
% 7.55/7.81 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 7.55/7.81 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 7.55/7.81 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 7.55/7.81 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 7.55/7.81 Found (eq_ref00 P) as proof of (P0 (f ((q f) x)))
% 7.55/7.81 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 7.55/7.81 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 7.55/7.81 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 7.55/7.81 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 7.55/7.81 Found (eq_ref00 P) as proof of (P0 (P (f ((q f) x))))
% 7.55/7.81 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 7.55/7.81 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 7.55/7.81 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 18.22/18.46 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 18.22/18.46 Found (eq_ref00 P) as proof of (P0 (P (f ((q f) x))))
% 18.22/18.46 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 18.22/18.46 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 18.22/18.46 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 18.22/18.46 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 18.22/18.46 Found (eq_ref00 P) as proof of (P0 (f ((q f) x)))
% 18.22/18.46 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 18.22/18.46 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 18.22/18.46 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 18.22/18.46 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 18.22/18.46 Found (eq_ref00 P) as proof of (P0 (P (f ((q f) x))))
% 18.22/18.46 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 18.22/18.46 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 18.22/18.46 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 18.22/18.46 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 18.22/18.46 Found (eq_ref00 P) as proof of (P0 (f ((q f) x)))
% 18.22/18.46 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 18.22/18.46 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 18.22/18.46 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 18.22/18.46 Found eq_ref00:=(eq_ref0 (f ((q f) x))):(((eq Prop) (f ((q f) x))) (f ((q f) x)))
% 18.22/18.46 Found (eq_ref0 (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 18.22/18.46 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 18.22/18.46 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 18.22/18.46 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 18.22/18.46 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 18.22/18.46 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 18.22/18.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 18.22/18.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 18.22/18.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 18.22/18.46 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 18.22/18.46 Found (eq_ref00 P) as proof of (P0 (f ((q f) x)))
% 18.22/18.46 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 18.22/18.46 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 18.22/18.46 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 18.22/18.46 Found eq_ref00:=(eq_ref0 (f ((q f) x))):(((eq Prop) (f ((q f) x))) (f ((q f) x)))
% 18.22/18.46 Found (eq_ref0 (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 18.22/18.46 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 18.22/18.46 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 18.22/18.46 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 18.22/18.46 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 18.22/18.46 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 18.22/18.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 18.22/18.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 18.22/18.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 18.22/18.46 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 18.22/18.46 Found (eq_ref00 P) as proof of (P0 (f ((q f) x)))
% 18.22/18.46 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 18.22/18.46 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 18.22/18.46 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 18.22/18.46 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 18.22/18.46 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 18.22/18.46 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 18.22/18.46 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 18.22/18.46 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 18.22/18.46 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 18.22/18.46 Found (eq_ref0 b) as proof of (((eq Prop) b) (f ((q f) x)))
% 18.22/18.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 18.22/18.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 18.22/18.46 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 18.22/18.46 Found eq_ref00:=(eq_ref0 (f ((q f) x))):(((eq Prop) (f ((q f) x))) (f ((q f) x)))
% 18.22/18.46 Found (eq_ref0 (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 18.22/18.46 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 27.76/28.05 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 27.76/28.05 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 27.76/28.05 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 27.76/28.05 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 27.76/28.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 27.76/28.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 27.76/28.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 27.76/28.05 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 27.76/28.05 Found (eq_ref00 P) as proof of (P0 (f ((q f) x)))
% 27.76/28.05 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 27.76/28.05 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 27.76/28.05 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 27.76/28.05 Found eq_ref00:=(eq_ref0 (f ((q f) x))):(((eq Prop) (f ((q f) x))) (f ((q f) x)))
% 27.76/28.05 Found (eq_ref0 (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 27.76/28.05 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 27.76/28.05 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 27.76/28.05 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 27.76/28.05 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 27.76/28.05 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 27.76/28.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 27.76/28.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 27.76/28.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 27.76/28.05 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 27.76/28.05 Found (eq_ref00 P) as proof of (P0 (P (f ((q f) x))))
% 27.76/28.05 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 27.76/28.05 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 27.76/28.05 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 27.76/28.05 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 27.76/28.05 Found (eq_ref00 P) as proof of (P0 (P (f ((q f) x))))
% 27.76/28.05 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 27.76/28.05 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 27.76/28.05 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 27.76/28.05 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 27.76/28.05 Found (eq_ref00 P) as proof of (P0 (f ((q f) x)))
% 27.76/28.05 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 27.76/28.05 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 27.76/28.05 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 27.76/28.05 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 27.76/28.05 Found (eq_ref00 P) as proof of (P0 (P (f ((q f) x))))
% 27.76/28.05 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 27.76/28.05 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 27.76/28.05 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 27.76/28.05 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 27.76/28.05 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 27.76/28.05 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 27.76/28.05 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 27.76/28.05 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 27.76/28.05 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 27.76/28.05 Found (eq_ref0 b) as proof of (((eq Prop) b) (f ((q f) x)))
% 27.76/28.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 27.76/28.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 27.76/28.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 27.76/28.05 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 27.76/28.05 Found (eq_ref00 P) as proof of (P0 (P (f ((q f) x))))
% 27.76/28.05 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 27.76/28.05 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 27.76/28.05 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 27.76/28.05 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 27.76/28.05 Found (eq_ref00 P) as proof of (P0 (f ((q f) x)))
% 27.76/28.05 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 27.76/28.05 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 27.76/28.05 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 37.84/38.12 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 37.84/38.12 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 37.84/38.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 37.84/38.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 37.84/38.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 37.84/38.12 Found eq_ref00:=(eq_ref0 ((q f) x)):(((eq Prop) ((q f) x)) ((q f) x))
% 37.84/38.12 Found (eq_ref0 ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 37.84/38.12 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 37.84/38.12 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 37.84/38.12 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 37.84/38.12 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 37.84/38.12 Found (eq_ref00 P) as proof of (P0 ((P (f x))->(P (f x))))
% 37.84/38.12 Found ((eq_ref0 (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 37.84/38.12 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 37.84/38.12 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 37.84/38.12 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 37.84/38.12 Found (eq_ref00 P) as proof of (P0 (f x))
% 37.84/38.12 Found ((eq_ref0 (f x)) P) as proof of (P0 (f x))
% 37.84/38.12 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 37.84/38.12 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 37.84/38.12 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 37.84/38.12 Found (eq_ref00 P) as proof of (P0 x)
% 37.84/38.12 Found ((eq_ref0 (f x)) P) as proof of (P0 x)
% 37.84/38.12 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 37.84/38.12 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 37.84/38.12 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 37.84/38.12 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 37.84/38.12 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 37.84/38.12 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 37.84/38.12 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 37.84/38.12 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 37.84/38.12 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 37.84/38.12 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 37.84/38.12 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 37.84/38.12 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 37.84/38.12 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 37.84/38.12 Found (eq_ref00 P) as proof of (P0 (P (f ((q f) x))))
% 37.84/38.12 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 37.84/38.12 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 37.84/38.12 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 37.84/38.12 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 37.84/38.12 Found (eq_ref00 P) as proof of (P0 (f ((q f) x)))
% 37.84/38.12 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 37.84/38.12 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 37.84/38.12 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 37.84/38.12 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 37.84/38.12 Found (eq_ref00 P) as proof of (P0 (P (f ((q f) x))))
% 37.84/38.12 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 37.84/38.12 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 37.84/38.12 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 37.84/38.12 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 37.84/38.12 Found (eq_ref00 P) as proof of (P0 (f ((q f) x)))
% 37.84/38.12 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 37.84/38.12 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 37.84/38.12 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 37.84/38.12 Found eq_ref00:=(eq_ref0 (f ((q f) x))):(((eq Prop) (f ((q f) x))) (f ((q f) x)))
