TSTP Solution File: SYO526^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO526^1 : TPTP v7.5.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 00:52:02 EDT 2022
% Result : Timeout 299.20s 299.67s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYO526^1 : TPTP v7.5.0. Released v5.2.0.
% 0.10/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n018.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 : Sun Mar 13 16:11:56 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.34 Python 2.7.5
% 14.55/14.78 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 14.55/14.78 FOF formula (<kernel.Constant object at 0x11c8170>, <kernel.Sort object at 0x2ad3f3917638>) of role type named a
% 14.55/14.78 Using role type
% 14.55/14.78 Declaring a:Prop
% 14.55/14.78 FOF formula (<kernel.Constant object at 0x11c85a8>, <kernel.Sort object at 0x2ad3f3917638>) of role type named b
% 14.55/14.78 Using role type
% 14.55/14.78 Declaring b:Prop
% 14.55/14.78 FOF formula ((iff a) b) of role axiom named ab
% 14.55/14.78 A new axiom: ((iff a) b)
% 14.55/14.78 FOF formula (<kernel.Constant object at 0x11c83b0>, <kernel.DependentProduct object at 0x11a2b00>) of role type named f
% 14.55/14.78 Using role type
% 14.55/14.78 Declaring f:(fofType->Prop)
% 14.55/14.78 FOF formula (<kernel.Constant object at 0x11c7950>, <kernel.DependentProduct object at 0x11a2b90>) of role type named g
% 14.55/14.78 Using role type
% 14.55/14.78 Declaring g:(fofType->Prop)
% 14.55/14.78 FOF formula (((eq (fofType->Prop)) f) g) of role axiom named fg
% 14.55/14.78 A new axiom: (((eq (fofType->Prop)) f) g)
% 14.55/14.78 FOF formula (((eq (fofType->Prop)) f) (fun (X:fofType)=> a)) of role axiom named fa
% 14.55/14.78 A new axiom: (((eq (fofType->Prop)) f) (fun (X:fofType)=> a))
% 14.55/14.78 FOF formula (((eq (fofType->Prop)) g) (fun (X:fofType)=> b)) of role conjecture named gb
% 14.55/14.78 Conjecture to prove = (((eq (fofType->Prop)) g) (fun (X:fofType)=> b)):Prop
% 14.55/14.78 Parameter fofType_DUMMY:fofType.
% 14.55/14.78 We need to prove ['(((eq (fofType->Prop)) g) (fun (X:fofType)=> b))']
% 14.55/14.78 Parameter a:Prop.
% 14.55/14.78 Parameter b:Prop.
% 14.55/14.78 Axiom ab:((iff a) b).
% 14.55/14.78 Parameter fofType:Type.
% 14.55/14.78 Parameter f:(fofType->Prop).
% 14.55/14.78 Parameter g:(fofType->Prop).
% 14.55/14.78 Axiom fg:(((eq (fofType->Prop)) f) g).
% 14.55/14.78 Axiom fa:(((eq (fofType->Prop)) f) (fun (X:fofType)=> a)).
% 14.55/14.78 Trying to prove (((eq (fofType->Prop)) g) (fun (X:fofType)=> b))
% 14.55/14.78 Found fg__eq_sym:=((((eq_sym (fofType->Prop)) f) g) fg):(((eq (fofType->Prop)) g) f)
% 14.55/14.78 Instantiate: b0:=f:(fofType->Prop)
% 14.55/14.78 Found fg__eq_sym as proof of (((eq (fofType->Prop)) g) b0)
% 14.55/14.78 Found eq_ref00:=(eq_ref0 b0):(((eq (fofType->Prop)) b0) b0)
% 14.55/14.78 Found (eq_ref0 b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 14.55/14.78 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 14.55/14.78 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 14.55/14.78 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 14.55/14.78 Found fg0:=(fg (fun (x:(fofType->Prop))=> (P g))):((P g)->(P g))
% 14.55/14.78 Found (fg (fun (x:(fofType->Prop))=> (P g))) as proof of (P0 g)
% 14.55/14.78 Found (fg (fun (x:(fofType->Prop))=> (P g))) as proof of (P0 g)
% 14.55/14.78 Found fg0:=(fg (fun (x:(fofType->Prop))=> (P g))):((P g)->(P g))
% 14.55/14.78 Found (fg (fun (x:(fofType->Prop))=> (P g))) as proof of (P0 g)
% 14.55/14.78 Found (fg (fun (x:(fofType->Prop))=> (P g))) as proof of (P0 g)
% 14.55/14.78 Found fg0:=(fg (fun (x:(fofType->Prop))=> (P g))):((P g)->(P g))
% 14.55/14.78 Found (fg (fun (x:(fofType->Prop))=> (P g))) as proof of (P0 g)
% 14.55/14.78 Found (fg (fun (x:(fofType->Prop))=> (P g))) as proof of (P0 g)
% 14.55/14.78 Found fg:(((eq (fofType->Prop)) f) g)
% 14.55/14.78 Instantiate: b0:=g:(fofType->Prop)
% 14.55/14.78 Found fg as proof of (((eq (fofType->Prop)) f) b0)
% 14.55/14.78 Found eta_expansion000:=(eta_expansion00 b0):(((eq (fofType->Prop)) b0) (fun (x:fofType)=> (b0 x)))
% 14.55/14.78 Found (eta_expansion00 b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 14.55/14.78 Found ((eta_expansion0 Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 14.55/14.78 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 14.55/14.78 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 14.55/14.78 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 14.55/14.78 Found eq_ref00:=(eq_ref0 g):(((eq (fofType->Prop)) g) g)
% 14.55/14.78 Found (eq_ref0 g) as proof of (((eq (fofType->Prop)) g) g)
% 14.55/14.78 Found ((eq_ref (fofType->Prop)) g) as proof of (((eq (fofType->Prop)) g) g)
% 14.55/14.78 Found (fun (x00:(b->a))=> ((eq_ref (fofType->Prop)) g)) as proof of (((eq (fofType->Prop)) g) g)
% 14.55/14.78 Found (fun (x00:(b->a))=> ((eq_ref (fofType->Prop)) g)) as proof of (P g)
% 14.55/14.78 Found eq_ref000:=(eq_ref00 P):((P f)->(P f))
% 14.55/14.78 Found (eq_ref00 P) as proof of (P0 f)
% 14.55/14.78 Found ((eq_ref0 f) P) as proof of (P0 f)
% 14.55/14.78 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 29.85/30.08 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 29.85/30.08 Found fg__eq_sym:=((((eq_sym (fofType->Prop)) f) g) fg):(((eq (fofType->Prop)) g) f)
% 29.85/30.08 Instantiate: b0:=f:(fofType->Prop)
% 29.85/30.08 Found fg__eq_sym as proof of (((eq (fofType->Prop)) g) b0)
% 29.85/30.08 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (fofType->Prop)) b0) (fun (x:fofType)=> (b0 x)))
% 29.85/30.08 Found (eta_expansion_dep00 b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 29.85/30.08 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 29.85/30.08 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 29.85/30.08 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 29.85/30.08 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 29.85/30.08 Found eq_ref000:=(eq_ref00 P):((P f)->(P f))
% 29.85/30.08 Found (eq_ref00 P) as proof of (P0 f)
% 29.85/30.08 Found ((eq_ref0 f) P) as proof of (P0 f)
% 29.85/30.08 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 29.85/30.08 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 29.85/30.08 Found eq_ref000:=(eq_ref00 P):((P f)->(P f))
% 29.85/30.08 Found (eq_ref00 P) as proof of (P0 f)
% 29.85/30.08 Found ((eq_ref0 f) P) as proof of (P0 f)
% 29.85/30.08 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 29.85/30.08 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 29.85/30.08 Found eq_ref00:=(eq_ref0 g):(((eq (fofType->Prop)) g) g)
% 29.85/30.08 Found (eq_ref0 g) as proof of (((eq (fofType->Prop)) g) g)
% 29.85/30.08 Found ((eq_ref (fofType->Prop)) g) as proof of (((eq (fofType->Prop)) g) g)
% 29.85/30.08 Found (fun (x00:(b->a))=> ((eq_ref (fofType->Prop)) g)) as proof of (((eq (fofType->Prop)) g) g)
% 29.85/30.08 Found (fun (x2:(a->b)) (x00:(b->a))=> ((eq_ref (fofType->Prop)) g)) as proof of ((b->a)->(((eq (fofType->Prop)) g) g))
% 29.85/30.08 Found (fun (x2:(a->b)) (x00:(b->a))=> ((eq_ref (fofType->Prop)) g)) as proof of (P g)
% 29.85/30.08 Found fa0:=(fa (fun (x1:(fofType->Prop))=> (P g))):((P g)->(P g))
% 29.85/30.08 Found (fa (fun (x1:(fofType->Prop))=> (P g))) as proof of (P0 g)
% 29.85/30.08 Found (fa (fun (x1:(fofType->Prop))=> (P g))) as proof of (P0 g)
% 29.85/30.08 Found fg0:=(fg (fun (x1:(fofType->Prop))=> (P g))):((P g)->(P g))
% 29.85/30.08 Found (fg (fun (x1:(fofType->Prop))=> (P g))) as proof of (P0 g)
% 29.85/30.08 Found (fg (fun (x1:(fofType->Prop))=> (P g))) as proof of (P0 g)
% 29.85/30.08 Found fg:(((eq (fofType->Prop)) f) g)
% 29.85/30.08 Instantiate: b0:=f:(fofType->Prop)
% 29.85/30.08 Found fg as proof of (((eq (fofType->Prop)) b0) g)
% 29.85/30.08 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> b)):(((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (x:fofType)=> b))
% 29.85/30.08 Found (eta_expansion_dep00 (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 29.85/30.08 Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 29.85/30.08 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 29.85/30.08 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 29.85/30.08 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 29.85/30.08 Found fg:(((eq (fofType->Prop)) f) g)
