TSTP Solution File: SYO191^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO191^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/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 00:50:52 EDT 2022
% Result : Timeout 290.55s 290.92s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYO191^5 : TPTP v7.5.0. Released v4.0.0.
% 0.03/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % RAMPerCPU : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Fri Mar 11 17:31:11 EST 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.13/0.34 Python 2.7.5
% 1.09/1.26 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 1.09/1.26 FOF formula ((ex Prop) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) of role conjecture named cCT14
% 1.09/1.26 Conjecture to prove = ((ex Prop) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))):Prop
% 1.09/1.26 We need to prove ['((ex Prop) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))))']
% 1.09/1.26 Trying to prove ((ex Prop) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))))
% 1.09/1.26 Found False:Prop
% 1.09/1.26 Found False as proof of Prop
% 1.09/1.26 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 1.09/1.26 Found (eq_ref0 x) as proof of (((eq Prop) x) x)
% 1.09/1.26 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x)
% 1.09/1.26 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) x)
% 1.09/1.26 Found (ex_intro010 ((eq_ref Prop) x)) as proof of ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 1.09/1.26 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))):(((eq (Prop->Prop)) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) (fun (x:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))))
% 1.09/1.26 Found (eta_expansion_dep00 (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) as proof of (((eq (Prop->Prop)) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) b)
% 1.09/1.26 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) as proof of (((eq (Prop->Prop)) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) b)
% 1.09/1.26 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) as proof of (((eq (Prop->Prop)) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) b)
% 1.09/1.26 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) as proof of (((eq (Prop->Prop)) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) b)
% 1.09/1.26 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) as proof of (((eq (Prop->Prop)) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) b)
% 1.09/1.26 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 1.09/1.26 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))
% 1.09/1.26 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))
% 1.09/1.26 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))
% 1.09/1.26 Found (fun (x:Prop)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))
% 1.09/1.26 Found (fun (x:Prop)=> ((eq_ref Prop) (f x))) as proof of (forall (x:Prop), (((eq Prop) (f x)) ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))))
% 1.09/1.26 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 1.09/1.26 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))
% 1.09/1.26 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))
% 1.09/1.26 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))
% 1.09/1.26 Found (fun (x:Prop)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))
% 1.09/1.26 Found (fun (x:Prop)=> ((eq_ref Prop) (f x))) as proof of (forall (x:Prop), (((eq Prop) (f x)) ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))))
% 1.09/1.26 Found eq_ref00:=(eq_ref0 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))):(((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 1.09/1.26 Found (eq_ref0 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b)
% 1.09/1.26 Found ((eq_ref (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b)
% 1.09/1.26 Found ((eq_ref (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b)
% 1.95/2.12 Found ((eq_ref (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b)
% 1.95/2.12 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 1.95/2.12 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (((eq Prop) x) x))
% 1.95/2.12 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq Prop) x) x))
% 1.95/2.12 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq Prop) x) x))
% 1.95/2.12 Found (fun (x:Prop)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (((eq Prop) x) x))
% 1.95/2.12 Found (fun (x:Prop)=> ((eq_ref Prop) (f x))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (((eq Prop) x) x)))
% 1.95/2.12 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 1.95/2.12 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (((eq Prop) x) x))
% 1.95/2.12 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq Prop) x) x))
% 1.95/2.12 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq Prop) x) x))
% 1.95/2.12 Found (fun (x:Prop)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (((eq Prop) x) x))
% 1.95/2.12 Found (fun (x:Prop)=> ((eq_ref Prop) (f x))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (((eq Prop) x) x)))
% 1.95/2.12 Found eta_expansion000:=(eta_expansion00 a):(((eq (Prop->Prop)) a) (fun (x:Prop)=> (a x)))
% 1.95/2.12 Found (eta_expansion00 a) as proof of (((eq (Prop->Prop)) a) b)
% 1.95/2.12 Found ((eta_expansion0 Prop) a) as proof of (((eq (Prop->Prop)) a) b)
% 1.95/2.12 Found (((eta_expansion Prop) Prop) a) as proof of (((eq (Prop->Prop)) a) b)
% 1.95/2.12 Found (((eta_expansion Prop) Prop) a) as proof of (((eq (Prop->Prop)) a) b)
% 1.95/2.12 Found (((eta_expansion Prop) Prop) a) as proof of (((eq (Prop->Prop)) a) b)
% 1.95/2.12 Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (Prop->Prop)) b) (fun (x:Prop)=> (b x)))
% 1.95/2.12 Found (eta_expansion_dep00 b) as proof of (((eq (Prop->Prop)) b) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))))
% 1.95/2.12 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))))
% 1.95/2.12 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))))
% 1.95/2.12 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))))
% 1.95/2.12 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))))
% 1.95/2.12 Found eq_ref00:=(eq_ref0 b):(((eq (Prop->Prop)) b) b)
% 1.95/2.12 Found (eq_ref0 b) as proof of (((eq (Prop->Prop)) b) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))))
% 1.95/2.12 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))))
% 1.95/2.12 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))))
% 1.95/2.12 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))))
% 1.95/2.12 Found eq_ref00:=(eq_ref0 a):(((eq (Prop->Prop)) a) a)
% 1.95/2.12 Found (eq_ref0 a) as proof of (((eq (Prop->Prop)) a) b)
% 1.95/2.12 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 1.95/2.12 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 1.95/2.12 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 1.95/2.12 Found eq_ref00:=(eq_ref0 b):(((eq (Prop->Prop)) b) b)
% 1.95/2.12 Found (eq_ref0 b) as proof of (((eq (Prop->Prop)) b) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 1.95/2.12 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 1.95/2.12 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 1.95/2.12 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 1.95/2.12 Found x0:(P0 x)
% 1.95/2.12 Found (fun (x0:(P0 x))=> x0) as proof of (P0 x)
% 1.95/2.12 Found (fun (P0:(Prop->Prop)) (x0:(P0 x))=> x0) as proof of ((P0 x)->(P0 x))
% 1.95/2.12 Found (fun (P0:(Prop->Prop)) (x0:(P0 x))=> x0) as proof of (b x)
% 4.10/4.32 Found (ex_intro010 (fun (P0:(Prop->Prop)) (x0:(P0 x))=> x0)) as proof of ((ex Prop) b)
% 4.10/4.32 Found x0:(P0 x)
% 4.10/4.32 Found (fun (x0:(P0 x))=> x0) as proof of (P0 x)
% 4.10/4.32 Found (fun (P0:(Prop->Prop)) (x0:(P0 x))=> x0) as proof of ((P0 x)->(P0 x))
% 4.10/4.32 Found (fun (P0:(Prop->Prop)) (x0:(P0 x))=> x0) as proof of (f x)
% 4.10/4.32 Found (ex_intro010 (fun (P0:(Prop->Prop)) (x0:(P0 x))=> x0)) as proof of ((ex Prop) f)
% 4.10/4.32 Found x0:(P0 x)
% 4.10/4.32 Found (fun (x0:(P0 x))=> x0) as proof of (P0 x)
% 4.10/4.32 Found (fun (P0:(Prop->Prop)) (x0:(P0 x))=> x0) as proof of ((P0 x)->(P0 x))
% 4.10/4.32 Found (fun (P0:(Prop->Prop)) (x0:(P0 x))=> x0) as proof of (f x)
% 4.10/4.32 Found (ex_intro010 (fun (P0:(Prop->Prop)) (x0:(P0 x))=> x0)) as proof of ((ex Prop) f)
% 4.10/4.32 Found x0:(P0 x)
% 4.10/4.32 Found (fun (x0:(P0 x))=> x0) as proof of (P0 x)
% 4.10/4.32 Found (fun (P0:(Prop->Prop)) (x0:(P0 x))=> x0) as proof of ((P0 x)->(P0 x))
% 4.10/4.32 Found (fun (P0:(Prop->Prop)) (x0:(P0 x))=> x0) as proof of (a x)
% 4.10/4.32 Found (ex_intro010 (fun (P0:(Prop->Prop)) (x0:(P0 x))=> x0)) as proof of ((ex Prop) a)
% 4.10/4.32 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))):(((eq (Prop->Prop)) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) (fun (x:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))))
% 4.10/4.32 Found (eta_expansion_dep00 (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) as proof of (((eq (Prop->Prop)) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) b0)
% 4.10/4.32 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) as proof of (((eq (Prop->Prop)) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) b0)
% 4.10/4.32 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) as proof of (((eq (Prop->Prop)) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) b0)
% 4.10/4.32 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) as proof of (((eq (Prop->Prop)) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) b0)
% 4.10/4.32 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) as proof of (((eq (Prop->Prop)) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) b0)
% 4.10/4.32 Found eq_ref00:=(eq_ref0 x0):(((eq Prop) x0) x0)
% 4.10/4.32 Found (eq_ref0 x0) as proof of (((eq Prop) x0) x0)
% 4.10/4.32 Found ((eq_ref Prop) x0) as proof of (((eq Prop) x0) x0)
% 4.10/4.32 Found ((eq_ref Prop) x0) as proof of (((eq Prop) x0) x0)
% 4.10/4.32 Found (ex_intro010 ((eq_ref Prop) x0)) as proof of ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 4.10/4.32 Found eq_ref00:=(eq_ref0 x0):(((eq Prop) x0) x0)
% 4.10/4.32 Found (eq_ref0 x0) as proof of (((eq Prop) x0) x0)
% 4.10/4.32 Found ((eq_ref Prop) x0) as proof of (((eq Prop) x0) x0)
% 4.10/4.32 Found ((eq_ref Prop) x0) as proof of (((eq Prop) x0) x0)
% 4.10/4.32 Found (ex_intro010 ((eq_ref Prop) x0)) as proof of ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 4.10/4.32 Found eq_ref00:=(eq_ref0 x0):(((eq Prop) x0) x0)
% 4.10/4.32 Found (eq_ref0 x0) as proof of (((eq Prop) x0) x0)
% 4.10/4.32 Found ((eq_ref Prop) x0) as proof of (((eq Prop) x0) x0)
% 4.10/4.32 Found ((eq_ref Prop) x0) as proof of (((eq Prop) x0) x0)
% 4.10/4.32 Found (ex_intro010 ((eq_ref Prop) x0)) as proof of ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 4.10/4.32 Found eq_ref00:=(eq_ref0 x0):(((eq Prop) x0) x0)
% 4.10/4.32 Found (eq_ref0 x0) as proof of (((eq Prop) x0) x0)
% 4.10/4.32 Found ((eq_ref Prop) x0) as proof of (((eq Prop) x0) x0)
% 4.10/4.32 Found ((eq_ref Prop) x0) as proof of (((eq Prop) x0) x0)
% 4.10/4.32 Found (ex_intro010 ((eq_ref Prop) x0)) as proof of ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 4.10/4.32 Found eq_ref00:=(eq_ref0 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))):(((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 4.10/4.32 Found (eq_ref0 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 4.10/4.32 Found ((eq_ref (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 4.10/4.32 Found ((eq_ref (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 4.79/5.03 Found ((eq_ref (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 4.79/5.03 Found eq_ref00:=(eq_ref0 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))):(((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 4.79/5.03 Found (eq_ref0 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b)
% 4.79/5.03 Found ((eq_ref (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b)
% 4.79/5.03 Found ((eq_ref (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b)
% 4.79/5.03 Found ((eq_ref (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b)
% 4.79/5.03 Found eq_ref00:=(eq_ref0 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))):(((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 4.79/5.03 Found (eq_ref0 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b)
% 4.79/5.03 Found ((eq_ref (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b)
% 4.79/5.03 Found ((eq_ref (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b)
% 4.79/5.03 Found ((eq_ref (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b)
% 4.79/5.03 Found eq_ref00:=(eq_ref0 (f0 x0)):(((eq Prop) (f0 x0)) (f0 x0))
% 4.79/5.03 Found (eq_ref0 (f0 x0)) as proof of (((eq Prop) (f0 x0)) (((eq Prop) x0) x0))
% 4.79/5.03 Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (((eq Prop) x0) x0))
% 4.79/5.03 Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (((eq Prop) x0) x0))
% 4.79/5.03 Found (fun (x0:Prop)=> ((eq_ref Prop) (f0 x0))) as proof of (((eq Prop) (f0 x0)) (((eq Prop) x0) x0))
% 4.79/5.03 Found (fun (x0:Prop)=> ((eq_ref Prop) (f0 x0))) as proof of (forall (x:Prop), (((eq Prop) (f0 x)) (((eq Prop) x) x)))
% 4.79/5.03 Found eq_ref00:=(eq_ref0 (f0 x0)):(((eq Prop) (f0 x0)) (f0 x0))
% 4.79/5.03 Found (eq_ref0 (f0 x0)) as proof of (((eq Prop) (f0 x0)) (((eq Prop) x0) x0))
% 4.79/5.03 Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (((eq Prop) x0) x0))
% 4.79/5.03 Found ((eq_ref Prop) (f0 x0)) as proof of (((eq Prop) (f0 x0)) (((eq Prop) x0) x0))
% 4.79/5.03 Found (fun (x0:Prop)=> ((eq_ref Prop) (f0 x0))) as proof of (((eq Prop) (f0 x0)) (((eq Prop) x0) x0))
% 4.79/5.03 Found (fun (x0:Prop)=> ((eq_ref Prop) (f0 x0))) as proof of (forall (x:Prop), (((eq Prop) (f0 x)) (((eq Prop) x) x)))
% 4.79/5.03 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 4.79/5.03 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x0) x0))
% 4.79/5.03 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x0) x0))
% 4.79/5.03 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x0) x0))
% 4.79/5.03 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq Prop) x0) x0))
% 4.79/5.03 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (((eq Prop) x) x)))
% 4.79/5.03 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 4.79/5.03 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x0) x0))
% 4.79/5.03 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x0) x0))
% 4.79/5.03 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x0) x0))
% 4.79/5.03 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq Prop) x0) x0))
% 4.79/5.03 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (((eq Prop) x) x)))
% 4.79/5.03 Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (Prop->Prop)) a) (fun (x:Prop)=> (a x)))
% 4.79/5.03 Found (eta_expansion_dep00 a) as proof of (((eq (Prop->Prop)) a) b)
% 4.79/5.03 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 4.79/5.03 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 10.20/10.36 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 10.20/10.36 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 10.20/10.36 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 10.20/10.36 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 10.20/10.36 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 10.20/10.36 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 10.20/10.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 10.20/10.36 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 10.20/10.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 10.20/10.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 10.20/10.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 10.20/10.36 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 10.20/10.36 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 10.20/10.36 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 10.20/10.36 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 10.20/10.36 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 10.20/10.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 10.20/10.36 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 10.20/10.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 10.20/10.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 10.20/10.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 10.20/10.36 Found x10:(P1 (f x0))
% 10.20/10.36 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P1 (f x0))
% 10.20/10.36 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P2 (f x0))
% 10.20/10.36 Found x10:(P1 (f x0))
% 10.20/10.36 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P1 (f x0))
% 10.20/10.36 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P2 (f x0))
% 10.20/10.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 10.20/10.36 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 10.20/10.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 10.20/10.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 10.20/10.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 10.20/10.36 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 10.20/10.36 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 10.20/10.36 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 10.20/10.36 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 10.20/10.36 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 10.20/10.36 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 10.20/10.36 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 10.20/10.36 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 10.20/10.36 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 10.20/10.36 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 10.20/10.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 10.20/10.36 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 10.20/10.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 10.20/10.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 10.20/10.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 10.20/10.36 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 10.20/10.36 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 10.20/10.36 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 10.20/10.36 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 10.20/10.36 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 10.20/10.36 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 10.20/10.36 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 10.20/10.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 10.20/10.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 10.20/10.36 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 10.20/10.36 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 10.20/10.36 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 10.20/10.36 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 10.20/10.36 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 10.20/10.36 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 17.33/17.54 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 17.33/17.54 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 17.33/17.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 17.33/17.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 17.33/17.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 17.33/17.54 Found x10:(P1 (f x0))
% 17.33/17.54 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P1 (f x0))
% 17.33/17.54 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P2 (f x0))
% 17.33/17.54 Found x10:(P1 (f x0))
% 17.33/17.54 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P1 (f x0))
% 17.33/17.54 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P2 (f x0))
% 17.33/17.54 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 17.33/17.54 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 17.33/17.54 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 17.33/17.54 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 17.33/17.54 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 17.33/17.54 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 17.33/17.54 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 17.33/17.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 17.33/17.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 17.33/17.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 17.33/17.54 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 17.33/17.54 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 17.33/17.54 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 17.33/17.54 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 17.33/17.54 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 17.33/17.54 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 17.33/17.54 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 17.33/17.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 17.33/17.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 17.33/17.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 17.33/17.54 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 17.33/17.54 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 17.33/17.54 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 17.33/17.54 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 17.33/17.54 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 17.33/17.54 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 17.33/17.54 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 17.33/17.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 17.33/17.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 17.33/17.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 17.33/17.54 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 17.33/17.54 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 17.33/17.54 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 17.33/17.54 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 17.33/17.54 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 17.33/17.54 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 17.33/17.54 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 17.33/17.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 17.33/17.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 17.33/17.54 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 17.33/17.54 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))):(((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) (fun (x:Prop)=> (((eq Prop) x) x)))