% 37.84/38.12 Found (eq_ref0 (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 37.84/38.12 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 37.84/38.12 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 37.84/38.12 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 37.84/38.12 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 37.84/38.12 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 37.84/38.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 37.84/38.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 37.84/38.12 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 37.84/38.12 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 37.84/38.12 Found (eq_ref00 P) as proof of (P0 (P (f ((q f) x))))
% 37.84/38.12 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 45.58/45.90 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 45.58/45.90 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 45.58/45.90 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 45.58/45.90 Found (eq_ref00 P) as proof of (P0 (f ((q f) x)))
% 45.58/45.90 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 45.58/45.90 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 45.58/45.90 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 45.58/45.90 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 45.58/45.90 Found (eq_ref00 P) as proof of (P0 (f ((q f) x)))
% 45.58/45.90 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 45.58/45.90 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 45.58/45.90 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 45.58/45.90 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 45.58/45.90 Found (eq_ref0 (f x)) as proof of (P x)
% 45.58/45.90 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 45.58/45.90 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 45.58/45.90 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 45.58/45.90 Found (eq_ref0 (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 45.58/45.90 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 45.58/45.90 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 45.58/45.90 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 45.58/45.90 Found (eq_ref00 P) as proof of (P0 (P (f ((q f) x))))
% 45.58/45.90 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 45.58/45.90 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 45.58/45.90 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 45.58/45.90 Found eq_ref00:=(eq_ref0 (f ((q f) x))):(((eq Prop) (f ((q f) x))) (f ((q f) x)))
% 45.58/45.90 Found (eq_ref0 (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 45.58/45.90 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 45.58/45.90 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 45.58/45.90 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 45.58/45.90 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 45.58/45.90 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 45.58/45.90 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 45.58/45.90 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 45.58/45.90 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 45.58/45.90 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 45.58/45.90 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 45.58/45.90 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 45.58/45.90 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 45.58/45.90 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 45.58/45.90 Found eq_ref00:=(eq_ref0 ((q f) x)):(((eq Prop) ((q f) x)) ((q f) x))
% 45.58/45.90 Found (eq_ref0 ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 45.58/45.90 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 45.58/45.90 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 45.58/45.90 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 45.58/45.90 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 45.58/45.90 Found (eq_ref00 P) as proof of (P0 ((P (f x))->(P (f x))))
% 45.58/45.90 Found ((eq_ref0 (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 45.58/45.90 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 45.58/45.90 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 45.58/45.90 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 45.58/45.90 Found (eq_ref00 P) as proof of (P0 (f x))
% 45.58/45.90 Found ((eq_ref0 (f x)) P) as proof of (P0 (f x))
% 45.58/45.90 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 45.58/45.90 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 45.58/45.90 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 45.58/45.90 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 45.58/45.90 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 45.58/45.90 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 45.58/45.90 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 45.58/45.90 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 45.58/45.90 Found (eq_ref00 P) as proof of (P0 x)
% 45.58/45.90 Found ((eq_ref0 (f x)) P) as proof of (P0 x)
% 45.58/45.90 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 45.58/45.90 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 45.58/45.90 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 45.58/45.90 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 45.58/45.90 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 56.47/56.79 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 56.47/56.79 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 56.47/56.79 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 56.47/56.79 Found (eq_ref00 P) as proof of (P0 (f ((q f) x)))
% 56.47/56.79 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 56.47/56.79 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 56.47/56.79 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 56.47/56.79 Found eq_ref00:=(eq_ref0 (f ((q f) x))):(((eq Prop) (f ((q f) x))) (f ((q f) x)))
% 56.47/56.79 Found (eq_ref0 (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 56.47/56.79 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 56.47/56.79 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 56.47/56.79 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 56.47/56.79 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 56.47/56.79 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 56.47/56.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 56.47/56.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 56.47/56.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 56.47/56.79 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 56.47/56.79 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 56.47/56.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 56.47/56.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 56.47/56.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 56.47/56.79 Found eq_ref00:=(eq_ref0 ((q f) x)):(((eq Prop) ((q f) x)) ((q f) x))
% 56.47/56.79 Found (eq_ref0 ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 56.47/56.79 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 56.47/56.79 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 56.47/56.79 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 56.47/56.79 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 56.47/56.79 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 56.47/56.79 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 56.47/56.79 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 56.47/56.79 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 56.47/56.79 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 56.47/56.79 Found (eq_ref0 b) as proof of (((eq Prop) b) (f ((q f) x)))
% 56.47/56.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 56.47/56.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 56.47/56.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 56.47/56.79 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 56.47/56.79 Found (eq_ref00 P) as proof of (P0 (f ((q f) x)))
% 56.47/56.79 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 56.47/56.79 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 56.47/56.79 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 56.47/56.79 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 56.47/56.79 Found (eq_ref0 (f x)) as proof of (P x)
% 56.47/56.79 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 56.47/56.79 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 56.47/56.79 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 56.47/56.79 Found (eq_ref0 (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 56.47/56.79 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 56.47/56.79 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 56.47/56.79 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 56.47/56.79 Found (eq_ref00 P) as proof of (P0 (P (f ((q f) x))))
% 56.47/56.79 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 56.47/56.79 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 56.47/56.79 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 56.47/56.79 Found eq_ref00:=(eq_ref0 (f ((q f) x))):(((eq Prop) (f ((q f) x))) (f ((q f) x)))
% 56.47/56.79 Found (eq_ref0 (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 56.47/56.79 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 56.47/56.79 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 56.47/56.79 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 56.47/56.79 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 56.47/56.79 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 56.47/56.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 56.47/56.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 56.47/56.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 75.98/76.26 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 75.98/76.26 Found (eq_ref00 P) as proof of (P0 (f ((q f) x)))
% 75.98/76.26 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 75.98/76.26 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 75.98/76.26 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 75.98/76.26 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 75.98/76.26 Found (eq_ref00 P) as proof of (P0 (P (f ((q f) x))))
% 75.98/76.26 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 75.98/76.26 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 75.98/76.26 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 75.98/76.26 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 75.98/76.26 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 75.98/76.26 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 75.98/76.26 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 75.98/76.26 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 75.98/76.26 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 75.98/76.26 Found (eq_ref0 b) as proof of (((eq Prop) b) (f ((q f) x)))
% 75.98/76.26 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 75.98/76.26 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 75.98/76.26 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 75.98/76.26 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 75.98/76.26 Found (eq_ref00 P) as proof of (P0 (P (f ((q f) x))))
% 75.98/76.26 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 75.98/76.26 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 75.98/76.26 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 75.98/76.26 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 75.98/76.26 Found (eq_ref00 P) as proof of (P0 (f ((q f) x)))
% 75.98/76.26 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 75.98/76.26 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 75.98/76.26 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 75.98/76.26 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 75.98/76.26 Found (eq_ref00 P) as proof of (P0 (P (f ((q f) x))))
% 75.98/76.26 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 75.98/76.26 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 75.98/76.26 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 75.98/76.26 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 75.98/76.26 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 75.98/76.26 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 75.98/76.26 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 75.98/76.26 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 75.98/76.26 Found eq_ref00:=(eq_ref0 ((q f) x)):(((eq Prop) ((q f) x)) ((q f) x))
% 75.98/76.26 Found (eq_ref0 ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 75.98/76.26 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 75.98/76.26 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 75.98/76.26 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 75.98/76.26 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 75.98/76.26 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 75.98/76.26 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 75.98/76.26 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 75.98/76.26 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 75.98/76.26 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 75.98/76.26 Found (eq_ref0 b) as proof of (((eq Prop) b) (f ((q f) x)))
% 75.98/76.26 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 75.98/76.26 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 75.98/76.26 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 75.98/76.26 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 75.98/76.26 Found (eq_ref00 P) as proof of (P0 (P (f ((q f) x))))