% 29.85/30.08 Instantiate: b0:=g:(fofType->Prop)
% 29.85/30.08 Found fg as proof of (((eq (fofType->Prop)) f) b0)
% 29.85/30.08 Found eta_expansion000:=(eta_expansion00 b0):(((eq (fofType->Prop)) b0) (fun (x:fofType)=> (b0 x)))
% 29.85/30.08 Found (eta_expansion00 b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 29.85/30.08 Found ((eta_expansion0 Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 29.85/30.08 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 29.85/30.08 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 29.85/30.08 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 29.85/30.08 Found fg0:=(fg (fun (x1:(fofType->Prop))=> (P g))):((P g)->(P g))
% 29.85/30.08 Found (fg (fun (x1:(fofType->Prop))=> (P g))) as proof of (P0 g)
% 48.73/48.97 Found (fg (fun (x1:(fofType->Prop))=> (P g))) as proof of (P0 g)
% 48.73/48.97 Found fg:(((eq (fofType->Prop)) f) g)
% 48.73/48.97 Instantiate: b0:=g:(fofType->Prop)
% 48.73/48.97 Found fg as proof of (((eq (fofType->Prop)) f) b0)
% 48.73/48.97 Found eq_ref00:=(eq_ref0 b0):(((eq (fofType->Prop)) b0) b0)
% 48.73/48.97 Found (eq_ref0 b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 48.73/48.97 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 48.73/48.97 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 48.73/48.97 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 48.73/48.97 Found fg:(((eq (fofType->Prop)) f) g)
% 48.73/48.97 Instantiate: b0:=g:(fofType->Prop)
% 48.73/48.97 Found fg as proof of (((eq (fofType->Prop)) f) b0)
% 48.73/48.97 Found eq_ref00:=(eq_ref0 b0):(((eq (fofType->Prop)) b0) b0)
% 48.73/48.97 Found (eq_ref0 b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 48.73/48.97 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 48.73/48.97 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 48.73/48.97 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 48.73/48.97 Found eq_ref00:=(eq_ref0 f):(((eq (fofType->Prop)) f) f)
% 48.73/48.97 Found (eq_ref0 f) as proof of (((eq (fofType->Prop)) f) f)
% 48.73/48.97 Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) f)
% 48.73/48.97 Found (fun (x00:(b->a))=> ((eq_ref (fofType->Prop)) f)) as proof of (((eq (fofType->Prop)) f) f)
% 48.73/48.97 Found (fun (x00:(b->a))=> ((eq_ref (fofType->Prop)) f)) as proof of (P f)
% 48.73/48.97 Found eq_ref00:=(eq_ref0 f):(((eq (fofType->Prop)) f) f)
% 48.73/48.97 Found (eq_ref0 f) as proof of (((eq (fofType->Prop)) f) f)
% 48.73/48.97 Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) f)
% 48.73/48.97 Found (fun (x00:(b->a))=> ((eq_ref (fofType->Prop)) f)) as proof of (((eq (fofType->Prop)) f) f)
% 48.73/48.97 Found (fun (x00:(b->a))=> ((eq_ref (fofType->Prop)) f)) as proof of (P f)
% 48.73/48.97 Found fg:(((eq (fofType->Prop)) f) g)
% 48.73/48.97 Instantiate: b0:=g:(fofType->Prop)
% 48.73/48.97 Found fg as proof of (((eq (fofType->Prop)) f) b0)
% 48.73/48.97 Found eq_ref00:=(eq_ref0 b0):(((eq (fofType->Prop)) b0) b0)
% 48.73/48.97 Found (eq_ref0 b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 48.73/48.97 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 48.73/48.97 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 48.73/48.97 Found ((eq_ref (fofType->Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 48.73/48.97 Found eq_ref000:=(eq_ref00 P):((P f)->(P f))
% 48.73/48.97 Found (eq_ref00 P) as proof of (P0 f)
% 48.73/48.97 Found ((eq_ref0 f) P) as proof of (P0 f)
% 48.73/48.97 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 48.73/48.97 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 48.73/48.97 Found eq_ref000:=(eq_ref00 P):((P f)->(P f))
% 48.73/48.97 Found (eq_ref00 P) as proof of (P0 f)
% 48.73/48.97 Found ((eq_ref0 f) P) as proof of (P0 f)
% 48.73/48.97 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 48.73/48.97 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 48.73/48.97 Found eq_ref000:=(eq_ref00 P):((P f)->(P f))
% 48.73/48.97 Found (eq_ref00 P) as proof of (P0 f)
% 48.73/48.97 Found ((eq_ref0 f) P) as proof of (P0 f)
% 48.73/48.97 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 48.73/48.97 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 48.73/48.97 Found eq_ref00:=(eq_ref0 f):(((eq (fofType->Prop)) f) f)
% 48.73/48.97 Found (eq_ref0 f) as proof of (((eq (fofType->Prop)) f) f)
% 48.73/48.97 Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) f)
% 48.73/48.97 Found (fun (x00:(b->a))=> ((eq_ref (fofType->Prop)) f)) as proof of (((eq (fofType->Prop)) f) f)
% 48.73/48.97 Found (fun (x00:(b->a))=> ((eq_ref (fofType->Prop)) f)) as proof of (P f)
% 48.73/48.97 Found fa0:=(fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))):((P (fun (X:fofType)=> b))->(P (fun (X:fofType)=> b)))
% 48.73/48.97 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 48.73/48.97 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 48.73/48.97 Found fg0:=(fg (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))):((P (fun (X:fofType)=> b))->(P (fun (X:fofType)=> b)))
% 48.73/48.97 Found (fg (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 58.51/58.74 Found (fg (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 58.51/58.74 Found fg__eq_sym:=((((eq_sym (fofType->Prop)) f) g) fg):(((eq (fofType->Prop)) g) f)
% 58.51/58.74 Instantiate: b0:=g:(fofType->Prop)
% 58.51/58.74 Found fg__eq_sym as proof of (((eq (fofType->Prop)) b0) f)
% 58.51/58.74 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> b)):(((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (x:fofType)=> b))
% 58.51/58.74 Found (eta_expansion_dep00 (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 58.51/58.74 Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 58.51/58.74 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 58.51/58.74 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 58.51/58.74 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 58.51/58.74 Found fg__eq_sym:=((((eq_sym (fofType->Prop)) f) g) fg):(((eq (fofType->Prop)) g) f)
% 58.51/58.74 Instantiate: b0:=g:(fofType->Prop)
% 58.51/58.74 Found fg__eq_sym as proof of (((eq (fofType->Prop)) b0) f)
% 58.51/58.74 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> b)):(((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (x:fofType)=> b))
% 58.51/58.74 Found (eta_expansion_dep00 (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 58.51/58.74 Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 58.51/58.74 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 58.51/58.74 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 58.51/58.74 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 58.51/58.74 Found fa0:=(fa (fun (x0:(fofType->Prop))=> (P (g x)))):((P (g x))->(P (g x)))
% 58.51/58.74 Found (fa (fun (x0:(fofType->Prop))=> (P (g x)))) as proof of (P0 (g x))
% 58.51/58.74 Found (fa (fun (x0:(fofType->Prop))=> (P (g x)))) as proof of (P0 (g x))
% 58.51/58.74 Found fa0:=(fa (fun (x0:(fofType->Prop))=> (P (g x)))):((P (g x))->(P (g x)))
% 58.51/58.74 Found (fa (fun (x0:(fofType->Prop))=> (P (g x)))) as proof of (P0 (g x))
% 58.51/58.74 Found (fa (fun (x0:(fofType->Prop))=> (P (g x)))) as proof of (P0 (g x))
% 58.51/58.74 Found eq_ref000:=(eq_ref00 P):((P f)->(P f))
% 58.51/58.74 Found (eq_ref00 P) as proof of (P0 f)
% 58.51/58.74 Found ((eq_ref0 f) P) as proof of (P0 f)
% 58.51/58.74 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 58.51/58.74 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 58.51/58.74 Found eq_ref000:=(eq_ref00 P):((P f)->(P f))
% 58.51/58.74 Found (eq_ref00 P) as proof of (P0 f)
% 58.51/58.74 Found ((eq_ref0 f) P) as proof of (P0 f)
% 58.51/58.74 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 58.51/58.74 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 58.51/58.74 Found eq_ref000:=(eq_ref00 P):((P f)->(P f))
% 58.51/58.74 Found (eq_ref00 P) as proof of (P0 f)
% 58.51/58.74 Found ((eq_ref0 f) P) as proof of (P0 f)