% 17.33/17.54 Found (eta_expansion_dep00 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 17.33/17.54 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 17.33/17.54 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 18.98/19.17 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 18.98/19.17 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 18.98/19.17 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 18.98/19.17 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x0) x0))
% 18.98/19.17 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x0) x0))
% 18.98/19.17 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x0) x0))
% 18.98/19.17 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq Prop) x0) x0))
% 18.98/19.17 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (((eq Prop) x) x)))
% 18.98/19.17 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 18.98/19.17 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x0) x0))
% 18.98/19.17 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x0) x0))
% 18.98/19.17 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq Prop) x0) x0))
% 18.98/19.17 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq Prop) x0) x0))
% 18.98/19.17 Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (((eq Prop) x) x)))
% 18.98/19.17 Found eta_expansion000:=(eta_expansion00 b0):(((eq (Prop->Prop)) b0) (fun (x:Prop)=> (b0 x)))
% 18.98/19.17 Found (eta_expansion00 b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 18.98/19.17 Found ((eta_expansion0 Prop) b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 18.98/19.17 Found (((eta_expansion Prop) Prop) b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 18.98/19.17 Found (((eta_expansion Prop) Prop) b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 18.98/19.17 Found (((eta_expansion Prop) Prop) b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 18.98/19.17 Found eta_expansion000:=(eta_expansion00 a):(((eq (Prop->Prop)) a) (fun (x:Prop)=> (a x)))
% 18.98/19.17 Found (eta_expansion00 a) as proof of (((eq (Prop->Prop)) a) b0)
% 18.98/19.17 Found ((eta_expansion0 Prop) a) as proof of (((eq (Prop->Prop)) a) b0)
% 18.98/19.17 Found (((eta_expansion Prop) Prop) a) as proof of (((eq (Prop->Prop)) a) b0)
% 18.98/19.17 Found (((eta_expansion Prop) Prop) a) as proof of (((eq (Prop->Prop)) a) b0)
% 18.98/19.17 Found (((eta_expansion Prop) Prop) a) as proof of (((eq (Prop->Prop)) a) b0)
% 18.98/19.17 Found eq_ref00:=(eq_ref0 a):(((eq (Prop->Prop)) a) a)
% 18.98/19.17 Found (eq_ref0 a) as proof of (((eq (Prop->Prop)) a) b0)
% 18.98/19.17 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b0)
% 18.98/19.17 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b0)
% 18.98/19.17 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b0)
% 18.98/19.17 Found eq_ref00:=(eq_ref0 b):(((eq (Prop->Prop)) b) b)
% 18.98/19.17 Found (eq_ref0 b) as proof of (((eq (Prop->Prop)) b) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 18.98/19.17 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 18.98/19.17 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 18.98/19.17 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 18.98/19.17 Found eta_expansion000:=(eta_expansion00 a):(((eq (Prop->Prop)) a) (fun (x:Prop)=> (a x)))
% 18.98/19.17 Found (eta_expansion00 a) as proof of (((eq (Prop->Prop)) a) b)
% 18.98/19.17 Found ((eta_expansion0 Prop) a) as proof of (((eq (Prop->Prop)) a) b)
% 18.98/19.17 Found (((eta_expansion Prop) Prop) a) as proof of (((eq (Prop->Prop)) a) b)
% 18.98/19.17 Found (((eta_expansion Prop) Prop) a) as proof of (((eq (Prop->Prop)) a) b)
% 18.98/19.17 Found (((eta_expansion Prop) Prop) a) as proof of (((eq (Prop->Prop)) a) b)
% 18.98/19.17 Found eq_ref00:=(eq_ref0 a):(((eq (Prop->Prop)) a) a)
% 18.98/19.17 Found (eq_ref0 a) as proof of (((eq (Prop->Prop)) a) b)
% 18.98/19.17 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 18.98/19.17 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 24.56/24.74 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 24.56/24.74 Found eq_ref00:=(eq_ref0 b):(((eq (Prop->Prop)) b) b)
% 24.56/24.74 Found (eq_ref0 b) as proof of (((eq (Prop->Prop)) b) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 24.56/24.74 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 24.56/24.74 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 24.56/24.74 Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 24.56/24.74 Found eq_ref00:=(eq_ref0 a):(((eq (Prop->Prop)) a) a)
% 24.56/24.74 Found (eq_ref0 a) as proof of (((eq (Prop->Prop)) a) b)
% 24.56/24.74 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 24.56/24.74 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 24.56/24.74 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b)
% 24.56/24.74 Found eta_expansion000:=(eta_expansion00 b0):(((eq (Prop->Prop)) b0) (fun (x:Prop)=> (b0 x)))
% 24.56/24.74 Found (eta_expansion00 b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 24.56/24.74 Found ((eta_expansion0 Prop) b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 24.56/24.74 Found (((eta_expansion Prop) Prop) b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 24.56/24.74 Found (((eta_expansion Prop) Prop) b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 24.56/24.74 Found (((eta_expansion Prop) Prop) b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 24.56/24.74 Found eta_expansion000:=(eta_expansion00 a):(((eq (Prop->Prop)) a) (fun (x:Prop)=> (a x)))
% 24.56/24.74 Found (eta_expansion00 a) as proof of (((eq (Prop->Prop)) a) b0)
% 24.56/24.74 Found ((eta_expansion0 Prop) a) as proof of (((eq (Prop->Prop)) a) b0)
% 24.56/24.74 Found (((eta_expansion Prop) Prop) a) as proof of (((eq (Prop->Prop)) a) b0)
% 24.56/24.74 Found (((eta_expansion Prop) Prop) a) as proof of (((eq (Prop->Prop)) a) b0)
% 24.56/24.74 Found (((eta_expansion Prop) Prop) a) as proof of (((eq (Prop->Prop)) a) b0)
% 24.56/24.74 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))):(((eq (Prop->Prop)) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) (fun (x:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))))
% 24.56/24.74 Found (eta_expansion_dep00 (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) as proof of (((eq (Prop->Prop)) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) b1)
% 24.56/24.74 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) as proof of (((eq (Prop->Prop)) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) b1)
% 24.56/24.74 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) as proof of (((eq (Prop->Prop)) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) b1)
% 24.56/24.74 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) as proof of (((eq (Prop->Prop)) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) b1)
% 24.56/24.74 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) as proof of (((eq (Prop->Prop)) (fun (Xz:Prop)=> ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))) b1)
% 24.56/24.74 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 24.56/24.74 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 24.56/24.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 24.56/24.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 24.56/24.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 24.56/24.74 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 24.56/24.74 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 24.56/24.74 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 24.56/24.74 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 24.56/24.74 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 24.56/24.74 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 29.80/29.98 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 29.80/29.98 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 29.80/29.98 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 29.80/29.98 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 29.80/29.98 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 29.80/29.98 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 29.80/29.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 29.80/29.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 29.80/29.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 29.80/29.98 Found x1:(P1 (f x0))
% 29.80/29.98 Instantiate: b:=(f x0):Prop
% 29.80/29.98 Found x1 as proof of (P2 b)
% 29.80/29.98 Found x1:(P1 (f x0))
% 29.80/29.98 Instantiate: b:=(f x0):Prop
% 29.80/29.98 Found x1 as proof of (P2 b)
% 29.80/29.98 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 29.80/29.98 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 29.80/29.98 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 29.80/29.98 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 29.80/29.98 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 29.80/29.98 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 29.80/29.98 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 29.80/29.98 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 29.80/29.98 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 29.80/29.98 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 29.80/29.98 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 29.80/29.98 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 29.80/29.98 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 29.80/29.98 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 29.80/29.98 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 29.80/29.98 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 29.80/29.98 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 29.80/29.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 29.80/29.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 29.80/29.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 29.80/29.98 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 29.80/29.98 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 29.80/29.98 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 29.80/29.98 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 29.80/29.98 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 29.80/29.98 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 29.80/29.98 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 29.80/29.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 29.80/29.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 29.80/29.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 29.80/29.98 Found x10:(P1 (f x0))
% 29.80/29.98 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P1 (f x0))
% 29.80/29.98 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P2 (f x0))
% 29.80/29.98 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 29.80/29.98 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 29.80/29.98 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 29.80/29.98 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 29.80/29.98 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 29.80/29.98 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 29.80/29.98 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 29.80/29.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 29.80/29.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 29.80/29.98 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 29.80/29.98 Found x10:(P1 (f x0))
% 29.80/29.98 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P1 (f x0))
% 29.80/29.98 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P2 (f x0))
% 29.80/29.98 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 29.80/29.98 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 32.43/32.67 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 32.43/32.67 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 32.43/32.67 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 32.43/32.67 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 32.43/32.67 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 32.43/32.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 32.43/32.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 32.43/32.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 32.43/32.67 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 32.43/32.67 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 32.43/32.67 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 32.43/32.67 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 32.43/32.67 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 32.43/32.67 Found x1:(P2 b)
% 32.43/32.67 Instantiate: b:=((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))):Prop
% 32.43/32.67 Found (fun (x1:(P2 b))=> x1) as proof of (P2 (f x0))
% 32.43/32.67 Found (fun (P2:(Prop->Prop)) (x1:(P2 b))=> x1) as proof of ((P2 b)->(P2 (f x0)))
% 32.43/32.67 Found (fun (P2:(Prop->Prop)) (x1:(P2 b))=> x1) as proof of (P1 b)
% 32.43/32.67 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 32.43/32.67 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 32.43/32.67 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 32.43/32.67 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 32.43/32.67 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 32.43/32.67 Found x1:(P2 b)
% 32.43/32.67 Instantiate: b:=((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))):Prop
% 32.43/32.67 Found (fun (x1:(P2 b))=> x1) as proof of (P2 (f x0))
% 32.43/32.67 Found (fun (P2:(Prop->Prop)) (x1:(P2 b))=> x1) as proof of ((P2 b)->(P2 (f x0)))
% 32.43/32.67 Found (fun (P2:(Prop->Prop)) (x1:(P2 b))=> x1) as proof of (P1 b)
% 32.43/32.67 Found x1:(P1 x0)
% 32.43/32.67 Found (fun (x1:(P1 x0))=> x1) as proof of (P1 x0)
% 32.43/32.67 Found (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1) as proof of ((P1 x0)->(P1 x0))
% 32.43/32.67 Found (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1) as proof of (b0 x0)
% 32.43/32.67 Found (ex_intro010 (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1)) as proof of ((ex Prop) b0)
% 32.43/32.67 Found x1:(P1 x0)
% 32.43/32.67 Found (fun (x1:(P1 x0))=> x1) as proof of (P1 x0)
% 32.43/32.67 Found (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1) as proof of ((P1 x0)->(P1 x0))
% 32.43/32.67 Found (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1) as proof of (f0 x0)
% 32.43/32.67 Found (ex_intro010 (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1)) as proof of ((ex Prop) f0)
% 32.43/32.67 Found x1:(P1 x0)
% 32.43/32.67 Found (fun (x1:(P1 x0))=> x1) as proof of (P1 x0)
% 32.43/32.67 Found (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1) as proof of ((P1 x0)->(P1 x0))
% 32.43/32.67 Found (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1) as proof of (f0 x0)
% 32.43/32.67 Found (ex_intro010 (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1)) as proof of ((ex Prop) f0)
% 32.43/32.67 Found x1:(P1 x0)
% 32.43/32.67 Found (fun (x1:(P1 x0))=> x1) as proof of (P1 x0)
% 32.43/32.67 Found (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1) as proof of ((P1 x0)->(P1 x0))
% 32.43/32.67 Found (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1) as proof of (b x0)
% 32.43/32.67 Found (ex_intro010 (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1)) as proof of ((ex Prop) b)
% 32.43/32.67 Found x1:(P1 x0)
% 32.43/32.67 Found (fun (x1:(P1 x0))=> x1) as proof of (P1 x0)
% 32.43/32.67 Found (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1) as proof of ((P1 x0)->(P1 x0))
% 32.43/32.67 Found (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1) as proof of (b x0)
% 32.43/32.67 Found (ex_intro010 (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1)) as proof of ((ex Prop) b)
% 32.43/32.67 Found x1:(P1 x0)
% 32.43/32.67 Found (fun (x1:(P1 x0))=> x1) as proof of (P1 x0)
% 32.43/32.67 Found (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1) as proof of ((P1 x0)->(P1 x0))
% 32.43/32.67 Found (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1) as proof of (f x0)
% 32.43/32.67 Found (ex_intro010 (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1)) as proof of ((ex Prop) f)
% 32.43/32.67 Found x1:(P1 x0)
% 32.43/32.67 Found (fun (x1:(P1 x0))=> x1) as proof of (P1 x0)
% 32.43/32.67 Found (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1) as proof of ((P1 x0)->(P1 x0))
% 32.43/32.67 Found (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1) as proof of (f x0)
% 32.43/32.67 Found (ex_intro010 (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1)) as proof of ((ex Prop) f)
% 37.79/38.01 Found x1:(P1 (((eq Prop) x0) x0))
% 37.79/38.01 Instantiate: b:=(((eq Prop) x0) x0):Prop
% 37.79/38.01 Found x1 as proof of (P2 b)
% 37.79/38.01 Found x1:(P1 (((eq Prop) x0) x0))
% 37.79/38.01 Instantiate: b:=(((eq Prop) x0) x0):Prop
% 37.79/38.01 Found x1 as proof of (P2 b)
% 37.79/38.01 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 37.79/38.01 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 37.79/38.01 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 37.79/38.01 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 37.79/38.01 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 37.79/38.01 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 37.79/38.01 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 37.79/38.01 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 37.79/38.01 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 37.79/38.01 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 37.79/38.01 Found eq_ref00:=(eq_ref0 a):(((eq (Prop->Prop)) a) a)
% 37.79/38.01 Found (eq_ref0 a) as proof of (((eq (Prop->Prop)) a) b0)
% 37.79/38.01 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b0)
% 37.79/38.01 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b0)
% 37.79/38.01 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b0)
% 37.79/38.01 Found eta_expansion000:=(eta_expansion00 b0):(((eq (Prop->Prop)) b0) (fun (x:Prop)=> (b0 x)))
% 37.79/38.01 Found (eta_expansion00 b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 37.79/38.01 Found ((eta_expansion0 Prop) b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 37.79/38.01 Found (((eta_expansion Prop) Prop) b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 37.79/38.01 Found (((eta_expansion Prop) Prop) b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 37.79/38.01 Found (((eta_expansion Prop) Prop) b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 37.79/38.01 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 37.79/38.01 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 37.79/38.01 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 37.79/38.01 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 37.79/38.01 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 37.79/38.01 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 37.79/38.01 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 37.79/38.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 37.79/38.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 37.79/38.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 37.79/38.01 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 37.79/38.01 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 37.79/38.01 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 37.79/38.01 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 37.79/38.01 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 37.79/38.01 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 37.79/38.01 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 37.79/38.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 37.79/38.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 37.79/38.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 37.79/38.01 Found x00:(P1 b)
% 37.79/38.01 Found (fun (x00:(P1 b))=> x00) as proof of (P1 b)
% 37.79/38.01 Found (fun (x00:(P1 b))=> x00) as proof of (P2 b)
% 37.79/38.01 Found eq_ref00:=(eq_ref0 x0):(((eq Prop) x0) x0)
% 37.79/38.01 Found (eq_ref0 x0) as proof of (((eq Prop) x0) x0)
% 37.79/38.01 Found ((eq_ref Prop) x0) as proof of (((eq Prop) x0) x0)
% 37.79/38.01 Found ((eq_ref Prop) x0) as proof of (((eq Prop) x0) x0)
% 37.79/38.01 Found (ex_intro010 ((eq_ref Prop) x0)) as proof of ((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 37.79/38.01 Found x00:(P1 b)
% 37.79/38.01 Found (fun (x00:(P1 b))=> x00) as proof of (P1 b)
% 37.79/38.01 Found (fun (x00:(P1 b))=> x00) as proof of (P2 b)
