TSTP Solution File: SYO373^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO373^5 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue Mar 29 00:51:17 EDT 2022
% Result : Timeout 291.61s 292.01s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYO373^5 : TPTP v7.5.0. Released v4.0.0.
% 0.03/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % RAMPerCPU : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sat Mar 12 08:40:10 EST 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.35 Python 2.7.5
% 5.67/5.88 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 5.67/5.88 FOF formula (<kernel.Constant object at 0x1955638>, <kernel.Type object at 0x1955fc8>) of role type named b_type
% 5.67/5.88 Using role type
% 5.67/5.88 Declaring b:Type
% 5.67/5.88 FOF formula (<kernel.Constant object at 0x1959dd0>, <kernel.DependentProduct object at 0x1955488>) of role type named g
% 5.67/5.88 Using role type
% 5.67/5.88 Declaring g:(b->Prop)
% 5.67/5.88 FOF formula (<kernel.Constant object at 0x19557e8>, <kernel.DependentProduct object at 0x19583f8>) of role type named f
% 5.67/5.88 Using role type
% 5.67/5.88 Declaring f:(b->Prop)
% 5.67/5.88 FOF formula ((forall (Xx:b), ((iff (f Xx)) (g Xx)))->(forall (Xq:((b->Prop)->Prop)), ((Xq f)->(Xq g)))) of role conjecture named cEXT_SET
% 5.67/5.88 Conjecture to prove = ((forall (Xx:b), ((iff (f Xx)) (g Xx)))->(forall (Xq:((b->Prop)->Prop)), ((Xq f)->(Xq g)))):Prop
% 5.67/5.88 Parameter b_DUMMY:b.
% 5.67/5.88 We need to prove ['((forall (Xx:b), ((iff (f Xx)) (g Xx)))->(forall (Xq:((b->Prop)->Prop)), ((Xq f)->(Xq g))))']
% 5.67/5.88 Parameter b:Type.
% 5.67/5.88 Parameter g:(b->Prop).
% 5.67/5.88 Parameter f:(b->Prop).
% 5.67/5.88 Trying to prove ((forall (Xx:b), ((iff (f Xx)) (g Xx)))->(forall (Xq:((b->Prop)->Prop)), ((Xq f)->(Xq g))))
% 5.67/5.88 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 5.67/5.88 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) g)
% 5.67/5.88 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 5.67/5.88 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 5.67/5.88 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 5.67/5.88 Found eta_expansion000:=(eta_expansion00 f):(((eq (b->Prop)) f) (fun (x:b)=> (f x)))
% 5.67/5.88 Found (eta_expansion00 f) as proof of (((eq (b->Prop)) f) b0)
% 5.67/5.88 Found ((eta_expansion0 Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 5.67/5.88 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 5.67/5.88 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 5.67/5.88 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 5.67/5.88 Found x00:(P f)
% 5.67/5.88 Found (fun (x00:(P f))=> x00) as proof of (P f)
% 5.67/5.88 Found (fun (x00:(P f))=> x00) as proof of (P0 f)
% 5.67/5.88 Found x00:(P f)
% 5.67/5.88 Found (fun (x00:(P f))=> x00) as proof of (P f)
% 5.67/5.88 Found (fun (x00:(P f))=> x00) as proof of (P0 f)
% 5.67/5.88 Found x00:(P f)
% 5.67/5.88 Found (fun (x00:(P f))=> x00) as proof of (P f)
% 5.67/5.88 Found (fun (x00:(P f))=> x00) as proof of (P0 f)
% 5.67/5.88 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 5.67/5.88 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 5.67/5.88 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 5.67/5.88 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 5.67/5.88 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 5.67/5.88 Found eta_expansion000:=(eta_expansion00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 5.67/5.88 Found (eta_expansion00 g) as proof of (((eq (b->Prop)) g) b0)
% 5.67/5.88 Found ((eta_expansion0 Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 5.67/5.88 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 5.67/5.88 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 5.67/5.88 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 5.67/5.88 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 5.67/5.88 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 5.67/5.88 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 5.67/5.88 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 5.67/5.88 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 5.67/5.88 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 5.67/5.88 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 5.67/5.88 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 5.67/5.88 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 5.67/5.88 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 5.67/5.88 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 5.67/5.88 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 5.67/5.88 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 5.67/5.88 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 5.67/5.88 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 5.67/5.88 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 5.67/5.88 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 5.67/5.88 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 5.67/5.88 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 15.73/15.95 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 15.73/15.95 Found x00:(P g)
% 15.73/15.95 Found (fun (x00:(P g))=> x00) as proof of (P g)
% 15.73/15.95 Found (fun (x00:(P g))=> x00) as proof of (P0 g)
% 15.73/15.95 Found x00:(P g)
% 15.73/15.95 Found (fun (x00:(P g))=> x00) as proof of (P g)
% 15.73/15.95 Found (fun (x00:(P g))=> x00) as proof of (P0 g)
% 15.73/15.95 Found x10:(P (f x0))
% 15.73/15.95 Found (fun (x10:(P (f x0)))=> x10) as proof of (P (f x0))
% 15.73/15.95 Found (fun (x10:(P (f x0)))=> x10) as proof of (P0 (f x0))
% 15.73/15.95 Found x10:(P (f x0))
% 15.73/15.95 Found (fun (x10:(P (f x0)))=> x10) as proof of (P (f x0))
% 15.73/15.95 Found (fun (x10:(P (f x0)))=> x10) as proof of (P0 (f x0))
% 15.73/15.95 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 15.73/15.95 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 15.73/15.95 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 15.73/15.95 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 15.73/15.95 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 15.73/15.95 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 15.73/15.95 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 15.73/15.95 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 15.73/15.95 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 15.73/15.95 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 15.73/15.95 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 15.73/15.95 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 15.73/15.95 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 15.73/15.95 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 15.73/15.95 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 15.73/15.95 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 15.73/15.95 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 15.73/15.95 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 15.73/15.95 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 15.73/15.95 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 15.73/15.95 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 15.73/15.95 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 15.73/15.95 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 15.73/15.95 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 15.73/15.95 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 15.73/15.95 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 15.73/15.95 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 15.73/15.95 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 15.73/15.95 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 15.73/15.95 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 15.73/15.95 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 15.73/15.95 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 15.73/15.95 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 15.73/15.95 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 15.73/15.95 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 15.73/15.95 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 15.73/15.95 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 15.73/15.95 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 15.73/15.95 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 15.73/15.95 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 15.73/15.95 Found x10:(P (g x0))
% 15.73/15.95 Found (fun (x10:(P (g x0)))=> x10) as proof of (P (g x0))
% 15.73/15.95 Found (fun (x10:(P (g x0)))=> x10) as proof of (P0 (g x0))
% 15.73/15.95 Found x10:(P (g x0))
% 15.73/15.95 Found (fun (x10:(P (g x0)))=> x10) as proof of (P (g x0))
% 15.73/15.95 Found (fun (x10:(P (g x0)))=> x10) as proof of (P0 (g x0))
% 15.73/15.95 Found x0:(P f)
% 15.73/15.95 Instantiate: b0:=f:(b->Prop)
% 15.73/15.95 Found x0 as proof of (P0 b0)
% 15.73/15.95 Found eta_expansion_dep000:=(eta_expansion_dep00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 15.73/15.95 Found (eta_expansion_dep00 g) as proof of (((eq (b->Prop)) g) b0)
% 15.73/15.95 Found ((eta_expansion_dep0 (fun (x2:b)=> Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 15.73/15.95 Found (((eta_expansion_dep b) (fun (x2:b)=> Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 15.73/15.95 Found (((eta_expansion_dep b) (fun (x2:b)=> Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 15.73/15.95 Found (((eta_expansion_dep b) (fun (x2:b)=> Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 15.73/15.95 Found x0:(P f)
% 15.73/15.95 Instantiate: f0:=f:(b->Prop)
% 15.73/15.95 Found x0 as proof of (P0 f0)
% 15.73/15.95 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 15.73/15.95 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (g x1))
% 15.73/15.95 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (g x1))
% 21.46/21.72 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (g x1))
% 21.46/21.72 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (g x1))
% 21.46/21.72 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:b), (((eq Prop) (f0 x)) (g x)))
% 21.46/21.72 Found x0:(P f)
% 21.46/21.72 Instantiate: f0:=f:(b->Prop)
% 21.46/21.72 Found x0 as proof of (P0 f0)
% 21.46/21.72 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 21.46/21.72 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (g x1))
% 21.46/21.72 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (g x1))
% 21.46/21.72 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (g x1))
% 21.46/21.72 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (g x1))
% 21.46/21.72 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:b), (((eq Prop) (f0 x)) (g x)))
% 21.46/21.72 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 21.46/21.72 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) g)
% 21.46/21.72 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 21.46/21.72 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 21.46/21.72 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 21.46/21.72 Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq (b->Prop)) f) (fun (x:b)=> (f x)))
% 21.46/21.72 Found (eta_expansion_dep00 f) as proof of (((eq (b->Prop)) f) b0)
% 21.46/21.72 Found ((eta_expansion_dep0 (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 21.46/21.72 Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 21.46/21.72 Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 21.46/21.72 Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 21.46/21.72 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 21.46/21.72 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 21.46/21.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 21.46/21.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 21.46/21.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 21.46/21.72 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 21.46/21.72 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 21.46/21.72 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 21.46/21.72 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 21.46/21.72 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 21.46/21.72 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 21.46/21.72 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 21.46/21.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 21.46/21.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 21.46/21.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 21.46/21.72 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 21.46/21.72 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 21.46/21.72 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 21.46/21.72 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 21.46/21.72 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 21.46/21.72 Found eta_expansion000:=(eta_expansion00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 21.46/21.72 Found (eta_expansion00 g) as proof of (((eq (b->Prop)) g) b0)
% 21.46/21.72 Found ((eta_expansion0 Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 21.46/21.72 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 21.46/21.72 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 21.46/21.72 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 21.46/21.72 Found x0:(P0 b0)
% 21.46/21.72 Instantiate: b0:=f:(b->Prop)
% 21.46/21.72 Found (fun (x0:(P0 b0))=> x0) as proof of (P0 f)
% 21.46/21.72 Found (fun (P0:((b->Prop)->Prop)) (x0:(P0 b0))=> x0) as proof of ((P0 b0)->(P0 f))
% 21.46/21.72 Found (fun (P0:((b->Prop)->Prop)) (x0:(P0 b0))=> x0) as proof of (P b0)
% 21.46/21.72 Found x00:(P f)
% 21.46/21.72 Found (fun (x00:(P f))=> x00) as proof of (P f)
% 21.46/21.72 Found (fun (x00:(P f))=> x00) as proof of (P0 f)
% 21.46/21.72 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 21.46/21.72 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) g)
% 21.46/21.72 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 21.46/21.72 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 21.46/21.72 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 21.46/21.72 Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq (b->Prop)) f) (fun (x:b)=> (f x)))
% 21.46/21.72 Found (eta_expansion_dep00 f) as proof of (((eq (b->Prop)) f) b0)
% 21.46/21.72 Found ((eta_expansion_dep0 (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 27.38/27.60 Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 27.38/27.60 Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 27.38/27.60 Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) f) as proof of (((eq (b->Prop)) f) b0)
% 27.38/27.60 Found x0:(P g)
% 27.38/27.60 Instantiate: b0:=g:(b->Prop)
% 27.38/27.60 Found x0 as proof of (P0 b0)
% 27.38/27.60 Found eta_expansion000:=(eta_expansion00 f):(((eq (b->Prop)) f) (fun (x:b)=> (f x)))
% 27.38/27.60 Found (eta_expansion00 f) as proof of (((eq (b->Prop)) f) b0)
% 27.38/27.60 Found ((eta_expansion0 Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 27.38/27.60 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 27.38/27.60 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 27.38/27.60 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 27.38/27.60 Found eq_ref00:=(eq_ref0 b00):(((eq (b->Prop)) b00) b00)
% 27.38/27.60 Found (eq_ref0 b00) as proof of (((eq (b->Prop)) b00) b0)
% 27.38/27.60 Found ((eq_ref (b->Prop)) b00) as proof of (((eq (b->Prop)) b00) b0)
% 27.38/27.60 Found ((eq_ref (b->Prop)) b00) as proof of (((eq (b->Prop)) b00) b0)
% 27.38/27.60 Found ((eq_ref (b->Prop)) b00) as proof of (((eq (b->Prop)) b00) b0)
% 27.38/27.60 Found eta_expansion000:=(eta_expansion00 f):(((eq (b->Prop)) f) (fun (x:b)=> (f x)))
% 27.38/27.60 Found (eta_expansion00 f) as proof of (((eq (b->Prop)) f) b00)
% 27.38/27.60 Found ((eta_expansion0 Prop) f) as proof of (((eq (b->Prop)) f) b00)
% 27.38/27.60 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b00)
% 27.38/27.60 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b00)
% 27.38/27.60 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b00)
% 27.38/27.60 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 27.38/27.60 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) g)
% 27.38/27.60 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 27.38/27.60 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 27.38/27.60 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 27.38/27.60 Found eta_expansion000:=(eta_expansion00 f):(((eq (b->Prop)) f) (fun (x:b)=> (f x)))
% 27.38/27.60 Found (eta_expansion00 f) as proof of (((eq (b->Prop)) f) b0)
% 27.38/27.60 Found ((eta_expansion0 Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 27.38/27.60 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 27.38/27.60 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 27.38/27.60 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 27.38/27.60 Found x0:(P g)
% 27.38/27.60 Instantiate: f0:=g:(b->Prop)
% 27.38/27.60 Found x0 as proof of (P0 f0)
% 27.38/27.60 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 27.38/27.60 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 27.38/27.60 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 27.38/27.60 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 27.38/27.60 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1))
% 27.38/27.60 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:b), (((eq Prop) (f0 x)) (f x)))
% 27.38/27.60 Found x0:(P g)
% 27.38/27.60 Instantiate: f0:=g:(b->Prop)
% 27.38/27.60 Found x0 as proof of (P0 f0)
% 27.38/27.60 Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% 27.38/27.60 Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 27.38/27.60 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 27.38/27.60 Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% 27.38/27.60 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1))
% 27.38/27.60 Found (fun (x1:b)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:b), (((eq Prop) (f0 x)) (f x)))
% 27.38/27.60 Found x30:(P f)
% 27.38/27.60 Found (fun (x30:(P f))=> x30) as proof of (P f)
% 27.38/27.60 Found (fun (x30:(P f))=> x30) as proof of (P0 f)
% 27.38/27.60 Found x1:(P (f x0))
% 27.38/27.60 Instantiate: b0:=(f x0):Prop
% 27.38/27.60 Found x1 as proof of (P0 b0)
% 27.38/27.60 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 27.38/27.60 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 27.38/27.60 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 27.38/27.60 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 27.38/27.60 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 27.38/27.60 Found x1:(P (f x0))
% 27.38/27.60 Instantiate: b0:=(f x0):Prop
% 27.38/27.60 Found x1 as proof of (P0 b0)
% 27.38/27.60 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 27.38/27.60 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 35.35/35.58 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 35.35/35.58 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 35.35/35.58 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 35.35/35.58 Found x30:(P f)
% 35.35/35.58 Found (fun (x30:(P f))=> x30) as proof of (P f)
% 35.35/35.58 Found (fun (x30:(P f))=> x30) as proof of (P0 f)
% 35.35/35.58 Found x30:(P f)
% 35.35/35.58 Found (fun (x30:(P f))=> x30) as proof of (P f)
% 35.35/35.58 Found (fun (x30:(P f))=> x30) as proof of (P0 f)
% 35.35/35.58 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 35.35/35.58 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 35.35/35.58 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 35.35/35.58 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 35.35/35.58 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 35.35/35.58 Found eta_expansion000:=(eta_expansion00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 35.35/35.58 Found (eta_expansion00 g) as proof of (((eq (b->Prop)) g) b0)
% 35.35/35.58 Found ((eta_expansion0 Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 35.35/35.58 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 35.35/35.58 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 35.35/35.58 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 35.35/35.58 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 35.35/35.58 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 35.35/35.58 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 35.35/35.58 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 35.35/35.58 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 35.35/35.58 Found eq_ref00:=(eq_ref0 g):(((eq (b->Prop)) g) g)