% 58.51/58.74 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 58.51/58.74 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 58.51/58.74 Found eq_ref000:=(eq_ref00 P):((P f)->(P f))
% 58.51/58.74 Found (eq_ref00 P) as proof of (P0 f)
% 58.51/58.74 Found ((eq_ref0 f) P) as proof of (P0 f)
% 58.51/58.74 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 58.51/58.74 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 58.51/58.74 Found eq_ref000:=(eq_ref00 P):((P f)->(P f))
% 58.51/58.74 Found (eq_ref00 P) as proof of (P0 f)
% 58.51/58.74 Found ((eq_ref0 f) P) as proof of (P0 f)
% 58.51/58.74 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 58.51/58.74 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 58.51/58.74 Found eq_ref000:=(eq_ref00 P):((P f)->(P f))
% 58.51/58.74 Found (eq_ref00 P) as proof of (P0 f)
% 58.51/58.74 Found ((eq_ref0 f) P) as proof of (P0 f)
% 58.51/58.74 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 58.51/58.74 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 58.51/58.74 Found eq_ref000:=(eq_ref00 P):((P f)->(P f))
% 79.48/79.77 Found (eq_ref00 P) as proof of (P0 f)
% 79.48/79.77 Found ((eq_ref0 f) P) as proof of (P0 f)
% 79.48/79.77 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 79.48/79.77 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 79.48/79.77 Found fa0:=(fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))):((P (fun (X:fofType)=> b))->(P (fun (X:fofType)=> b)))
% 79.48/79.77 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 79.48/79.77 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 79.48/79.77 Found eq_ref00:=(eq_ref0 f):(((eq (fofType->Prop)) f) f)
% 79.48/79.77 Found (eq_ref0 f) as proof of (((eq (fofType->Prop)) f) f)
% 79.48/79.77 Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) f)
% 79.48/79.77 Found (fun (x00:(b->a))=> ((eq_ref (fofType->Prop)) f)) as proof of (((eq (fofType->Prop)) f) f)
% 79.48/79.77 Found (fun (x00:(b->a))=> ((eq_ref (fofType->Prop)) f)) as proof of (P f)
% 79.48/79.77 Found eq_ref00:=(eq_ref0 f):(((eq (fofType->Prop)) f) f)
% 79.48/79.77 Found (eq_ref0 f) as proof of (((eq (fofType->Prop)) f) f)
% 79.48/79.77 Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) f)
% 79.48/79.77 Found (fun (x00:(b->a))=> ((eq_ref (fofType->Prop)) f)) as proof of (((eq (fofType->Prop)) f) f)
% 79.48/79.77 Found (fun (x10:(a->b)) (x00:(b->a))=> ((eq_ref (fofType->Prop)) f)) as proof of ((b->a)->(((eq (fofType->Prop)) f) f))
% 79.48/79.77 Found (fun (x10:(a->b)) (x00:(b->a))=> ((eq_ref (fofType->Prop)) f)) as proof of (P f)
% 79.48/79.77 Found eq_ref00:=(eq_ref0 (g x)):(((eq Prop) (g x)) (g x))
% 79.48/79.77 Found (eq_ref0 (g x)) as proof of (((eq Prop) (g x)) b0)
% 79.48/79.77 Found ((eq_ref Prop) (g x)) as proof of (((eq Prop) (g x)) b0)
% 79.48/79.77 Found ((eq_ref Prop) (g x)) as proof of (((eq Prop) (g x)) b0)
% 79.48/79.77 Found ((eq_ref Prop) (g x)) as proof of (((eq Prop) (g x)) b0)
% 79.48/79.77 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 79.48/79.77 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 79.48/79.77 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 79.48/79.77 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 79.48/79.77 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 79.48/79.77 Found eq_ref00:=(eq_ref0 (g x)):(((eq Prop) (g x)) (g x))
% 79.48/79.77 Found (eq_ref0 (g x)) as proof of (((eq Prop) (g x)) b0)
% 79.48/79.77 Found ((eq_ref Prop) (g x)) as proof of (((eq Prop) (g x)) b0)
% 79.48/79.77 Found ((eq_ref Prop) (g x)) as proof of (((eq Prop) (g x)) b0)
% 79.48/79.77 Found ((eq_ref Prop) (g x)) as proof of (((eq Prop) (g x)) b0)
% 79.48/79.77 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 79.48/79.77 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 79.48/79.77 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 79.48/79.77 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 79.48/79.77 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 79.48/79.77 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> a)):(((eq (fofType->Prop)) (fun (X:fofType)=> a)) (fun (x:fofType)=> a))
% 79.48/79.77 Found (eta_expansion_dep00 (fun (X:fofType)=> a)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> a)) (fun (X:fofType)=> a))
% 79.48/79.77 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> a)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> a)) (fun (X:fofType)=> a))
% 79.48/79.77 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> a)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> a)) (fun (X:fofType)=> a))
% 79.48/79.77 Found (fun (x00:(b->a))=> (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> a))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> a)) (fun (X:fofType)=> a))
% 79.48/79.77 Found (fun (x00:(b->a))=> (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> a))) as proof of (P (fun (X:fofType)=> a))
% 79.48/79.77 Found eq_ref000:=(eq_ref00 P):((P f)->(P f))
% 79.48/79.77 Found (eq_ref00 P) as proof of (P0 f)
% 79.48/79.77 Found ((eq_ref0 f) P) as proof of (P0 f)
% 79.48/79.77 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 79.48/79.77 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 79.48/79.77 Found eq_ref000:=(eq_ref00 P):((P f)->(P f))
% 79.48/79.77 Found (eq_ref00 P) as proof of (P0 f)
% 79.48/79.77 Found ((eq_ref0 f) P) as proof of (P0 f)
% 79.48/79.77 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 79.48/79.77 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 79.48/79.77 Found eq_ref00:=(eq_ref0 f):(((eq (fofType->Prop)) f) f)
% 79.48/79.77 Found (eq_ref0 f) as proof of (((eq (fofType->Prop)) f) f)
% 79.48/79.77 Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) f)
% 94.53/94.82 Found (fun (x00:(b->a))=> ((eq_ref (fofType->Prop)) f)) as proof of (((eq (fofType->Prop)) f) f)
% 94.53/94.82 Found (fun (x00:(b->a))=> ((eq_ref (fofType->Prop)) f)) as proof of (P f)
% 94.53/94.82 Found eq_ref00:=(eq_ref0 f):(((eq (fofType->Prop)) f) f)
% 94.53/94.82 Found (eq_ref0 f) as proof of (((eq (fofType->Prop)) f) f)
% 94.53/94.82 Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) f)
% 94.53/94.82 Found (fun (x00:(b->a))=> ((eq_ref (fofType->Prop)) f)) as proof of (((eq (fofType->Prop)) f) f)
% 94.53/94.82 Found (fun (x2:(a->b)) (x00:(b->a))=> ((eq_ref (fofType->Prop)) f)) as proof of ((b->a)->(((eq (fofType->Prop)) f) f))
% 94.53/94.82 Found (fun (x2:(a->b)) (x00:(b->a))=> ((eq_ref (fofType->Prop)) f)) as proof of (P f)
% 94.53/94.82 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> a)):(((eq (fofType->Prop)) (fun (X:fofType)=> a)) (fun (x:fofType)=> a))
% 94.53/94.82 Found (eta_expansion_dep00 (fun (X:fofType)=> a)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> a)) (fun (X:fofType)=> a))
% 94.53/94.82 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> a)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> a)) (fun (X:fofType)=> a))
% 94.53/94.82 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> a)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> a)) (fun (X:fofType)=> a))
% 94.53/94.82 Found (fun (x00:(b->a))=> (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> a))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> a)) (fun (X:fofType)=> a))
% 94.53/94.82 Found (fun (x00:(b->a))=> (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> a))) as proof of (P (fun (X:fofType)=> a))
% 94.53/94.82 Found fg:(((eq (fofType->Prop)) f) g)
% 94.53/94.82 Instantiate: b0:=f:(fofType->Prop)
% 94.53/94.82 Found fg as proof of (((eq (fofType->Prop)) b0) g)
% 94.53/94.82 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> b)):(((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (x:fofType)=> b))
% 94.53/94.82 Found (eta_expansion_dep00 (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 94.53/94.82 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 94.53/94.82 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 94.53/94.82 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 94.53/94.82 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 94.53/94.82 Found fa0:=(fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))):((P (fun (X:fofType)=> b))->(P (fun (X:fofType)=> b)))