% 37.79/38.01 Found x00:(P1 b)
% 37.79/38.01 Found (fun (x00:(P1 b))=> x00) as proof of (P1 b)
% 37.79/38.01 Found (fun (x00:(P1 b))=> x00) as proof of (P2 b)
% 37.79/38.01 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 37.79/38.01 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 37.79/38.01 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 37.79/38.01 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 38.92/39.16 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 38.92/39.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 38.92/39.16 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 38.92/39.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 38.92/39.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 38.92/39.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 38.92/39.16 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 38.92/39.16 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 38.92/39.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 38.92/39.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 38.92/39.16 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 38.92/39.16 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 38.92/39.16 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 38.92/39.16 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 38.92/39.16 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 38.92/39.17 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 38.92/39.17 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 38.92/39.17 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 38.92/39.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 38.92/39.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 38.92/39.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 38.92/39.17 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 38.92/39.17 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 38.92/39.17 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 38.92/39.17 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 38.92/39.17 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 38.92/39.17 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 38.92/39.17 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 38.92/39.17 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 38.92/39.17 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 38.92/39.17 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 38.92/39.17 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 38.92/39.17 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 38.92/39.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 38.92/39.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 38.92/39.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 38.92/39.17 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 38.92/39.17 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 38.92/39.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 38.92/39.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 38.92/39.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 38.92/39.17 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 38.92/39.17 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 38.92/39.17 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 38.92/39.17 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 38.92/39.17 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 38.92/39.17 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 38.92/39.17 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 38.92/39.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 38.92/39.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 38.92/39.17 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 38.92/39.17 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 38.92/39.17 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 38.92/39.17 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 38.92/39.17 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 38.92/39.17 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 38.92/39.17 Found x10:(P1 b)
% 38.92/39.17 Found (fun (x10:(P1 b))=> x10) as proof of (P1 b)
% 43.40/43.59 Found (fun (x10:(P1 b))=> x10) as proof of (P2 b)
% 43.40/43.59 Found x10:(P1 b)
% 43.40/43.59 Found (fun (x10:(P1 b))=> x10) as proof of (P1 b)
% 43.40/43.59 Found (fun (x10:(P1 b))=> x10) as proof of (P2 b)
% 43.40/43.59 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x0) x0))->(P1 (((eq Prop) x0) x0)))
% 43.40/43.59 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x0) x0))
% 43.40/43.59 Found ((eq_ref0 (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 43.40/43.59 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 43.40/43.59 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 43.40/43.59 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 43.40/43.59 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 43.40/43.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 43.40/43.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 43.40/43.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 43.40/43.59 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 43.40/43.59 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 43.40/43.59 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 43.40/43.59 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 43.40/43.59 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 43.40/43.59 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x0) x0))->(P1 (((eq Prop) x0) x0)))
% 43.40/43.59 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x0) x0))
% 43.40/43.59 Found ((eq_ref0 (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 43.40/43.59 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 43.40/43.59 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 43.40/43.59 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 43.40/43.59 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 43.40/43.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 43.40/43.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 43.40/43.59 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 43.40/43.59 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 43.40/43.59 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 43.40/43.59 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 43.40/43.59 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 43.40/43.59 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 43.40/43.59 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))):(((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) (fun (x:Prop)=> (((eq Prop) x) x)))
% 43.40/43.59 Found (eta_expansion_dep00 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 43.40/43.59 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 43.40/43.59 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 43.40/43.59 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 43.40/43.59 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 43.40/43.59 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (Prop->Prop)) b0) (fun (x:Prop)=> (b0 x)))
% 43.40/43.59 Found (eta_expansion_dep00 b0) as proof of (((eq (Prop->Prop)) b0) b)
% 43.40/43.59 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 43.40/43.59 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 43.40/43.59 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 43.40/43.59 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 43.40/43.59 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 43.40/43.59 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 47.22/47.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 47.22/47.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 47.22/47.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 47.22/47.41 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 47.22/47.41 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 47.22/47.41 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 47.22/47.41 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 47.22/47.41 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 47.22/47.41 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 47.22/47.41 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 47.22/47.41 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 47.22/47.41 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 47.22/47.41 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 47.22/47.41 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 47.22/47.41 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 47.22/47.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 47.22/47.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 47.22/47.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 47.22/47.41 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))->(P1 (fun (x:Prop)=> (((eq Prop) x) x))))
% 47.22/47.41 Found (eta_expansion_dep000 P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 47.22/47.41 Found ((eta_expansion_dep00 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 47.22/47.41 Found (((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 47.22/47.41 Found ((((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 47.22/47.41 Found ((((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 47.22/47.41 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))->(P1 (fun (x:Prop)=> (((eq Prop) x) x))))
% 47.22/47.41 Found (eta_expansion_dep000 P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 47.22/47.41 Found ((eta_expansion_dep00 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 47.22/47.41 Found (((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 47.22/47.41 Found ((((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 47.22/47.41 Found ((((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 47.22/47.41 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 47.22/47.41 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 47.22/47.41 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 47.22/47.41 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 47.22/47.41 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 47.22/47.41 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 47.22/47.41 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 47.22/47.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 47.22/47.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 47.22/47.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 47.22/47.41 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 47.22/47.41 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 47.22/47.41 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 47.22/47.41 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 60.56/60.80 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 60.56/60.80 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 60.56/60.80 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 60.56/60.80 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 60.56/60.80 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 60.56/60.80 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 60.56/60.80 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 60.56/60.80 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 60.56/60.80 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 60.56/60.80 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 60.56/60.80 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 60.56/60.80 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 60.56/60.80 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 60.56/60.80 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 60.56/60.80 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 60.56/60.80 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 60.56/60.80 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 60.56/60.80 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 60.56/60.80 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 60.56/60.80 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 60.56/60.80 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 60.56/60.80 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 60.56/60.80 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 60.56/60.80 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 60.56/60.80 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 60.56/60.80 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 60.56/60.80 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x0) x0))->(P1 (((eq Prop) x0) x0)))
% 60.56/60.80 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x0) x0))
% 60.56/60.80 Found ((eq_ref0 (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 60.56/60.80 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 60.56/60.80 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 60.56/60.80 Found x10:(P1 b)
% 60.56/60.80 Found (fun (x10:(P1 b))=> x10) as proof of (P1 b)
% 60.56/60.80 Found (fun (x10:(P1 b))=> x10) as proof of (P2 b)
% 60.56/60.80 Found x10:(P1 (b x0))
% 60.56/60.80 Found (fun (x10:(P1 (b x0)))=> x10) as proof of (P1 (b x0))
% 60.56/60.80 Found (fun (x10:(P1 (b x0)))=> x10) as proof of (P2 (b x0))
% 60.56/60.80 Found x10:(P1 (b x0))
% 60.56/60.80 Found (fun (x10:(P1 (b x0)))=> x10) as proof of (P1 (b x0))
% 60.56/60.80 Found (fun (x10:(P1 (b x0)))=> x10) as proof of (P2 (b x0))
% 60.56/60.80 Found x1:(P1 (f x0))
% 60.56/60.80 Instantiate: b:=(f x0):Prop
% 60.56/60.80 Found x1 as proof of (P2 b)
% 60.56/60.80 Found x1:(P1 (f x0))
% 60.56/60.80 Instantiate: b:=(f x0):Prop
% 60.56/60.80 Found x1 as proof of (P2 b)
% 60.56/60.80 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 60.56/60.80 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 60.56/60.80 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 60.56/60.80 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 60.56/60.80 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 60.56/60.80 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 60.56/60.80 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 60.56/60.80 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 60.56/60.80 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 60.56/60.80 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 60.56/60.80 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 60.56/60.80 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 60.56/60.80 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 60.56/60.80 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 60.56/60.80 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 60.56/60.80 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 60.56/60.80 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 60.56/60.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 60.56/60.80 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 65.85/66.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 65.85/66.05 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 65.85/66.05 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 65.85/66.05 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 65.85/66.05 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 65.85/66.05 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 65.85/66.05 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 65.85/66.05 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 65.85/66.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 65.85/66.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 65.85/66.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 65.85/66.05 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 65.85/66.05 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 65.85/66.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 65.85/66.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 65.85/66.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 65.85/66.05 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 65.85/66.05 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 65.85/66.05 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 65.85/66.05 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 65.85/66.05 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 65.85/66.05 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 65.85/66.05 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 65.85/66.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 65.85/66.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 65.85/66.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 65.85/66.05 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 65.85/66.05 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 65.85/66.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 65.85/66.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 65.85/66.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 65.85/66.05 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 65.85/66.05 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 65.85/66.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 65.85/66.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 65.85/66.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 65.85/66.05 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 65.85/66.05 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 65.85/66.05 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 65.85/66.05 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 65.85/66.05 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 65.85/66.05 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 65.85/66.05 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 65.85/66.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 65.85/66.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 65.85/66.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 65.85/66.05 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 65.85/66.05 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 65.85/66.05 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 65.85/66.05 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 65.85/66.05 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 65.85/66.05 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 65.85/66.05 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 65.85/66.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 65.85/66.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 65.85/66.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 65.85/66.05 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 65.85/66.05 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 65.85/66.05 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 65.85/66.05 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 65.85/66.05 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 69.34/69.62 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 69.34/69.62 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 69.34/69.62 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 69.34/69.62 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 69.34/69.62 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 69.34/69.62 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 69.34/69.62 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 69.34/69.62 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 69.34/69.62 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 69.34/69.62 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 69.34/69.62 Found x10:(P1 (f x0))
% 69.34/69.62 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P1 (f x0))
% 69.34/69.62 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P2 (f x0))
% 69.34/69.62 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 69.34/69.62 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 69.34/69.62 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 69.34/69.62 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 69.34/69.62 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 69.34/69.62 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 69.34/69.62 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 69.34/69.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 69.34/69.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 69.34/69.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 69.34/69.62 Found x10:(P1 (f x0))
% 69.34/69.62 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P1 (f x0))
% 69.34/69.62 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P2 (f x0))
% 69.34/69.62 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 69.34/69.62 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 69.34/69.62 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 69.34/69.62 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 69.34/69.62 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 69.34/69.62 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 69.34/69.62 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 69.34/69.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 69.34/69.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 69.34/69.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 69.34/69.62 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 69.34/69.62 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 69.34/69.62 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 69.34/69.62 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 69.34/69.62 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 69.34/69.62 Found x1:(P2 b)