% 35.35/35.58 Found (eq_ref0 g) as proof of (((eq (b->Prop)) g) b0)
% 35.35/35.58 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 35.35/35.58 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 35.35/35.58 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 35.35/35.58 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 35.35/35.58 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 35.35/35.58 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 35.35/35.58 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 35.35/35.58 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 35.35/35.58 Found eq_ref00:=(eq_ref0 g):(((eq (b->Prop)) g) g)
% 35.35/35.58 Found (eq_ref0 g) as proof of (((eq (b->Prop)) g) b0)
% 35.35/35.58 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 35.35/35.58 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 35.35/35.58 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 35.35/35.58 Found x00:(P f)
% 35.35/35.58 Found (fun (x00:(P f))=> x00) as proof of (P f)
% 35.35/35.58 Found (fun (x00:(P f))=> x00) as proof of (P0 f)
% 35.35/35.58 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 35.35/35.58 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 35.35/35.58 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 35.35/35.58 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 35.35/35.58 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 35.35/35.58 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 35.35/35.58 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 35.35/35.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 35.35/35.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 35.35/35.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 35.35/35.58 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 35.35/35.58 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 35.35/35.58 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 35.35/35.58 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 35.35/35.58 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 35.35/35.58 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 35.35/35.58 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 35.35/35.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 35.35/35.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 35.35/35.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 35.35/35.58 Found x00:(P f)
% 35.35/35.58 Found (fun (x00:(P f))=> x00) as proof of (P f)
% 35.35/35.58 Found (fun (x00:(P f))=> x00) as proof of (P0 f)
% 35.35/35.58 Found x00:(P f)
% 35.35/35.58 Found (fun (x00:(P f))=> x00) as proof of (P f)
% 35.35/35.58 Found (fun (x00:(P f))=> x00) as proof of (P0 f)
% 35.35/35.58 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 35.35/35.58 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 35.35/35.58 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 41.45/41.67 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 41.45/41.67 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 41.45/41.67 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 41.45/41.67 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 41.45/41.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 41.45/41.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 41.45/41.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 41.45/41.67 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 41.45/41.67 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 41.45/41.67 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 41.45/41.67 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 41.45/41.67 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 41.45/41.67 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 41.45/41.67 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 41.45/41.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 41.45/41.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 41.45/41.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 41.45/41.67 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 41.45/41.67 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 41.45/41.67 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 41.45/41.67 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 41.45/41.67 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 41.45/41.67 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 41.45/41.67 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 41.45/41.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 41.45/41.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 41.45/41.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 41.45/41.67 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 41.45/41.67 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 41.45/41.67 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 41.45/41.67 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 41.45/41.67 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 41.45/41.67 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 41.45/41.67 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 41.45/41.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 41.45/41.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 41.45/41.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 41.45/41.67 Found x00:(P1 g)
% 41.45/41.67 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 41.45/41.67 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 41.45/41.67 Found x00:(P1 g)
% 41.45/41.67 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 41.45/41.67 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 41.45/41.67 Found x00:(P1 g)
% 41.45/41.67 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 41.45/41.67 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 41.45/41.67 Found x00:(P1 g)
% 41.45/41.67 Found (fun (x00:(P1 g))=> x00) as proof of (P1 g)
% 41.45/41.67 Found (fun (x00:(P1 g))=> x00) as proof of (P2 g)
% 41.45/41.67 Found x00:(P g)
% 41.45/41.67 Found (fun (x00:(P g))=> x00) as proof of (P g)
% 41.45/41.67 Found (fun (x00:(P g))=> x00) as proof of (P0 g)
% 41.45/41.67 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 41.45/41.67 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 41.45/41.67 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 41.45/41.67 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 41.45/41.67 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 41.45/41.67 Found eta_expansion000:=(eta_expansion00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 41.45/41.67 Found (eta_expansion00 g) as proof of (((eq (b->Prop)) g) b0)
% 41.45/41.67 Found ((eta_expansion0 Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 41.45/41.67 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 41.45/41.67 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 41.45/41.67 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 41.45/41.67 Found x10:(P1 (f x0))
% 41.45/41.67 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P1 (f x0))
% 41.45/41.67 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P2 (f x0))
% 41.45/41.67 Found x10:(P1 (f x0))
% 41.45/41.67 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P1 (f x0))
% 41.45/41.67 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P2 (f x0))
% 41.45/41.67 Found x10:(P1 (f x0))
% 41.45/41.67 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P1 (f x0))
% 41.45/41.67 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P2 (f x0))
% 41.45/41.67 Found x10:(P1 (f x0))
% 41.45/41.67 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P1 (f x0))
% 41.45/41.67 Found (fun (x10:(P1 (f x0)))=> x10) as proof of (P2 (f x0))
% 50.33/50.55 Found eq_ref00:=(eq_ref0 b00):(((eq (b->Prop)) b00) b00)
% 50.33/50.55 Found (eq_ref0 b00) as proof of (((eq (b->Prop)) b00) b0)
% 50.33/50.55 Found ((eq_ref (b->Prop)) b00) as proof of (((eq (b->Prop)) b00) b0)
% 50.33/50.55 Found ((eq_ref (b->Prop)) b00) as proof of (((eq (b->Prop)) b00) b0)
% 50.33/50.55 Found ((eq_ref (b->Prop)) b00) as proof of (((eq (b->Prop)) b00) b0)
% 50.33/50.55 Found eq_ref00:=(eq_ref0 g):(((eq (b->Prop)) g) g)
% 50.33/50.55 Found (eq_ref0 g) as proof of (((eq (b->Prop)) g) b00)
% 50.33/50.55 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b00)
% 50.33/50.55 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b00)
% 50.33/50.55 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b00)
% 50.33/50.55 Found x10:(P (f x0))
% 50.33/50.55 Found (fun (x10:(P (f x0)))=> x10) as proof of (P (f x0))
% 50.33/50.55 Found (fun (x10:(P (f x0)))=> x10) as proof of (P0 (f x0))
% 50.33/50.55 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 50.33/50.55 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 50.33/50.55 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 50.33/50.55 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 50.33/50.55 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 50.33/50.55 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 50.33/50.55 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 50.33/50.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 50.33/50.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 50.33/50.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 50.33/50.55 Found x10:(P (f x0))
% 50.33/50.55 Found (fun (x10:(P (f x0)))=> x10) as proof of (P (f x0))
% 50.33/50.55 Found (fun (x10:(P (f x0)))=> x10) as proof of (P0 (f x0))
% 50.33/50.55 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 50.33/50.55 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 50.33/50.55 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 50.33/50.55 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 50.33/50.55 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 50.33/50.55 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 50.33/50.55 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 50.33/50.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 50.33/50.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 50.33/50.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 50.33/50.55 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 50.33/50.55 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 50.33/50.55 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 50.33/50.55 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 50.33/50.55 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 50.33/50.55 Found x1:(P0 b0)
% 50.33/50.55 Instantiate: b0:=(f x0):Prop
% 50.33/50.55 Found (fun (x1:(P0 b0))=> x1) as proof of (P0 (f x0))
% 50.33/50.55 Found (fun (P0:(Prop->Prop)) (x1:(P0 b0))=> x1) as proof of ((P0 b0)->(P0 (f x0)))
% 50.33/50.55 Found (fun (P0:(Prop->Prop)) (x1:(P0 b0))=> x1) as proof of (P b0)
% 50.33/50.55 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 50.33/50.55 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 50.33/50.55 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 50.33/50.55 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 50.33/50.55 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 50.33/50.55 Found x1:(P0 b0)
% 50.33/50.55 Instantiate: b0:=(f x0):Prop
% 50.33/50.55 Found (fun (x1:(P0 b0))=> x1) as proof of (P0 (f x0))
% 50.33/50.55 Found (fun (P0:(Prop->Prop)) (x1:(P0 b0))=> x1) as proof of ((P0 b0)->(P0 (f x0)))
% 50.33/50.55 Found (fun (P0:(Prop->Prop)) (x1:(P0 b0))=> x1) as proof of (P b0)
% 50.33/50.55 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 50.33/50.55 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 50.33/50.55 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 50.33/50.55 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 50.33/50.55 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 50.33/50.55 Found eta_expansion000:=(eta_expansion00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 50.33/50.55 Found (eta_expansion00 g) as proof of (((eq (b->Prop)) g) b0)
% 50.33/50.55 Found ((eta_expansion0 Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 50.33/50.55 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 50.33/50.55 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 50.33/50.55 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 50.33/50.55 Found eq_ref00:=(eq_ref0 g):(((eq (b->Prop)) g) g)
% 50.33/50.55 Found (eq_ref0 g) as proof of (((eq (b->Prop)) g) b0)
% 58.47/58.70 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 58.47/58.70 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 58.47/58.70 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 58.47/58.70 Found x1:(P0 (b0 x0))
% 58.47/58.70 Instantiate: b0:=f:(b->Prop)
% 58.47/58.70 Found (fun (x1:(P0 (b0 x0)))=> x1) as proof of (P0 (f x0))
% 58.47/58.70 Found (fun (P0:(Prop->Prop)) (x1:(P0 (b0 x0)))=> x1) as proof of ((P0 (b0 x0))->(P0 (f x0)))
% 58.47/58.70 Found (fun (P0:(Prop->Prop)) (x1:(P0 (b0 x0)))=> x1) as proof of (P b0)
% 58.47/58.70 Found eta_expansion_dep000:=(eta_expansion_dep00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 58.47/58.70 Found (eta_expansion_dep00 g) as proof of (((eq (b->Prop)) g) b0)
% 58.47/58.70 Found ((eta_expansion_dep0 (fun (x2:b)=> Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 58.47/58.70 Found (((eta_expansion_dep b) (fun (x2:b)=> Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 58.47/58.70 Found (((eta_expansion_dep b) (fun (x2:b)=> Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 58.47/58.70 Found (((eta_expansion_dep b) (fun (x2:b)=> Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 58.47/58.70 Found x1:(P0 (b0 x0))
% 58.47/58.70 Instantiate: b0:=f:(b->Prop)
% 58.47/58.70 Found (fun (x1:(P0 (b0 x0)))=> x1) as proof of (P0 (f x0))
% 58.47/58.70 Found (fun (P0:(Prop->Prop)) (x1:(P0 (b0 x0)))=> x1) as proof of ((P0 (b0 x0))->(P0 (f x0)))
% 58.47/58.70 Found (fun (P0:(Prop->Prop)) (x1:(P0 (b0 x0)))=> x1) as proof of (P b0)
% 58.47/58.70 Found x1:(P (g x0))
% 58.47/58.70 Instantiate: b0:=(g x0):Prop
% 58.47/58.70 Found x1 as proof of (P0 b0)
% 58.47/58.70 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 58.47/58.70 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 58.47/58.70 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 58.47/58.70 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 58.47/58.70 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 58.47/58.70 Found eq_ref00:=(eq_ref0 b00):(((eq (b->Prop)) b00) b00)
% 58.47/58.70 Found (eq_ref0 b00) as proof of (((eq (b->Prop)) b00) f)
% 58.47/58.70 Found ((eq_ref (b->Prop)) b00) as proof of (((eq (b->Prop)) b00) f)
% 58.47/58.70 Found ((eq_ref (b->Prop)) b00) as proof of (((eq (b->Prop)) b00) f)
% 58.47/58.70 Found ((eq_ref (b->Prop)) b00) as proof of (((eq (b->Prop)) b00) f)
% 58.47/58.70 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (b->Prop)) b0) (fun (x:b)=> (b0 x)))
% 58.47/58.70 Found (eta_expansion_dep00 b0) as proof of (((eq (b->Prop)) b0) b00)
% 58.47/58.70 Found ((eta_expansion_dep0 (fun (x1:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) b00)
% 58.47/58.70 Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) b00)
% 58.47/58.70 Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) b00)
% 58.47/58.70 Found (((eta_expansion_dep b) (fun (x1:b)=> Prop)) b0) as proof of (((eq (b->Prop)) b0) b00)
% 58.47/58.70 Found x1:(P (g x0))
% 58.47/58.70 Instantiate: b0:=(g x0):Prop
% 58.47/58.70 Found x1 as proof of (P0 b0)
% 58.47/58.70 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 58.47/58.70 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 58.47/58.70 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 58.47/58.70 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 58.47/58.70 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 58.47/58.70 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 58.47/58.70 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) g)
% 58.47/58.70 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 58.47/58.70 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 58.47/58.70 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 58.47/58.70 Found eta_expansion000:=(eta_expansion00 f):(((eq (b->Prop)) f) (fun (x:b)=> (f x)))
% 58.47/58.70 Found (eta_expansion00 f) as proof of (((eq (b->Prop)) f) b0)
% 58.47/58.70 Found ((eta_expansion0 Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 58.47/58.70 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 58.47/58.70 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 58.47/58.70 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 58.47/58.70 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 58.47/58.70 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 58.47/58.70 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 58.47/58.70 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 58.47/58.70 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 58.47/58.70 Found eq_ref00:=(eq_ref0 g):(((eq (b->Prop)) g) g)
% 58.47/58.70 Found (eq_ref0 g) as proof of (((eq (b->Prop)) g) b0)
% 58.47/58.70 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 71.05/71.29 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 71.05/71.29 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 71.05/71.29 Found x20:=(x2 x30):(g Xx)
% 71.05/71.29 Found (x2 x30) as proof of (g Xx)
% 71.05/71.29 Found (x2 x30) as proof of (g Xx)
% 71.05/71.29 Found x30:=(x3 x20):(f Xx)
% 71.05/71.29 Found (x3 x20) as proof of (f Xx)
% 71.05/71.29 Found (x3 x20) as proof of (f Xx)
% 71.05/71.29 Found x1:(P (g x0))
% 71.05/71.29 Instantiate: b0:=(g x0):Prop
% 71.05/71.29 Found x1 as proof of (P0 b0)
% 71.05/71.29 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 71.05/71.29 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 71.05/71.29 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 71.05/71.29 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 71.05/71.29 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 71.05/71.29 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 71.05/71.29 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) b0)
% 71.05/71.29 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) b0)
% 71.05/71.29 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) b0)
% 71.05/71.29 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) b0)
% 71.05/71.29 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 71.05/71.29 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x3))
% 71.05/71.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x3))
% 71.05/71.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x3))
% 71.05/71.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x3))
% 71.05/71.29 Found x1:(P (g x0))
% 71.05/71.29 Instantiate: b0:=(g x0):Prop
% 71.05/71.29 Found x1 as proof of (P0 b0)
% 71.05/71.29 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 71.05/71.29 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 71.05/71.29 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 71.05/71.29 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 71.05/71.29 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 71.05/71.29 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 71.05/71.29 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) b0)
% 71.05/71.29 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) b0)
% 71.05/71.29 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) b0)
% 71.05/71.29 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) b0)
% 71.05/71.29 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 71.05/71.29 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x3))
% 71.05/71.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x3))
% 71.05/71.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x3))
% 71.05/71.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x3))
% 71.05/71.29 Found x00:(P g)
% 71.05/71.29 Found (fun (x00:(P g))=> x00) as proof of (P g)
% 71.05/71.29 Found (fun (x00:(P g))=> x00) as proof of (P0 g)
% 71.05/71.29 Found eq_ref00:=(eq_ref0 a):(((eq b) a) a)
% 71.05/71.29 Found (eq_ref0 a) as proof of (((eq b) a) x0)
% 71.05/71.29 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 71.05/71.29 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 71.05/71.29 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 71.05/71.29 Found eq_ref00:=(eq_ref0 a):(((eq b) a) a)
% 71.05/71.29 Found (eq_ref0 a) as proof of (((eq b) a) x0)
% 71.05/71.29 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 71.05/71.29 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 71.05/71.29 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 71.05/71.29 Found eq_ref00:=(eq_ref0 a):(((eq b) a) a)