% 75.98/76.26 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 75.98/76.26 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 75.98/76.26 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 75.98/76.26 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 75.98/76.26 Found (eq_ref0 b) as proof of (((eq Prop) b) (f ((q f) x)))
% 75.98/76.26 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 75.98/76.26 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 87.24/87.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 87.24/87.54 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 87.24/87.54 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 87.24/87.54 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 87.24/87.54 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 87.24/87.54 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 87.24/87.54 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 87.24/87.54 Found (eq_ref00 P) as proof of (P0 x)
% 87.24/87.54 Found ((eq_ref0 x) P) as proof of (P0 x)
% 87.24/87.54 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 87.24/87.54 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 87.24/87.54 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 87.24/87.54 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 87.24/87.54 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 87.24/87.54 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 87.24/87.54 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 87.24/87.54 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 87.24/87.54 Found (eq_ref0 b) as proof of (((eq Prop) b) (f ((q f) x)))
% 87.24/87.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 87.24/87.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 87.24/87.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 87.24/87.54 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 87.24/87.54 Found (eq_ref00 P) as proof of (P0 (f ((q f) x)))
% 87.24/87.54 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 87.24/87.54 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 87.24/87.54 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 87.24/87.54 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 87.24/87.54 Found (eq_ref00 P) as proof of (P0 (P (f ((q f) x))))
% 87.24/87.54 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 87.24/87.54 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 87.24/87.54 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 87.24/87.54 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 87.24/87.54 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 87.24/87.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 87.24/87.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 87.24/87.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 87.24/87.54 Found eq_ref00:=(eq_ref0 ((q f) x)):(((eq Prop) ((q f) x)) ((q f) x))
% 87.24/87.54 Found (eq_ref0 ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 87.24/87.54 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 87.24/87.54 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 87.24/87.54 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 87.24/87.54 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 87.24/87.54 Found (eq_ref00 P) as proof of (P0 (P (f ((q f) x))))
% 87.24/87.54 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 87.24/87.54 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 87.24/87.54 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 87.24/87.54 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 87.24/87.54 Found (eq_ref00 P) as proof of (P0 ((P (f x))->(P (f x))))
% 87.24/87.54 Found ((eq_ref0 (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 87.24/87.54 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 87.24/87.54 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 87.24/87.54 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 87.24/87.54 Found (eq_ref00 P) as proof of (P0 x)
% 87.24/87.54 Found ((eq_ref0 (f x)) P) as proof of (P0 x)
% 87.24/87.54 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 87.24/87.54 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 87.24/87.54 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 87.24/87.54 Found (eq_ref00 P) as proof of (P0 (f x))
% 87.24/87.54 Found ((eq_ref0 (f x)) P) as proof of (P0 (f x))
% 87.24/87.54 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 87.24/87.54 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 87.24/87.54 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 87.24/87.54 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 87.24/87.54 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 87.24/87.54 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 87.24/87.54 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 87.24/87.54 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 87.24/87.54 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 87.24/87.54 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 87.24/87.54 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 100.82/101.10 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 100.82/101.10 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 100.82/101.10 Found (eq_ref00 P) as proof of (P0 (P (f ((q f) x))))
% 100.82/101.10 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 100.82/101.10 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 100.82/101.10 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (P (f ((q f) x))))
% 100.82/101.10 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 100.82/101.10 Found (eq_ref00 P) as proof of (P0 (f ((q f) x)))
% 100.82/101.10 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 100.82/101.10 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 100.82/101.10 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 100.82/101.10 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 100.82/101.10 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 100.82/101.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 100.82/101.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 100.82/101.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 100.82/101.10 Found eq_ref00:=(eq_ref0 ((q f) x)):(((eq Prop) ((q f) x)) ((q f) x))
% 100.82/101.10 Found (eq_ref0 ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 100.82/101.10 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 100.82/101.10 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 100.82/101.10 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 100.82/101.10 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 100.82/101.10 Found (eq_ref00 P) as proof of (P0 ((P (f x))->(P (f x))))
% 100.82/101.10 Found ((eq_ref0 (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 100.82/101.10 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 100.82/101.10 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 100.82/101.10 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 100.82/101.10 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 100.82/101.10 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 100.82/101.10 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 100.82/101.10 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 100.82/101.10 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 100.82/101.10 Found (eq_ref00 P) as proof of (P0 x)
% 100.82/101.10 Found ((eq_ref0 (f x)) P) as proof of (P0 x)
% 100.82/101.10 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 100.82/101.10 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 100.82/101.10 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 100.82/101.10 Found (eq_ref00 P) as proof of (P0 (f x))
% 100.82/101.10 Found ((eq_ref0 (f x)) P) as proof of (P0 (f x))
% 100.82/101.10 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 100.82/101.10 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 100.82/101.10 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 100.82/101.10 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 100.82/101.10 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 100.82/101.10 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 100.82/101.10 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 100.82/101.10 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 100.82/101.10 Found (eq_ref0 (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 100.82/101.10 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 100.82/101.10 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 100.82/101.10 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 100.82/101.10 Found (eq_ref0 (f x)) as proof of (P x)
% 100.82/101.10 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 100.82/101.10 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 100.82/101.10 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 100.82/101.10 Found (eq_ref0 b) as proof of (((eq Prop) b) (f ((q f) x)))
% 100.82/101.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 100.82/101.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 100.82/101.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 100.82/101.10 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 100.82/101.10 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 100.82/101.10 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 100.82/101.10 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 100.82/101.10 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 100.82/101.10 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 100.82/101.10 Found (eq_ref0 b) as proof of (((eq Prop) b) ((q f) x))
% 100.82/101.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 100.82/101.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 100.82/101.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 100.82/101.10 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 100.82/101.10 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 116.70/116.98 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 116.70/116.98 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 116.70/116.98 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 116.70/116.98 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 116.70/116.98 Found (eq_ref0 b) as proof of (((eq Prop) b) ((q f) x))
% 116.70/116.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 116.70/116.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 116.70/116.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 116.70/116.98 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 116.70/116.98 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 116.70/116.98 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 116.70/116.98 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 116.70/116.98 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 116.70/116.98 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 116.70/116.98 Found (eq_ref00 P) as proof of (P0 x)
% 116.70/116.98 Found ((eq_ref0 x) P) as proof of (P0 x)
% 116.70/116.98 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 116.70/116.98 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 116.70/116.98 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 116.70/116.98 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 116.70/116.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 116.70/116.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 116.70/116.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 116.70/116.98 Found eq_ref00:=(eq_ref0 ((q f) x)):(((eq Prop) ((q f) x)) ((q f) x))
% 116.70/116.98 Found (eq_ref0 ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 116.70/116.98 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 116.70/116.98 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 116.70/116.98 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 116.70/116.98 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 116.70/116.98 Found (eq_ref0 b) as proof of (((eq Prop) b) (f ((q f) x)))
% 116.70/116.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 116.70/116.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 116.70/116.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 116.70/116.98 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 116.70/116.98 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 116.70/116.98 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 116.70/116.98 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 116.70/116.98 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 116.70/116.98 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 116.70/116.98 Found (eq_ref0 (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 116.70/116.98 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 116.70/116.98 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 116.70/116.98 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 116.70/116.98 Found (eq_ref00 P) as proof of (P0 ((P (f x))->(P (f x))))
% 116.70/116.98 Found ((eq_ref0 (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 116.70/116.98 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 116.70/116.98 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 116.70/116.98 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 116.70/116.98 Found (eq_ref0 (f x)) as proof of (P x)