% 94.53/94.82 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 94.53/94.82 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 94.53/94.82 Found fa0:=(fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))):((P (fun (X:fofType)=> b))->(P (fun (X:fofType)=> b)))
% 94.53/94.82 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 94.53/94.82 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 94.53/94.82 Found fa0:=(fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))):((P (fun (X:fofType)=> b))->(P (fun (X:fofType)=> b)))
% 94.53/94.82 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 94.53/94.82 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 94.53/94.82 Found fa0:=(fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))):((P (fun (X:fofType)=> b))->(P (fun (X:fofType)=> b)))
% 94.53/94.82 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 94.53/94.82 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 94.53/94.82 Found fa__eq_sym:=((((eq_sym (fofType->Prop)) f) (fun (X:fofType)=> a)) fa):(((eq (fofType->Prop)) (fun (X:fofType)=> a)) f)
% 94.53/94.82 Instantiate: b0:=f:(fofType->Prop)
% 100.16/100.45 Found fa__eq_sym as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> a)) b0)
% 100.16/100.45 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (fofType->Prop)) b0) (fun (x:fofType)=> (b0 x)))
% 100.16/100.45 Found (eta_expansion_dep00 b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 100.16/100.45 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 100.16/100.45 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 100.16/100.45 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 100.16/100.45 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 100.16/100.45 Found fa__eq_sym:=((((eq_sym (fofType->Prop)) f) (fun (X:fofType)=> a)) fa):(((eq (fofType->Prop)) (fun (X:fofType)=> a)) f)
% 100.16/100.45 Instantiate: b0:=f:(fofType->Prop)
% 100.16/100.45 Found fa__eq_sym as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> a)) b0)
% 100.16/100.45 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (fofType->Prop)) b0) (fun (x:fofType)=> (b0 x)))
% 100.16/100.45 Found (eta_expansion_dep00 b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 100.16/100.45 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 100.16/100.45 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 100.16/100.45 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 100.16/100.45 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 100.16/100.45 Found fa__eq_sym:=((((eq_sym (fofType->Prop)) f) (fun (X:fofType)=> a)) fa):(((eq (fofType->Prop)) (fun (X:fofType)=> a)) f)
% 100.16/100.45 Instantiate: b0:=f:(fofType->Prop)
% 100.16/100.45 Found fa__eq_sym as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> a)) b0)
% 100.16/100.45 Found eta_expansion000:=(eta_expansion00 b0):(((eq (fofType->Prop)) b0) (fun (x:fofType)=> (b0 x)))
% 100.16/100.45 Found (eta_expansion00 b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 100.16/100.45 Found ((eta_expansion0 Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 100.16/100.45 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 100.16/100.45 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 100.16/100.45 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 100.16/100.45 Found fa0:=(fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))):((P (fun (X:fofType)=> b))->(P (fun (X:fofType)=> b)))
% 100.16/100.45 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 100.16/100.45 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 100.16/100.45 Found fa0:=(fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))):((P (fun (X:fofType)=> b))->(P (fun (X:fofType)=> b)))
% 100.16/100.45 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 100.16/100.45 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 100.16/100.45 Found eq_ref00:=(eq_ref0 (fun (X:fofType)=> b)):(((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (X:fofType)=> b))
% 100.16/100.45 Found (eq_ref0 (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (X:fofType)=> b))
% 100.16/100.45 Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (X:fofType)=> b))
% 100.16/100.45 Found (fun (x00:(b->a))=> ((eq_ref (fofType->Prop)) (fun (X:fofType)=> b))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (X:fofType)=> b))
% 100.16/100.45 Found (fun (x00:(b->a))=> ((eq_ref (fofType->Prop)) (fun (X:fofType)=> b))) as proof of (P (fun (X:fofType)=> b))
% 100.16/100.45 Found eq_ref000:=(eq_ref00 P):((P (f x1))->(P (f x1)))
% 100.16/100.45 Found (eq_ref00 P) as proof of (P0 (f x1))
% 100.16/100.45 Found ((eq_ref0 (f x1)) P) as proof of (P0 (f x1))
% 100.16/100.45 Found (((eq_ref Prop) (f x1)) P) as proof of (P0 (f x1))
% 100.16/100.45 Found (((eq_ref Prop) (f x1)) P) as proof of (P0 (f x1))
% 116.26/116.59 Found eq_ref000:=(eq_ref00 P):((P (f x1))->(P (f x1)))
% 116.26/116.59 Found (eq_ref00 P) as proof of (P0 (f x1))
% 116.26/116.59 Found ((eq_ref0 (f x1)) P) as proof of (P0 (f x1))
% 116.26/116.59 Found (((eq_ref Prop) (f x1)) P) as proof of (P0 (f x1))
% 116.26/116.59 Found (((eq_ref Prop) (f x1)) P) as proof of (P0 (f x1))
% 116.26/116.59 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 116.26/116.59 Found (eq_ref00 P) as proof of (P0 (f x))
% 116.26/116.59 Found ((eq_ref0 (f x)) P) as proof of (P0 (f x))
% 116.26/116.59 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 116.26/116.59 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 116.26/116.59 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 116.26/116.59 Found (eq_ref00 P) as proof of (P0 (f x))
% 116.26/116.59 Found ((eq_ref0 (f x)) P) as proof of (P0 (f x))
% 116.26/116.59 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 116.26/116.59 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 116.26/116.59 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 116.26/116.59 Found (eq_ref00 P) as proof of (P0 (f x))
% 116.26/116.59 Found ((eq_ref0 (f x)) P) as proof of (P0 (f x))
% 116.26/116.59 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 116.26/116.59 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 116.26/116.59 Found eq_ref000:=(eq_ref00 P):((P (f x))->(P (f x)))
% 116.26/116.59 Found (eq_ref00 P) as proof of (P0 (f x))
% 116.26/116.59 Found ((eq_ref0 (f x)) P) as proof of (P0 (f x))
% 116.26/116.59 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 116.26/116.59 Found (((eq_ref Prop) (f x)) P) as proof of (P0 (f x))
% 116.26/116.59 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 116.26/116.59 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) b0)
% 116.26/116.59 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b0)
% 116.26/116.59 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b0)
% 116.26/116.59 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b0)
% 116.26/116.59 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 116.26/116.59 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 116.26/116.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 116.26/116.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 116.26/116.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 116.26/116.59 Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 116.26/116.59 Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) b0)
% 116.26/116.59 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b0)
% 116.26/116.59 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b0)
% 116.26/116.59 Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) b0)
% 116.26/116.59 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 116.26/116.59 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 116.26/116.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 116.26/116.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 116.26/116.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 116.26/116.59 Found fa__eq_sym:=((((eq_sym (fofType->Prop)) f) (fun (X:fofType)=> a)) fa):(((eq (fofType->Prop)) (fun (X:fofType)=> a)) f)
% 116.26/116.59 Instantiate: b0:=f:(fofType->Prop)