% 71.05/71.29 Found (eq_ref0 a) as proof of (((eq b) a) x0)
% 71.05/71.29 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 71.05/71.29 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 71.05/71.29 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 71.05/71.29 Found eq_ref00:=(eq_ref0 a):(((eq b) a) a)
% 71.05/71.29 Found (eq_ref0 a) as proof of (((eq b) a) x0)
% 71.05/71.29 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 71.05/71.29 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 71.05/71.29 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 71.05/71.29 Found x00:(P f)
% 71.05/71.29 Found (fun (x00:(P f))=> x00) as proof of (P f)
% 71.05/71.29 Found (fun (x00:(P f))=> x00) as proof of (P0 f)
% 71.05/71.29 Found x30:=(x3 x20):(f Xx)
% 71.05/71.29 Found (x3 x20) as proof of (f Xx)
% 71.05/71.29 Found (x3 x20) as proof of (f Xx)
% 71.05/71.29 Found x30:(P g)
% 71.05/71.29 Found (fun (x30:(P g))=> x30) as proof of (P g)
% 71.05/71.29 Found (fun (x30:(P g))=> x30) as proof of (P0 g)
% 71.05/71.29 Found x30:(P g)
% 71.05/71.29 Found (fun (x30:(P g))=> x30) as proof of (P g)
% 71.05/71.29 Found (fun (x30:(P g))=> x30) as proof of (P0 g)
% 71.05/71.29 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 71.05/71.29 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 71.05/71.29 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 71.05/71.29 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 71.05/71.29 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 79.13/79.35 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 79.13/79.35 Found (eq_ref0 b1) as proof of (((eq Prop) b1) (b0 x0))
% 79.13/79.35 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (b0 x0))
% 79.13/79.35 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (b0 x0))
% 79.13/79.35 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (b0 x0))
% 79.13/79.35 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 79.13/79.35 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 79.13/79.35 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 79.13/79.35 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 79.13/79.35 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 79.13/79.35 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 79.13/79.35 Found (eq_ref0 b1) as proof of (((eq Prop) b1) (b0 x0))
% 79.13/79.35 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (b0 x0))
% 79.13/79.35 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (b0 x0))
% 79.13/79.35 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (b0 x0))
% 79.13/79.35 Found x00:(P f)
% 79.13/79.35 Found (fun (x00:(P f))=> x00) as proof of (P f)
% 79.13/79.35 Found (fun (x00:(P f))=> x00) as proof of (P0 f)
% 79.13/79.35 Found x00:(P f)
% 79.13/79.35 Found (fun (x00:(P f))=> x00) as proof of (P f)
% 79.13/79.35 Found (fun (x00:(P f))=> x00) as proof of (P0 f)
% 79.13/79.35 Found x40:(P (f x3))
% 79.13/79.35 Found (fun (x40:(P (f x3)))=> x40) as proof of (P (f x3))
% 79.13/79.35 Found (fun (x40:(P (f x3)))=> x40) as proof of (P0 (f x3))
% 79.13/79.35 Found x40:(P (f x3))
% 79.13/79.35 Found (fun (x40:(P (f x3)))=> x40) as proof of (P (f x3))
% 79.13/79.35 Found (fun (x40:(P (f x3)))=> x40) as proof of (P0 (f x3))
% 79.13/79.35 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 79.13/79.35 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 79.13/79.35 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 79.13/79.35 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 79.13/79.35 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 79.13/79.35 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 79.13/79.35 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 79.13/79.35 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 79.13/79.35 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 79.13/79.35 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 79.13/79.35 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 79.13/79.35 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 79.13/79.35 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 79.13/79.35 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 79.13/79.35 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 79.13/79.35 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 79.13/79.35 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 79.13/79.35 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 79.13/79.35 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 79.13/79.35 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 79.13/79.35 Found x20:=(x2 x10):(f Xx)
% 79.13/79.35 Found (x2 x10) as proof of (f Xx)
% 79.13/79.35 Found (x2 x10) as proof of (f Xx)
% 79.13/79.35 Found x10:=(x1 x20):(g Xx)
% 79.13/79.35 Found (x1 x20) as proof of (g Xx)
% 79.13/79.35 Found (x1 x20) as proof of (g Xx)
% 79.13/79.35 Found x00:(P g)
% 79.13/79.35 Found (fun (x00:(P g))=> x00) as proof of (P g)
% 79.13/79.35 Found (fun (x00:(P g))=> x00) as proof of (P0 g)
% 79.13/79.35 Found x00:(P g)
% 79.13/79.35 Found (fun (x00:(P g))=> x00) as proof of (P g)
% 79.13/79.35 Found (fun (x00:(P g))=> x00) as proof of (P0 g)
% 79.13/79.35 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 79.13/79.35 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 79.13/79.35 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 79.13/79.35 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 79.13/79.35 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 79.13/79.35 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 79.13/79.35 Found (eq_ref0 b1) as proof of (((eq Prop) b1) (g x0))
% 79.13/79.35 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (g x0))
% 79.13/79.35 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (g x0))
% 79.13/79.35 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (g x0))
% 79.13/79.35 Found x00:(P b0)
% 79.13/79.35 Found (fun (x00:(P b0))=> x00) as proof of (P b0)
% 79.13/79.35 Found (fun (x00:(P b0))=> x00) as proof of (P0 b0)
% 79.13/79.35 Found x00:(P b0)
% 79.13/79.35 Found (fun (x00:(P b0))=> x00) as proof of (P b0)
% 79.13/79.35 Found (fun (x00:(P b0))=> x00) as proof of (P0 b0)
% 79.13/79.35 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 79.13/79.35 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 79.13/79.35 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 79.13/79.35 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 81.05/81.29 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 81.05/81.29 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 81.05/81.29 Found (eq_ref0 b1) as proof of (((eq Prop) b1) (g x0))
% 81.05/81.29 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (g x0))
% 81.05/81.29 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (g x0))
% 81.05/81.29 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (g x0))
% 81.05/81.29 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 81.05/81.29 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 81.05/81.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 81.05/81.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 81.05/81.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 81.05/81.29 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 81.05/81.29 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 81.05/81.29 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 81.05/81.29 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 81.05/81.29 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 81.05/81.29 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 81.05/81.29 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 81.05/81.29 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 81.05/81.29 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 81.05/81.29 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 81.05/81.29 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 81.05/81.29 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 81.05/81.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 81.05/81.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 81.05/81.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 81.05/81.29 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 81.05/81.29 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 81.05/81.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 81.05/81.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 81.05/81.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 81.05/81.29 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 81.05/81.29 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 81.05/81.29 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 81.05/81.29 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 81.05/81.29 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 81.05/81.29 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 81.05/81.29 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 81.05/81.29 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 81.05/81.29 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 81.05/81.29 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 81.05/81.29 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 81.05/81.29 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 81.05/81.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 81.05/81.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 81.05/81.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 81.05/81.29 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 81.05/81.29 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 81.05/81.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 81.05/81.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 81.05/81.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 81.05/81.29 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 81.05/81.29 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 81.05/81.29 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 81.05/81.29 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 81.05/81.29 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 81.05/81.29 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 81.05/81.29 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 81.05/81.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 81.05/81.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 81.05/81.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 81.05/81.29 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 81.05/81.29 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 81.05/81.29 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 81.05/81.29 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 81.05/81.29 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 81.05/81.29 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 81.05/81.29 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 82.12/82.36 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 82.12/82.36 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 82.12/82.36 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 82.12/82.36 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 82.12/82.36 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 82.12/82.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 82.12/82.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 82.12/82.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 82.12/82.36 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 82.12/82.36 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 82.12/82.36 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 82.12/82.36 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 82.12/82.36 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 82.12/82.36 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 82.12/82.36 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 82.12/82.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 82.12/82.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 82.12/82.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 82.12/82.36 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 82.12/82.36 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 82.12/82.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 82.12/82.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 82.12/82.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 82.12/82.36 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 82.12/82.36 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 82.12/82.36 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 82.12/82.36 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 82.12/82.36 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 82.12/82.36 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 82.12/82.36 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 82.12/82.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 82.12/82.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 82.12/82.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 82.12/82.36 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 82.12/82.36 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 82.12/82.36 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 82.12/82.36 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 82.12/82.36 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 82.12/82.36 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 82.12/82.36 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 82.12/82.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 82.12/82.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 82.12/82.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 82.12/82.36 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 82.12/82.36 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 82.12/82.36 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 82.12/82.36 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 82.12/82.36 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 82.12/82.36 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 82.12/82.36 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 82.12/82.36 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 82.12/82.36 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 82.12/82.36 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 82.12/82.36 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 82.12/82.36 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 82.12/82.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 82.12/82.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 82.12/82.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 82.12/82.36 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 82.12/82.36 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 82.12/82.36 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 82.12/82.36 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 82.12/82.36 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 82.12/82.36 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 82.12/82.36 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 82.12/82.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 82.12/82.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 82.12/82.36 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 83.45/83.69 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 83.45/83.69 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 83.45/83.69 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 83.45/83.69 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 83.45/83.69 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 83.45/83.69 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 83.45/83.69 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 83.45/83.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 83.45/83.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 83.45/83.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 83.45/83.69 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 83.45/83.69 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 83.45/83.69 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 83.45/83.69 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 83.45/83.69 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 83.45/83.69 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 83.45/83.69 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 83.45/83.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 83.45/83.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 83.45/83.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 83.45/83.69 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 83.45/83.69 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 83.45/83.69 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 83.45/83.69 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 83.45/83.69 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 83.45/83.69 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 83.45/83.69 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 83.45/83.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 83.45/83.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 83.45/83.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 83.45/83.69 Found x30:(P g)
% 83.45/83.69 Found (fun (x30:(P g))=> x30) as proof of (P g)
% 83.45/83.69 Found (fun (x30:(P g))=> x30) as proof of (P0 g)
% 83.45/83.69 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 83.45/83.69 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 83.45/83.69 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 83.45/83.69 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 83.45/83.69 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 83.45/83.69 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 83.45/83.69 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 83.45/83.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 83.45/83.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 83.45/83.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 83.45/83.69 Found x30:(P g)
% 83.45/83.69 Found (fun (x30:(P g))=> x30) as proof of (P g)
% 83.45/83.69 Found (fun (x30:(P g))=> x30) as proof of (P0 g)
% 83.45/83.69 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 83.45/83.69 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 83.45/83.69 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 83.45/83.69 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 83.45/83.69 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 83.45/83.69 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 83.45/83.69 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 83.45/83.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 83.45/83.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 83.45/83.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 83.45/83.69 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 83.45/83.69 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 83.45/83.69 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 83.45/83.69 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 83.45/83.69 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 83.45/83.69 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 83.45/83.69 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 83.45/83.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 83.45/83.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 83.45/83.69 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 83.45/83.69 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 83.45/83.69 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 83.45/83.69 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 83.45/83.69 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 100.43/100.67 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 100.43/100.67 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 100.43/100.67 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 100.43/100.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 100.43/100.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 100.43/100.67 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 100.43/100.67 Found x20:=(x2 x10):(f Xx)
% 100.43/100.67 Found (x2 x10) as proof of (f Xx)
% 100.43/100.67 Found (x2 x10) as proof of (f Xx)
% 100.43/100.67 Found x10:=(x1 x20):(g Xx)
% 100.43/100.67 Found (x1 x20) as proof of (g Xx)
% 100.43/100.67 Found (x1 x20) as proof of (g Xx)
% 100.43/100.67 Found x10:(P b0)