% 116.70/116.98 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 116.70/116.98 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 116.70/116.98 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 116.70/116.98 Found (eq_ref00 P) as proof of (P0 (f x))
% 116.70/116.98 Found ((eq_ref0 (f x)) P) as proof of (P0 (f x))
% 116.70/116.98 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 116.70/116.98 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 116.70/116.98 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 116.70/116.98 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 116.70/116.98 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 116.70/116.98 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 116.70/116.98 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 116.70/116.98 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 116.70/116.98 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 116.70/116.98 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 116.70/116.98 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 116.70/116.98 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 116.70/116.98 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 116.70/116.98 Found (eq_ref00 P) as proof of (P0 x)
% 116.70/116.98 Found ((eq_ref0 (f x)) P) as proof of (P0 x)
% 116.70/116.98 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 116.70/116.98 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 116.70/116.98 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 116.70/116.98 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 116.70/116.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 125.92/126.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 125.92/126.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 125.92/126.24 Found eq_ref00:=(eq_ref0 ((q f) x)):(((eq Prop) ((q f) x)) ((q f) x))
% 125.92/126.24 Found (eq_ref0 ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 125.92/126.24 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 125.92/126.24 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 125.92/126.24 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 125.92/126.24 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 125.92/126.24 Found (eq_ref00 P) as proof of (P0 x)
% 125.92/126.24 Found ((eq_ref0 x) P) as proof of (P0 x)
% 125.92/126.24 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 125.92/126.24 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 125.92/126.24 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 125.92/126.24 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 125.92/126.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 125.92/126.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 125.92/126.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 125.92/126.24 Found eq_ref00:=(eq_ref0 ((q f) x)):(((eq Prop) ((q f) x)) ((q f) x))
% 125.92/126.24 Found (eq_ref0 ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 125.92/126.24 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 125.92/126.24 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 125.92/126.24 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 125.92/126.24 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 125.92/126.24 Found (eq_ref00 P) as proof of (P0 ((P (f x))->(P (f x))))
% 125.92/126.24 Found ((eq_ref0 (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 125.92/126.24 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 125.92/126.24 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 125.92/126.24 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 125.92/126.24 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 125.92/126.24 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 125.92/126.24 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 125.92/126.24 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 125.92/126.24 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 125.92/126.24 Found (eq_ref00 P) as proof of (P0 x)
% 125.92/126.24 Found ((eq_ref0 (f x)) P) as proof of (P0 x)
% 125.92/126.24 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 125.92/126.24 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 125.92/126.24 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 125.92/126.24 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 125.92/126.24 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 125.92/126.24 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 125.92/126.24 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 125.92/126.24 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 125.92/126.24 Found (eq_ref00 P) as proof of (P0 (f x))
% 125.92/126.24 Found ((eq_ref0 (f x)) P) as proof of (P0 (f x))
% 125.92/126.24 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 125.92/126.24 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 125.92/126.24 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 125.92/126.24 Found (eq_ref0 b) as proof of (((eq Prop) b) (f ((q f) x)))
% 125.92/126.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 125.92/126.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 125.92/126.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 125.92/126.24 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 125.92/126.24 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 125.92/126.24 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 125.92/126.24 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 125.92/126.24 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 125.92/126.24 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 125.92/126.24 Found (eq_ref00 P) as proof of (P0 ((P (f x))->(P (f x))))
% 125.92/126.24 Found ((eq_ref0 (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 125.92/126.24 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 125.92/126.24 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 125.92/126.24 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 125.92/126.24 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 125.92/126.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 125.92/126.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 125.92/126.24 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 125.92/126.24 Found eq_ref00:=(eq_ref0 ((q f) x)):(((eq Prop) ((q f) x)) ((q f) x))
% 125.92/126.24 Found (eq_ref0 ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 125.92/126.24 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 125.92/126.24 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 125.92/126.24 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 139.08/139.41 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 139.08/139.41 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 139.08/139.41 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 139.08/139.41 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 139.08/139.41 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 139.08/139.41 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 139.08/139.41 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 139.08/139.41 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 139.08/139.41 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 139.08/139.41 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 139.08/139.41 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 139.08/139.41 Found (eq_ref00 P) as proof of (P0 x)
% 139.08/139.41 Found ((eq_ref0 (f x)) P) as proof of (P0 x)
% 139.08/139.41 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 139.08/139.41 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 139.08/139.41 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 139.08/139.41 Found (eq_ref00 P) as proof of (P0 (f x))
% 139.08/139.41 Found ((eq_ref0 (f x)) P) as proof of (P0 (f x))
% 139.08/139.41 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 139.08/139.41 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 139.08/139.41 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 139.08/139.41 Found (eq_ref0 (f x)) as proof of (P x)
% 139.08/139.41 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 139.08/139.41 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 139.08/139.41 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 139.08/139.41 Found (eq_ref0 (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 139.08/139.41 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 139.08/139.41 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 139.08/139.41 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 139.08/139.41 Found (eq_ref0 b) as proof of (((eq Prop) b) ((q f) x))
% 139.08/139.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 139.08/139.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 139.08/139.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 139.08/139.41 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 139.08/139.41 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 139.08/139.41 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 139.08/139.41 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 139.08/139.41 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 139.08/139.41 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 139.08/139.41 Found (eq_ref0 b) as proof of (((eq Prop) b) ((q f) x))
% 139.08/139.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 139.08/139.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 139.08/139.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 139.08/139.41 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 139.08/139.41 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 139.08/139.41 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 139.08/139.41 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 139.08/139.41 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 139.08/139.41 Found x01:(P (f ((q f) x)))
% 139.08/139.41 Instantiate: b:=(f ((q f) x)):Prop
% 139.08/139.41 Found x01 as proof of (P0 b)
% 139.08/139.41 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 139.08/139.41 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 139.08/139.41 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 139.08/139.41 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 139.08/139.41 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 139.08/139.41 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 139.08/139.41 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 139.08/139.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 139.08/139.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 139.08/139.41 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 139.08/139.41 Found eq_ref00:=(eq_ref0 ((q f) x)):(((eq Prop) ((q f) x)) ((q f) x))
% 139.08/139.41 Found (eq_ref0 ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 139.08/139.41 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 139.08/139.41 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 139.08/139.41 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 139.08/139.41 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 139.08/139.41 Found (eq_ref0 (f x)) as proof of (P x)
% 139.08/139.41 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 139.08/139.41 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 139.08/139.41 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 139.08/139.41 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 139.08/139.41 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 139.08/139.41 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 139.08/139.41 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 154.66/155.04 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 154.66/155.04 Found (eq_ref0 b) as proof of (((eq Prop) b) (f ((q f) x)))
% 154.66/155.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 154.66/155.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 154.66/155.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 154.66/155.04 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 154.66/155.04 Found (eq_ref0 (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 154.66/155.04 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 154.66/155.04 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 154.66/155.04 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 154.66/155.04 Found (eq_ref0 (f x)) as proof of (P x)
% 154.66/155.04 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 154.66/155.04 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 154.66/155.04 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 154.66/155.04 Found (eq_ref0 (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 154.66/155.04 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 154.66/155.04 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 154.66/155.04 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 154.66/155.04 Found (eq_ref0 b) as proof of (((eq Prop) b) ((q f) x))
% 154.66/155.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 154.66/155.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 154.66/155.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 154.66/155.04 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 154.66/155.04 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 154.66/155.04 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 154.66/155.04 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 154.66/155.04 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 154.66/155.04 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 154.66/155.04 Found (eq_ref0 b) as proof of (((eq Prop) b) ((q f) x))