% 69.34/69.62 Instantiate: b:=((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))):Prop
% 69.34/69.62 Found (fun (x1:(P2 b))=> x1) as proof of (P2 (f x0))
% 69.34/69.62 Found (fun (P2:(Prop->Prop)) (x1:(P2 b))=> x1) as proof of ((P2 b)->(P2 (f x0)))
% 69.34/69.62 Found (fun (P2:(Prop->Prop)) (x1:(P2 b))=> x1) as proof of (P1 b)
% 69.34/69.62 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 69.34/69.62 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 69.34/69.62 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 69.34/69.62 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 69.34/69.62 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 69.34/69.62 Found x1:(P2 b)
% 69.34/69.62 Instantiate: b:=((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))):Prop
% 69.34/69.62 Found (fun (x1:(P2 b))=> x1) as proof of (P2 (f x0))
% 69.34/69.62 Found (fun (P2:(Prop->Prop)) (x1:(P2 b))=> x1) as proof of ((P2 b)->(P2 (f x0)))
% 69.34/69.62 Found (fun (P2:(Prop->Prop)) (x1:(P2 b))=> x1) as proof of (P1 b)
% 69.34/69.62 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x0) x0))->(P1 (((eq Prop) x0) x0)))
% 69.34/69.62 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x0) x0))
% 69.34/69.62 Found ((eq_ref0 (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 69.34/69.62 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 86.98/87.20 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 86.98/87.20 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x0) x0))->(P1 (((eq Prop) x0) x0)))
% 86.98/87.20 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x0) x0))
% 86.98/87.20 Found ((eq_ref0 (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 86.98/87.20 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 86.98/87.20 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 86.98/87.20 Found x1:(P1 (((eq Prop) x0) x0))
% 86.98/87.20 Instantiate: b:=(((eq Prop) x0) x0):Prop
% 86.98/87.20 Found x1 as proof of (P2 b)
% 86.98/87.20 Found x1:(P1 (((eq Prop) x0) x0))
% 86.98/87.20 Instantiate: b:=(((eq Prop) x0) x0):Prop
% 86.98/87.20 Found x1 as proof of (P2 b)
% 86.98/87.20 Found x1:(P1 (((eq Prop) x0) x0))
% 86.98/87.20 Instantiate: b:=(((eq Prop) x0) x0):Prop
% 86.98/87.20 Found x1 as proof of (P2 b)
% 86.98/87.20 Found x1:(P1 (((eq Prop) x0) x0))
% 86.98/87.20 Instantiate: b:=(((eq Prop) x0) x0):Prop
% 86.98/87.20 Found x1 as proof of (P2 b)
% 86.98/87.20 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 86.98/87.20 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 86.98/87.20 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 86.98/87.20 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 86.98/87.20 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 86.98/87.20 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 86.98/87.20 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 86.98/87.20 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 86.98/87.20 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 86.98/87.20 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 86.98/87.20 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 86.98/87.20 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 86.98/87.20 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 86.98/87.20 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 86.98/87.20 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 86.98/87.20 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 86.98/87.20 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 86.98/87.20 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 86.98/87.20 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 86.98/87.20 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 86.98/87.20 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 86.98/87.20 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 86.98/87.20 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 86.98/87.20 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 86.98/87.20 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 86.98/87.20 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 86.98/87.20 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 86.98/87.20 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 86.98/87.20 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 86.98/87.20 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 86.98/87.20 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 86.98/87.20 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 86.98/87.20 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 86.98/87.20 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 86.98/87.20 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 86.98/87.20 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 86.98/87.20 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 86.98/87.20 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 86.98/87.20 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 86.98/87.20 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 86.98/87.20 Found x00:(P1 b)
% 86.98/87.20 Found (fun (x00:(P1 b))=> x00) as proof of (P1 b)
% 86.98/87.20 Found (fun (x00:(P1 b))=> x00) as proof of (P2 b)
% 86.98/87.20 Found x00:(P1 b)
% 86.98/87.20 Found (fun (x00:(P1 b))=> x00) as proof of (P1 b)
% 86.98/87.20 Found (fun (x00:(P1 b))=> x00) as proof of (P2 b)
% 86.98/87.20 Found x00:(P1 b)
% 86.98/87.20 Found (fun (x00:(P1 b))=> x00) as proof of (P1 b)
% 86.98/87.20 Found (fun (x00:(P1 b))=> x00) as proof of (P2 b)
% 86.98/87.20 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 86.98/87.20 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 86.98/87.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 86.98/87.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 86.98/87.20 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 86.98/87.20 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 88.42/88.64 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 88.42/88.64 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 88.42/88.64 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 88.42/88.64 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 88.42/88.64 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 88.42/88.64 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 88.42/88.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 88.42/88.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 88.42/88.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 88.42/88.64 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 88.42/88.64 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 88.42/88.64 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 88.42/88.64 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 88.42/88.64 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 88.42/88.64 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 88.42/88.64 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 88.42/88.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 88.42/88.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 88.42/88.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 88.42/88.64 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 88.42/88.64 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 88.42/88.64 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 88.42/88.64 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 88.42/88.64 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 88.42/88.64 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 88.42/88.64 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 88.42/88.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 88.42/88.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 88.42/88.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 88.42/88.64 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 88.42/88.64 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 88.42/88.64 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 88.42/88.64 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 88.42/88.64 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 88.42/88.64 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 88.42/88.64 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 88.42/88.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 88.42/88.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 88.42/88.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 88.42/88.64 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 88.42/88.64 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 88.42/88.64 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 88.42/88.64 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 88.42/88.64 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 88.42/88.64 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 88.42/88.64 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 88.42/88.64 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 88.42/88.64 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 88.42/88.64 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 88.42/88.64 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 88.42/88.64 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 88.42/88.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 88.42/88.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 88.42/88.64 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 89.65/89.89 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 89.65/89.89 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 89.65/89.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 89.65/89.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 89.65/89.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 89.65/89.89 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 89.65/89.89 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 89.65/89.89 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 89.65/89.89 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 89.65/89.89 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 89.65/89.89 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 89.65/89.89 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 89.65/89.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 89.65/89.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 89.65/89.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 89.65/89.89 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 89.65/89.89 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 89.65/89.89 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 89.65/89.89 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 89.65/89.89 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 89.65/89.89 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 89.65/89.89 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 89.65/89.89 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 89.65/89.89 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 89.65/89.89 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 89.65/89.89 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 89.65/89.89 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 89.65/89.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 89.65/89.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 89.65/89.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 89.65/89.89 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 89.65/89.89 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 89.65/89.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 89.65/89.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 89.65/89.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 89.65/89.89 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 89.65/89.89 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 89.65/89.89 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 89.65/89.89 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 89.65/89.89 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 89.65/89.89 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 89.65/89.89 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 89.65/89.89 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 89.65/89.89 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 89.65/89.89 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 89.65/89.89 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 89.65/89.89 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 89.65/89.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 89.65/89.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 89.65/89.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 89.65/89.89 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 89.65/89.89 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 89.65/89.89 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 89.65/89.89 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 89.65/89.89 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 92.99/93.23 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 92.99/93.23 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 92.99/93.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 92.99/93.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 92.99/93.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 92.99/93.23 Found x10:(P1 b)
% 92.99/93.23 Found (fun (x10:(P1 b))=> x10) as proof of (P1 b)
% 92.99/93.23 Found (fun (x10:(P1 b))=> x10) as proof of (P2 b)
% 92.99/93.23 Found x10:(P1 b)
% 92.99/93.23 Found (fun (x10:(P1 b))=> x10) as proof of (P1 b)
% 92.99/93.23 Found (fun (x10:(P1 b))=> x10) as proof of (P2 b)
% 92.99/93.23 Found x10:(P1 b)
% 92.99/93.23 Found (fun (x10:(P1 b))=> x10) as proof of (P1 b)
% 92.99/93.23 Found (fun (x10:(P1 b))=> x10) as proof of (P2 b)
% 92.99/93.23 Found x10:(P1 b)
% 92.99/93.23 Found (fun (x10:(P1 b))=> x10) as proof of (P1 b)
% 92.99/93.23 Found (fun (x10:(P1 b))=> x10) as proof of (P2 b)
% 92.99/93.23 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x0) x0))->(P1 (((eq Prop) x0) x0)))
% 92.99/93.23 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x0) x0))
% 92.99/93.23 Found ((eq_ref0 (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 92.99/93.23 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 92.99/93.23 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 92.99/93.23 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 92.99/93.23 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 92.99/93.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 92.99/93.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 92.99/93.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 92.99/93.23 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 92.99/93.23 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 92.99/93.23 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 92.99/93.23 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 92.99/93.23 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 92.99/93.23 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x0) x0))->(P1 (((eq Prop) x0) x0)))
% 92.99/93.23 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x0) x0))
% 92.99/93.23 Found ((eq_ref0 (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 92.99/93.23 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 92.99/93.23 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 92.99/93.23 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 92.99/93.23 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 92.99/93.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 92.99/93.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 92.99/93.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 92.99/93.23 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 92.99/93.23 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 92.99/93.23 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 92.99/93.23 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 92.99/93.23 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 92.99/93.23 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x0) x0))->(P1 (((eq Prop) x0) x0)))
% 92.99/93.23 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x0) x0))
% 92.99/93.23 Found ((eq_ref0 (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 92.99/93.23 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 92.99/93.23 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 92.99/93.23 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 92.99/93.23 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 92.99/93.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 92.99/93.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 92.99/93.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 92.99/93.23 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 92.99/93.23 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 92.99/93.23 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 92.99/93.23 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 92.99/93.23 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 97.82/98.05 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x0) x0))->(P1 (((eq Prop) x0) x0)))
% 97.82/98.05 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x0) x0))
% 97.82/98.05 Found ((eq_ref0 (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 97.82/98.05 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 97.82/98.05 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 97.82/98.05 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 97.82/98.05 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 97.82/98.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 97.82/98.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 97.82/98.05 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 97.82/98.05 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 97.82/98.05 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 97.82/98.05 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 97.82/98.05 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 97.82/98.05 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 97.82/98.05 Found eq_ref00:=(eq_ref0 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))):(((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 97.82/98.05 Found (eq_ref0 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 97.82/98.05 Found ((eq_ref (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 97.82/98.05 Found ((eq_ref (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 97.82/98.05 Found ((eq_ref (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 97.82/98.05 Found eq_ref00:=(eq_ref0 b0):(((eq (Prop->Prop)) b0) b0)
% 97.82/98.05 Found (eq_ref0 b0) as proof of (((eq (Prop->Prop)) b0) b)
% 97.82/98.05 Found ((eq_ref (Prop->Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 97.82/98.05 Found ((eq_ref (Prop->Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 97.82/98.05 Found ((eq_ref (Prop->Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 97.82/98.05 Found eta_expansion000:=(eta_expansion00 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))):(((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) (fun (x:Prop)=> (((eq Prop) x) x)))
% 97.82/98.05 Found (eta_expansion00 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 97.82/98.05 Found ((eta_expansion0 Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 97.82/98.05 Found (((eta_expansion Prop) Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 97.82/98.05 Found (((eta_expansion Prop) Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 97.82/98.05 Found (((eta_expansion Prop) Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 97.82/98.05 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (Prop->Prop)) b0) (fun (x:Prop)=> (b0 x)))
% 97.82/98.05 Found (eta_expansion_dep00 b0) as proof of (((eq (Prop->Prop)) b0) b)