% 100.43/100.67 Found (fun (x10:(P b0))=> x10) as proof of (P b0)
% 100.43/100.67 Found (fun (x10:(P b0))=> x10) as proof of (P0 b0)
% 100.43/100.67 Found x10:(P b0)
% 100.43/100.67 Found (fun (x10:(P b0))=> x10) as proof of (P b0)
% 100.43/100.67 Found (fun (x10:(P b0))=> x10) as proof of (P0 b0)
% 100.43/100.67 Found x20:=(x2 x10):(f Xx)
% 100.43/100.67 Found (x2 x10) as proof of (f Xx)
% 100.43/100.67 Found (x2 x10) as proof of (f Xx)
% 100.43/100.67 Found x10:(P (f x0))
% 100.43/100.67 Found (fun (x10:(P (f x0)))=> x10) as proof of (P (f x0))
% 100.43/100.67 Found (fun (x10:(P (f x0)))=> x10) as proof of (P0 (f x0))
% 100.43/100.67 Found x10:(P (f x0))
% 100.43/100.67 Found (fun (x10:(P (f x0)))=> x10) as proof of (P (f x0))
% 100.43/100.67 Found (fun (x10:(P (f x0)))=> x10) as proof of (P0 (f x0))
% 100.43/100.67 Found x20:=(x2 x30):(g Xx)
% 100.43/100.67 Found (x2 x30) as proof of (g Xx)
% 100.43/100.67 Found (x2 x30) as proof of (g Xx)
% 100.43/100.67 Found x10:=(x1 x20):(g Xx)
% 100.43/100.67 Found (x1 x20) as proof of (g Xx)
% 100.43/100.67 Found (x1 x20) as proof of (g Xx)
% 100.43/100.67 Found x30:=(x3 x20):(f Xx)
% 100.43/100.67 Found (x3 x20) as proof of (f Xx)
% 100.43/100.67 Found (x3 x20) as proof of (f Xx)
% 100.43/100.67 Found x20:=(x2 x10):(f Xx)
% 100.43/100.67 Found (x2 x10) as proof of (f Xx)
% 100.43/100.67 Found (x2 x10) as proof of (f Xx)
% 100.43/100.67 Found x40:(P (f x0))
% 100.43/100.67 Found (fun (x40:(P (f x0)))=> x40) as proof of (P (f x0))
% 100.43/100.67 Found (fun (x40:(P (f x0)))=> x40) as proof of (P0 (f x0))
% 100.43/100.67 Found x40:(P (f x0))
% 100.43/100.67 Found (fun (x40:(P (f x0)))=> x40) as proof of (P (f x0))
% 100.43/100.67 Found (fun (x40:(P (f x0)))=> x40) as proof of (P0 (f x0))
% 100.43/100.67 Found x10:=(x1 x20):(g Xx)
% 100.43/100.67 Found (x1 x20) as proof of (g Xx)
% 100.43/100.67 Found (x1 x20) as proof of (g Xx)
% 100.43/100.67 Found x20:=(x2 x10):(f Xx)
% 100.43/100.67 Found (x2 x10) as proof of (f Xx)
% 100.43/100.67 Found (x2 x10) as proof of (f Xx)
% 100.43/100.67 Found x10:(P1 (g x0))
% 100.43/100.67 Found (fun (x10:(P1 (g x0)))=> x10) as proof of (P1 (g x0))
% 100.43/100.67 Found (fun (x10:(P1 (g x0)))=> x10) as proof of (P2 (g x0))
% 100.43/100.67 Found x10:(P1 (g x0))
% 100.43/100.67 Found (fun (x10:(P1 (g x0)))=> x10) as proof of (P1 (g x0))
% 100.43/100.67 Found (fun (x10:(P1 (g x0)))=> x10) as proof of (P2 (g x0))
% 100.43/100.67 Found x10:(P1 (g x0))
% 100.43/100.67 Found (fun (x10:(P1 (g x0)))=> x10) as proof of (P1 (g x0))
% 100.43/100.67 Found (fun (x10:(P1 (g x0)))=> x10) as proof of (P2 (g x0))
% 100.43/100.67 Found x10:(P1 (g x0))
% 100.43/100.67 Found (fun (x10:(P1 (g x0)))=> x10) as proof of (P1 (g x0))
% 100.43/100.67 Found (fun (x10:(P1 (g x0)))=> x10) as proof of (P2 (g x0))
% 100.43/100.67 Found x10:(P1 (g x0))
% 100.43/100.67 Found (fun (x10:(P1 (g x0)))=> x10) as proof of (P1 (g x0))
% 100.43/100.67 Found (fun (x10:(P1 (g x0)))=> x10) as proof of (P2 (g x0))
% 100.43/100.67 Found x10:(P1 (g x0))
% 100.43/100.67 Found (fun (x10:(P1 (g x0)))=> x10) as proof of (P1 (g x0))
% 100.43/100.67 Found (fun (x10:(P1 (g x0)))=> x10) as proof of (P2 (g x0))
% 100.43/100.67 Found x10:(P1 (g x0))
% 100.43/100.67 Found (fun (x10:(P1 (g x0)))=> x10) as proof of (P1 (g x0))
% 100.43/100.67 Found (fun (x10:(P1 (g x0)))=> x10) as proof of (P2 (g x0))
% 100.43/100.67 Found x10:(P1 (g x0))
% 100.43/100.67 Found (fun (x10:(P1 (g x0)))=> x10) as proof of (P1 (g x0))
% 100.43/100.67 Found (fun (x10:(P1 (g x0)))=> x10) as proof of (P2 (g x0))
% 100.43/100.67 Found x30:=(x3 x20):(f Xx)
% 100.43/100.67 Found (x3 x20) as proof of (f Xx)
% 100.43/100.67 Found (x3 x20) as proof of (f Xx)
% 100.43/100.67 Found x10:=(x1 x20):(g Xx)
% 100.43/100.67 Found (x1 x20) as proof of (g Xx)
% 100.43/100.67 Found (x1 x20) as proof of (g Xx)
% 100.43/100.67 Found x20:=(x2 x10):(f Xx)
% 100.43/100.67 Found (x2 x10) as proof of (f Xx)
% 100.43/100.67 Found (x2 x10) as proof of (f Xx)
% 100.43/100.67 Found x20:=(x2 x10):(f Xx)
% 100.43/100.67 Found (x2 x10) as proof of (f Xx)
% 100.43/100.67 Found (x2 x10) as proof of (f Xx)
% 100.43/100.67 Found eq_ref00:=(eq_ref0 b00):(((eq (b->Prop)) b00) b00)
% 100.43/100.67 Found (eq_ref0 b00) as proof of (((eq (b->Prop)) b00) g)
% 100.43/100.67 Found ((eq_ref (b->Prop)) b00) as proof of (((eq (b->Prop)) b00) g)
% 100.43/100.67 Found ((eq_ref (b->Prop)) b00) as proof of (((eq (b->Prop)) b00) g)
% 100.43/100.67 Found ((eq_ref (b->Prop)) b00) as proof of (((eq (b->Prop)) b00) g)
% 100.43/100.67 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 100.43/100.67 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) b00)
% 100.43/100.67 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) b00)
% 100.43/100.67 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) b00)
% 108.01/108.26 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) b00)
% 108.01/108.26 Found x10:(P (g x0))
% 108.01/108.26 Found (fun (x10:(P (g x0)))=> x10) as proof of (P (g x0))
% 108.01/108.26 Found (fun (x10:(P (g x0)))=> x10) as proof of (P0 (g x0))
% 108.01/108.26 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 108.01/108.26 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 108.01/108.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 108.01/108.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 108.01/108.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 108.01/108.26 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 108.01/108.26 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 108.01/108.26 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 108.01/108.26 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 108.01/108.26 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 108.01/108.26 Found x10:(P (g x0))
% 108.01/108.26 Found (fun (x10:(P (g x0)))=> x10) as proof of (P (g x0))
% 108.01/108.26 Found (fun (x10:(P (g x0)))=> x10) as proof of (P0 (g x0))
% 108.01/108.26 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 108.01/108.26 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 108.01/108.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 108.01/108.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 108.01/108.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 108.01/108.26 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 108.01/108.26 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 108.01/108.26 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 108.01/108.26 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 108.01/108.26 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 108.01/108.26 Found x10:(P (g x0))
% 108.01/108.26 Found (fun (x10:(P (g x0)))=> x10) as proof of (P (g x0))
% 108.01/108.26 Found (fun (x10:(P (g x0)))=> x10) as proof of (P0 (g x0))
% 108.01/108.26 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 108.01/108.26 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 108.01/108.26 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 108.01/108.26 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 108.01/108.26 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 108.01/108.26 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 108.01/108.26 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 108.01/108.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 108.01/108.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 108.01/108.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 108.01/108.26 Found x10:(P (g x0))
% 108.01/108.26 Found (fun (x10:(P (g x0)))=> x10) as proof of (P (g x0))
% 108.01/108.26 Found (fun (x10:(P (g x0)))=> x10) as proof of (P0 (g x0))
% 108.01/108.26 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 108.01/108.26 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 108.01/108.26 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 108.01/108.26 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 108.01/108.26 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 108.01/108.26 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 108.01/108.26 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 108.01/108.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 108.01/108.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 108.01/108.26 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 108.01/108.26 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 108.01/108.26 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 108.01/108.26 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 108.01/108.26 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 108.01/108.26 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 108.01/108.26 Found eta_expansion000:=(eta_expansion00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 108.01/108.26 Found (eta_expansion00 g) as proof of (((eq (b->Prop)) g) b0)
% 108.01/108.26 Found ((eta_expansion0 Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 108.01/108.26 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 108.01/108.26 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 108.01/108.26 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 108.01/108.26 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 108.01/108.26 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) f)
% 108.01/108.26 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 108.01/108.26 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 108.01/108.26 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) f)
% 108.01/108.26 Found eta_expansion000:=(eta_expansion00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 118.63/118.89 Found (eta_expansion00 g) as proof of (((eq (b->Prop)) g) b0)
% 118.63/118.89 Found ((eta_expansion0 Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 118.63/118.89 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 118.63/118.89 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 118.63/118.89 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 118.63/118.89 Found x20:=(x2 x10):(f Xx)
% 118.63/118.89 Found (x2 x10) as proof of (f Xx)
% 118.63/118.89 Found (x2 x10) as proof of (f Xx)
% 118.63/118.89 Found x10:=(x1 x20):(g Xx)
% 118.63/118.89 Found (x1 x20) as proof of (g Xx)
% 118.63/118.89 Found (x1 x20) as proof of (g Xx)
% 118.63/118.89 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 118.63/118.89 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 118.63/118.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 118.63/118.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 118.63/118.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 118.63/118.89 Found x1:(P0 b0)
% 118.63/118.89 Instantiate: b0:=(g x0):Prop
% 118.63/118.89 Found (fun (x1:(P0 b0))=> x1) as proof of (P0 (g x0))
% 118.63/118.89 Found (fun (P0:(Prop->Prop)) (x1:(P0 b0))=> x1) as proof of ((P0 b0)->(P0 (g x0)))
% 118.63/118.89 Found (fun (P0:(Prop->Prop)) (x1:(P0 b0))=> x1) as proof of (P b0)
% 118.63/118.89 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 118.63/118.89 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 118.63/118.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 118.63/118.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 118.63/118.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 118.63/118.89 Found x1:(P0 b0)
% 118.63/118.89 Instantiate: b0:=(g x0):Prop
% 118.63/118.89 Found (fun (x1:(P0 b0))=> x1) as proof of (P0 (g x0))
% 118.63/118.89 Found (fun (P0:(Prop->Prop)) (x1:(P0 b0))=> x1) as proof of ((P0 b0)->(P0 (g x0)))
% 118.63/118.89 Found (fun (P0:(Prop->Prop)) (x1:(P0 b0))=> x1) as proof of (P b0)
% 118.63/118.89 Found x20:=(x2 x10):(f Xx)
% 118.63/118.89 Found (x2 x10) as proof of (f Xx)
% 118.63/118.89 Found (x2 x10) as proof of (f Xx)
% 118.63/118.89 Found x1:(P (f x0))
% 118.63/118.89 Instantiate: b0:=(f x0):Prop
% 118.63/118.89 Found x1 as proof of (P0 b0)
% 118.63/118.89 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 118.63/118.89 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 118.63/118.89 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 118.63/118.89 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 118.63/118.89 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 118.63/118.89 Found x1:(P (f x0))
% 118.63/118.89 Instantiate: b0:=(f x0):Prop
% 118.63/118.89 Found x1 as proof of (P0 b0)
% 118.63/118.89 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 118.63/118.89 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 118.63/118.89 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 118.63/118.89 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 118.63/118.89 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 118.63/118.89 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 118.63/118.89 Found (eq_ref0 b1) as proof of (((eq Prop) b1) b0)
% 118.63/118.89 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 118.63/118.89 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 118.63/118.89 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 118.63/118.89 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 118.63/118.89 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 118.63/118.89 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 118.63/118.89 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 118.63/118.89 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 118.63/118.89 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 118.63/118.89 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 118.63/118.89 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 118.63/118.89 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 118.63/118.89 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 118.63/118.89 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 118.63/118.89 Found (eq_ref0 b1) as proof of (((eq Prop) b1) b0)
% 118.63/118.89 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 118.63/118.89 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 118.63/118.89 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 118.63/118.89 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 118.63/118.89 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 118.63/118.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 118.63/118.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 118.63/118.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 129.18/129.51 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 129.18/129.51 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 129.18/129.51 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 129.18/129.51 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 129.18/129.51 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 129.18/129.51 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 129.18/129.51 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 129.18/129.51 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 129.18/129.51 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 129.18/129.51 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 129.18/129.51 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 129.18/129.51 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 129.18/129.51 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 129.18/129.51 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 129.18/129.51 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 129.18/129.51 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 129.18/129.51 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 129.18/129.51 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 129.18/129.51 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 129.18/129.51 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 129.18/129.51 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 129.18/129.51 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 129.18/129.51 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 129.18/129.51 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 129.18/129.51 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 129.18/129.51 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 129.18/129.51 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 129.18/129.51 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 129.18/129.51 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 129.18/129.51 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 129.18/129.51 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 129.18/129.51 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 129.18/129.51 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 129.18/129.51 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 129.18/129.51 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 129.18/129.51 Found eq_ref00:=(eq_ref0 a):(((eq b) a) a)
% 129.18/129.51 Found (eq_ref0 a) as proof of (((eq b) a) x0)
% 129.18/129.51 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 129.18/129.51 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 129.18/129.51 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 129.18/129.51 Found eq_ref00:=(eq_ref0 a):(((eq b) a) a)
% 129.18/129.51 Found (eq_ref0 a) as proof of (((eq b) a) x0)
% 129.18/129.51 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 129.18/129.51 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 129.18/129.51 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 129.18/129.51 Found eq_ref00:=(eq_ref0 a):(((eq b) a) a)
% 129.18/129.51 Found (eq_ref0 a) as proof of (((eq b) a) x0)
% 129.18/129.51 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 129.18/129.51 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 129.18/129.51 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 129.18/129.51 Found eq_ref00:=(eq_ref0 a):(((eq b) a) a)
% 129.18/129.51 Found (eq_ref0 a) as proof of (((eq b) a) x0)
% 129.18/129.51 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 129.18/129.51 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 129.18/129.51 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 129.18/129.51 Found x00:(P g)
% 129.18/129.51 Found (fun (x00:(P g))=> x00) as proof of (P g)
% 129.18/129.51 Found (fun (x00:(P g))=> x00) as proof of (P0 g)
% 129.18/129.51 Found x00:(P g)
% 129.18/129.51 Found (fun (x00:(P g))=> x00) as proof of (P g)
% 129.18/129.51 Found (fun (x00:(P g))=> x00) as proof of (P0 g)
% 129.18/129.51 Found x00:(P g)
% 129.18/129.51 Found (fun (x00:(P g))=> x00) as proof of (P g)
% 129.18/129.51 Found (fun (x00:(P g))=> x00) as proof of (P0 g)
% 129.18/129.51 Found x00:(P g)
% 129.18/129.51 Found (fun (x00:(P g))=> x00) as proof of (P g)
% 129.18/129.51 Found (fun (x00:(P g))=> x00) as proof of (P0 g)
% 129.18/129.51 Found eq_ref00:=(eq_ref0 a):(((eq b) a) a)
% 129.18/129.51 Found (eq_ref0 a) as proof of (((eq b) a) x0)
% 129.18/129.51 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 129.18/129.51 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 129.18/129.51 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 129.18/129.51 Found eq_ref00:=(eq_ref0 a):(((eq b) a) a)
% 129.18/129.51 Found (eq_ref0 a) as proof of (((eq b) a) x0)
% 129.18/129.51 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 129.18/129.51 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 129.18/129.51 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 129.18/129.51 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 129.18/129.51 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 129.18/129.51 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 134.12/134.41 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 134.12/134.41 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 134.12/134.41 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 134.12/134.41 Found (eq_ref0 b1) as proof of (((eq Prop) b1) b0)
% 134.12/134.41 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 134.12/134.41 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 134.12/134.41 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 134.12/134.41 Found eq_ref00:=(eq_ref0 a):(((eq b) a) a)
% 134.12/134.41 Found (eq_ref0 a) as proof of (((eq b) a) x0)
% 134.12/134.41 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 134.12/134.41 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 134.12/134.41 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 134.12/134.41 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 134.12/134.41 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 134.12/134.41 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 134.12/134.41 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 134.12/134.41 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 134.12/134.41 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 134.12/134.41 Found (eq_ref0 b1) as proof of (((eq Prop) b1) b0)