% 154.66/155.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 154.66/155.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 154.66/155.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 154.66/155.04 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 154.66/155.04 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 154.66/155.04 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 154.66/155.04 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 154.66/155.04 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 154.66/155.04 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 154.66/155.04 Found (eq_ref00 P) as proof of (P0 x)
% 154.66/155.04 Found ((eq_ref0 x) P) as proof of (P0 x)
% 154.66/155.04 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 154.66/155.04 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 154.66/155.04 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 154.66/155.04 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 154.66/155.04 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 154.66/155.04 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 154.66/155.04 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 154.66/155.04 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 154.66/155.04 Found (eq_ref0 b) as proof of (((eq Prop) b) (f ((q f) x)))
% 154.66/155.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 154.66/155.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 154.66/155.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 154.66/155.04 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 154.66/155.04 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 154.66/155.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 154.66/155.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 154.66/155.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 154.66/155.04 Found eq_ref00:=(eq_ref0 ((q f) x)):(((eq Prop) ((q f) x)) ((q f) x))
% 154.66/155.04 Found (eq_ref0 ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 154.66/155.04 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 154.66/155.04 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 154.66/155.04 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 154.66/155.04 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 154.66/155.04 Found (eq_ref00 P) as proof of (P0 ((P (f x))->(P (f x))))
% 154.66/155.04 Found ((eq_ref0 (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 154.66/155.04 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 154.66/155.04 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 154.66/155.04 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 154.66/155.04 Found (eq_ref0 b) as proof of (((eq Prop) b) (f ((q f) x)))
% 154.66/155.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 154.66/155.04 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 166.87/167.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 166.87/167.21 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 166.87/167.21 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 166.87/167.21 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 166.87/167.21 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 166.87/167.21 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 166.87/167.21 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 166.87/167.21 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 166.87/167.21 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 166.87/167.21 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 166.87/167.21 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 166.87/167.21 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 166.87/167.21 Found (eq_ref00 P) as proof of (P0 x)
% 166.87/167.21 Found ((eq_ref0 (f x)) P) as proof of (P0 x)
% 166.87/167.21 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 166.87/167.21 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 166.87/167.21 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 166.87/167.21 Found (eq_ref00 P) as proof of (P0 (f x))
% 166.87/167.21 Found ((eq_ref0 (f x)) P) as proof of (P0 (f x))
% 166.87/167.21 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 166.87/167.21 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 166.87/167.21 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 166.87/167.21 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 166.87/167.21 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 166.87/167.21 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 166.87/167.21 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 166.87/167.21 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 166.87/167.21 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 166.87/167.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 166.87/167.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 166.87/167.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 166.87/167.21 Found eq_ref00:=(eq_ref0 ((q f) x)):(((eq Prop) ((q f) x)) ((q f) x))
% 166.87/167.21 Found (eq_ref0 ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 166.87/167.21 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 166.87/167.21 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 166.87/167.21 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 166.87/167.21 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 166.87/167.21 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 166.87/167.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 166.87/167.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 166.87/167.21 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 166.87/167.21 Found eq_ref00:=(eq_ref0 ((q f) x)):(((eq Prop) ((q f) x)) ((q f) x))
% 166.87/167.21 Found (eq_ref0 ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 166.87/167.21 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 166.87/167.21 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 166.87/167.21 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 166.87/167.21 Found x01:(P (f ((q f) x)))
% 166.87/167.21 Instantiate: b:=(f ((q f) x)):Prop
% 166.87/167.21 Found x01 as proof of (P0 b)
% 166.87/167.21 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 166.87/167.21 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 166.87/167.21 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 166.87/167.21 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 166.87/167.21 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 166.87/167.21 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 166.87/167.21 Found (eq_ref00 P) as proof of (P0 ((P (f x))->(P (f x))))
% 166.87/167.21 Found ((eq_ref0 (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 166.87/167.21 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 166.87/167.21 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 166.87/167.21 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 166.87/167.21 Found (eq_ref00 P) as proof of (P0 x)
% 166.87/167.21 Found ((eq_ref0 (f x)) P) as proof of (P0 x)
% 166.87/167.21 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 166.87/167.21 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 166.87/167.21 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 166.87/167.21 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 166.87/167.21 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 166.87/167.21 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 166.87/167.21 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 166.87/167.21 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 166.87/167.21 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 166.87/167.21 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 166.87/167.21 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 166.87/167.21 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 178.83/179.14 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 178.83/179.14 Found (eq_ref00 P) as proof of (P0 (f x))
% 178.83/179.14 Found ((eq_ref0 (f x)) P) as proof of (P0 (f x))
% 178.83/179.14 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 178.83/179.14 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 178.83/179.14 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 178.83/179.14 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 178.83/179.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 178.83/179.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 178.83/179.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 178.83/179.14 Found eq_ref00:=(eq_ref0 ((q f) x)):(((eq Prop) ((q f) x)) ((q f) x))
% 178.83/179.14 Found (eq_ref0 ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 178.83/179.14 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 178.83/179.14 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 178.83/179.14 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 178.83/179.14 Found eq_ref00:=(eq_ref0 (f ((q f) x))):(((eq Prop) (f ((q f) x))) (f ((q f) x)))
% 178.83/179.14 Found (eq_ref0 (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 178.83/179.14 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 178.83/179.14 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 178.83/179.14 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 178.83/179.14 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 178.83/179.14 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 178.83/179.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 178.83/179.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 178.83/179.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 178.83/179.14 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 178.83/179.14 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 178.83/179.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 178.83/179.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 178.83/179.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 178.83/179.14 Found eq_ref00:=(eq_ref0 ((q f) x)):(((eq Prop) ((q f) x)) ((q f) x))
% 178.83/179.14 Found (eq_ref0 ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 178.83/179.14 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 178.83/179.14 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 178.83/179.14 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 178.83/179.14 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 178.83/179.14 Found (eq_ref00 P) as proof of (P0 (f ((q f) x)))
% 178.83/179.14 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 178.83/179.14 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 178.83/179.14 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 178.83/179.14 Found eq_ref00:=(eq_ref0 (f ((q f) x))):(((eq Prop) (f ((q f) x))) (f ((q f) x)))
% 178.83/179.14 Found (eq_ref0 (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 178.83/179.14 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 178.83/179.14 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 178.83/179.14 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 178.83/179.14 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 178.83/179.14 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 178.83/179.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 178.83/179.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 178.83/179.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 178.83/179.14 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 178.83/179.14 Found (eq_ref0 (f x)) as proof of (P x)
% 178.83/179.14 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 178.83/179.14 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 178.83/179.14 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 178.83/179.14 Found (eq_ref0 (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 178.83/179.14 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 178.83/179.14 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 178.83/179.14 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 178.83/179.14 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 178.83/179.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 178.83/179.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 178.83/179.14 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 178.83/179.14 Found eq_ref00:=(eq_ref0 ((q f) x)):(((eq Prop) ((q f) x)) ((q f) x))
% 178.83/179.14 Found (eq_ref0 ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 178.83/179.14 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 178.83/179.14 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 178.83/179.14 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 189.83/190.20 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 189.83/190.20 Found (eq_ref00 P) as proof of (P0 ((P (f x))->(P (f x))))
% 189.83/190.20 Found ((eq_ref0 (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 189.83/190.20 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 189.83/190.20 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 189.83/190.20 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 189.83/190.20 Found (eq_ref00 P) as proof of (P0 (f x))