% 97.82/98.05 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 97.82/98.05 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 97.82/98.05 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 97.82/98.05 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 97.82/98.05 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 97.82/98.05 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 97.82/98.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 97.82/98.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 97.82/98.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 97.82/98.05 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 97.82/98.05 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 109.94/110.17 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 109.94/110.17 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 109.94/110.17 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 109.94/110.17 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 109.94/110.17 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 109.94/110.17 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 109.94/110.17 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 109.94/110.17 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 109.94/110.17 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 109.94/110.17 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 109.94/110.17 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 109.94/110.17 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 109.94/110.17 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 109.94/110.17 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 109.94/110.17 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 109.94/110.17 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 109.94/110.17 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 109.94/110.17 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 109.94/110.17 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 109.94/110.17 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 109.94/110.17 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 109.94/110.17 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 109.94/110.17 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 109.94/110.17 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 109.94/110.17 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 109.94/110.17 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 109.94/110.17 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 109.94/110.17 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 109.94/110.17 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 109.94/110.17 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 109.94/110.17 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 109.94/110.17 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 109.94/110.17 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 109.94/110.17 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 109.94/110.17 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 109.94/110.17 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 109.94/110.17 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 109.94/110.17 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 109.94/110.17 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 109.94/110.17 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 109.94/110.17 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 109.94/110.17 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 109.94/110.17 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 109.94/110.17 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 109.94/110.17 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 109.94/110.17 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 109.94/110.17 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 109.94/110.17 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 109.94/110.17 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 109.94/110.17 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 109.94/110.17 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 109.94/110.17 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 109.94/110.17 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 109.94/110.17 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))->(P1 (fun (x:Prop)=> (((eq Prop) x) x))))
% 109.94/110.17 Found (eta_expansion_dep000 P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 109.94/110.17 Found ((eta_expansion_dep00 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 111.43/111.70 Found (((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 111.43/111.70 Found ((((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 111.43/111.70 Found ((((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 111.43/111.70 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))->(P1 (fun (x:Prop)=> (((eq Prop) x) x))))
% 111.43/111.70 Found (eta_expansion_dep000 P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 111.43/111.70 Found ((eta_expansion_dep00 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 111.43/111.70 Found (((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 111.43/111.70 Found ((((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 111.43/111.70 Found ((((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 111.43/111.70 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))->(P1 (fun (x:Prop)=> (((eq Prop) x) x))))
% 111.43/111.70 Found (eta_expansion_dep000 P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 111.43/111.70 Found ((eta_expansion_dep00 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 111.43/111.70 Found (((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 111.43/111.70 Found ((((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 111.43/111.70 Found ((((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 111.43/111.70 Found eta_expansion_dep0000:=(eta_expansion_dep000 P1):((P1 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))->(P1 (fun (x:Prop)=> (((eq Prop) x) x))))
% 111.43/111.70 Found (eta_expansion_dep000 P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 111.43/111.70 Found ((eta_expansion_dep00 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 111.43/111.70 Found (((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 111.43/111.70 Found ((((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 111.43/111.70 Found ((((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 111.43/111.70 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 111.43/111.70 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 111.43/111.70 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 111.43/111.70 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 111.43/111.70 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 111.43/111.70 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 111.43/111.70 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 111.43/111.70 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 111.43/111.70 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 111.43/111.70 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 111.43/111.70 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 111.43/111.70 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 111.43/111.70 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 111.43/111.70 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 113.54/113.83 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 113.54/113.83 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 113.54/113.83 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 113.54/113.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 113.54/113.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 113.54/113.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 113.54/113.83 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 113.54/113.83 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 113.54/113.83 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 113.54/113.83 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 113.54/113.83 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 113.54/113.83 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 113.54/113.83 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 113.54/113.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 113.54/113.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 113.54/113.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 113.54/113.83 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 113.54/113.83 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 113.54/113.83 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 113.54/113.83 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 113.54/113.83 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 113.54/113.83 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 113.54/113.83 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 113.54/113.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 113.54/113.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 113.54/113.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 113.54/113.83 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 113.54/113.83 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 113.54/113.83 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 113.54/113.83 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 113.54/113.83 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 113.54/113.83 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 113.54/113.83 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 113.54/113.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 113.54/113.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 113.54/113.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 113.54/113.83 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 113.54/113.83 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 113.54/113.83 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 113.54/113.83 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 113.54/113.83 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 113.54/113.83 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 113.54/113.83 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 113.54/113.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 113.54/113.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 113.54/113.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 113.54/113.83 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 113.54/113.83 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 113.54/113.83 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 113.54/113.83 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 113.54/113.83 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 113.54/113.83 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 113.54/113.83 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 113.54/113.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 113.54/113.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 113.54/113.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 113.54/113.83 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 113.54/113.83 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 113.54/113.83 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 146.41/146.73 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 146.41/146.73 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 146.41/146.73 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 146.41/146.73 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 146.41/146.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 146.41/146.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 146.41/146.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 146.41/146.73 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 146.41/146.73 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 146.41/146.73 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 146.41/146.73 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 146.41/146.73 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 146.41/146.73 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 146.41/146.73 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 146.41/146.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 146.41/146.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 146.41/146.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 146.41/146.73 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 146.41/146.73 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 146.41/146.73 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 146.41/146.73 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 146.41/146.73 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 146.41/146.73 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 146.41/146.73 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 146.41/146.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 146.41/146.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 146.41/146.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 146.41/146.73 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x0) x0))->(P1 (((eq Prop) x0) x0)))
% 146.41/146.73 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x0) x0))
% 146.41/146.73 Found ((eq_ref0 (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 146.41/146.73 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 146.41/146.73 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 146.41/146.73 Found x10:(P1 b)
% 146.41/146.73 Found (fun (x10:(P1 b))=> x10) as proof of (P1 b)
% 146.41/146.73 Found (fun (x10:(P1 b))=> x10) as proof of (P2 b)
% 146.41/146.73 Found x10:(P1 b)
% 146.41/146.73 Found (fun (x10:(P1 b))=> x10) as proof of (P1 b)
% 146.41/146.73 Found (fun (x10:(P1 b))=> x10) as proof of (P2 b)
% 146.41/146.73 Found x10:(P1 b)
% 146.41/146.73 Found (fun (x10:(P1 b))=> x10) as proof of (P1 b)
% 146.41/146.73 Found (fun (x10:(P1 b))=> x10) as proof of (P2 b)
% 146.41/146.73 Found x10:(P1 b)
% 146.41/146.73 Found (fun (x10:(P1 b))=> x10) as proof of (P1 b)
% 146.41/146.73 Found (fun (x10:(P1 b))=> x10) as proof of (P2 b)
% 146.41/146.73 Found x10:(P1 b)
% 146.41/146.73 Found (fun (x10:(P1 b))=> x10) as proof of (P1 b)
% 146.41/146.73 Found (fun (x10:(P1 b))=> x10) as proof of (P2 b)
% 146.41/146.73 Found x10:(P1 (b x0))
% 146.41/146.73 Found (fun (x10:(P1 (b x0)))=> x10) as proof of (P1 (b x0))
% 146.41/146.73 Found (fun (x10:(P1 (b x0)))=> x10) as proof of (P2 (b x0))
% 146.41/146.73 Found x10:(P1 (b x0))
% 146.41/146.73 Found (fun (x10:(P1 (b x0)))=> x10) as proof of (P1 (b x0))
% 146.41/146.73 Found (fun (x10:(P1 (b x0)))=> x10) as proof of (P2 (b x0))
% 146.41/146.73 Found x10:(P1 (b x0))
% 146.41/146.73 Found (fun (x10:(P1 (b x0)))=> x10) as proof of (P1 (b x0))
% 146.41/146.73 Found (fun (x10:(P1 (b x0)))=> x10) as proof of (P2 (b x0))
% 146.41/146.73 Found x10:(P1 (b x0))
% 146.41/146.73 Found (fun (x10:(P1 (b x0)))=> x10) as proof of (P1 (b x0))
% 146.41/146.73 Found (fun (x10:(P1 (b x0)))=> x10) as proof of (P2 (b x0))
% 146.41/146.73 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 146.41/146.73 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 146.41/146.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 146.41/146.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 146.41/146.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 146.41/146.73 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 146.41/146.73 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 146.41/146.73 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 146.41/146.73 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 146.41/146.73 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 146.41/146.73 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 146.41/146.73 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 146.41/146.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 146.41/146.73 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 153.36/153.63 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 153.36/153.63 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 153.36/153.63 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.36/153.63 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.36/153.63 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.36/153.63 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.36/153.63 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 153.36/153.63 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 153.36/153.63 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 153.36/153.63 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 153.36/153.63 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 153.36/153.63 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 153.36/153.63 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.36/153.63 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.36/153.63 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.36/153.63 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.36/153.63 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 153.36/153.63 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 153.36/153.63 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 153.36/153.63 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 153.36/153.63 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 153.36/153.63 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 153.36/153.63 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 153.36/153.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 153.36/153.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 153.36/153.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 153.36/153.63 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 153.36/153.63 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 153.36/153.63 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 153.36/153.63 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 153.36/153.63 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 153.36/153.63 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 153.36/153.63 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.36/153.63 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.36/153.63 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.36/153.63 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.36/153.63 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 153.36/153.63 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 153.36/153.63 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 153.36/153.63 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 153.36/153.63 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 153.36/153.63 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 153.36/153.63 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.36/153.63 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.36/153.63 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.36/153.63 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.36/153.63 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 153.36/153.63 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 153.36/153.63 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 153.36/153.63 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 153.36/153.63 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 153.36/153.63 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 153.36/153.63 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.36/153.63 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.36/153.63 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.36/153.63 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.36/153.63 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 153.36/153.63 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 153.36/153.63 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 153.36/153.63 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 153.36/153.63 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 153.36/153.63 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 153.36/153.63 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.36/153.63 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.36/153.63 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.36/153.63 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 153.36/153.63 Found eta_expansion000:=(eta_expansion00 b0):(((eq (Prop->Prop)) b0) (fun (x:Prop)=> (b0 x)))
% 153.36/153.63 Found (eta_expansion00 b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 155.13/155.41 Found ((eta_expansion0 Prop) b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 155.13/155.41 Found (((eta_expansion Prop) Prop) b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 155.13/155.41 Found (((eta_expansion Prop) Prop) b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 155.13/155.41 Found (((eta_expansion Prop) Prop) b0) as proof of (((eq (Prop->Prop)) b0) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 155.13/155.41 Found eq_ref00:=(eq_ref0 a0):(((eq (Prop->Prop)) a0) a0)
% 155.13/155.41 Found (eq_ref0 a0) as proof of (((eq (Prop->Prop)) a0) b0)
% 155.13/155.41 Found ((eq_ref (Prop->Prop)) a0) as proof of (((eq (Prop->Prop)) a0) b0)
% 155.13/155.41 Found ((eq_ref (Prop->Prop)) a0) as proof of (((eq (Prop->Prop)) a0) b0)
% 155.13/155.41 Found ((eq_ref (Prop->Prop)) a0) as proof of (((eq (Prop->Prop)) a0) b0)