% 134.12/134.41 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 134.12/134.41 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 134.12/134.41 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 134.12/134.41 Found eq_ref00:=(eq_ref0 a):(((eq b) a) a)
% 134.12/134.41 Found (eq_ref0 a) as proof of (((eq b) a) x0)
% 134.12/134.41 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 134.12/134.41 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 134.12/134.41 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 134.12/134.41 Found eq_ref00:=(eq_ref0 (g x3)):(((eq Prop) (g x3)) (g x3))
% 134.12/134.41 Found (eq_ref0 (g x3)) as proof of (((eq Prop) (g x3)) b0)
% 134.12/134.41 Found ((eq_ref Prop) (g x3)) as proof of (((eq Prop) (g x3)) b0)
% 134.12/134.41 Found ((eq_ref Prop) (g x3)) as proof of (((eq Prop) (g x3)) b0)
% 134.12/134.41 Found ((eq_ref Prop) (g x3)) as proof of (((eq Prop) (g x3)) b0)
% 134.12/134.41 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 134.12/134.41 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x3))
% 134.12/134.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x3))
% 134.12/134.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x3))
% 134.12/134.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x3))
% 134.12/134.41 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 134.12/134.41 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x3))
% 134.12/134.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x3))
% 134.12/134.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x3))
% 134.12/134.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x3))
% 134.12/134.41 Found eq_ref00:=(eq_ref0 (g x3)):(((eq Prop) (g x3)) (g x3))
% 134.12/134.41 Found (eq_ref0 (g x3)) as proof of (((eq Prop) (g x3)) b0)
% 134.12/134.41 Found ((eq_ref Prop) (g x3)) as proof of (((eq Prop) (g x3)) b0)
% 134.12/134.41 Found ((eq_ref Prop) (g x3)) as proof of (((eq Prop) (g x3)) b0)
% 134.12/134.41 Found ((eq_ref Prop) (g x3)) as proof of (((eq Prop) (g x3)) b0)
% 134.12/134.41 Found eq_ref00:=(eq_ref0 (g x3)):(((eq Prop) (g x3)) (g x3))
% 134.12/134.41 Found (eq_ref0 (g x3)) as proof of (((eq Prop) (g x3)) b0)
% 134.12/134.41 Found ((eq_ref Prop) (g x3)) as proof of (((eq Prop) (g x3)) b0)
% 134.12/134.41 Found ((eq_ref Prop) (g x3)) as proof of (((eq Prop) (g x3)) b0)
% 134.12/134.41 Found ((eq_ref Prop) (g x3)) as proof of (((eq Prop) (g x3)) b0)
% 134.12/134.41 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 134.12/134.41 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x3))
% 134.12/134.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x3))
% 134.12/134.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x3))
% 134.12/134.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x3))
% 134.12/134.41 Found eq_ref00:=(eq_ref0 (g x3)):(((eq Prop) (g x3)) (g x3))
% 134.12/134.41 Found (eq_ref0 (g x3)) as proof of (((eq Prop) (g x3)) b0)
% 134.12/134.41 Found ((eq_ref Prop) (g x3)) as proof of (((eq Prop) (g x3)) b0)
% 134.12/134.41 Found ((eq_ref Prop) (g x3)) as proof of (((eq Prop) (g x3)) b0)
% 134.12/134.41 Found ((eq_ref Prop) (g x3)) as proof of (((eq Prop) (g x3)) b0)
% 134.12/134.41 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 134.12/134.41 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x3))
% 134.12/134.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x3))
% 134.12/134.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x3))
% 134.12/134.41 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x3))
% 134.12/134.41 Found x10:(P (f x0))
% 134.12/134.41 Found (fun (x10:(P (f x0)))=> x10) as proof of (P (f x0))
% 134.12/134.41 Found (fun (x10:(P (f x0)))=> x10) as proof of (P0 (f x0))
% 134.12/134.41 Found x10:(P (f x0))
% 134.12/134.41 Found (fun (x10:(P (f x0)))=> x10) as proof of (P (f x0))
% 146.28/146.56 Found (fun (x10:(P (f x0)))=> x10) as proof of (P0 (f x0))
% 146.28/146.56 Found x10:(P (f x0))
% 146.28/146.56 Found (fun (x10:(P (f x0)))=> x10) as proof of (P (f x0))
% 146.28/146.56 Found (fun (x10:(P (f x0)))=> x10) as proof of (P0 (f x0))
% 146.28/146.56 Found x10:(P (f x0))
% 146.28/146.56 Found (fun (x10:(P (f x0)))=> x10) as proof of (P (f x0))
% 146.28/146.56 Found (fun (x10:(P (f x0)))=> x10) as proof of (P0 (f x0))
% 146.28/146.56 Found x1:(P (f x0))
% 146.28/146.56 Instantiate: b0:=f:(b->Prop)
% 146.28/146.56 Found x1 as proof of (P0 b0)
% 146.28/146.56 Found eta_expansion_dep000:=(eta_expansion_dep00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 146.28/146.56 Found (eta_expansion_dep00 g) as proof of (((eq (b->Prop)) g) b0)
% 146.28/146.56 Found ((eta_expansion_dep0 (fun (x3:b)=> Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 146.28/146.56 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 146.28/146.56 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 146.28/146.56 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 146.28/146.56 Found x1:(P (f x0))
% 146.28/146.56 Instantiate: b0:=f:(b->Prop)
% 146.28/146.56 Found x1 as proof of (P0 b0)
% 146.28/146.56 Found eta_expansion_dep000:=(eta_expansion_dep00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 146.28/146.56 Found (eta_expansion_dep00 g) as proof of (((eq (b->Prop)) g) b0)
% 146.28/146.56 Found ((eta_expansion_dep0 (fun (x3:b)=> Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 146.28/146.56 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 146.28/146.56 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 146.28/146.56 Found (((eta_expansion_dep b) (fun (x3:b)=> Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 146.28/146.56 Found x20:=(x2 x10):(f Xx)
% 146.28/146.56 Found (x2 x10) as proof of (f Xx)
% 146.28/146.56 Found (x2 x10) as proof of (f Xx)
% 146.28/146.56 Found x10:=(x1 x20):(g Xx)
% 146.28/146.56 Found (x1 x20) as proof of (g Xx)
% 146.28/146.56 Found (x1 x20) as proof of (g Xx)
% 146.28/146.56 Found x00:(P b0)
% 146.28/146.56 Found (fun (x00:(P b0))=> x00) as proof of (P b0)
% 146.28/146.56 Found (fun (x00:(P b0))=> x00) as proof of (P0 b0)
% 146.28/146.56 Found x00:(P b0)
% 146.28/146.56 Found (fun (x00:(P b0))=> x00) as proof of (P b0)
% 146.28/146.56 Found (fun (x00:(P b0))=> x00) as proof of (P0 b0)
% 146.28/146.56 Found eq_ref00:=(eq_ref0 g):(((eq (b->Prop)) g) g)
% 146.28/146.56 Found (eq_ref0 g) as proof of (((eq (b->Prop)) g) b0)
% 146.28/146.56 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 146.28/146.56 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 146.28/146.56 Found ((eq_ref (b->Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 146.28/146.56 Found x1:(P0 (f x0))
% 146.28/146.56 Instantiate: b0:=f:(b->Prop)
% 146.28/146.56 Found (fun (x1:(P0 (f x0)))=> x1) as proof of (P0 (b0 x0))
% 146.28/146.56 Found (fun (P0:(Prop->Prop)) (x1:(P0 (f x0)))=> x1) as proof of ((P0 (f x0))->(P0 (b0 x0)))
% 146.28/146.56 Found (fun (P0:(Prop->Prop)) (x1:(P0 (f x0)))=> x1) as proof of (P b0)
% 146.28/146.56 Found eta_expansion000:=(eta_expansion00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 146.28/146.56 Found (eta_expansion00 g) as proof of (((eq (b->Prop)) g) b0)
% 146.28/146.56 Found ((eta_expansion0 Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 146.28/146.56 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 146.28/146.56 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 146.28/146.56 Found (((eta_expansion b) Prop) g) as proof of (((eq (b->Prop)) g) b0)
% 146.28/146.56 Found x1:(P0 (f x0))
% 146.28/146.56 Instantiate: b0:=f:(b->Prop)
% 146.28/146.56 Found (fun (x1:(P0 (f x0)))=> x1) as proof of (P0 (b0 x0))
% 146.28/146.56 Found (fun (P0:(Prop->Prop)) (x1:(P0 (f x0)))=> x1) as proof of ((P0 (f x0))->(P0 (b0 x0)))
% 146.28/146.56 Found (fun (P0:(Prop->Prop)) (x1:(P0 (f x0)))=> x1) as proof of (P b0)
% 146.28/146.56 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 146.28/146.56 Found (eq_ref0 b1) as proof of (((eq Prop) b1) (f x0))
% 146.28/146.56 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (f x0))
% 146.28/146.56 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (f x0))
% 146.28/146.56 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (f x0))
% 146.28/146.56 Found eq_ref00:=(eq_ref0 (b0 x0)):(((eq Prop) (b0 x0)) (b0 x0))
% 146.28/146.56 Found (eq_ref0 (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 146.28/146.56 Found ((eq_ref Prop) (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 146.28/146.56 Found ((eq_ref Prop) (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 146.28/146.56 Found ((eq_ref Prop) (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 146.28/146.56 Found eq_ref00:=(eq_ref0 (b0 x0)):(((eq Prop) (b0 x0)) (b0 x0))
% 146.28/146.56 Found (eq_ref0 (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 146.28/146.56 Found ((eq_ref Prop) (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 146.28/146.56 Found ((eq_ref Prop) (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 153.43/153.71 Found ((eq_ref Prop) (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 153.43/153.71 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 153.43/153.71 Found (eq_ref0 b1) as proof of (((eq Prop) b1) (f x0))
% 153.43/153.71 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (f x0))
% 153.43/153.71 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (f x0))
% 153.43/153.71 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (f x0))
% 153.43/153.71 Found eq_ref00:=(eq_ref0 (b0 x0)):(((eq Prop) (b0 x0)) (b0 x0))
% 153.43/153.71 Found (eq_ref0 (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 153.43/153.71 Found ((eq_ref Prop) (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 153.43/153.71 Found ((eq_ref Prop) (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 153.43/153.71 Found ((eq_ref Prop) (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 153.43/153.71 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 153.43/153.71 Found (eq_ref0 b1) as proof of (((eq Prop) b1) (f x0))
% 153.43/153.71 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (f x0))
% 153.43/153.71 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (f x0))
% 153.43/153.71 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (f x0))
% 153.43/153.71 Found eq_ref00:=(eq_ref0 (b0 x0)):(((eq Prop) (b0 x0)) (b0 x0))
% 153.43/153.71 Found (eq_ref0 (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 153.43/153.71 Found ((eq_ref Prop) (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 153.43/153.71 Found ((eq_ref Prop) (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 153.43/153.71 Found ((eq_ref Prop) (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 153.43/153.71 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 153.43/153.71 Found (eq_ref0 b1) as proof of (((eq Prop) b1) (f x0))
% 153.43/153.71 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (f x0))
% 153.43/153.71 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (f x0))
% 153.43/153.71 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (f x0))
% 153.43/153.71 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 153.43/153.71 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 153.43/153.71 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 153.43/153.71 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 153.43/153.71 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 153.43/153.71 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 153.43/153.71 Found (eq_ref0 b1) as proof of (((eq Prop) b1) (b0 x0))
% 153.43/153.71 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (b0 x0))
% 153.43/153.71 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (b0 x0))
% 153.43/153.71 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (b0 x0))
% 153.43/153.71 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 153.43/153.71 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 153.43/153.71 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 153.43/153.71 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 153.43/153.71 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 153.43/153.71 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 153.43/153.71 Found (eq_ref0 b1) as proof of (((eq Prop) b1) (b0 x0))
% 153.43/153.71 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (b0 x0))
% 153.43/153.71 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (b0 x0))
% 153.43/153.71 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (b0 x0))
% 153.43/153.71 Found x20:=(x2 x10):(f Xx)
% 153.43/153.71 Found (x2 x10) as proof of (f Xx)
% 153.43/153.71 Found (x2 x10) as proof of (f Xx)
% 153.43/153.71 Found x20:=(x2 x10):(f Xx)
% 153.43/153.71 Found (x2 x10) as proof of (f Xx)
% 153.43/153.71 Found (x2 x10) as proof of (f Xx)
% 153.43/153.71 Found x10:=(x1 x20):(g Xx)
% 153.43/153.71 Found (x1 x20) as proof of (g Xx)
% 153.43/153.71 Found (x1 x20) as proof of (g Xx)
% 153.43/153.71 Found x10:=(x1 x20):(g Xx)
% 153.43/153.71 Found (x1 x20) as proof of (g Xx)
% 153.43/153.71 Found (x1 x20) as proof of (g Xx)
% 153.43/153.71 Found x10:=(x1 x20):(g Xx)
% 153.43/153.71 Found (x1 x20) as proof of (g Xx)
% 153.43/153.71 Found (x1 x20) as proof of (g Xx)
% 153.43/153.71 Found x20:=(x2 x10):(f Xx)
% 153.43/153.71 Found (x2 x10) as proof of (f Xx)
% 153.43/153.71 Found (x2 x10) as proof of (f Xx)
% 153.43/153.71 Found x10:(P (g x0))
% 153.43/153.71 Found (fun (x10:(P (g x0)))=> x10) as proof of (P (g x0))
% 153.43/153.71 Found (fun (x10:(P (g x0)))=> x10) as proof of (P0 (g x0))
% 153.43/153.71 Found x10:(P (g x0))
% 153.43/153.71 Found (fun (x10:(P (g x0)))=> x10) as proof of (P (g x0))
% 153.43/153.71 Found (fun (x10:(P (g x0)))=> x10) as proof of (P0 (g x0))
% 153.43/153.71 Found eq_ref00:=(eq_ref0 (g x3)):(((eq Prop) (g x3)) (g x3))
% 153.43/153.71 Found (eq_ref0 (g x3)) as proof of (((eq Prop) (g x3)) b0)
% 153.43/153.71 Found ((eq_ref Prop) (g x3)) as proof of (((eq Prop) (g x3)) b0)
% 153.43/153.71 Found ((eq_ref Prop) (g x3)) as proof of (((eq Prop) (g x3)) b0)
% 153.43/153.71 Found ((eq_ref Prop) (g x3)) as proof of (((eq Prop) (g x3)) b0)
% 153.43/153.71 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 153.43/153.71 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x3))
% 164.46/164.80 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x3))
% 164.46/164.80 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x3))
% 164.46/164.80 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x3))
% 164.46/164.80 Found eq_ref00:=(eq_ref0 (g x3)):(((eq Prop) (g x3)) (g x3))
% 164.46/164.80 Found (eq_ref0 (g x3)) as proof of (((eq Prop) (g x3)) b0)
% 164.46/164.80 Found ((eq_ref Prop) (g x3)) as proof of (((eq Prop) (g x3)) b0)
% 164.46/164.80 Found ((eq_ref Prop) (g x3)) as proof of (((eq Prop) (g x3)) b0)
% 164.46/164.80 Found ((eq_ref Prop) (g x3)) as proof of (((eq Prop) (g x3)) b0)
% 164.46/164.80 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 164.46/164.80 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x3))
% 164.46/164.80 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x3))
% 164.46/164.80 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x3))
% 164.46/164.80 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x3))
% 164.46/164.80 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 164.46/164.80 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 164.46/164.80 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 164.46/164.80 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 164.46/164.80 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 164.46/164.80 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 164.46/164.80 Found (eq_ref0 b1) as proof of (((eq Prop) b1) (f x0))
% 164.46/164.80 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (f x0))
% 164.46/164.80 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (f x0))
% 164.46/164.80 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (f x0))
% 164.46/164.80 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 164.46/164.80 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 164.46/164.80 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 164.46/164.80 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 164.46/164.80 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b1)
% 164.46/164.80 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 164.46/164.80 Found (eq_ref0 b1) as proof of (((eq Prop) b1) (f x0))
% 164.46/164.80 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (f x0))
% 164.46/164.80 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (f x0))
% 164.46/164.80 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (f x0))
% 164.46/164.80 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 164.46/164.80 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 164.46/164.80 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 164.46/164.80 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 164.46/164.80 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 164.46/164.80 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 164.46/164.80 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 164.46/164.80 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 164.46/164.80 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 164.46/164.80 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 164.46/164.80 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 164.46/164.80 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 164.46/164.80 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 164.46/164.80 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 164.46/164.80 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 164.46/164.80 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 164.46/164.80 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 164.46/164.80 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 164.46/164.80 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 164.46/164.80 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 164.46/164.80 Found x40:(P (g x3))
% 164.46/164.80 Found (fun (x40:(P (g x3)))=> x40) as proof of (P (g x3))
% 164.46/164.80 Found (fun (x40:(P (g x3)))=> x40) as proof of (P0 (g x3))
% 164.46/164.80 Found x40:(P (g x3))
% 164.46/164.80 Found (fun (x40:(P (g x3)))=> x40) as proof of (P (g x3))
% 164.46/164.80 Found (fun (x40:(P (g x3)))=> x40) as proof of (P0 (g x3))
% 164.46/164.80 Found x20:=(x2 x10):(f Xx)
% 164.46/164.80 Found (x2 x10) as proof of (f Xx)
% 164.46/164.80 Found (x2 x10) as proof of (f Xx)
% 164.46/164.80 Found x10:=(x1 x20):(g Xx)
% 164.46/164.80 Found (x1 x20) as proof of (g Xx)
% 164.46/164.80 Found (x1 x20) as proof of (g Xx)
% 164.46/164.80 Found x10:=(x1 x20):(g Xx)
% 164.46/164.80 Found (x1 x20) as proof of (g Xx)
% 164.46/164.80 Found (x1 x20) as proof of (g Xx)
% 164.46/164.80 Found x20:=(x2 x10):(f Xx)
% 164.46/164.80 Found (x2 x10) as proof of (f Xx)
% 164.46/164.80 Found (x2 x10) as proof of (f Xx)
% 164.46/164.80 Found x10:=(x1 x20):(g Xx)
% 164.46/164.80 Found (x1 x20) as proof of (g Xx)
% 164.46/164.80 Found (x1 x20) as proof of (g Xx)
% 164.46/164.80 Found x20:=(x2 x10):(f Xx)
% 164.46/164.80 Found (x2 x10) as proof of (f Xx)
% 164.46/164.80 Found (x2 x10) as proof of (f Xx)
% 164.46/164.80 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 164.46/164.80 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 166.55/166.89 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 166.55/166.89 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 166.55/166.89 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 166.55/166.89 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 166.55/166.89 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 166.55/166.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 166.55/166.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 166.55/166.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 166.55/166.89 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 166.55/166.89 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 166.55/166.89 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 166.55/166.89 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 166.55/166.89 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 166.55/166.89 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 166.55/166.89 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 166.55/166.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 166.55/166.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 166.55/166.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 166.55/166.89 Found x10:=(x1 x20):(g Xx)