% 189.83/190.20 Found ((eq_ref0 (f x)) P) as proof of (P0 (f x))
% 189.83/190.20 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 189.83/190.20 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 189.83/190.20 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 189.83/190.20 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 189.83/190.20 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 189.83/190.20 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 189.83/190.20 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 189.83/190.20 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 189.83/190.20 Found (eq_ref00 P) as proof of (P0 x)
% 189.83/190.20 Found ((eq_ref0 (f x)) P) as proof of (P0 x)
% 189.83/190.20 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 189.83/190.20 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 189.83/190.20 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 189.83/190.20 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 189.83/190.20 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 189.83/190.20 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 189.83/190.20 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 189.83/190.20 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 189.83/190.20 Found (eq_ref0 b) as proof of (((eq Prop) b) ((q f) x))
% 189.83/190.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 189.83/190.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 189.83/190.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 189.83/190.20 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 189.83/190.20 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 189.83/190.20 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 189.83/190.20 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 189.83/190.20 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 189.83/190.20 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 189.83/190.20 Found (eq_ref0 b) as proof of (((eq Prop) b) ((q f) x))
% 189.83/190.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 189.83/190.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 189.83/190.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 189.83/190.20 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 189.83/190.20 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 189.83/190.20 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 189.83/190.20 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 189.83/190.20 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 189.83/190.20 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 189.83/190.20 Found (eq_ref0 (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 189.83/190.20 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 189.83/190.20 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 189.83/190.20 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 189.83/190.20 Found (eq_ref0 (f x)) as proof of (P x)
% 189.83/190.20 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 189.83/190.20 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 189.83/190.20 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 189.83/190.20 Found (eq_ref0 b) as proof of (((eq Prop) b) (f ((q f) x)))
% 189.83/190.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 189.83/190.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 189.83/190.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f ((q f) x)))
% 189.83/190.20 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 189.83/190.20 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 189.83/190.20 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 189.83/190.20 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 189.83/190.20 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 189.83/190.20 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 189.83/190.20 Found (eq_ref00 P) as proof of (P0 x)
% 189.83/190.20 Found ((eq_ref0 x) P) as proof of (P0 x)
% 189.83/190.20 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 189.83/190.20 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 189.83/190.20 Found x01:(P (f ((q f) x)))
% 189.83/190.20 Instantiate: a:=((q f) x):Prop
% 189.83/190.20 Found x01 as proof of (P0 (P (f a)))
% 189.83/190.20 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 189.83/190.20 Found (eq_ref0 a) as proof of (((eq Prop) a) x)
% 189.83/190.20 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 189.83/190.20 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 189.83/190.20 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 211.54/211.93 Found x01:(P (f ((q f) x)))
% 211.54/211.93 Instantiate: a:=((q f) x):Prop
% 211.54/211.93 Found x01 as proof of (P0 a)
% 211.54/211.93 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 211.54/211.93 Found (eq_ref0 a) as proof of (((eq Prop) a) x)
% 211.54/211.93 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 211.54/211.93 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 211.54/211.93 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 211.54/211.93 Found x01:(P (f ((q f) x)))
% 211.54/211.93 Instantiate: a:=((q f) x):Prop
% 211.54/211.93 Found x01 as proof of (P0 (f a))
% 211.54/211.93 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 211.54/211.93 Found (eq_ref0 a) as proof of (((eq Prop) a) x)
% 211.54/211.93 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 211.54/211.93 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 211.54/211.93 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 211.54/211.93 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 211.54/211.93 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 211.54/211.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 211.54/211.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 211.54/211.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 211.54/211.93 Found eq_ref00:=(eq_ref0 ((q f) x)):(((eq Prop) ((q f) x)) ((q f) x))
% 211.54/211.93 Found (eq_ref0 ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 211.54/211.93 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 211.54/211.93 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 211.54/211.93 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 211.54/211.93 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 211.54/211.93 Found (eq_ref0 (f x)) as proof of (P x)
% 211.54/211.93 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 211.54/211.93 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 211.54/211.93 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 211.54/211.93 Found (eq_ref0 (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 211.54/211.93 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 211.54/211.93 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 211.54/211.93 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 211.54/211.93 Found (eq_ref00 P) as proof of (P0 ((P (f x))->(P (f x))))
% 211.54/211.93 Found ((eq_ref0 (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 211.54/211.93 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 211.54/211.93 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 211.54/211.93 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 211.54/211.93 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 211.54/211.93 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 211.54/211.93 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 211.54/211.93 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 211.54/211.93 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 211.54/211.93 Found (eq_ref00 P) as proof of (P0 (f x))
% 211.54/211.93 Found ((eq_ref0 (f x)) P) as proof of (P0 (f x))
% 211.54/211.93 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 211.54/211.93 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 211.54/211.93 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 211.54/211.93 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 211.54/211.93 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 211.54/211.93 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 211.54/211.93 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 211.54/211.93 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 211.54/211.93 Found (eq_ref00 P) as proof of (P0 x)
% 211.54/211.93 Found ((eq_ref0 (f x)) P) as proof of (P0 x)
% 211.54/211.93 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 211.54/211.93 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 211.54/211.93 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 211.54/211.93 Found (eq_ref00 P) as proof of (P0 x)
% 211.54/211.93 Found ((eq_ref0 x) P) as proof of (P0 x)
% 211.54/211.93 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 211.54/211.93 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 211.54/211.93 Found eq_ref00:=(eq_ref0 (f ((q f) x))):(((eq Prop) (f ((q f) x))) (f ((q f) x)))
% 211.54/211.93 Found (eq_ref0 (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 211.54/211.93 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 211.54/211.93 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 211.54/211.93 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 211.54/211.93 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 211.54/211.93 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 211.54/211.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 211.54/211.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 211.54/211.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 211.54/211.93 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 211.54/211.93 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 223.01/223.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 223.01/223.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 223.01/223.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 223.01/223.36 Found eq_ref00:=(eq_ref0 ((q f) x)):(((eq Prop) ((q f) x)) ((q f) x))
% 223.01/223.36 Found (eq_ref0 ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 223.01/223.36 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 223.01/223.36 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 223.01/223.36 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 223.01/223.36 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 223.01/223.36 Found (eq_ref00 P) as proof of (P0 (f ((q f) x)))
% 223.01/223.36 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 223.01/223.36 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 223.01/223.36 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 223.01/223.36 Found eq_ref00:=(eq_ref0 (f ((q f) x))):(((eq Prop) (f ((q f) x))) (f ((q f) x)))
% 223.01/223.36 Found (eq_ref0 (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 223.01/223.36 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 223.01/223.36 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 223.01/223.36 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 223.01/223.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 223.01/223.36 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 223.01/223.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 223.01/223.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 223.01/223.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 223.01/223.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 223.01/223.36 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 223.01/223.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 223.01/223.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 223.01/223.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 223.01/223.36 Found eq_ref00:=(eq_ref0 ((q f) x)):(((eq Prop) ((q f) x)) ((q f) x))
% 223.01/223.36 Found (eq_ref0 ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 223.01/223.36 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 223.01/223.36 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 223.01/223.36 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 223.01/223.36 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 223.01/223.36 Found (eq_ref00 P) as proof of (P0 ((P (f x))->(P (f x))))
% 223.01/223.36 Found ((eq_ref0 (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 223.01/223.36 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 223.01/223.36 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 223.01/223.36 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 223.01/223.36 Found (eq_ref00 P) as proof of (P0 x)
% 223.01/223.36 Found ((eq_ref0 (f x)) P) as proof of (P0 x)
% 223.01/223.36 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 223.01/223.36 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 223.01/223.36 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 223.01/223.36 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 223.01/223.36 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 223.01/223.36 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 223.01/223.36 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 223.01/223.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 223.01/223.36 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 223.01/223.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 223.01/223.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 223.01/223.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 223.01/223.36 Found eq_ref00:=(eq_ref0 ((q f) x)):(((eq Prop) ((q f) x)) ((q f) x))