% 116.26/116.59 Found fa__eq_sym as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> a)) b0)
% 116.26/116.59 Found eta_expansion000:=(eta_expansion00 b0):(((eq (fofType->Prop)) b0) (fun (x:fofType)=> (b0 x)))
% 116.26/116.59 Found (eta_expansion00 b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 116.26/116.59 Found ((eta_expansion0 Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 116.26/116.59 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 116.26/116.59 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 116.26/116.59 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 116.26/116.59 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 116.26/116.59 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b0)
% 116.26/116.59 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 116.26/116.59 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 116.26/116.59 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 116.26/116.59 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 116.26/116.59 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 116.26/116.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 116.26/116.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 116.26/116.59 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 116.26/116.59 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 116.26/116.59 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b0)
% 116.26/116.59 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 116.26/116.59 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 129.56/129.90 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 129.56/129.90 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 129.56/129.90 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 129.56/129.90 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 129.56/129.90 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 129.56/129.90 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 129.56/129.90 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 129.56/129.90 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b0)
% 129.56/129.90 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 129.56/129.90 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 129.56/129.90 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 129.56/129.90 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 129.56/129.90 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 129.56/129.90 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 129.56/129.90 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 129.56/129.90 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 129.56/129.90 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 129.56/129.90 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b0)
% 129.56/129.90 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 129.56/129.90 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 129.56/129.90 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 129.56/129.90 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 129.56/129.90 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 129.56/129.90 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 129.56/129.90 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 129.56/129.90 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 129.56/129.90 Found fa__eq_sym:=((((eq_sym (fofType->Prop)) f) (fun (X:fofType)=> a)) fa):(((eq (fofType->Prop)) (fun (X:fofType)=> a)) f)
% 129.56/129.90 Instantiate: b0:=f:(fofType->Prop)
% 129.56/129.90 Found fa__eq_sym as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> a)) b0)
% 129.56/129.90 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (fofType->Prop)) b0) (fun (x:fofType)=> (b0 x)))
% 129.56/129.90 Found (eta_expansion_dep00 b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 129.56/129.90 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 129.56/129.90 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 129.56/129.90 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 129.56/129.90 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 129.56/129.90 Found eq_ref00:=(eq_ref0 f):(((eq (fofType->Prop)) f) f)
% 129.56/129.90 Found (eq_ref0 f) as proof of (((eq (fofType->Prop)) f) f)
% 129.56/129.90 Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) f)
% 129.56/129.90 Found (fun (x00:(b->a))=> ((eq_ref (fofType->Prop)) f)) as proof of (((eq (fofType->Prop)) f) f)
% 129.56/129.90 Found (fun (x2:(a->b)) (x00:(b->a))=> ((eq_ref (fofType->Prop)) f)) as proof of ((b->a)->(((eq (fofType->Prop)) f) f))
% 129.56/129.90 Found (fun (x2:(a->b)) (x00:(b->a))=> ((eq_ref (fofType->Prop)) f)) as proof of (P f)
% 129.56/129.90 Found fg:(((eq (fofType->Prop)) f) g)
% 129.56/129.90 Instantiate: b0:=f:(fofType->Prop)
% 129.56/129.90 Found fg as proof of (((eq (fofType->Prop)) b0) g)
% 129.56/129.90 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> b)):(((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (x:fofType)=> b))
% 129.56/129.90 Found (eta_expansion_dep00 (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 129.56/129.90 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 129.56/129.90 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 129.56/129.90 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 129.56/129.90 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 129.56/129.90 Found fa0:=(fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> a)))):((P (fun (X:fofType)=> a))->(P (fun (X:fofType)=> a)))
% 129.56/129.90 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> a)))) as proof of (P0 (fun (X:fofType)=> a))
% 149.66/149.97 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> a)))) as proof of (P0 (fun (X:fofType)=> a))
% 149.66/149.97 Found fa0:=(fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> a)))):((P (fun (X:fofType)=> a))->(P (fun (X:fofType)=> a)))
% 149.66/149.97 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> a)))) as proof of (P0 (fun (X:fofType)=> a))
% 149.66/149.97 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> a)))) as proof of (P0 (fun (X:fofType)=> a))
% 149.66/149.97 Found fa0:=(fa (fun (x0:(fofType->Prop))=> (P (fun (X:fofType)=> a)))):((P (fun (X:fofType)=> a))->(P (fun (X:fofType)=> a)))
% 149.66/149.97 Found (fa (fun (x0:(fofType->Prop))=> (P (fun (X:fofType)=> a)))) as proof of (P0 (fun (X:fofType)=> a))
% 149.66/149.97 Found (fa (fun (x0:(fofType->Prop))=> (P (fun (X:fofType)=> a)))) as proof of (P0 (fun (X:fofType)=> a))
% 149.66/149.97 Found fg__eq_sym:=((((eq_sym (fofType->Prop)) f) g) fg):(((eq (fofType->Prop)) g) f)
% 149.66/149.97 Instantiate: b0:=f:(fofType->Prop)
% 149.66/149.97 Found fg__eq_sym as proof of (((eq (fofType->Prop)) g) b0)
% 149.66/149.97 Found eta_expansion000:=(eta_expansion00 b0):(((eq (fofType->Prop)) b0) (fun (x:fofType)=> (b0 x)))
% 149.66/149.97 Found (eta_expansion00 b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 149.66/149.97 Found ((eta_expansion0 Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 149.66/149.97 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 149.66/149.97 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 149.66/149.97 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 149.66/149.97 Found eq_ref00:=(eq_ref0 (fun (X:fofType)=> b)):(((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (X:fofType)=> b))
% 149.66/149.97 Found (eq_ref0 (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (X:fofType)=> b))
% 149.66/149.97 Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (X:fofType)=> b))
% 149.66/149.97 Found (fun (x00:(b->a))=> ((eq_ref (fofType->Prop)) (fun (X:fofType)=> b))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (X:fofType)=> b))
% 149.66/149.97 Found (fun (x2:(a->b)) (x00:(b->a))=> ((eq_ref (fofType->Prop)) (fun (X:fofType)=> b))) as proof of ((b->a)->(((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (X:fofType)=> b)))
% 149.66/149.97 Found (fun (x2:(a->b)) (x00:(b->a))=> ((eq_ref (fofType->Prop)) (fun (X:fofType)=> b))) as proof of (P (fun (X:fofType)=> b))