% 166.55/166.89 Found (x1 x20) as proof of (g Xx)
% 166.55/166.89 Found (x1 x20) as proof of (g Xx)
% 166.55/166.89 Found x20:=(x2 x10):(f Xx)
% 166.55/166.89 Found (x2 x10) as proof of (f Xx)
% 166.55/166.89 Found (x2 x10) as proof of (f Xx)
% 166.55/166.89 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 166.55/166.89 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 166.55/166.89 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 166.55/166.89 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 166.55/166.89 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 166.55/166.89 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 166.55/166.89 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 166.55/166.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 166.55/166.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 166.55/166.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 166.55/166.89 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 166.55/166.89 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 166.55/166.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 166.55/166.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 166.55/166.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 166.55/166.89 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 166.55/166.89 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 166.55/166.89 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 166.55/166.89 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 166.55/166.89 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 166.55/166.89 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 166.55/166.89 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 166.55/166.89 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 166.55/166.89 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 166.55/166.89 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 166.55/166.89 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 166.55/166.89 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 166.55/166.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 166.55/166.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 166.55/166.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 166.55/166.89 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 166.55/166.89 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 166.55/166.89 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 166.55/166.89 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 166.55/166.89 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 166.55/166.89 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 166.55/166.89 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 166.55/166.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 166.55/166.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 166.55/166.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 166.55/166.89 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 166.55/166.89 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 166.55/166.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 166.55/166.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 166.55/166.89 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 166.55/166.89 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 168.25/168.55 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 168.25/168.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 168.25/168.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 168.25/168.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 168.25/168.55 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 168.25/168.55 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 168.25/168.55 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 168.25/168.55 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 168.25/168.55 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 168.25/168.55 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 168.25/168.55 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 168.25/168.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 168.25/168.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 168.25/168.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 168.25/168.55 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 168.25/168.55 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 168.25/168.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 168.25/168.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 168.25/168.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 168.25/168.55 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 168.25/168.55 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 168.25/168.55 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 168.25/168.55 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 168.25/168.55 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 168.25/168.55 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 168.25/168.55 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 168.25/168.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 168.25/168.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 168.25/168.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 168.25/168.55 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 168.25/168.55 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 168.25/168.55 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 168.25/168.55 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 168.25/168.55 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 168.25/168.55 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 168.25/168.55 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 168.25/168.55 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 168.25/168.55 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 168.25/168.55 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 168.25/168.55 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 168.25/168.55 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 168.25/168.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 168.25/168.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 168.25/168.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 168.25/168.55 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 168.25/168.55 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 168.25/168.55 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 168.25/168.55 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 168.25/168.55 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 168.25/168.55 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 168.25/168.55 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 168.25/168.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 168.25/168.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 168.25/168.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 168.25/168.55 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 168.25/168.55 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 168.25/168.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 168.25/168.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 168.25/168.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 168.25/168.55 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 168.25/168.55 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 168.25/168.55 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 168.25/168.55 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 168.25/168.55 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 168.25/168.55 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 168.25/168.55 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 168.25/168.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 168.25/168.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 168.25/168.55 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 182.82/183.14 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 182.82/183.14 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 182.82/183.14 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 182.82/183.14 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 182.82/183.14 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 182.82/183.14 Found x10:=(x1 x20):(g Xx)
% 182.82/183.14 Found (x1 x20) as proof of (g Xx)
% 182.82/183.14 Found (x1 x20) as proof of (g Xx)
% 182.82/183.14 Found x20:=(x2 x10):(f Xx)
% 182.82/183.14 Found (x2 x10) as proof of (f Xx)
% 182.82/183.14 Found (x2 x10) as proof of (f Xx)
% 182.82/183.14 Found x10:(P b0)
% 182.82/183.14 Found (fun (x10:(P b0))=> x10) as proof of (P b0)
% 182.82/183.14 Found (fun (x10:(P b0))=> x10) as proof of (P0 b0)
% 182.82/183.14 Found x10:(P b0)
% 182.82/183.14 Found (fun (x10:(P b0))=> x10) as proof of (P b0)
% 182.82/183.14 Found (fun (x10:(P b0))=> x10) as proof of (P0 b0)
% 182.82/183.14 Found x20:=(x2 x10):(f Xx)
% 182.82/183.14 Found (x2 x10) as proof of (f Xx)
% 182.82/183.14 Found (x2 x10) as proof of (f Xx)
% 182.82/183.14 Found x20:=(x2 x10):(f Xx)
% 182.82/183.14 Found (x2 x10) as proof of (f Xx)
% 182.82/183.14 Found (x2 x10) as proof of (f Xx)
% 182.82/183.14 Found x10:=(x1 x20):(g Xx)
% 182.82/183.14 Found (x1 x20) as proof of (g Xx)
% 182.82/183.15 Found (x1 x20) as proof of (g Xx)
% 182.82/183.15 Found x10:(P (b0 x0))
% 182.82/183.15 Found (fun (x10:(P (b0 x0)))=> x10) as proof of (P (b0 x0))
% 182.82/183.15 Found (fun (x10:(P (b0 x0)))=> x10) as proof of (P0 (b0 x0))
% 182.82/183.15 Found x10:(P (b0 x0))
% 182.82/183.15 Found (fun (x10:(P (b0 x0)))=> x10) as proof of (P (b0 x0))
% 182.82/183.15 Found (fun (x10:(P (b0 x0)))=> x10) as proof of (P0 (b0 x0))
% 182.82/183.15 Found x10:(P (g x0))
% 182.82/183.15 Found (fun (x10:(P (g x0)))=> x10) as proof of (P (g x0))
% 182.82/183.15 Found (fun (x10:(P (g x0)))=> x10) as proof of (P0 (g x0))
% 182.82/183.15 Found x10:(P (g x0))
% 182.82/183.15 Found (fun (x10:(P (g x0)))=> x10) as proof of (P (g x0))
% 182.82/183.15 Found (fun (x10:(P (g x0)))=> x10) as proof of (P0 (g x0))
% 182.82/183.15 Found x10:=(x1 x20):(g Xx)
% 182.82/183.15 Found (x1 x20) as proof of (g Xx)
% 182.82/183.15 Found (x1 x20) as proof of (g Xx)
% 182.82/183.15 Found x10:=(x1 x20):(g Xx)
% 182.82/183.15 Found (x1 x20) as proof of (g Xx)
% 182.82/183.15 Found (x1 x20) as proof of (g Xx)
% 182.82/183.15 Found x20:=(x2 x10):(f Xx)
% 182.82/183.15 Found (x2 x10) as proof of (f Xx)
% 182.82/183.15 Found (x2 x10) as proof of (f Xx)
% 182.82/183.15 Found x20:=(x2 x10):(f Xx)
% 182.82/183.15 Found (x2 x10) as proof of (f Xx)
% 182.82/183.15 Found (x2 x10) as proof of (f Xx)
% 182.82/183.15 Found x10:=(x1 x20):(g Xx)
% 182.82/183.15 Found (x1 x20) as proof of (g Xx)
% 182.82/183.15 Found (x1 x20) as proof of (g Xx)
% 182.82/183.15 Found x10:=(x1 x20):(g Xx)
% 182.82/183.15 Found (x1 x20) as proof of (g Xx)
% 182.82/183.15 Found (x1 x20) as proof of (g Xx)
% 182.82/183.15 Found x20:=(x2 x10):(f Xx)
% 182.82/183.15 Found (x2 x10) as proof of (f Xx)
% 182.82/183.15 Found (x2 x10) as proof of (f Xx)
% 182.82/183.15 Found x20:=(x2 x10):(f Xx)
% 182.82/183.15 Found (x2 x10) as proof of (f Xx)
% 182.82/183.15 Found (x2 x10) as proof of (f Xx)
% 182.82/183.15 Found x20:=(x2 x10):(f Xx)
% 182.82/183.15 Found (x2 x10) as proof of (f Xx)
% 182.82/183.15 Found (x2 x10) as proof of (f Xx)
% 182.82/183.15 Found x10:=(x1 x20):(g Xx)
% 182.82/183.15 Found (x1 x20) as proof of (g Xx)
% 182.82/183.15 Found (x1 x20) as proof of (g Xx)
% 182.82/183.15 Found x40:(P (g x3))
% 182.82/183.15 Found (fun (x40:(P (g x3)))=> x40) as proof of (P (g x3))
% 182.82/183.15 Found (fun (x40:(P (g x3)))=> x40) as proof of (P0 (g x3))
% 182.82/183.15 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 182.82/183.15 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 182.82/183.15 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 182.82/183.15 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 182.82/183.15 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 182.82/183.15 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 182.82/183.15 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 182.82/183.15 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 182.82/183.15 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 182.82/183.15 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 182.82/183.15 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 182.82/183.15 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 182.82/183.15 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 182.82/183.15 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 182.82/183.15 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 182.82/183.15 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 182.82/183.15 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 182.82/183.15 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 182.82/183.15 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 182.82/183.15 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 182.82/183.15 Found x40:(P (g x3))
% 182.82/183.15 Found (fun (x40:(P (g x3)))=> x40) as proof of (P (g x3))
% 182.82/183.15 Found (fun (x40:(P (g x3)))=> x40) as proof of (P0 (g x3))
% 182.82/183.15 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 199.65/200.04 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 199.65/200.04 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 199.65/200.04 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 199.65/200.04 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 199.65/200.04 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 199.65/200.04 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 199.65/200.04 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 199.65/200.04 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 199.65/200.04 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 199.65/200.04 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 199.65/200.04 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 199.65/200.04 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 199.65/200.04 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 199.65/200.04 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 199.65/200.04 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 199.65/200.04 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 199.65/200.04 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 199.65/200.04 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 199.65/200.04 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 199.65/200.04 Found x30:=(x3 x20):(f Xx)
% 199.65/200.04 Found (x3 x20) as proof of (f Xx)
% 199.65/200.04 Found (x3 x20) as proof of (f Xx)
% 199.65/200.04 Found x20:=(x2 x30):(g Xx)
% 199.65/200.04 Found (x2 x30) as proof of (g Xx)
% 199.65/200.04 Found (x2 x30) as proof of (g Xx)
% 199.65/200.04 Found x10:=(x1 x20):(g Xx)
% 199.65/200.04 Found (x1 x20) as proof of (g Xx)
% 199.65/200.04 Found (x1 x20) as proof of (g Xx)
% 199.65/200.04 Found x20:=(x2 x10):(f Xx)
% 199.65/200.04 Found (x2 x10) as proof of (f Xx)
% 199.65/200.04 Found (x2 x10) as proof of (f Xx)
% 199.65/200.04 Found x10:=(x1 x20):(g Xx)
% 199.65/200.04 Found (x1 x20) as proof of (g Xx)
% 199.65/200.04 Found (x1 x20) as proof of (g Xx)
% 199.65/200.04 Found x20:=(x2 x10):(f Xx)
% 199.65/200.04 Found (x2 x10) as proof of (f Xx)
% 199.65/200.04 Found (x2 x10) as proof of (f Xx)
% 199.65/200.04 Found x10:=(x1 x20):(g Xx)
% 199.65/200.04 Found (x1 x20) as proof of (g Xx)
% 199.65/200.04 Found (x1 x20) as proof of (g Xx)
% 199.65/200.04 Found x20:=(x2 x10):(f Xx)
% 199.65/200.04 Found (x2 x10) as proof of (f Xx)
% 199.65/200.04 Found (x2 x10) as proof of (f Xx)
% 199.65/200.04 Found x20:=(x2 x10):(f Xx)
% 199.65/200.04 Found (x2 x10) as proof of (f Xx)
% 199.65/200.04 Found (x2 x10) as proof of (f Xx)
% 199.65/200.04 Found x10:=(x1 x20):(g Xx)
% 199.65/200.04 Found (x1 x20) as proof of (g Xx)
% 199.65/200.04 Found (x1 x20) as proof of (g Xx)
% 199.65/200.04 Found x10:=(x1 x20):(g Xx)
% 199.65/200.04 Found (x1 x20) as proof of (g Xx)
% 199.65/200.04 Found (x1 x20) as proof of (g Xx)
% 199.65/200.04 Found x10:=(x1 x20):(g Xx)
% 199.65/200.04 Found (x1 x20) as proof of (g Xx)
% 199.65/200.04 Found (x1 x20) as proof of (g Xx)
% 199.65/200.04 Found x20:=(x2 x10):(f Xx)
% 199.65/200.04 Found (x2 x10) as proof of (f Xx)
% 199.65/200.04 Found (x2 x10) as proof of (f Xx)
% 199.65/200.04 Found x20:=(x2 x10):(f Xx)
% 199.65/200.04 Found (x2 x10) as proof of (f Xx)
% 199.65/200.04 Found (x2 x10) as proof of (f Xx)
% 199.65/200.04 Found x20:=(x2 x30):(g Xx)
% 199.65/200.04 Found (x2 x30) as proof of (g Xx)
% 199.65/200.04 Found (x2 x30) as proof of (g Xx)
% 199.65/200.04 Found x20:=(x2 x30):(g Xx)
% 199.65/200.04 Found (x2 x30) as proof of (g Xx)
% 199.65/200.04 Found (x2 x30) as proof of (g Xx)
% 199.65/200.04 Found x30:=(x3 x20):(f Xx)
% 199.65/200.04 Found (x3 x20) as proof of (f Xx)
% 199.65/200.04 Found (x3 x20) as proof of (f Xx)
% 199.65/200.04 Found x30:=(x3 x20):(f Xx)
% 199.65/200.04 Found (x3 x20) as proof of (f Xx)
% 199.65/200.04 Found (x3 x20) as proof of (f Xx)
% 199.65/200.04 Found x10:=(x1 x20):(g Xx)
% 199.65/200.04 Found (x1 x20) as proof of (g Xx)
% 199.65/200.04 Found (x1 x20) as proof of (g Xx)
% 199.65/200.04 Found x20:=(x2 x10):(f Xx)
% 199.65/200.04 Found (x2 x10) as proof of (f Xx)
% 199.65/200.04 Found (x2 x10) as proof of (f Xx)
% 199.65/200.04 Found x20:=(x2 x10):(f Xx)
% 199.65/200.04 Found (x2 x10) as proof of (f Xx)
% 199.65/200.04 Found (x2 x10) as proof of (f Xx)
% 199.65/200.04 Found x30:=(x3 x20):(f Xx)
% 199.65/200.04 Found (x3 x20) as proof of (f Xx)
% 199.65/200.04 Found (x3 x20) as proof of (f Xx)
% 199.65/200.04 Found x20:=(x2 x10):(f Xx)
% 199.65/200.04 Found (x2 x10) as proof of (f Xx)
% 199.65/200.04 Found (x2 x10) as proof of (f Xx)
% 199.65/200.04 Found x10:=(x1 x20):(g Xx)
% 199.65/200.04 Found (x1 x20) as proof of (g Xx)
% 199.65/200.04 Found (x1 x20) as proof of (g Xx)
% 199.65/200.04 Found x20:=(x2 x10):(f Xx)
% 199.65/200.04 Found (x2 x10) as proof of (f Xx)
% 199.65/200.04 Found (x2 x10) as proof of (f Xx)
% 199.65/200.04 Found x10:=(x1 x20):(g Xx)
% 199.65/200.04 Found (x1 x20) as proof of (g Xx)
% 199.65/200.04 Found (x1 x20) as proof of (g Xx)
% 199.65/200.04 Found x10:=(x1 x20):(g Xx)
% 199.65/200.04 Found (x1 x20) as proof of (g Xx)
% 199.65/200.04 Found (x1 x20) as proof of (g Xx)
% 199.65/200.04 Found x20:=(x2 x10):(f Xx)
% 199.65/200.04 Found (x2 x10) as proof of (f Xx)
% 199.65/200.04 Found (x2 x10) as proof of (f Xx)
% 199.65/200.04 Found x20:=(x2 x10):(f Xx)
% 199.65/200.04 Found (x2 x10) as proof of (f Xx)
% 199.65/200.04 Found (x2 x10) as proof of (f Xx)
% 199.65/200.04 Found x20:=(x2 x10):(f Xx)
% 199.65/200.04 Found (x2 x10) as proof of (f Xx)
% 199.65/200.04 Found (x2 x10) as proof of (f Xx)
% 199.65/200.04 Found x10:=(x1 x20):(g Xx)
% 199.65/200.04 Found (x1 x20) as proof of (g Xx)
% 199.65/200.04 Found (x1 x20) as proof of (g Xx)
% 206.73/207.09 Found x10:=(x1 x20):(g Xx)
% 206.73/207.09 Found (x1 x20) as proof of (g Xx)
% 206.73/207.09 Found (x1 x20) as proof of (g Xx)
% 206.73/207.09 Found x30:=(x3 x20):(f Xx)
% 206.73/207.09 Found (x3 x20) as proof of (f Xx)
% 206.73/207.09 Found (x3 x20) as proof of (f Xx)
% 206.73/207.09 Found x30:=(x3 x20):(f Xx)
% 206.73/207.09 Found (x3 x20) as proof of (f Xx)
% 206.73/207.09 Found (x3 x20) as proof of (f Xx)
% 206.73/207.09 Found x20:=(x2 x30):(g Xx)
% 206.73/207.09 Found (x2 x30) as proof of (g Xx)
% 206.73/207.09 Found (x2 x30) as proof of (g Xx)
% 206.73/207.09 Found x20:=(x2 x30):(g Xx)
% 206.73/207.09 Found (x2 x30) as proof of (g Xx)
% 206.73/207.09 Found (x2 x30) as proof of (g Xx)
% 206.73/207.09 Found x30:=(x3 x20):(f Xx)
% 206.73/207.09 Found (x3 x20) as proof of (f Xx)
% 206.73/207.09 Found (x3 x20) as proof of (f Xx)
% 206.73/207.09 Found x30:=(x3 x20):(f Xx)
% 206.73/207.09 Found (x3 x20) as proof of (f Xx)
% 206.73/207.09 Found (x3 x20) as proof of (f Xx)
% 206.73/207.09 Found x10:(P (f x0))
% 206.73/207.09 Found (fun (x10:(P (f x0)))=> x10) as proof of (P (f x0))