% 223.01/223.36 Found (eq_ref0 ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 223.01/223.36 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 223.01/223.36 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 223.01/223.36 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 223.01/223.36 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 223.01/223.36 Found (eq_ref00 P) as proof of (P0 (f x))
% 223.01/223.36 Found ((eq_ref0 (f x)) P) as proof of (P0 (f x))
% 223.01/223.36 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 223.01/223.36 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 223.01/223.36 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 223.01/223.36 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 223.01/223.36 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 223.01/223.36 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 223.01/223.36 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 223.01/223.36 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 229.81/230.20 Found (eq_ref00 P) as proof of (P0 ((P (f x))->(P (f x))))
% 229.81/230.20 Found ((eq_ref0 (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 229.81/230.20 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 229.81/230.20 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 229.81/230.20 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 229.81/230.20 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 229.81/230.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 229.81/230.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 229.81/230.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 229.81/230.20 Found eq_ref00:=(eq_ref0 ((q f) x)):(((eq Prop) ((q f) x)) ((q f) x))
% 229.81/230.20 Found (eq_ref0 ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 229.81/230.20 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 229.81/230.20 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 229.81/230.20 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 229.81/230.20 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 229.81/230.20 Found (eq_ref00 P) as proof of (P0 (f x))
% 229.81/230.20 Found ((eq_ref0 (f x)) P) as proof of (P0 (f x))
% 229.81/230.20 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 229.81/230.20 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 229.81/230.20 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 229.81/230.20 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 229.81/230.20 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 229.81/230.20 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 229.81/230.20 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 229.81/230.20 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 229.81/230.20 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 229.81/230.20 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 229.81/230.20 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 229.81/230.20 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 229.81/230.20 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 229.81/230.20 Found (eq_ref00 P) as proof of (P0 x)
% 229.81/230.20 Found ((eq_ref0 (f x)) P) as proof of (P0 x)
% 229.81/230.20 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 229.81/230.20 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 229.81/230.20 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 229.81/230.20 Found (eq_ref0 b) as proof of (((eq Prop) b) ((q f) x))
% 229.81/230.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 229.81/230.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 229.81/230.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 229.81/230.20 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 229.81/230.20 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 229.81/230.20 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 229.81/230.20 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 229.81/230.20 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 229.81/230.20 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 229.81/230.20 Found (eq_ref0 b) as proof of (((eq Prop) b) ((q f) x))
% 229.81/230.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 229.81/230.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 229.81/230.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 229.81/230.20 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 229.81/230.20 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 229.81/230.20 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 229.81/230.20 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 229.81/230.20 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 229.81/230.20 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 229.81/230.20 Found (eq_ref0 (f x)) as proof of (P x)
% 229.81/230.20 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 229.81/230.20 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 229.81/230.20 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 229.81/230.20 Found (eq_ref0 (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 229.81/230.20 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 229.81/230.20 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 229.81/230.20 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 229.81/230.20 Found (eq_ref00 P) as proof of (P0 x)
% 229.81/230.20 Found ((eq_ref0 x) P) as proof of (P0 x)
% 229.81/230.20 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 229.81/230.20 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 229.81/230.20 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 229.81/230.20 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 229.81/230.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 229.81/230.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 229.81/230.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 229.81/230.20 Found eq_ref00:=(eq_ref0 ((q f) x)):(((eq Prop) ((q f) x)) ((q f) x))
% 229.81/230.20 Found (eq_ref0 ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 229.81/230.20 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 246.59/246.95 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 246.59/246.95 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 246.59/246.95 Found x01:(P (f ((q f) x)))
% 246.59/246.95 Instantiate: a:=((q f) x):Prop
% 246.59/246.95 Found x01 as proof of (P0 (f a))
% 246.59/246.95 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 246.59/246.95 Found (eq_ref0 a) as proof of (((eq Prop) a) x)
% 246.59/246.95 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 246.59/246.95 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 246.59/246.95 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 246.59/246.95 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 246.59/246.95 Found (eq_ref0 b) as proof of (P b)
% 246.59/246.95 Found ((eq_ref Prop) b) as proof of (P b)
% 246.59/246.95 Found ((eq_ref Prop) b) as proof of (P b)
% 246.59/246.95 Found ((eq_ref Prop) b) as proof of (P b)
% 246.59/246.95 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 246.59/246.95 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 246.59/246.95 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 246.59/246.95 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 246.59/246.95 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 246.59/246.95 Found x01:(P (f ((q f) x)))
% 246.59/246.95 Instantiate: a:=((q f) x):Prop
% 246.59/246.95 Found x01 as proof of (P0 a)
% 246.59/246.95 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 246.59/246.95 Found (eq_ref0 a) as proof of (((eq Prop) a) x)
% 246.59/246.95 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 246.59/246.95 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 246.59/246.95 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 246.59/246.95 Found x01:(P (f ((q f) x)))
% 246.59/246.95 Instantiate: a:=((q f) x):Prop
% 246.59/246.95 Found x01 as proof of (P0 (P (f a)))
% 246.59/246.95 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 246.59/246.95 Found (eq_ref0 a) as proof of (((eq Prop) a) x)
% 246.59/246.95 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 246.59/246.95 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 246.59/246.95 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 246.59/246.95 Found x03:(P (f ((q f) x)))
% 246.59/246.95 Instantiate: b:=(f ((q f) x)):Prop
% 246.59/246.95 Found x03 as proof of (P0 b)
% 246.59/246.95 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 246.59/246.95 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 246.59/246.95 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 246.59/246.95 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 246.59/246.95 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 246.59/246.95 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 246.59/246.95 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 246.59/246.95 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 246.59/246.95 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 246.59/246.95 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 246.59/246.95 Found eq_ref00:=(eq_ref0 ((q f) x)):(((eq Prop) ((q f) x)) ((q f) x))
% 246.59/246.95 Found (eq_ref0 ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 246.59/246.95 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 246.59/246.95 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 246.59/246.95 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 246.59/246.95 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 246.59/246.95 Found (eq_ref0 (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 246.59/246.95 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 246.59/246.95 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 246.59/246.95 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 246.59/246.95 Found (eq_ref0 (f x)) as proof of (P x)
% 246.59/246.95 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 246.59/246.95 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 246.59/246.95 Found x01:(P (f x))
% 246.59/246.95 Instantiate: b:=(f x):Prop
% 246.59/246.95 Found x01 as proof of (P0 b)
% 246.59/246.95 Found eq_ref00:=(eq_ref0 (f ((q f) x))):(((eq Prop) (f ((q f) x))) (f ((q f) x)))
% 246.59/246.95 Found (eq_ref0 (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 246.59/246.95 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 246.59/246.95 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 246.59/246.95 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 246.59/246.95 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 246.59/246.95 Found (eq_ref00 P) as proof of (P0 x)
% 246.59/246.95 Found ((eq_ref0 x) P) as proof of (P0 x)
% 246.59/246.95 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 246.59/246.95 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 246.59/246.95 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 246.59/246.95 Found (eq_ref0 b) as proof of (((eq Prop) b) ((q f) x))
% 246.59/246.95 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 246.59/246.95 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 246.59/246.95 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 267.79/268.17 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 267.79/268.17 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 267.79/268.17 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 267.79/268.17 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 267.79/268.17 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 267.79/268.17 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 267.79/268.17 Found (eq_ref0 b) as proof of (((eq Prop) b) ((q f) x))
% 267.79/268.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 267.79/268.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 267.79/268.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 267.79/268.17 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 267.79/268.17 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 267.79/268.17 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 267.79/268.17 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 267.79/268.17 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 267.79/268.17 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 267.79/268.17 Found (eq_ref0 (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 267.79/268.17 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 267.79/268.17 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 267.79/268.17 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 267.79/268.17 Found (eq_ref0 (f x)) as proof of (P x)
% 267.79/268.17 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 267.79/268.17 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 267.79/268.17 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 267.79/268.17 Found (eq_ref00 P) as proof of (P0 x)
% 267.79/268.17 Found ((eq_ref0 x) P) as proof of (P0 x)