% 149.66/149.97 Found fa0:=(fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))):((P (fun (X:fofType)=> b))->(P (fun (X:fofType)=> b)))
% 149.66/149.97 Found (fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 149.66/149.97 Found (fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 149.66/149.97 Found fg__eq_sym:=((((eq_sym (fofType->Prop)) f) g) fg):(((eq (fofType->Prop)) g) f)
% 149.66/149.97 Instantiate: b0:=g:(fofType->Prop)
% 149.66/149.97 Found fg__eq_sym as proof of (((eq (fofType->Prop)) b0) f)
% 149.66/149.97 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> b)):(((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (x:fofType)=> b))
% 149.66/149.97 Found (eta_expansion_dep00 (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 149.66/149.97 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 149.66/149.97 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 149.66/149.97 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 149.66/149.97 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 149.66/149.97 Found fa0:=(fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))):((P (fun (X:fofType)=> b))->(P (fun (X:fofType)=> b)))
% 149.66/149.97 Found (fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 149.66/149.97 Found (fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 160.22/160.52 Found fg__eq_sym:=((((eq_sym (fofType->Prop)) f) g) fg):(((eq (fofType->Prop)) g) f)
% 160.22/160.52 Instantiate: b0:=g:(fofType->Prop)
% 160.22/160.52 Found fg__eq_sym as proof of (((eq (fofType->Prop)) b0) f)
% 160.22/160.52 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> b)):(((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (x:fofType)=> b))
% 160.22/160.52 Found (eta_expansion_dep00 (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 160.22/160.52 Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 160.22/160.52 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 160.22/160.52 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 160.22/160.52 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 160.22/160.52 Found fg__eq_sym:=((((eq_sym (fofType->Prop)) f) g) fg):(((eq (fofType->Prop)) g) f)
% 160.22/160.52 Instantiate: b0:=g:(fofType->Prop)
% 160.22/160.52 Found fg__eq_sym as proof of (((eq (fofType->Prop)) b0) f)
% 160.22/160.52 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> b)):(((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (x:fofType)=> b))
% 160.22/160.52 Found (eta_expansion_dep00 (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 160.22/160.52 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 160.22/160.52 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 160.22/160.52 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 160.22/160.52 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 160.22/160.52 Found fa0:=(fa (fun (x0:(fofType->Prop))=> (P (fun (X:fofType)=> a)))):((P (fun (X:fofType)=> a))->(P (fun (X:fofType)=> a)))
% 160.22/160.52 Found (fa (fun (x0:(fofType->Prop))=> (P (fun (X:fofType)=> a)))) as proof of (P0 (fun (X:fofType)=> a))
% 160.22/160.52 Found (fa (fun (x0:(fofType->Prop))=> (P (fun (X:fofType)=> a)))) as proof of (P0 (fun (X:fofType)=> a))
% 160.22/160.52 Found fa0:=(fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> a)))):((P (fun (X:fofType)=> a))->(P (fun (X:fofType)=> a)))
% 160.22/160.52 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> a)))) as proof of (P0 (fun (X:fofType)=> a))
% 160.22/160.52 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> a)))) as proof of (P0 (fun (X:fofType)=> a))
% 160.22/160.52 Found fg__eq_sym:=((((eq_sym (fofType->Prop)) f) g) fg):(((eq (fofType->Prop)) g) f)
% 160.22/160.52 Instantiate: b0:=g:(fofType->Prop)
% 160.22/160.52 Found fg__eq_sym as proof of (((eq (fofType->Prop)) b0) f)
% 160.22/160.52 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> b)):(((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (x:fofType)=> b))
% 160.22/160.52 Found (eta_expansion_dep00 (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 160.22/160.52 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 160.22/160.52 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 160.22/160.52 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 160.22/160.52 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 160.22/160.52 Found fa0:=(fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> a)))):((P (fun (X:fofType)=> a))->(P (fun (X:fofType)=> a)))
% 160.22/160.52 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> a)))) as proof of (P0 (fun (X:fofType)=> a))
% 160.22/160.52 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> a)))) as proof of (P0 (fun (X:fofType)=> a))
% 160.22/160.52 Found fa0:=(fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> a)))):((P (fun (X:fofType)=> a))->(P (fun (X:fofType)=> a)))
% 168.82/169.13 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> a)))) as proof of (P0 (fun (X:fofType)=> a))
% 168.82/169.13 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> a)))) as proof of (P0 (fun (X:fofType)=> a))
% 168.82/169.13 Found fa0:=(fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> a)))):((P (fun (X:fofType)=> a))->(P (fun (X:fofType)=> a)))
% 168.82/169.13 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> a)))) as proof of (P0 (fun (X:fofType)=> a))
% 168.82/169.13 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> a)))) as proof of (P0 (fun (X:fofType)=> a))
% 168.82/169.13 Found fa0:=(fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> a)))):((P (fun (X:fofType)=> a))->(P (fun (X:fofType)=> a)))
% 168.82/169.13 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> a)))) as proof of (P0 (fun (X:fofType)=> a))
% 168.82/169.13 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> a)))) as proof of (P0 (fun (X:fofType)=> a))
% 168.82/169.13 Found fa0:=(fa (fun (x0:(fofType->Prop))=> (P (fun (X:fofType)=> a)))):((P (fun (X:fofType)=> a))->(P (fun (X:fofType)=> a)))
% 168.82/169.13 Found (fa (fun (x0:(fofType->Prop))=> (P (fun (X:fofType)=> a)))) as proof of (P0 (fun (X:fofType)=> a))
% 168.82/169.13 Found (fa (fun (x0:(fofType->Prop))=> (P (fun (X:fofType)=> a)))) as proof of (P0 (fun (X:fofType)=> a))
% 168.82/169.13 Found fa0:=(fa (fun (x0:(fofType->Prop))=> (P (fun (X:fofType)=> a)))):((P (fun (X:fofType)=> a))->(P (fun (X:fofType)=> a)))
% 168.82/169.13 Found (fa (fun (x0:(fofType->Prop))=> (P (fun (X:fofType)=> a)))) as proof of (P0 (fun (X:fofType)=> a))
% 168.82/169.13 Found (fa (fun (x0:(fofType->Prop))=> (P (fun (X:fofType)=> a)))) as proof of (P0 (fun (X:fofType)=> a))
% 168.82/169.13 Found fg:(((eq (fofType->Prop)) f) g)
% 168.82/169.13 Instantiate: b0:=g:(fofType->Prop)
% 168.82/169.13 Found fg as proof of (((eq (fofType->Prop)) f) b0)
% 168.82/169.13 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (fofType->Prop)) b0) (fun (x:fofType)=> (b0 x)))
% 168.82/169.13 Found (eta_expansion_dep00 b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 168.82/169.13 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 168.82/169.13 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 168.82/169.13 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 168.82/169.13 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 168.82/169.13 Found fg:(((eq (fofType->Prop)) f) g)
% 168.82/169.13 Instantiate: b0:=g:(fofType->Prop)
% 168.82/169.13 Found fg as proof of (((eq (fofType->Prop)) f) b0)
% 168.82/169.13 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (fofType->Prop)) b0) (fun (x:fofType)=> (b0 x)))
% 168.82/169.13 Found (eta_expansion_dep00 b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 168.82/169.13 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 168.82/169.13 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 168.82/169.13 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 168.82/169.13 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 168.82/169.13 Found fg:(((eq (fofType->Prop)) f) g)
% 168.82/169.13 Instantiate: b0:=g:(fofType->Prop)
% 168.82/169.13 Found fg as proof of (((eq (fofType->Prop)) f) b0)