% 155.13/155.41 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 155.13/155.41 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 155.13/155.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 155.13/155.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 155.13/155.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 155.13/155.41 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 155.13/155.41 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 155.13/155.41 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 155.13/155.41 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 155.13/155.41 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 155.13/155.41 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 155.13/155.41 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 155.13/155.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 155.13/155.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 155.13/155.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 155.13/155.41 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 155.13/155.41 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 155.13/155.41 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 155.13/155.41 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 155.13/155.41 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 155.13/155.41 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 155.13/155.41 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 155.13/155.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 155.13/155.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 155.13/155.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 155.13/155.41 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 155.13/155.41 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 155.13/155.41 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 155.13/155.41 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 155.13/155.41 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 155.13/155.41 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 155.13/155.41 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 155.13/155.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 155.13/155.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 155.13/155.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 155.13/155.41 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 155.13/155.41 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 155.13/155.41 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 155.13/155.41 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 155.13/155.41 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 155.13/155.41 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 155.13/155.41 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 155.13/155.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 155.13/155.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 155.13/155.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 155.13/155.41 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 156.37/156.66 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 156.37/156.66 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 156.37/156.66 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 156.37/156.66 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 156.37/156.66 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 156.37/156.66 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 156.37/156.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 156.37/156.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 156.37/156.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 156.37/156.66 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 156.37/156.66 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 156.37/156.66 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 156.37/156.66 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 156.37/156.66 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 156.37/156.66 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 156.37/156.66 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 156.37/156.66 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 156.37/156.66 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 156.37/156.66 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 156.37/156.66 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 156.37/156.66 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 156.37/156.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 156.37/156.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 156.37/156.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 156.37/156.66 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 156.37/156.66 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 156.37/156.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 156.37/156.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 156.37/156.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 156.37/156.66 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 156.37/156.66 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 156.37/156.66 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 156.37/156.66 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 156.37/156.66 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 156.37/156.66 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 156.37/156.66 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 156.37/156.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 156.37/156.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 156.37/156.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 156.37/156.66 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 156.37/156.66 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 156.37/156.66 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 156.37/156.66 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 156.37/156.66 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 156.37/156.66 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 156.37/156.66 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 156.37/156.66 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 156.37/156.66 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 156.37/156.66 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 156.37/156.66 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 156.37/156.66 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 156.37/156.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 156.37/156.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 169.52/169.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 169.52/169.81 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 169.52/169.81 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 169.52/169.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 169.52/169.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 169.52/169.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 169.52/169.81 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 169.52/169.81 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 169.52/169.81 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 169.52/169.81 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 169.52/169.81 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 169.52/169.81 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 169.52/169.81 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 169.52/169.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 169.52/169.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 169.52/169.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 169.52/169.81 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 169.52/169.81 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 169.52/169.81 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 169.52/169.81 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 169.52/169.81 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 169.52/169.81 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x0) x0))->(P1 (((eq Prop) x0) x0)))
% 169.52/169.81 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x0) x0))
% 169.52/169.81 Found ((eq_ref0 (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 169.52/169.81 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 169.52/169.81 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 169.52/169.81 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x0) x0))->(P1 (((eq Prop) x0) x0)))
% 169.52/169.81 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x0) x0))
% 169.52/169.81 Found ((eq_ref0 (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 169.52/169.81 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 169.52/169.81 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 169.52/169.81 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x0) x0))->(P1 (((eq Prop) x0) x0)))
% 169.52/169.81 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x0) x0))
% 169.52/169.81 Found ((eq_ref0 (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 169.52/169.81 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 169.52/169.81 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 169.52/169.81 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x0) x0))->(P1 (((eq Prop) x0) x0)))
% 169.52/169.81 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x0) x0))
% 169.52/169.81 Found ((eq_ref0 (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 169.52/169.81 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 169.52/169.81 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 169.52/169.81 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x0) x0))->(P1 (((eq Prop) x0) x0)))
% 169.52/169.81 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x0) x0))
% 169.52/169.81 Found ((eq_ref0 (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 169.52/169.81 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 169.52/169.81 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 169.52/169.81 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x0) x0))->(P1 (((eq Prop) x0) x0)))
% 169.52/169.81 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x0) x0))
% 169.52/169.81 Found ((eq_ref0 (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 169.52/169.81 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 169.52/169.81 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 169.52/169.81 Found x1:(P1 (((eq Prop) x0) x0))
% 169.52/169.81 Instantiate: b:=(((eq Prop) x0) x0):Prop
% 169.52/169.81 Found x1 as proof of (P2 b)
% 169.52/169.81 Found x1:(P1 (((eq Prop) x0) x0))
% 169.52/169.81 Instantiate: b:=(((eq Prop) x0) x0):Prop
% 169.52/169.81 Found x1 as proof of (P2 b)
% 169.52/169.81 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 186.68/187.01 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 186.68/187.01 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 186.68/187.01 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 186.68/187.01 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 186.68/187.01 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 186.68/187.01 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b)
% 186.68/187.01 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 186.68/187.01 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 186.68/187.01 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b)
% 186.68/187.01 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 186.68/187.01 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 186.68/187.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 186.68/187.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 186.68/187.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 186.68/187.01 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 186.68/187.01 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 186.68/187.01 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 186.68/187.01 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 186.68/187.01 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 186.68/187.01 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 186.68/187.01 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 186.68/187.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 186.68/187.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 186.68/187.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 186.68/187.01 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 186.68/187.01 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 186.68/187.01 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 186.68/187.01 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 186.68/187.01 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 186.68/187.01 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 186.68/187.01 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 186.68/187.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 186.68/187.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 186.68/187.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 186.68/187.01 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 186.68/187.01 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 186.68/187.01 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 186.68/187.01 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 186.68/187.01 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 186.68/187.01 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 186.68/187.01 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 186.68/187.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 186.68/187.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 186.68/187.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 186.68/187.01 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 186.68/187.01 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 186.68/187.01 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 186.68/187.01 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 186.68/187.01 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 186.68/187.01 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 186.68/187.01 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 186.68/187.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 186.68/187.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 186.68/187.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 186.68/187.01 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 186.68/187.01 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 186.68/187.01 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 186.68/187.01 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 191.99/192.28 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 191.99/192.28 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 191.99/192.28 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 191.99/192.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 191.99/192.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 191.99/192.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 191.99/192.28 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 191.99/192.28 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 191.99/192.28 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 191.99/192.28 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 191.99/192.28 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 191.99/192.28 Found x10:(P1 b)
% 191.99/192.28 Found (fun (x10:(P1 b))=> x10) as proof of (P1 b)
% 191.99/192.28 Found (fun (x10:(P1 b))=> x10) as proof of (P2 b)
% 191.99/192.28 Found x10:(P1 b)
% 191.99/192.28 Found (fun (x10:(P1 b))=> x10) as proof of (P1 b)
% 191.99/192.28 Found (fun (x10:(P1 b))=> x10) as proof of (P2 b)
% 191.99/192.28 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x0) x0))->(P1 (((eq Prop) x0) x0)))
% 191.99/192.28 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x0) x0))
% 191.99/192.28 Found ((eq_ref0 (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 191.99/192.28 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 191.99/192.28 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 191.99/192.28 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 191.99/192.28 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 191.99/192.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 191.99/192.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 191.99/192.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 191.99/192.28 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 191.99/192.28 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 191.99/192.28 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 191.99/192.28 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 191.99/192.28 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 191.99/192.28 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x0) x0))->(P1 (((eq Prop) x0) x0)))
% 191.99/192.28 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x0) x0))
% 191.99/192.28 Found ((eq_ref0 (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 191.99/192.28 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 191.99/192.28 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 191.99/192.28 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 191.99/192.28 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x0))
% 191.99/192.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 191.99/192.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 191.99/192.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x0))
% 191.99/192.28 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 191.99/192.28 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 191.99/192.28 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 191.99/192.28 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 191.99/192.28 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 191.99/192.28 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))):(((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) (fun (x:Prop)=> (((eq Prop) x) x)))
% 191.99/192.28 Found (eta_expansion_dep00 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 191.99/192.28 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 191.99/192.28 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 191.99/192.28 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 200.66/200.97 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 200.66/200.97 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (Prop->Prop)) b0) (fun (x:Prop)=> (b0 x)))
% 200.66/200.97 Found (eta_expansion_dep00 b0) as proof of (((eq (Prop->Prop)) b0) b)
% 200.66/200.97 Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 200.66/200.97 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 200.66/200.97 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 200.66/200.97 Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) b0) as proof of (((eq (Prop->Prop)) b0) b)
% 200.66/200.97 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 200.66/200.97 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 200.66/200.97 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 200.66/200.97 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 200.66/200.97 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 200.66/200.97 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 200.66/200.97 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 200.66/200.97 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 200.66/200.97 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 200.66/200.97 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 200.66/200.97 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 200.66/200.97 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 200.66/200.97 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 200.66/200.97 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 200.66/200.97 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 200.66/200.97 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 200.66/200.97 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 200.66/200.97 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 200.66/200.97 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 200.66/200.97 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 200.66/200.97 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 200.66/200.97 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 200.66/200.97 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 200.66/200.97 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 200.66/200.97 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 200.66/200.97 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 200.66/200.97 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 200.66/200.97 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 200.66/200.97 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 200.66/200.97 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 200.66/200.97 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 200.66/200.97 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 200.66/200.97 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 200.66/200.97 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 200.66/200.97 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 200.66/200.97 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 200.66/200.97 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 200.66/200.97 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 200.66/200.97 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 200.66/200.97 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 200.66/200.97 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 200.66/200.97 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 200.66/200.97 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 200.66/200.97 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 200.66/200.97 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 200.66/200.97 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 200.66/200.97 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 200.66/200.97 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 200.66/200.97 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 200.66/200.97 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 212.98/213.28 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 212.98/213.28 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 212.98/213.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 212.98/213.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 212.98/213.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 212.98/213.28 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 212.98/213.28 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 212.98/213.28 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 212.98/213.28 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 212.98/213.28 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 212.98/213.28 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 212.98/213.28 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 212.98/213.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 212.98/213.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 212.98/213.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 212.98/213.28 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 212.98/213.28 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 212.98/213.28 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 212.98/213.28 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 212.98/213.28 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 212.98/213.28 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 212.98/213.28 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 212.98/213.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 212.98/213.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 212.98/213.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 212.98/213.28 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 212.98/213.28 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 212.98/213.28 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 212.98/213.28 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 212.98/213.28 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 212.98/213.28 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 212.98/213.28 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 212.98/213.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 212.98/213.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 212.98/213.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 212.98/213.28 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 212.98/213.28 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 212.98/213.28 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 212.98/213.28 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 212.98/213.28 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 212.98/213.28 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 212.98/213.28 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 212.98/213.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 212.98/213.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 212.98/213.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 212.98/213.28 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 212.98/213.28 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 212.98/213.28 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 212.98/213.28 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 212.98/213.28 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 212.98/213.28 Found eq_ref00:=(eq_ref0 b1):(((eq (Prop->Prop)) b1) b1)