% 206.73/207.09 Found (fun (x10:(P (f x0)))=> x10) as proof of (P0 (f x0))
% 206.73/207.09 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 206.73/207.09 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 206.73/207.09 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 206.73/207.09 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 206.73/207.09 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 206.73/207.09 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 206.73/207.09 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 206.73/207.09 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 206.73/207.09 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 206.73/207.09 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 206.73/207.09 Found x10:(P (f x0))
% 206.73/207.09 Found (fun (x10:(P (f x0)))=> x10) as proof of (P (f x0))
% 206.73/207.09 Found (fun (x10:(P (f x0)))=> x10) as proof of (P0 (f x0))
% 206.73/207.09 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 206.73/207.09 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x0))
% 206.73/207.09 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 206.73/207.09 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 206.73/207.09 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x0))
% 206.73/207.09 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 206.73/207.09 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 206.73/207.09 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 206.73/207.09 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 206.73/207.09 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b0)
% 206.73/207.09 Found x10:=(x1 x20):(g Xx)
% 206.73/207.09 Found (x1 x20) as proof of (g Xx)
% 206.73/207.09 Found (x1 x20) as proof of (g Xx)
% 206.73/207.09 Found x20:=(x2 x10):(f Xx)
% 206.73/207.09 Found (x2 x10) as proof of (f Xx)
% 206.73/207.09 Found (x2 x10) as proof of (f Xx)
% 206.73/207.09 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 206.73/207.09 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 206.73/207.09 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 206.73/207.09 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 206.73/207.09 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 206.73/207.09 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 206.73/207.09 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 206.73/207.09 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 206.73/207.09 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 206.73/207.09 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 206.73/207.09 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 206.73/207.09 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 206.73/207.09 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 206.73/207.09 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 206.73/207.09 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 206.73/207.09 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 206.73/207.09 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 206.73/207.09 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 206.73/207.09 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 206.73/207.09 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 206.73/207.09 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 206.73/207.09 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 206.73/207.09 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 206.73/207.09 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 206.73/207.09 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 206.73/207.09 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 206.73/207.09 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 206.73/207.09 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 206.73/207.09 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 208.93/209.28 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 208.93/209.28 Found x40:(P (g x0))
% 208.93/209.28 Found (fun (x40:(P (g x0)))=> x40) as proof of (P (g x0))
% 208.93/209.28 Found (fun (x40:(P (g x0)))=> x40) as proof of (P0 (g x0))
% 208.93/209.28 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 208.93/209.28 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 208.93/209.28 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 208.93/209.28 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 208.93/209.28 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 208.93/209.28 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 208.93/209.28 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 208.93/209.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 208.93/209.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 208.93/209.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 208.93/209.28 Found x40:(P (g x0))
% 208.93/209.28 Found (fun (x40:(P (g x0)))=> x40) as proof of (P (g x0))
% 208.93/209.28 Found (fun (x40:(P (g x0)))=> x40) as proof of (P0 (g x0))
% 208.93/209.28 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 208.93/209.28 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 208.93/209.28 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 208.93/209.28 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 208.93/209.28 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 208.93/209.28 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 208.93/209.28 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 208.93/209.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 208.93/209.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 208.93/209.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 208.93/209.28 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 208.93/209.28 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 208.93/209.28 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 208.93/209.28 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 208.93/209.28 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 208.93/209.28 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 208.93/209.28 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 208.93/209.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 208.93/209.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 208.93/209.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 208.93/209.28 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 208.93/209.28 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 208.93/209.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 208.93/209.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 208.93/209.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 208.93/209.28 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 208.93/209.28 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 208.93/209.28 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 208.93/209.28 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 208.93/209.28 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 208.93/209.28 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 208.93/209.28 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 208.93/209.28 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 208.93/209.28 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 208.93/209.28 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 208.93/209.28 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 208.93/209.28 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 208.93/209.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 208.93/209.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 208.93/209.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 208.93/209.28 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 208.93/209.28 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 208.93/209.28 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 208.93/209.28 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 208.93/209.28 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 208.93/209.28 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 208.93/209.28 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 208.93/209.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 208.93/209.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 208.93/209.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 208.93/209.28 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 208.93/209.28 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 208.93/209.28 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 220.24/220.58 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 220.24/220.58 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 220.24/220.58 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 220.24/220.58 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 220.24/220.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 220.24/220.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 220.24/220.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 220.24/220.58 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 220.24/220.58 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 220.24/220.58 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 220.24/220.58 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 220.24/220.58 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 220.24/220.58 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 220.24/220.58 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 220.24/220.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 220.24/220.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 220.24/220.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 220.24/220.58 Found eq_ref00:=(eq_ref0 (g x0)):(((eq Prop) (g x0)) (g x0))
% 220.24/220.58 Found (eq_ref0 (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 220.24/220.58 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 220.24/220.58 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 220.24/220.58 Found ((eq_ref Prop) (g x0)) as proof of (((eq Prop) (g x0)) b0)
% 220.24/220.58 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 220.24/220.58 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x0))
% 220.24/220.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 220.24/220.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 220.24/220.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x0))
% 220.24/220.58 Found x20:=(x2 x10):(f Xx)
% 220.24/220.58 Found (x2 x10) as proof of (f Xx)
% 220.24/220.58 Found (x2 x10) as proof of (f Xx)
% 220.24/220.58 Found x10:=(x1 x20):(g Xx)
% 220.24/220.58 Found (x1 x20) as proof of (g Xx)
% 220.24/220.58 Found (x1 x20) as proof of (g Xx)
% 220.24/220.58 Found x20:=(x2 x10):(f Xx)
% 220.24/220.58 Found (x2 x10) as proof of (f Xx)
% 220.24/220.58 Found (x2 x10) as proof of (f Xx)
% 220.24/220.58 Found x10:=(x1 x20):(g Xx)
% 220.24/220.58 Found (x1 x20) as proof of (g Xx)
% 220.24/220.58 Found (x1 x20) as proof of (g Xx)
% 220.24/220.58 Found x20:=(x2 x10):(f Xx)
% 220.24/220.58 Found (x2 x10) as proof of (f Xx)
% 220.24/220.58 Found (x2 x10) as proof of (f Xx)
% 220.24/220.58 Found x10:=(x1 x20):(g Xx)
% 220.24/220.58 Found (x1 x20) as proof of (g Xx)
% 220.24/220.58 Found (x1 x20) as proof of (g Xx)
% 220.24/220.58 Found x20:=(x2 x10):(f Xx)
% 220.24/220.58 Found (x2 x10) as proof of (f Xx)
% 220.24/220.58 Found (x2 x10) as proof of (f Xx)
% 220.24/220.58 Found x20:=(x2 x30):(g Xx)
% 220.24/220.58 Found (x2 x30) as proof of (g Xx)
% 220.24/220.58 Found (x2 x30) as proof of (g Xx)
% 220.24/220.58 Found x30:=(x3 x20):(f Xx)
% 220.24/220.58 Found (x3 x20) as proof of (f Xx)
% 220.24/220.58 Found (x3 x20) as proof of (f Xx)
% 220.24/220.58 Found x30:=(x3 x20):(f Xx)
% 220.24/220.58 Found (x3 x20) as proof of (f Xx)
% 220.24/220.58 Found (x3 x20) as proof of (f Xx)
% 220.24/220.58 Found x20:=(x2 x30):(g Xx)
% 220.24/220.58 Found (x2 x30) as proof of (g Xx)
% 220.24/220.58 Found (x2 x30) as proof of (g Xx)
% 220.24/220.58 Found x30:=(x3 x20):(f Xx)
% 220.24/220.58 Found (x3 x20) as proof of (f Xx)
% 220.24/220.58 Found (x3 x20) as proof of (f Xx)
% 220.24/220.58 Found x30:=(x3 x20):(f Xx)
% 220.24/220.58 Found (x3 x20) as proof of (f Xx)
% 220.24/220.58 Found (x3 x20) as proof of (f Xx)
% 220.24/220.58 Found x20:=(x2 x30):(g Xx)
% 220.24/220.58 Found (x2 x30) as proof of (g Xx)
% 220.24/220.58 Found (x2 x30) as proof of (g Xx)
% 220.24/220.58 Found x20:=(x2 x30):(g Xx)
% 220.24/220.58 Found (x2 x30) as proof of (g Xx)
% 220.24/220.58 Found (x2 x30) as proof of (g Xx)
% 220.24/220.58 Found x30:=(x3 x40):(g Xx)
% 220.24/220.58 Found (x3 x40) as proof of (g Xx)
% 220.24/220.58 Found (x3 x40) as proof of (g Xx)
% 220.24/220.58 Found x40:=(x4 x30):(f Xx)
% 220.24/220.58 Found (x4 x30) as proof of (f Xx)
% 220.24/220.58 Found (x4 x30) as proof of (f Xx)
% 220.24/220.58 Found x40:=(x4 x30):(f Xx)
% 220.24/220.58 Found (x4 x30) as proof of (f Xx)
% 220.24/220.58 Found (x4 x30) as proof of (f Xx)
% 220.24/220.58 Found x30:=(x3 x40):(g Xx)
% 220.24/220.58 Found (x3 x40) as proof of (g Xx)
% 220.24/220.58 Found (x3 x40) as proof of (g Xx)
% 220.24/220.58 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 220.24/220.58 Found (eq_ref0 b1) as proof of (((eq Prop) b1) (g x0))
% 220.24/220.58 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (g x0))
% 220.24/220.58 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (g x0))
% 220.24/220.58 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (g x0))
% 220.24/220.58 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 220.24/220.58 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b1)
% 220.24/220.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b1)
% 220.24/220.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b1)
% 220.24/220.58 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b1)
% 220.24/220.58 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 220.24/220.58 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b1)
% 229.53/229.93 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b1)
% 229.53/229.93 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b1)
% 229.53/229.93 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b1)
% 229.53/229.93 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 229.53/229.93 Found (eq_ref0 b1) as proof of (((eq Prop) b1) (g x0))
% 229.53/229.93 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (g x0))
% 229.53/229.93 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (g x0))
% 229.53/229.93 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (g x0))
% 229.53/229.93 Found x20:=(x2 x10):(f Xx)
% 229.53/229.93 Found (x2 x10) as proof of (f Xx)
% 229.53/229.93 Found (x2 x10) as proof of (f Xx)
% 229.53/229.93 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 229.53/229.93 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 229.53/229.93 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 229.53/229.93 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 229.53/229.93 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 229.53/229.93 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 229.53/229.93 Found (eq_ref0 b1) as proof of (((eq Prop) b1) b0)
% 229.53/229.93 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 229.53/229.93 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 229.53/229.93 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 229.53/229.93 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 229.53/229.93 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 229.53/229.93 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 229.53/229.93 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 229.53/229.93 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 229.53/229.93 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 229.53/229.93 Found (eq_ref0 b1) as proof of (((eq Prop) b1) b0)
% 229.53/229.93 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 229.53/229.93 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 229.53/229.93 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 229.53/229.93 Found x10:=(x1 x20):(g Xx)
% 229.53/229.93 Found (x1 x20) as proof of (g Xx)
% 229.53/229.93 Found (x1 x20) as proof of (g Xx)
% 229.53/229.93 Found x20:=(x2 x10):(f Xx)
% 229.53/229.93 Found (x2 x10) as proof of (f Xx)
% 229.53/229.93 Found (x2 x10) as proof of (f Xx)
% 229.53/229.93 Found x10:=(x1 x20):(g Xx)
% 229.53/229.93 Found (x1 x20) as proof of (g Xx)
% 229.53/229.93 Found (x1 x20) as proof of (g Xx)
% 229.53/229.93 Found x20:=(x2 x10):(f Xx)
% 229.53/229.93 Found (x2 x10) as proof of (f Xx)
% 229.53/229.93 Found (x2 x10) as proof of (f Xx)
% 229.53/229.93 Found x30:=(x3 x20):(f Xx)
% 229.53/229.93 Found (x3 x20) as proof of (f Xx)
% 229.53/229.93 Found (x3 x20) as proof of (f Xx)
% 229.53/229.93 Found x30:=(x3 x20):(f Xx)
% 229.53/229.93 Found (x3 x20) as proof of (f Xx)
% 229.53/229.93 Found (x3 x20) as proof of (f Xx)
% 229.53/229.93 Found x20:=(x2 x30):(g Xx)
% 229.53/229.93 Found (x2 x30) as proof of (g Xx)
% 229.53/229.93 Found (x2 x30) as proof of (g Xx)
% 229.53/229.93 Found x30:=(x3 x20):(f Xx)
% 229.53/229.93 Found (x3 x20) as proof of (f Xx)
% 229.53/229.93 Found (x3 x20) as proof of (f Xx)
% 229.53/229.93 Found x20:=(x2 x30):(g Xx)
% 229.53/229.93 Found (x2 x30) as proof of (g Xx)
% 229.53/229.93 Found (x2 x30) as proof of (g Xx)
% 229.53/229.93 Found x30:=(x3 x20):(f Xx)
% 229.53/229.93 Found (x3 x20) as proof of (f Xx)
% 229.53/229.93 Found (x3 x20) as proof of (f Xx)
% 229.53/229.93 Found x40:=(x4 x30):(f Xx)
% 229.53/229.93 Found (x4 x30) as proof of (f Xx)
% 229.53/229.93 Found (x4 x30) as proof of (f Xx)
% 229.53/229.93 Found x20:=(x2 x10):(f Xx)
% 229.53/229.93 Found (x2 x10) as proof of (f Xx)
% 229.53/229.93 Found (x2 x10) as proof of (f Xx)
% 229.53/229.93 Found x10:=(x1 x20):(g Xx)
% 229.53/229.93 Found (x1 x20) as proof of (g Xx)
% 229.53/229.93 Found (x1 x20) as proof of (g Xx)
% 229.53/229.93 Found x20:=(x2 x10):(f Xx)
% 229.53/229.93 Found (x2 x10) as proof of (f Xx)
% 229.53/229.93 Found (x2 x10) as proof of (f Xx)
% 229.53/229.93 Found x10:=(x1 x20):(g Xx)
% 229.53/229.93 Found (x1 x20) as proof of (g Xx)
% 229.53/229.93 Found (x1 x20) as proof of (g Xx)
% 229.53/229.93 Found x40:=(x4 x30):(f Xx)
% 229.53/229.93 Found (x4 x30) as proof of (f Xx)
% 229.53/229.93 Found (x4 x30) as proof of (f Xx)
% 229.53/229.93 Found x10:=(x1 x20):(g Xx)
% 229.53/229.93 Found (x1 x20) as proof of (g Xx)
% 229.53/229.93 Found (x1 x20) as proof of (g Xx)
% 229.53/229.93 Found x20:=(x2 x10):(f Xx)
% 229.53/229.93 Found (x2 x10) as proof of (f Xx)
% 229.53/229.93 Found (x2 x10) as proof of (f Xx)
% 229.53/229.93 Found x10:(P (g x0))
% 229.53/229.93 Found (fun (x10:(P (g x0)))=> x10) as proof of (P (g x0))
% 229.53/229.93 Found (fun (x10:(P (g x0)))=> x10) as proof of (P0 (g x0))
% 229.53/229.93 Found x10:(P (g x0))
% 229.53/229.93 Found (fun (x10:(P (g x0)))=> x10) as proof of (P (g x0))
% 229.53/229.93 Found (fun (x10:(P (g x0)))=> x10) as proof of (P0 (g x0))
% 229.53/229.93 Found x10:(P (g x0))
% 229.53/229.93 Found (fun (x10:(P (g x0)))=> x10) as proof of (P (g x0))
% 229.53/229.93 Found (fun (x10:(P (g x0)))=> x10) as proof of (P0 (g x0))
% 229.53/229.93 Found x10:(P (g x0))
% 229.53/229.93 Found (fun (x10:(P (g x0)))=> x10) as proof of (P (g x0))
% 229.53/229.93 Found (fun (x10:(P (g x0)))=> x10) as proof of (P0 (g x0))
% 229.53/229.93 Found x10:(P (g x0))
% 229.53/229.93 Found (fun (x10:(P (g x0)))=> x10) as proof of (P (g x0))
% 242.89/243.30 Found (fun (x10:(P (g x0)))=> x10) as proof of (P0 (g x0))
% 242.89/243.30 Found x10:(P (g x0))
% 242.89/243.30 Found (fun (x10:(P (g x0)))=> x10) as proof of (P (g x0))
% 242.89/243.30 Found (fun (x10:(P (g x0)))=> x10) as proof of (P0 (g x0))
% 242.89/243.30 Found x20:=(x2 x10):(f Xx)
% 242.89/243.30 Found (x2 x10) as proof of (f Xx)
% 242.89/243.30 Found (x2 x10) as proof of (f Xx)
% 242.89/243.30 Found x20:=(x2 x10):(f Xx)
% 242.89/243.30 Found (x2 x10) as proof of (f Xx)
% 242.89/243.30 Found (x2 x10) as proof of (f Xx)
% 242.89/243.30 Found eq_ref00:=(eq_ref0 a):(((eq b) a) a)
% 242.89/243.30 Found (eq_ref0 a) as proof of (((eq b) a) x0)
% 242.89/243.30 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 242.89/243.30 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 242.89/243.30 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 242.89/243.30 Found x20:=(x2 x10):(f Xx)
% 242.89/243.30 Found (x2 x10) as proof of (f Xx)
% 242.89/243.30 Found (x2 x10) as proof of (f Xx)