% 168.82/169.13 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (fofType->Prop)) b0) (fun (x:fofType)=> (b0 x)))
% 168.82/169.13 Found (eta_expansion_dep00 b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 168.82/169.13 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 168.82/169.13 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 168.82/169.13 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 168.82/169.13 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 183.16/183.52 Found fg:(((eq (fofType->Prop)) f) g)
% 183.16/183.52 Instantiate: b0:=g:(fofType->Prop)
% 183.16/183.52 Found fg as proof of (((eq (fofType->Prop)) f) b0)
% 183.16/183.52 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (fofType->Prop)) b0) (fun (x:fofType)=> (b0 x)))
% 183.16/183.52 Found (eta_expansion_dep00 b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 183.16/183.52 Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 183.16/183.52 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 183.16/183.52 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 183.16/183.52 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 183.16/183.52 Found fg0:=(fg (fun (x2:(fofType->Prop))=> (P (g x1)))):((P (g x1))->(P (g x1)))
% 183.16/183.52 Found (fg (fun (x2:(fofType->Prop))=> (P (g x1)))) as proof of (P0 (g x1))
% 183.16/183.52 Found (fg (fun (x2:(fofType->Prop))=> (P (g x1)))) as proof of (P0 (g x1))
% 183.16/183.52 Found fg__eq_sym:=((((eq_sym (fofType->Prop)) f) g) fg):(((eq (fofType->Prop)) g) f)
% 183.16/183.52 Instantiate: b0:=f:(fofType->Prop)
% 183.16/183.52 Found fg__eq_sym as proof of (((eq (fofType->Prop)) g) b0)
% 183.16/183.52 Found eta_expansion000:=(eta_expansion00 b0):(((eq (fofType->Prop)) b0) (fun (x:fofType)=> (b0 x)))
% 183.16/183.52 Found (eta_expansion00 b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 183.16/183.52 Found ((eta_expansion0 Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 183.16/183.52 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 183.16/183.52 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 183.16/183.52 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 183.16/183.52 Found fg0:=(fg (fun (x2:(fofType->Prop))=> (P (g x1)))):((P (g x1))->(P (g x1)))
% 183.16/183.52 Found (fg (fun (x2:(fofType->Prop))=> (P (g x1)))) as proof of (P0 (g x1))
% 183.16/183.52 Found (fg (fun (x2:(fofType->Prop))=> (P (g x1)))) as proof of (P0 (g x1))
% 183.16/183.52 Found fg__eq_sym:=((((eq_sym (fofType->Prop)) f) g) fg):(((eq (fofType->Prop)) g) f)
% 183.16/183.52 Instantiate: b0:=f:(fofType->Prop)
% 183.16/183.52 Found fg__eq_sym as proof of (((eq (fofType->Prop)) g) b0)
% 183.16/183.52 Found eta_expansion000:=(eta_expansion00 b0):(((eq (fofType->Prop)) b0) (fun (x:fofType)=> (b0 x)))
% 183.16/183.52 Found (eta_expansion00 b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 183.16/183.52 Found ((eta_expansion0 Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 183.16/183.52 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 183.16/183.52 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 183.16/183.52 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 183.16/183.52 Found fa0:=(fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))):((P (fun (X:fofType)=> b))->(P (fun (X:fofType)=> b)))
% 183.16/183.52 Found (fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 183.16/183.52 Found (fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 183.16/183.52 Found fg__eq_sym:=((((eq_sym (fofType->Prop)) f) g) fg):(((eq (fofType->Prop)) g) f)
% 183.16/183.52 Instantiate: b0:=g:(fofType->Prop)
% 183.16/183.52 Found fg__eq_sym as proof of (((eq (fofType->Prop)) b0) f)
% 183.16/183.52 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> b)):(((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (x:fofType)=> b))
% 183.16/183.52 Found (eta_expansion_dep00 (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 183.16/183.52 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 183.16/183.52 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 183.16/183.52 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 183.16/183.52 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 207.48/207.83 Found eq_ref00:=(eq_ref0 (g x1)):(((eq Prop) (g x1)) (g x1))
% 207.48/207.83 Found (eq_ref0 (g x1)) as proof of (((eq Prop) (g x1)) b0)
% 207.48/207.83 Found ((eq_ref Prop) (g x1)) as proof of (((eq Prop) (g x1)) b0)
% 207.48/207.83 Found ((eq_ref Prop) (g x1)) as proof of (((eq Prop) (g x1)) b0)
% 207.48/207.83 Found ((eq_ref Prop) (g x1)) as proof of (((eq Prop) (g x1)) b0)
% 207.48/207.83 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 207.48/207.83 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 207.48/207.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 207.48/207.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 207.48/207.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 207.48/207.83 Found eq_ref00:=(eq_ref0 (g x1)):(((eq Prop) (g x1)) (g x1))
% 207.48/207.83 Found (eq_ref0 (g x1)) as proof of (((eq Prop) (g x1)) b0)
% 207.48/207.83 Found ((eq_ref Prop) (g x1)) as proof of (((eq Prop) (g x1)) b0)
% 207.48/207.83 Found ((eq_ref Prop) (g x1)) as proof of (((eq Prop) (g x1)) b0)
% 207.48/207.83 Found ((eq_ref Prop) (g x1)) as proof of (((eq Prop) (g x1)) b0)
% 207.48/207.83 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 207.48/207.83 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 207.48/207.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 207.48/207.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 207.48/207.83 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 207.48/207.83 Found fa0:=(fa (fun (x:(fofType->Prop))=> (P g))):((P g)->(P g))
% 207.48/207.83 Found (fa (fun (x:(fofType->Prop))=> (P g))) as proof of (P0 g)
% 207.48/207.83 Found (fa (fun (x:(fofType->Prop))=> (P g))) as proof of (P0 g)
% 207.48/207.83 Found fa0:=(fa (fun (x0:(fofType->Prop))=> (P (fun (X:fofType)=> a)))):((P (fun (X:fofType)=> a))->(P (fun (X:fofType)=> a)))
% 207.48/207.83 Found (fa (fun (x0:(fofType->Prop))=> (P (fun (X:fofType)=> a)))) as proof of (P0 (fun (X:fofType)=> a))
% 207.48/207.83 Found (fa (fun (x0:(fofType->Prop))=> (P (fun (X:fofType)=> a)))) as proof of (P0 (fun (X:fofType)=> a))
% 207.48/207.83 Found fa0:=(fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> a)))):((P (fun (X:fofType)=> a))->(P (fun (X:fofType)=> a)))
% 207.48/207.83 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> a)))) as proof of (P0 (fun (X:fofType)=> a))
% 207.48/207.83 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> a)))) as proof of (P0 (fun (X:fofType)=> a))
% 207.48/207.83 Found fa0:=(fa (fun (x0:(fofType->Prop))=> (P (fun (X:fofType)=> a)))):((P (fun (X:fofType)=> a))->(P (fun (X:fofType)=> a)))
% 207.48/207.83 Found (fa (fun (x0:(fofType->Prop))=> (P (fun (X:fofType)=> a)))) as proof of (P0 (fun (X:fofType)=> a))
% 207.48/207.83 Found (fa (fun (x0:(fofType->Prop))=> (P (fun (X:fofType)=> a)))) as proof of (P0 (fun (X:fofType)=> a))
% 207.48/207.83 Found fa0:=(fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> a)))):((P (fun (X:fofType)=> a))->(P (fun (X:fofType)=> a)))
% 207.48/207.83 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> a)))) as proof of (P0 (fun (X:fofType)=> a))
% 207.48/207.83 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> a)))) as proof of (P0 (fun (X:fofType)=> a))
% 207.48/207.83 Found fg:(((eq (fofType->Prop)) f) g)
% 207.48/207.83 Instantiate: b0:=g:(fofType->Prop)
% 207.48/207.83 Found fg as proof of (((eq (fofType->Prop)) f) b0)
% 207.48/207.83 Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq (fofType->Prop)) b0) (fun (x:fofType)=> (b0 x)))
% 207.48/207.83 Found (eta_expansion_dep00 b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 207.48/207.83 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 207.48/207.83 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 207.48/207.83 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 207.48/207.83 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 207.48/207.83 Found fg__eq_sym:=((((eq_sym (fofType->Prop)) f) g) fg):(((eq (fofType->Prop)) g) f)