% 212.98/213.28 Found (eq_ref0 b1) as proof of (((eq (Prop->Prop)) b1) b0)
% 212.98/213.28 Found ((eq_ref (Prop->Prop)) b1) as proof of (((eq (Prop->Prop)) b1) b0)
% 212.98/213.28 Found ((eq_ref (Prop->Prop)) b1) as proof of (((eq (Prop->Prop)) b1) b0)
% 212.98/213.28 Found ((eq_ref (Prop->Prop)) b1) as proof of (((eq (Prop->Prop)) b1) b0)
% 212.98/213.28 Found eq_ref00:=(eq_ref0 a):(((eq (Prop->Prop)) a) a)
% 212.98/213.28 Found (eq_ref0 a) as proof of (((eq (Prop->Prop)) a) b1)
% 212.98/213.28 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b1)
% 212.98/213.28 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b1)
% 212.98/213.28 Found ((eq_ref (Prop->Prop)) a) as proof of (((eq (Prop->Prop)) a) b1)
% 212.98/213.28 Found eq_ref000:=(eq_ref00 P1):((P1 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))->(P1 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))
% 214.96/215.31 Found (eq_ref00 P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 214.96/215.31 Found ((eq_ref0 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 214.96/215.31 Found (((eq_ref (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 214.96/215.31 Found (((eq_ref (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 214.96/215.31 Found eq_ref000:=(eq_ref00 P1):((P1 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))->(P1 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))))
% 214.96/215.31 Found (eq_ref00 P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 214.96/215.31 Found ((eq_ref0 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 214.96/215.31 Found (((eq_ref (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 214.96/215.31 Found (((eq_ref (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) P1) as proof of (P2 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx)))
% 214.96/215.31 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 214.96/215.31 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 214.96/215.31 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 214.96/215.31 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 214.96/215.31 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 214.96/215.31 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 214.96/215.31 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 214.96/215.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 214.96/215.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 214.96/215.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 214.96/215.31 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 214.96/215.31 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 214.96/215.31 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 214.96/215.31 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 214.96/215.31 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 214.96/215.31 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 214.96/215.31 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 214.96/215.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 214.96/215.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 214.96/215.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 214.96/215.31 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 214.96/215.31 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 214.96/215.31 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 214.96/215.31 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 214.96/215.31 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 214.96/215.31 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 214.96/215.31 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 214.96/215.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 214.96/215.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 214.96/215.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 214.96/215.31 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 214.96/215.31 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 214.96/215.31 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 214.96/215.31 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 214.96/215.31 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 214.96/215.31 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 214.96/215.31 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 214.96/215.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 214.96/215.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 214.96/215.31 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 214.96/215.31 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 244.34/244.66 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 244.34/244.66 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 244.34/244.66 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 244.34/244.66 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 244.34/244.66 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 244.34/244.66 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 244.34/244.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 244.34/244.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 244.34/244.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 244.34/244.66 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 244.34/244.66 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 244.34/244.66 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 244.34/244.66 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 244.34/244.66 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 244.34/244.66 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 244.34/244.66 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 244.34/244.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 244.34/244.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 244.34/244.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 244.34/244.66 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 244.34/244.66 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 244.34/244.66 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 244.34/244.66 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 244.34/244.66 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 244.34/244.66 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 244.34/244.66 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 244.34/244.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 244.34/244.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 244.34/244.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 244.34/244.66 Found eq_ref00:=(eq_ref0 (b x0)):(((eq Prop) (b x0)) (b x0))
% 244.34/244.66 Found (eq_ref0 (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 244.34/244.66 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 244.34/244.66 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 244.34/244.66 Found ((eq_ref Prop) (b x0)) as proof of (((eq Prop) (b x0)) b0)
% 244.34/244.66 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 244.34/244.66 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 244.34/244.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 244.34/244.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 244.34/244.66 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 244.34/244.66 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x0) x0))->(P1 (((eq Prop) x0) x0)))
% 244.34/244.66 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x0) x0))
% 244.34/244.66 Found ((eq_ref0 (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 244.34/244.66 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 244.34/244.66 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 244.34/244.66 Found x10:(P1 b)
% 244.34/244.66 Found (fun (x10:(P1 b))=> x10) as proof of (P1 b)
% 244.34/244.66 Found (fun (x10:(P1 b))=> x10) as proof of (P2 b)
% 244.34/244.66 Found x10:(P1 b)
% 244.34/244.66 Found (fun (x10:(P1 b))=> x10) as proof of (P1 b)
% 244.34/244.66 Found (fun (x10:(P1 b))=> x10) as proof of (P2 b)
% 244.34/244.66 Found x10:(P1 b)
% 244.34/244.66 Found (fun (x10:(P1 b))=> x10) as proof of (P1 b)
% 244.34/244.66 Found (fun (x10:(P1 b))=> x10) as proof of (P2 b)
% 244.34/244.66 Found x10:(P1 b)
% 244.34/244.66 Found (fun (x10:(P1 b))=> x10) as proof of (P1 b)
% 244.34/244.66 Found (fun (x10:(P1 b))=> x10) as proof of (P2 b)
% 244.34/244.66 Found x10:(P1 b)
% 244.34/244.66 Found (fun (x10:(P1 b))=> x10) as proof of (P1 b)
% 244.34/244.66 Found (fun (x10:(P1 b))=> x10) as proof of (P2 b)
% 244.34/244.66 Found x10:(P1 (b x0))
% 244.34/244.66 Found (fun (x10:(P1 (b x0)))=> x10) as proof of (P1 (b x0))
% 244.34/244.66 Found (fun (x10:(P1 (b x0)))=> x10) as proof of (P2 (b x0))
% 244.34/244.66 Found x10:(P1 (b x0))
% 244.34/244.66 Found (fun (x10:(P1 (b x0)))=> x10) as proof of (P1 (b x0))
% 244.34/244.66 Found (fun (x10:(P1 (b x0)))=> x10) as proof of (P2 (b x0))
% 244.34/244.66 Found x00:(P1 a)
% 244.34/244.66 Found (fun (x00:(P1 a))=> x00) as proof of (P1 a)
% 244.34/244.66 Found (fun (x00:(P1 a))=> x00) as proof of (P2 a)
% 244.34/244.66 Found x00:(P1 a)
% 244.34/244.66 Found (fun (x00:(P1 a))=> x00) as proof of (P1 a)
% 264.40/264.74 Found (fun (x00:(P1 a))=> x00) as proof of (P2 a)
% 264.40/264.74 Found x00:(P1 a)
% 264.40/264.74 Found (fun (x00:(P1 a))=> x00) as proof of (P1 a)
% 264.40/264.74 Found (fun (x00:(P1 a))=> x00) as proof of (P2 a)
% 264.40/264.74 Found x1:(P1 (f x0))
% 264.40/264.74 Instantiate: a:=(f x0):Prop
% 264.40/264.74 Found x1 as proof of (P2 a)
% 264.40/264.74 Found x1:(P1 (f x0))
% 264.40/264.74 Instantiate: a:=(f x0):Prop
% 264.40/264.74 Found x1 as proof of (P2 a)
% 264.40/264.74 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 264.40/264.74 Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% 264.40/264.74 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 264.40/264.74 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 264.40/264.74 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 264.40/264.74 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 264.40/264.74 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 264.40/264.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 264.40/264.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 264.40/264.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 264.40/264.74 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 264.40/264.74 Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% 264.40/264.74 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 264.40/264.74 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 264.40/264.74 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 264.40/264.74 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 264.40/264.74 Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% 264.40/264.74 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 264.40/264.74 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 264.40/264.74 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 264.40/264.74 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 264.40/264.74 Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 264.40/264.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 264.40/264.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 264.40/264.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq Prop) x0) x0))
% 264.40/264.74 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 264.40/264.74 Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% 264.40/264.74 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 264.40/264.74 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 264.40/264.74 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% 264.40/264.74 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 264.40/264.74 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 264.40/264.74 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 264.40/264.74 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 264.40/264.74 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 264.40/264.74 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 264.40/264.74 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 264.40/264.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 264.40/264.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 264.40/264.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 264.40/264.74 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 264.40/264.74 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 264.40/264.74 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 264.40/264.74 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 264.40/264.74 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 264.40/264.74 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 264.40/264.74 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 264.40/264.74 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 264.40/264.74 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 264.40/264.74 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 264.40/264.74 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 264.40/264.74 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 264.40/264.74 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 264.40/264.74 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 264.40/264.74 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 264.40/264.74 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 264.40/264.74 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 264.40/264.74 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 264.40/264.74 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 264.40/264.74 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 264.40/264.74 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 264.40/264.74 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 264.40/264.74 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 264.40/264.74 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 264.40/264.74 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 264.40/264.74 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 265.50/265.84 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 265.50/265.84 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 265.50/265.84 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 265.50/265.84 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 265.50/265.84 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 265.50/265.84 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 265.50/265.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 265.50/265.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 265.50/265.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 265.50/265.84 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 265.50/265.84 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 265.50/265.84 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 265.50/265.84 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 265.50/265.84 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 265.50/265.84 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 265.50/265.84 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 265.50/265.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 265.50/265.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 265.50/265.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 265.50/265.84 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 265.50/265.84 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 265.50/265.84 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 265.50/265.84 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 265.50/265.84 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 265.50/265.84 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 265.50/265.84 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 265.50/265.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 265.50/265.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 265.50/265.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 265.50/265.84 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 265.50/265.84 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 265.50/265.84 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 265.50/265.84 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 265.50/265.84 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 265.50/265.84 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 265.50/265.84 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 265.50/265.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 265.50/265.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 265.50/265.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 265.50/265.84 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 265.50/265.84 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 265.50/265.84 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 265.50/265.84 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 265.50/265.84 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 265.50/265.84 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 265.50/265.84 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 265.50/265.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 265.50/265.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 265.50/265.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 265.50/265.84 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 265.50/265.84 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 265.50/265.84 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 265.50/265.84 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 265.50/265.84 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 265.50/265.84 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 265.50/265.84 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 265.50/265.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 265.50/265.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 265.50/265.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 265.50/265.84 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 265.50/265.84 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 265.50/265.84 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 265.50/265.84 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 265.50/265.84 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 265.50/265.84 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 265.50/265.84 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 265.50/265.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 265.50/265.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 265.50/265.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq Prop) x0) x0))