% 242.89/243.30 Found eq_ref00:=(eq_ref0 a):(((eq b) a) a)
% 242.89/243.30 Found (eq_ref0 a) as proof of (((eq b) a) x0)
% 242.89/243.30 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 242.89/243.30 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 242.89/243.30 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 242.89/243.30 Found eq_ref00:=(eq_ref0 a):(((eq b) a) a)
% 242.89/243.30 Found (eq_ref0 a) as proof of (((eq b) a) x0)
% 242.89/243.30 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 242.89/243.30 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 242.89/243.30 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 242.89/243.30 Found eq_ref00:=(eq_ref0 a):(((eq b) a) a)
% 242.89/243.30 Found (eq_ref0 a) as proof of (((eq b) a) x0)
% 242.89/243.30 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 242.89/243.30 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 242.89/243.30 Found ((eq_ref b) a) as proof of (((eq b) a) x0)
% 242.89/243.30 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 242.89/243.30 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) g)
% 242.89/243.30 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 242.89/243.30 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 242.89/243.30 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 242.89/243.30 Found eta_expansion000:=(eta_expansion00 f):(((eq (b->Prop)) f) (fun (x:b)=> (f x)))
% 242.89/243.30 Found (eta_expansion00 f) as proof of (((eq (b->Prop)) f) b0)
% 242.89/243.30 Found ((eta_expansion0 Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 242.89/243.30 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 242.89/243.30 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 242.89/243.30 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 242.89/243.30 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 242.89/243.30 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 242.89/243.30 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 242.89/243.30 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 242.89/243.30 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 242.89/243.30 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 242.89/243.30 Found (eq_ref0 b1) as proof of (((eq Prop) b1) b0)
% 242.89/243.30 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 242.89/243.30 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 242.89/243.30 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 242.89/243.30 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 242.89/243.30 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 242.89/243.30 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 242.89/243.30 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 242.89/243.30 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 242.89/243.30 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 242.89/243.30 Found (eq_ref0 b1) as proof of (((eq Prop) b1) b0)
% 242.89/243.30 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 242.89/243.30 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 242.89/243.30 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) b0)
% 242.89/243.30 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 242.89/243.30 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) g)
% 242.89/243.30 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 242.89/243.30 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 242.89/243.30 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 242.89/243.30 Found eta_expansion000:=(eta_expansion00 f):(((eq (b->Prop)) f) (fun (x:b)=> (f x)))
% 242.89/243.30 Found (eta_expansion00 f) as proof of (((eq (b->Prop)) f) b0)
% 242.89/243.30 Found ((eta_expansion0 Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 242.89/243.30 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 242.89/243.30 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 242.89/243.30 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 242.89/243.30 Found x30:=(x3 x20):(f Xx)
% 258.61/259.05 Found (x3 x20) as proof of (f Xx)
% 258.61/259.05 Found (x3 x20) as proof of (f Xx)
% 258.61/259.05 Found x30:=(x3 x20):(f Xx)
% 258.61/259.05 Found (x3 x20) as proof of (f Xx)
% 258.61/259.05 Found (x3 x20) as proof of (f Xx)
% 258.61/259.05 Found x20:=(x2 x30):(g Xx)
% 258.61/259.05 Found (x2 x30) as proof of (g Xx)
% 258.61/259.05 Found (x2 x30) as proof of (g Xx)
% 258.61/259.05 Found x20:=(x2 x30):(g Xx)
% 258.61/259.05 Found (x2 x30) as proof of (g Xx)
% 258.61/259.05 Found (x2 x30) as proof of (g Xx)
% 258.61/259.05 Found eq_ref00:=(eq_ref0 (b0 x0)):(((eq Prop) (b0 x0)) (b0 x0))
% 258.61/259.05 Found (eq_ref0 (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 258.61/259.05 Found ((eq_ref Prop) (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 258.61/259.05 Found ((eq_ref Prop) (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 258.61/259.05 Found ((eq_ref Prop) (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 258.61/259.05 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 258.61/259.05 Found (eq_ref0 b1) as proof of (((eq Prop) b1) (g x0))
% 258.61/259.05 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (g x0))
% 258.61/259.05 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (g x0))
% 258.61/259.05 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (g x0))
% 258.61/259.05 Found eq_ref00:=(eq_ref0 (b0 x0)):(((eq Prop) (b0 x0)) (b0 x0))
% 258.61/259.05 Found (eq_ref0 (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 258.61/259.05 Found ((eq_ref Prop) (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 258.61/259.05 Found ((eq_ref Prop) (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 258.61/259.05 Found ((eq_ref Prop) (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 258.61/259.05 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 258.61/259.05 Found (eq_ref0 b1) as proof of (((eq Prop) b1) (g x0))
% 258.61/259.05 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (g x0))
% 258.61/259.05 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (g x0))
% 258.61/259.05 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (g x0))
% 258.61/259.05 Found x20:=(x2 x10):(f Xx)
% 258.61/259.05 Found (x2 x10) as proof of (f Xx)
% 258.61/259.05 Found (x2 x10) as proof of (f Xx)
% 258.61/259.05 Found x10:=(x1 x20):(g Xx)
% 258.61/259.05 Found (x1 x20) as proof of (g Xx)
% 258.61/259.05 Found (x1 x20) as proof of (g Xx)
% 258.61/259.05 Found x20:=(x2 x10):(f Xx)
% 258.61/259.05 Found (x2 x10) as proof of (f Xx)
% 258.61/259.05 Found (x2 x10) as proof of (f Xx)
% 258.61/259.05 Found x10:=(x1 x20):(g Xx)
% 258.61/259.05 Found (x1 x20) as proof of (g Xx)
% 258.61/259.05 Found (x1 x20) as proof of (g Xx)
% 258.61/259.05 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 258.61/259.05 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) b0)
% 258.61/259.05 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) b0)
% 258.61/259.05 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) b0)
% 258.61/259.05 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) b0)
% 258.61/259.05 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 258.61/259.05 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x3))
% 258.61/259.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x3))
% 258.61/259.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x3))
% 258.61/259.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x3))
% 258.61/259.05 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 258.61/259.05 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x3))
% 258.61/259.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x3))
% 258.61/259.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x3))
% 258.61/259.05 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x3))
% 258.61/259.05 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 258.61/259.05 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) b0)
% 258.61/259.05 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) b0)
% 258.61/259.05 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) b0)
% 258.61/259.05 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) b0)
% 258.61/259.05 Found eq_ref00:=(eq_ref0 b0):(((eq (b->Prop)) b0) b0)
% 258.61/259.05 Found (eq_ref0 b0) as proof of (((eq (b->Prop)) b0) g)
% 258.61/259.05 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 258.61/259.05 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 258.61/259.05 Found ((eq_ref (b->Prop)) b0) as proof of (((eq (b->Prop)) b0) g)
% 258.61/259.05 Found eta_expansion000:=(eta_expansion00 f):(((eq (b->Prop)) f) (fun (x:b)=> (f x)))
% 258.61/259.05 Found (eta_expansion00 f) as proof of (((eq (b->Prop)) f) b0)
% 258.61/259.05 Found ((eta_expansion0 Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 258.61/259.05 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 258.61/259.05 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 258.61/259.05 Found (((eta_expansion b) Prop) f) as proof of (((eq (b->Prop)) f) b0)
% 258.61/259.05 Found x30:=(x3 x20):(f Xx)
% 258.61/259.05 Found (x3 x20) as proof of (f Xx)
% 258.61/259.05 Found (x3 x20) as proof of (f Xx)
% 258.61/259.05 Found x30:=(x3 x20):(f Xx)
% 258.61/259.05 Found (x3 x20) as proof of (f Xx)
% 258.61/259.05 Found (x3 x20) as proof of (f Xx)
% 275.23/275.61 Found x10:=(x1 x20):(g Xx)
% 275.23/275.61 Found (x1 x20) as proof of (g Xx)
% 275.23/275.61 Found (x1 x20) as proof of (g Xx)
% 275.23/275.61 Found x20:=(x2 x10):(f Xx)
% 275.23/275.61 Found (x2 x10) as proof of (f Xx)
% 275.23/275.61 Found (x2 x10) as proof of (f Xx)
% 275.23/275.61 Found x20:=(x2 x10):(f Xx)
% 275.23/275.61 Found (x2 x10) as proof of (f Xx)
% 275.23/275.61 Found (x2 x10) as proof of (f Xx)
% 275.23/275.61 Found x10:=(x1 x20):(g Xx)
% 275.23/275.61 Found (x1 x20) as proof of (g Xx)
% 275.23/275.61 Found (x1 x20) as proof of (g Xx)
% 275.23/275.61 Found x10:=(x1 x20):(g Xx)
% 275.23/275.61 Found (x1 x20) as proof of (g Xx)
% 275.23/275.61 Found (x1 x20) as proof of (g Xx)
% 275.23/275.61 Found x20:=(x2 x10):(f Xx)
% 275.23/275.61 Found (x2 x10) as proof of (f Xx)
% 275.23/275.61 Found (x2 x10) as proof of (f Xx)
% 275.23/275.61 Found x30:=(x3 x21):(f Xx)
% 275.23/275.61 Found (x3 x21) as proof of (f Xx)
% 275.23/275.61 Found (x3 x21) as proof of (f Xx)
% 275.23/275.61 Found x20:=(x2 x31):(g Xx)
% 275.23/275.61 Found (x2 x31) as proof of (g Xx)
% 275.23/275.61 Found (x2 x31) as proof of (g Xx)
% 275.23/275.61 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 275.23/275.61 Found (eq_ref0 b1) as proof of (((eq Prop) b1) (b0 x0))
% 275.23/275.61 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (b0 x0))
% 275.23/275.61 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (b0 x0))
% 275.23/275.61 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (b0 x0))
% 275.23/275.61 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 275.23/275.61 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 275.23/275.61 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 275.23/275.61 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 275.23/275.61 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 275.23/275.61 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 275.23/275.61 Found (eq_ref0 b1) as proof of (((eq Prop) b1) (b0 x0))
% 275.23/275.61 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (b0 x0))
% 275.23/275.61 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (b0 x0))
% 275.23/275.61 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (b0 x0))
% 275.23/275.61 Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 275.23/275.61 Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 275.23/275.61 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 275.23/275.61 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 275.23/275.61 Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) b1)
% 275.23/275.61 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 275.23/275.61 Found (eq_ref0 b1) as proof of (((eq Prop) b1) (g x0))
% 275.23/275.61 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (g x0))
% 275.23/275.61 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (g x0))
% 275.23/275.61 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (g x0))
% 275.23/275.61 Found eq_ref00:=(eq_ref0 (b0 x0)):(((eq Prop) (b0 x0)) (b0 x0))
% 275.23/275.61 Found (eq_ref0 (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 275.23/275.61 Found ((eq_ref Prop) (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 275.23/275.61 Found ((eq_ref Prop) (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 275.23/275.61 Found ((eq_ref Prop) (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 275.23/275.61 Found eq_ref00:=(eq_ref0 (b0 x0)):(((eq Prop) (b0 x0)) (b0 x0))
% 275.23/275.61 Found (eq_ref0 (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 275.23/275.61 Found ((eq_ref Prop) (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 275.23/275.61 Found ((eq_ref Prop) (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 275.23/275.61 Found ((eq_ref Prop) (b0 x0)) as proof of (((eq Prop) (b0 x0)) b1)
% 275.23/275.61 Found eq_ref00:=(eq_ref0 b1):(((eq Prop) b1) b1)
% 275.23/275.61 Found (eq_ref0 b1) as proof of (((eq Prop) b1) (g x0))
% 275.23/275.61 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (g x0))
% 275.23/275.61 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (g x0))
% 275.23/275.61 Found ((eq_ref Prop) b1) as proof of (((eq Prop) b1) (g x0))
% 275.23/275.61 Found x20:=(x2 x10):(f Xx)
% 275.23/275.61 Found (x2 x10) as proof of (f Xx)
% 275.23/275.61 Found (x2 x10) as proof of (f Xx)
% 275.23/275.61 Found x20:=(x2 x10):(f Xx)
% 275.23/275.61 Found (x2 x10) as proof of (f Xx)
% 275.23/275.61 Found (x2 x10) as proof of (f Xx)
% 275.23/275.61 Found x20:=(x2 x10):(f Xx)
% 275.23/275.61 Found (x2 x10) as proof of (f Xx)
% 275.23/275.61 Found (x2 x10) as proof of (f Xx)
% 275.23/275.61 Found x20:=(x2 x10):(f Xx)
% 275.23/275.61 Found (x2 x10) as proof of (f Xx)
% 275.23/275.61 Found (x2 x10) as proof of (f Xx)
% 275.23/275.61 Found x20:=(x2 x10):(f Xx)
% 275.23/275.61 Found (x2 x10) as proof of (f Xx)
% 275.23/275.61 Found (x2 x10) as proof of (f Xx)
% 275.23/275.61 Found x10:=(x1 x20):(g Xx)
% 275.23/275.61 Found (x1 x20) as proof of (g Xx)
% 275.23/275.61 Found (x1 x20) as proof of (g Xx)
% 275.23/275.61 Found x10:=(x1 x20):(g Xx)
% 275.23/275.61 Found (x1 x20) as proof of (g Xx)
% 275.23/275.61 Found (x1 x20) as proof of (g Xx)
% 275.23/275.61 Found x10:=(x1 x20):(g Xx)
% 275.23/275.61 Found (x1 x20) as proof of (g Xx)
% 275.23/275.61 Found (x1 x20) as proof of (g Xx)
% 275.23/275.61 Found x20:=(x2 x10):(f Xx)
% 275.23/275.61 Found (x2 x10) as proof of (f Xx)
% 275.23/275.61 Found (x2 x10) as proof of (f Xx)
% 275.23/275.61 Found x10:=(x1 x20):(g Xx)
% 275.23/275.61 Found (x1 x20) as proof of (g Xx)
% 291.61/292.01 Found (x1 x20) as proof of (g Xx)
% 291.61/292.01 Found x20:=(x2 x10):(f Xx)
% 291.61/292.01 Found (x2 x10) as proof of (f Xx)
% 291.61/292.01 Found (x2 x10) as proof of (f Xx)
% 291.61/292.01 Found x20:=(x2 x10):(f Xx)
% 291.61/292.01 Found (x2 x10) as proof of (f Xx)
% 291.61/292.01 Found (x2 x10) as proof of (f Xx)
% 291.61/292.01 Found x20:=(x2 x10):(f Xx)
% 291.61/292.01 Found (x2 x10) as proof of (f Xx)
% 291.61/292.01 Found (x2 x10) as proof of (f Xx)
% 291.61/292.01 Found x10:=(x1 x20):(g Xx)
% 291.61/292.01 Found (x1 x20) as proof of (g Xx)
% 291.61/292.01 Found (x1 x20) as proof of (g Xx)
% 291.61/292.01 Found x10:=(x1 x20):(g Xx)
% 291.61/292.01 Found (x1 x20) as proof of (g Xx)
% 291.61/292.01 Found (x1 x20) as proof of (g Xx)
% 291.61/292.01 Found x10:(P (f x0))
% 291.61/292.01 Found (fun (x10:(P (f x0)))=> x10) as proof of (P (f x0))
% 291.61/292.01 Found (fun (x10:(P (f x0)))=> x10) as proof of (P0 (f x0))
% 291.61/292.01 Found x10:(P (f x0))
% 291.61/292.01 Found (fun (x10:(P (f x0)))=> x10) as proof of (P (f x0))
% 291.61/292.01 Found (fun (x10:(P (f x0)))=> x10) as proof of (P0 (f x0))
% 291.61/292.01 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 291.61/292.01 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x3))
% 291.61/292.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x3))
% 291.61/292.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x3))
% 291.61/292.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x3))
% 291.61/292.01 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 291.61/292.01 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) b0)
% 291.61/292.01 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) b0)
% 291.61/292.01 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) b0)
% 291.61/292.01 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) b0)
% 291.61/292.01 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 291.61/292.01 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x3))
% 291.61/292.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x3))
% 291.61/292.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x3))
% 291.61/292.01 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x3))
% 291.61/292.01 Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% 291.61/292.01 Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) b0)
% 291.61/292.01 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) b0)
% 291.61/292.01 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) b0)
% 291.61/292.01 Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) b0)
% 291.61/292.01 Found x30:(P f)
% 291.61/292.01 Found (fun (x30:(P f))=> x30) as proof of (P f)
% 291.61/292.01 Found (fun (x30:(P f))=> x30) as proof of (P0 f)
% 291.61/292.01 Found x30:(P f)
% 291.61/292.01 Found (fun (x30:(P f))=> x30) as proof of (P f)
% 291.61/292.01 Found (fun (x30:(P f))=> x30) as proof of (P0 f)
% 291.61/292.01 Found x30:=(x3 x21):(f Xx)
% 291.61/292.01 Found (x3 x21) as proof of (f Xx)
% 291.61/292.01 Found (x3 x21) as proof of (f Xx)
% 291.61/292.01 Found x10:(P (b0 x0))
% 291.61/292.01 Found (fun (x10:(P (b0 x0)))=> x10) as proof of (P (b0 x0))
% 291.61/292.01 Found (fun (x10:(P (b0 x0)))=> x10) as proof of (P0 (b0 x0))
% 291.61/292.01 Found x10:(P (b0 x0))
% 291.61/292.01 Found (fun (x10:(P (b0 x0)))=> x10) as proof of (P (b0 x0))
% 291.61/292.01 Found (fun (x10:(P (b0 x0)))=> x10) as proof of (P0 (b0 x0))
% 291.61/292.01 Found x0:(P f)
% 291.61/292.01 Instantiate: b0:=f:(b->Prop)
% 291.61/292.01 Found x0 as proof of (P0 b0)
% 291.61/292.01 Found eta_expansion_dep000:=(eta_expansion_dep00 g):(((eq (b->Prop)) g) (fun (x:b)=> (g x)))
% 291.61/292.01 Found (eta_expansion_dep00 g) as proof of (((eq (b->Prop)) g) b0)
% 291.61/292.01 Found ((eta_expansion_dep0 (fun (x2:b)=> Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 291.61/292.01 Found (((eta_expansion_dep b) (fun (x2:b)=> Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 291.61/292.01 Found (((eta_expansion_dep b) (fun (x2:b)=> Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 291.61/292.01 Found (((eta_expansion_dep b) (fun (x2:b)=> Prop)) g) as proof of (((eq (b->Prop)) g) b0)
% 291.61/292.01 Found x10:=(x1 x20):(g Xx)
% 291.61/292.01 Found (x1 x20) as proof of (g Xx)
% 291.61/292.01 Found (x1 x20) as proof of (g Xx)
% 291.61/292.01 Found x10:=(x1 x20):(g Xx)
% 291.61/292.01 Found (x1 x20) as proof of (g Xx)
% 291.61/292.01 Found (x1 x20) as proof of (g Xx)
% 291.61/292.01 Found x20:=(x2 x10):(f Xx)
% 291.61/292.01 Found (x2 x10) as proof of (f Xx)
% 291.61/292.01 Found (x2 x10) as proof of (f Xx)
% 291.61/292.01 Found x20:=(x2 x10):(f Xx)
% 291.61/292.01 Found (x2 x10) as proof of (f Xx)
% 291.61/292.01 Found (x2 x10) as proof of (f Xx)
% 291.61/292.01 Found x10:=(x1 x20):(g Xx)
% 291.61/292.01 Found (x1 x20) as proof of (g Xx)
% 291.61/292.01 Found (x1 x20) as proof of (g Xx)
% 291.61/292.01 Found x20:=(x2 x10):(f Xx)
% 291.61/292.01 Found (x2 x10) as proof of (f Xx)
% 291.61/292.01 Found (x2 x10) as proof of (f Xx)
% 291.61/292.01 Found x20:=(x2 x10):(f Xx)
% 291.61/292.01 Found (x2 x10) as proof of (f Xx)
% 291.61/292.01 Found (x2 x10) as proof of (f Xx)
% 291.61/292.01 Found x10:=(x1 x20):(g Xx)
% 291.61/292.01 Found (x1 x20) as proof of (g Xx)
% 291.61/292.01 Found (x1 x20) as proof of (g Xx)
% 291.61/292.01 Found x10:=(x1 x20):(g Xx)
% 291.61/292.01 Found (x1 x20) as proof of (g Xx)
% 291.61/292.01 Found (x1 x20) as proof of (g Xx)
% 291.61/292.01 Found x20:=(x2 x10):(f Xx)
% 291.61/292.01 Found (x2 x
%------------------------------------------------------------------------------