% 267.79/268.17 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 267.79/268.17 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 267.79/268.17 Found x03:(P (f ((q f) x)))
% 267.79/268.17 Instantiate: b:=(f ((q f) x)):Prop
% 267.79/268.17 Found x03 as proof of (P0 b)
% 267.79/268.17 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 267.79/268.17 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 267.79/268.17 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 267.79/268.17 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 267.79/268.17 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 267.79/268.17 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 267.79/268.17 Found (eq_ref00 P) as proof of (P0 x)
% 267.79/268.17 Found ((eq_ref0 x) P) as proof of (P0 x)
% 267.79/268.17 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 267.79/268.17 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 267.79/268.17 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 267.79/268.17 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 267.79/268.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 267.79/268.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 267.79/268.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 267.79/268.17 Found eq_ref00:=(eq_ref0 ((q f) x)):(((eq Prop) ((q f) x)) ((q f) x))
% 267.79/268.17 Found (eq_ref0 ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 267.79/268.17 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 267.79/268.17 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 267.79/268.17 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 267.79/268.17 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 267.79/268.17 Found (eq_ref00 P) as proof of (P0 ((P (f x))->(P (f x))))
% 267.79/268.17 Found ((eq_ref0 (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 267.79/268.17 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 267.79/268.17 Found (((eq_ref Prop) (f x)) P) as proof of (P0 ((P (f x))->(P (f x))))
% 267.79/268.17 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 267.79/268.17 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 267.79/268.17 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 267.79/268.17 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 267.79/268.17 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 267.79/268.17 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 267.79/268.17 Found (eq_ref00 P) as proof of (P0 (P (f x)))
% 267.79/268.17 Found ((eq_ref0 (f x)) P) as proof of (P0 (P (f x)))
% 267.79/268.17 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 267.79/268.17 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (P (f x)))
% 267.79/268.17 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 267.79/268.17 Found (eq_ref00 P) as proof of (P0 x)
% 267.79/268.17 Found ((eq_ref0 (f x)) P) as proof of (P0 x)
% 267.79/268.17 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 267.79/268.17 Found (((eq_ref Prop) (f x)) P) as proof of (P0 x)
% 267.79/268.17 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 267.79/268.17 Found (eq_ref00 P) as proof of (P0 (f x))
% 267.79/268.17 Found ((eq_ref0 (f x)) P) as proof of (P0 (f x))
% 267.79/268.17 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 267.79/268.17 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 267.79/268.17 Found x01:(P (f ((q f) x)))
% 282.55/282.99 Instantiate: b:=(f ((q f) x)):Prop
% 282.55/282.99 Found x01 as proof of (P0 b)
% 282.55/282.99 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 282.55/282.99 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 282.55/282.99 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 282.55/282.99 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 282.55/282.99 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 282.55/282.99 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 282.55/282.99 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 282.55/282.99 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 282.55/282.99 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 282.55/282.99 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 282.55/282.99 Found eq_ref00:=(eq_ref0 ((q f) x)):(((eq Prop) ((q f) x)) ((q f) x))
% 282.55/282.99 Found (eq_ref0 ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 282.55/282.99 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 282.55/282.99 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 282.55/282.99 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 282.55/282.99 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 282.55/282.99 Found (eq_ref0 b) as proof of (((eq Prop) b) ((q f) x))
% 282.55/282.99 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 282.55/282.99 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 282.55/282.99 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 282.55/282.99 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 282.55/282.99 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 282.55/282.99 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 282.55/282.99 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 282.55/282.99 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 282.55/282.99 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 282.55/282.99 Found (eq_ref0 b) as proof of (((eq Prop) b) ((q f) x))
% 282.55/282.99 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 282.55/282.99 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 282.55/282.99 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 282.55/282.99 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 282.55/282.99 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 282.55/282.99 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 282.55/282.99 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 282.55/282.99 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 282.55/282.99 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 282.55/282.99 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 282.55/282.99 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 282.55/282.99 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 282.55/282.99 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 282.55/282.99 Found eq_ref00:=(eq_ref0 ((q f) x)):(((eq Prop) ((q f) x)) ((q f) x))
% 282.55/282.99 Found (eq_ref0 ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 282.55/282.99 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 282.55/282.99 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 282.55/282.99 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 282.55/282.99 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 282.55/282.99 Found (eq_ref0 b) as proof of (P b)
% 282.55/282.99 Found ((eq_ref Prop) b) as proof of (P b)
% 282.55/282.99 Found ((eq_ref Prop) b) as proof of (P b)
% 282.55/282.99 Found ((eq_ref Prop) b) as proof of (P b)
% 282.55/282.99 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 282.55/282.99 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 282.55/282.99 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 282.55/282.99 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 282.55/282.99 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 282.55/282.99 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 282.55/282.99 Found (eq_ref00 P) as proof of (P0 x)
% 282.55/282.99 Found ((eq_ref0 x) P) as proof of (P0 x)
% 282.55/282.99 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 282.55/282.99 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 282.55/282.99 Found x03:(P (f ((q f) x)))
% 282.55/282.99 Instantiate: b:=(f ((q f) x)):Prop
% 282.55/282.99 Found x03 as proof of (P0 b)
% 282.55/282.99 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 282.55/282.99 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 282.55/282.99 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 282.55/282.99 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 282.55/282.99 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 282.55/282.99 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 282.55/282.99 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 282.55/282.99 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 282.55/282.99 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 282.55/282.99 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 282.55/282.99 Found eq_ref00:=(eq_ref0 ((q f) x)):(((eq Prop) ((q f) x)) ((q f) x))
% 292.36/292.76 Found (eq_ref0 ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 292.36/292.76 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 292.36/292.76 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 292.36/292.76 Found ((eq_ref Prop) ((q f) x)) as proof of (((eq Prop) ((q f) x)) b)
% 292.36/292.76 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 292.36/292.76 Found (eq_ref0 b) as proof of (((eq Prop) b) ((q f) x))
% 292.36/292.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 292.36/292.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 292.36/292.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 292.36/292.76 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 292.36/292.76 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 292.36/292.76 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 292.36/292.76 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 292.36/292.76 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 292.36/292.76 Found eq_ref000:=(eq_ref00 P):((P (f ((q f) x)))->(P (f ((q f) x))))
% 292.36/292.76 Found (eq_ref00 P) as proof of (P0 (f ((q f) x)))
% 292.36/292.76 Found ((eq_ref0 (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 292.36/292.76 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 292.36/292.76 Found (((eq_ref Prop) (f ((q f) x))) P) as proof of (P0 (f ((q f) x)))
% 292.36/292.76 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 292.36/292.76 Found (eq_ref0 (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 292.36/292.76 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 292.36/292.76 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 292.36/292.76 Found eq_ref00:=(eq_ref0 (f ((q f) x))):(((eq Prop) (f ((q f) x))) (f ((q f) x)))
% 292.36/292.76 Found (eq_ref0 (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 292.36/292.76 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 292.36/292.76 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 292.36/292.76 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 292.36/292.76 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 292.36/292.76 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 292.36/292.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 292.36/292.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 292.36/292.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 292.36/292.76 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 292.36/292.76 Found (eq_ref0 (f x)) as proof of (P x)
% 292.36/292.76 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 292.36/292.76 Found ((eq_ref Prop) (f x)) as proof of (P x)
% 292.36/292.76 Found eq_ref00:=(eq_ref0 (f ((q f) x))):(((eq Prop) (f ((q f) x))) (f ((q f) x)))
% 292.36/292.76 Found (eq_ref0 (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 292.36/292.76 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 292.36/292.76 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 292.36/292.76 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 292.36/292.76 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 292.36/292.76 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 292.36/292.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 292.36/292.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 292.36/292.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 292.36/292.76 Found x01:(P (f x))
% 292.36/292.76 Instantiate: b:=(f x):Prop
% 292.36/292.76 Found x01 as proof of (P0 b)
% 292.36/292.76 Found eq_ref00:=(eq_ref0 (f ((q f) x))):(((eq Prop) (f ((q f) x))) (f ((q f) x)))
% 292.36/292.76 Found (eq_ref0 (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 292.36/292.76 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 292.36/292.76 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 292.36/292.76 Found ((eq_ref Prop) (f ((q f) x))) as proof of (((eq Prop) (f ((q f) x))) b)
% 292.36/292.76 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 292.36/292.76 Found (eq_ref00 P) as proof of (P0 x)
% 292.36/292.76 Found ((eq_ref0 x) P) as proof of (P0 x)
% 292.36/292.76 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 292.36/292.76 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 292.36/292.76 Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% 292.36/292.76 Found (eq_ref00 P) as proof of (P0 b)
% 292.36/292.76 Found ((eq_ref0 b) P) as proof of (P0 b)
% 292.36/292.76 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 292.36/292.76 Found (((eq_ref Prop) b) P) as proof of (P0 b)
% 292.36/292.76 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 292.36/292.76 Found (eq_ref0 b) as proof of (((eq Prop) b) ((q f) x))
% 292.36/292.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 292.36/292.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((q f) x))
% 292.36/292.76 Found ((eq_ref Prop) b) as proof of (
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