% 276.07/276.42 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 276.07/276.42 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 276.07/276.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 276.07/276.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 276.07/276.42 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 276.07/276.42 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 276.07/276.42 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 276.07/276.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 276.07/276.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 276.07/276.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 276.07/276.42 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 276.07/276.42 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 276.07/276.42 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 276.07/276.42 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 276.07/276.42 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 276.07/276.42 Found eta_expansion000:=(eta_expansion00 b0):(((eq (Prop->Prop)) b0) (fun (x:Prop)=> (b0 x)))
% 276.07/276.42 Found (eta_expansion00 b0) as proof of (((eq (Prop->Prop)) b0) b1)
% 276.07/276.42 Found ((eta_expansion0 Prop) b0) as proof of (((eq (Prop->Prop)) b0) b1)
% 276.07/276.42 Found (((eta_expansion Prop) Prop) b0) as proof of (((eq (Prop->Prop)) b0) b1)
% 276.07/276.42 Found (((eta_expansion Prop) Prop) b0) as proof of (((eq (Prop->Prop)) b0) b1)
% 276.07/276.42 Found (((eta_expansion Prop) Prop) b0) as proof of (((eq (Prop->Prop)) b0) b1)
% 276.07/276.42 Found eq_ref00:=(eq_ref0 b1):(((eq (Prop->Prop)) b1) b1)
% 276.07/276.42 Found (eq_ref0 b1) as proof of (((eq (Prop->Prop)) b1) a)
% 276.07/276.42 Found ((eq_ref (Prop->Prop)) b1) as proof of (((eq (Prop->Prop)) b1) a)
% 276.07/276.42 Found ((eq_ref (Prop->Prop)) b1) as proof of (((eq (Prop->Prop)) b1) a)
% 276.07/276.42 Found ((eq_ref (Prop->Prop)) b1) as proof of (((eq (Prop->Prop)) b1) a)
% 276.07/276.42 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 276.07/276.42 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 276.07/276.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 276.07/276.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 276.07/276.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 276.07/276.42 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 276.07/276.42 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 276.07/276.42 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 276.07/276.42 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 276.07/276.42 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 276.07/276.42 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 276.07/276.42 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 276.07/276.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 276.07/276.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 276.07/276.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 276.07/276.42 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 276.07/276.42 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 276.07/276.42 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 276.07/276.42 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 276.07/276.42 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 276.07/276.42 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 276.07/276.42 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 276.07/276.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 276.07/276.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 276.07/276.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 276.07/276.42 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 276.07/276.42 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 276.07/276.42 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 276.07/276.42 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 276.07/276.42 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 276.07/276.42 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 276.07/276.42 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 276.07/276.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 276.07/276.42 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 277.04/277.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 277.04/277.44 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 277.04/277.44 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 277.04/277.44 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 277.04/277.44 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 277.04/277.44 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 277.04/277.44 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 277.04/277.44 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 277.04/277.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 277.04/277.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 277.04/277.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 277.04/277.44 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 277.04/277.44 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 277.04/277.44 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 277.04/277.44 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 277.04/277.44 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 277.04/277.44 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 277.04/277.44 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 277.04/277.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 277.04/277.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 277.04/277.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 277.04/277.44 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 277.04/277.44 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 277.04/277.44 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 277.04/277.44 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 277.04/277.44 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 277.04/277.44 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 277.04/277.44 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 277.04/277.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 277.04/277.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 277.04/277.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 277.04/277.44 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 277.04/277.44 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 277.04/277.44 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 277.04/277.44 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 277.04/277.44 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 277.04/277.44 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 277.04/277.44 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 277.04/277.44 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 277.04/277.44 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 277.04/277.44 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 277.04/277.44 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 277.04/277.44 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 277.04/277.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 277.04/277.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 277.04/277.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 277.04/277.44 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 277.04/277.44 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 277.04/277.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 277.04/277.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 277.04/277.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 277.04/277.44 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 277.04/277.44 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 277.04/277.44 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 277.04/277.44 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 279.85/280.26 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 279.85/280.26 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 279.85/280.26 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 279.85/280.26 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 279.85/280.26 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 279.85/280.26 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 279.85/280.26 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 279.85/280.26 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 279.85/280.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 279.85/280.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 279.85/280.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 279.85/280.26 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 279.85/280.26 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 279.85/280.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 279.85/280.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 279.85/280.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 279.85/280.26 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 279.85/280.26 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 279.85/280.26 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 279.85/280.26 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 279.85/280.26 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 279.85/280.26 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 279.85/280.26 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 279.85/280.26 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 279.85/280.26 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 279.85/280.26 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b0)
% 279.85/280.26 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 279.85/280.26 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x0))
% 279.85/280.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 279.85/280.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 279.85/280.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x0))
% 279.85/280.26 Found x1:(P1 x0)
% 279.85/280.26 Found (fun (x1:(P1 x0))=> x1) as proof of (P1 x0)
% 279.85/280.26 Found (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1) as proof of ((P1 x0)->(P1 x0))
% 279.85/280.26 Found (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1) as proof of (b0 x0)
% 279.85/280.26 Found (ex_intro010 (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1)) as proof of ((ex Prop) b0)
% 279.85/280.26 Found x1:(P1 x0)
% 279.85/280.26 Found (fun (x1:(P1 x0))=> x1) as proof of (P1 x0)
% 279.85/280.26 Found (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1) as proof of ((P1 x0)->(P1 x0))
% 279.85/280.26 Found (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1) as proof of (a x0)
% 279.85/280.26 Found (ex_intro010 (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1)) as proof of ((ex Prop) a)
% 279.85/280.26 Found x0:(P1 b)
% 279.85/280.26 Instantiate: b0:=b:(Prop->Prop)
% 279.85/280.26 Found x0 as proof of (P2 b0)
% 279.85/280.26 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))):(((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) (fun (x:Prop)=> (((eq Prop) x) x)))
% 279.85/280.26 Found (eta_expansion_dep00 (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 279.85/280.26 Found ((eta_expansion_dep0 (fun (x2:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 279.85/280.26 Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 279.85/280.26 Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 279.85/280.26 Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) as proof of (((eq (Prop->Prop)) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))) b0)
% 279.85/280.26 Found x1:(P1 x0)
% 290.55/290.92 Found (fun (x1:(P1 x0))=> x1) as proof of (P1 x0)
% 290.55/290.92 Found (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1) as proof of ((P1 x0)->(P1 x0))
% 290.55/290.92 Found (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1) as proof of (f x0)
% 290.55/290.92 Found (ex_intro010 (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1)) as proof of ((ex Prop) f)
% 290.55/290.92 Found x1:(P1 x0)
% 290.55/290.92 Found (fun (x1:(P1 x0))=> x1) as proof of (P1 x0)
% 290.55/290.92 Found (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1) as proof of ((P1 x0)->(P1 x0))
% 290.55/290.92 Found (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1) as proof of (f x0)
% 290.55/290.92 Found (ex_intro010 (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1)) as proof of ((ex Prop) f)
% 290.55/290.92 Found x1:(P1 x0)
% 290.55/290.92 Found (fun (x1:(P1 x0))=> x1) as proof of (P1 x0)
% 290.55/290.92 Found (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1) as proof of ((P1 x0)->(P1 x0))
% 290.55/290.92 Found (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1) as proof of (a x0)
% 290.55/290.92 Found (ex_intro010 (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1)) as proof of ((ex Prop) a)
% 290.55/290.92 Found x1:(P1 x0)
% 290.55/290.92 Found (fun (x1:(P1 x0))=> x1) as proof of (P1 x0)
% 290.55/290.92 Found (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1) as proof of ((P1 x0)->(P1 x0))
% 290.55/290.92 Found (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1) as proof of (a x0)
% 290.55/290.92 Found (ex_intro010 (fun (P1:(Prop->Prop)) (x1:(P1 x0))=> x1)) as proof of ((ex Prop) a)
% 290.55/290.92 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x0) x0))->(P1 (((eq Prop) x0) x0)))
% 290.55/290.92 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x0) x0))
% 290.55/290.92 Found ((eq_ref0 (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 290.55/290.92 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 290.55/290.92 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 290.55/290.92 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x0) x0))->(P1 (((eq Prop) x0) x0)))
% 290.55/290.92 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x0) x0))
% 290.55/290.92 Found ((eq_ref0 (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 290.55/290.92 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 290.55/290.92 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 290.55/290.92 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x0) x0))->(P1 (((eq Prop) x0) x0)))
% 290.55/290.92 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x0) x0))
% 290.55/290.92 Found ((eq_ref0 (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 290.55/290.92 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 290.55/290.92 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 290.55/290.92 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x0) x0))->(P1 (((eq Prop) x0) x0)))
% 290.55/290.92 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x0) x0))
% 290.55/290.92 Found ((eq_ref0 (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 290.55/290.92 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 290.55/290.92 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 290.55/290.92 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x0) x0))->(P1 (((eq Prop) x0) x0)))
% 290.55/290.92 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x0) x0))
% 290.55/290.92 Found ((eq_ref0 (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 290.55/290.92 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 290.55/290.92 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 290.55/290.92 Found eq_ref000:=(eq_ref00 P1):((P1 (((eq Prop) x0) x0))->(P1 (((eq Prop) x0) x0)))
% 290.55/290.92 Found (eq_ref00 P1) as proof of (P2 (((eq Prop) x0) x0))
% 290.55/290.92 Found ((eq_ref0 (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 290.55/290.92 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 290.55/290.92 Found (((eq_ref Prop) (((eq Prop) x0) x0)) P1) as proof of (P2 (((eq Prop) x0) x0))
% 290.55/290.92 Found x0:(P1 b)
% 290.55/290.92 Instantiate: f:=b:(Prop->Prop)
% 290.55/290.92 Found x0 as proof of (P2 f)
% 290.55/290.92 Found x0:(P1 b)
% 290.55/290.92 Instantiate: f:=b:(Prop->Prop)
% 290.55/290.92 Found x0 as proof of (P2 f)
% 290.55/290.92 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 290.55/290.92 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 290.55/290.92 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 290.55/290.92 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 290.55/290.92 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 297.05/297.47 Found x1:(P4 b)
% 297.05/297.47 Instantiate: b:=((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))):Prop
% 297.05/297.47 Found (fun (x1:(P4 b))=> x1) as proof of (P4 (f x0))
% 297.05/297.47 Found (fun (P4:(Prop->Prop)) (x1:(P4 b))=> x1) as proof of ((P4 b)->(P4 (f x0)))
% 297.05/297.47 Found (fun (P4:(Prop->Prop)) (x1:(P4 b))=> x1) as proof of (P3 b)
% 297.05/297.47 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 297.05/297.47 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 297.05/297.47 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 297.05/297.47 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 297.05/297.47 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 297.05/297.47 Found x1:(P4 b)
% 297.05/297.47 Instantiate: b:=((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))):Prop
% 297.05/297.47 Found (fun (x1:(P4 b))=> x1) as proof of (P4 (f x0))
% 297.05/297.47 Found (fun (P4:(Prop->Prop)) (x1:(P4 b))=> x1) as proof of ((P4 b)->(P4 (f x0)))
% 297.05/297.47 Found (fun (P4:(Prop->Prop)) (x1:(P4 b))=> x1) as proof of (P3 b)
% 297.05/297.47 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 297.05/297.47 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 297.05/297.47 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 297.05/297.47 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 297.05/297.47 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 297.05/297.47 Found x1:(P4 b)
% 297.05/297.47 Instantiate: b:=((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))):Prop
% 297.05/297.47 Found (fun (x1:(P4 b))=> x1) as proof of (P4 (f x0))
% 297.05/297.47 Found (fun (P4:(Prop->Prop)) (x1:(P4 b))=> x1) as proof of ((P4 b)->(P4 (f x0)))
% 297.05/297.47 Found (fun (P4:(Prop->Prop)) (x1:(P4 b))=> x1) as proof of (P3 b)
% 297.05/297.47 Found eq_ref00:=(eq_ref0 (((eq Prop) x0) x0)):(((eq Prop) (((eq Prop) x0) x0)) (((eq Prop) x0) x0))
% 297.05/297.47 Found (eq_ref0 (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 297.05/297.47 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 297.05/297.47 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 297.05/297.47 Found ((eq_ref Prop) (((eq Prop) x0) x0)) as proof of (((eq Prop) (((eq Prop) x0) x0)) b)
% 297.05/297.47 Found x1:(P4 b)
% 297.05/297.47 Instantiate: b:=((ex Prop) (fun (Xx:Prop)=> (((eq Prop) Xx) Xx))):Prop
% 297.05/297.47 Found (fun (x1:(P4 b))=> x1) as proof of (P4 (f x0))
% 297.05/297.47 Found (fun (P4:(Prop->Prop)) (x1:(P4 b))=> x1) as proof of ((P4 b)->(P4 (f x0)))
% 297.05/297.47 Found (fun (P4:(Prop->Prop)) (x1:(P4 b))=> x1) as proof of (P3 b)
% 297.05/297.47 Found eq_ref00:=(eq_ref0 (a x0)):(((eq Prop) (a x0)) (a x0))
% 297.05/297.47 Found (eq_ref0 (a x0)) as proof of (((eq Prop) (a x0)) b1)
% 297.05/297.47 Found ((eq_ref Prop) (a x0)) as proof of (((eq Prop) (a x0)) b1)
% 297.05/297.47 Found ((eq_ref Prop) (a x0)) as proof of (((eq Prop) (a x0)) b1)
% 297.05/297.47 Found ((eq_ref Prop) (a x0)) as proof of (((eq Prop) (a x0)) b1)
% 297.05/297.47 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 297.05/297.47 Found (eq_ref0 b1) as proof of (((eq Prop) b1) (b0 x0))
% 297.05/297.47 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (b0 x0))
% 297.05/297.47 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (b0 x0))
% 297.05/297.47 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (b0 x0))
% 297.05/297.47 Found eq_ref00:=(eq_ref0 (a x0)):(((eq Prop) (a x0)) (a x0))
% 297.05/297.47 Found (eq_ref0 (a x0)) as proof of (((eq Prop) (a x0)) b1)
% 297.05/297.47 Found ((eq_ref Prop) (a x0)) as proof of (((eq Prop) (a x0)) b1)
% 297.05/297.47 Found ((eq_ref Prop) (a x0)) as proof of (((eq Prop) (a x0)) b1)
% 297.05/297.47 Found ((eq_ref Prop) (a x0)) as proof of (((eq Prop) (a x0)) b1)
% 297.05/297.47 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 297.05/297.47 Found (eq_ref0 b1) as proof of (((eq Prop) b1) (b0 x0))
% 297.05/297.47 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (b0 x0))
% 297.05/297.47 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (b0 x0))
% 297.05/297.47 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (b0 x0))
% 297.05/297.47 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 297.05/297.47 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (((eq Prop) x1) x1))
% 297.05/297.47 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq Prop) x1) x1))
% 297.05/297.47 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (((eq Prop) x1) x1))
% 297.05/297.47 Found (fun (x1:Prop)=> ((eq_ref Prop) (f
%------------------------------------------------------------------------------