% 207.48/207.83 Instantiate: b0:=g:(fofType->Prop)
% 207.48/207.83 Found fg__eq_sym as proof of (((eq (fofType->Prop)) b0) f)
% 207.48/207.83 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> b)):(((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (x:fofType)=> b))
% 207.48/207.83 Found (eta_expansion_dep00 (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 221.85/222.27 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 221.85/222.27 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 221.85/222.27 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 221.85/222.27 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 221.85/222.27 Found fa0:=(fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))):((P (fun (X:fofType)=> b))->(P (fun (X:fofType)=> b)))
% 221.85/222.27 Found (fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 221.85/222.27 Found (fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 221.85/222.27 Found fa0:=(fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))):((P (fun (X:fofType)=> b))->(P (fun (X:fofType)=> b)))
% 221.85/222.27 Found (fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 221.85/222.27 Found (fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 221.85/222.27 Found fg__eq_sym:=((((eq_sym (fofType->Prop)) f) g) fg):(((eq (fofType->Prop)) g) f)
% 221.85/222.27 Instantiate: b0:=g:(fofType->Prop)
% 221.85/222.27 Found fg__eq_sym as proof of (((eq (fofType->Prop)) b0) f)
% 221.85/222.27 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> b)):(((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (x:fofType)=> b))
% 221.85/222.27 Found (eta_expansion_dep00 (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 221.85/222.27 Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 221.85/222.27 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 221.85/222.27 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 221.85/222.27 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 221.85/222.27 Found fa:(((eq (fofType->Prop)) f) (fun (X:fofType)=> a))
% 221.85/222.27 Instantiate: b0:=f:(fofType->Prop)
% 221.85/222.27 Found fa as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> a))
% 221.85/222.27 Found eq_ref00:=(eq_ref0 (fun (X:fofType)=> b)):(((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (X:fofType)=> b))
% 221.85/222.27 Found (eq_ref0 (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 221.85/222.27 Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 221.85/222.27 Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 221.85/222.27 Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 221.85/222.27 Found fg:(((eq (fofType->Prop)) f) g)
% 221.85/222.27 Instantiate: b0:=f:(fofType->Prop)
% 221.85/222.27 Found fg as proof of (((eq (fofType->Prop)) b0) g)
% 221.85/222.27 Found eq_ref00:=(eq_ref0 (fun (X:fofType)=> b)):(((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (X:fofType)=> b))
% 221.85/222.27 Found (eq_ref0 (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 221.85/222.27 Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 221.85/222.27 Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 221.85/222.27 Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 221.85/222.27 Found fg__eq_sym:=((((eq_sym (fofType->Prop)) f) g) fg):(((eq (fofType->Prop)) g) f)
% 221.85/222.27 Instantiate: b0:=g:(fofType->Prop)
% 221.85/222.27 Found fg__eq_sym as proof of (((eq (fofType->Prop)) b0) f)
% 221.85/222.27 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> b)):(((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (x:fofType)=> b))
% 221.85/222.27 Found (eta_expansion_dep00 (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 237.64/238.02 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 237.64/238.02 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 237.64/238.02 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 237.64/238.02 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 237.64/238.02 Found fa:(((eq (fofType->Prop)) f) (fun (X:fofType)=> a))
% 237.64/238.02 Instantiate: b0:=f:(fofType->Prop)
% 237.64/238.02 Found fa as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> a))
% 237.64/238.02 Found eq_ref00:=(eq_ref0 (fun (X:fofType)=> b)):(((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (X:fofType)=> b))
% 237.64/238.02 Found (eq_ref0 (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 237.64/238.02 Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 237.64/238.02 Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 237.64/238.02 Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 237.64/238.02 Found eq_ref000:=(eq_ref00 P):((P f)->(P f))
% 237.64/238.02 Found (eq_ref00 P) as proof of (P0 f)
% 237.64/238.02 Found ((eq_ref0 f) P) as proof of (P0 f)
% 237.64/238.02 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 237.64/238.02 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 237.64/238.02 Found fa0:=(fa (fun (x:(fofType->Prop))=> (P g))):((P g)->(P g))
% 237.64/238.02 Found (fa (fun (x:(fofType->Prop))=> (P g))) as proof of (P0 g)
% 237.64/238.02 Found (fa (fun (x:(fofType->Prop))=> (P g))) as proof of (P0 g)
% 237.64/238.02 Found fa0:=(fa (fun (x0:(fofType->Prop))=> (P g))):((P g)->(P g))
% 237.64/238.02 Found (fa (fun (x0:(fofType->Prop))=> (P g))) as proof of (P0 g)
% 237.64/238.02 Found (fa (fun (x0:(fofType->Prop))=> (P g))) as proof of (P0 g)
% 237.64/238.02 Found fa0:=(fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))):((P (fun (X:fofType)=> b))->(P (fun (X:fofType)=> b)))
% 237.64/238.02 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 237.64/238.02 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 237.64/238.02 Found eq_ref000:=(eq_ref00 P):((P f)->(P f))
% 237.64/238.02 Found (eq_ref00 P) as proof of (P0 f)
% 237.64/238.02 Found ((eq_ref0 f) P) as proof of (P0 f)
% 237.64/238.02 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 237.64/238.02 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 237.64/238.02 Found eq_ref000:=(eq_ref00 P):((P f)->(P f))
% 237.64/238.02 Found (eq_ref00 P) as proof of (P0 f)
% 237.64/238.02 Found ((eq_ref0 f) P) as proof of (P0 f)
% 237.64/238.02 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 237.64/238.02 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 237.64/238.02 Found fa0:=(fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))):((P (fun (X:fofType)=> b))->(P (fun (X:fofType)=> b)))
% 237.64/238.02 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 237.64/238.02 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 237.64/238.02 Found eq_ref00:=(eq_ref0 (fun (X:fofType)=> b)):(((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (X:fofType)=> b))
% 237.64/238.02 Found (eq_ref0 (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (X:fofType)=> b))
% 237.64/238.02 Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (X:fofType)=> b))
% 237.64/238.02 Found (fun (x00:(b->a))=> ((eq_ref (fofType->Prop)) (fun (X:fofType)=> b))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (X:fofType)=> b))
% 237.64/238.02 Found (fun (x00:(b->a))=> ((eq_ref (fofType->Prop)) (fun (X:fofType)=> b))) as proof of (P (fun (X:fofType)=> b))
% 237.64/238.02 Found fa0:=(fa (fun (x0:(fofType->Prop))=> (P (fun (X:fofType)=> b)))):((P (fun (X:fofType)=> b))->(P (fun (X:fofType)=> b)))
% 237.64/238.02 Found (fa (fun (x0:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 237.64/238.02 Found (fa (fun (x0:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 259.81/260.25 Found eq_ref000:=(eq_ref00 P):((P f)->(P f))
% 259.81/260.25 Found (eq_ref00 P) as proof of (P0 f)
% 259.81/260.25 Found ((eq_ref0 f) P) as proof of (P0 f)
% 259.81/260.25 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 259.81/260.25 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 259.81/260.25 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> b)):(((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (x:fofType)=> b))
% 259.81/260.25 Found (eta_expansion_dep00 (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (X:fofType)=> b))
% 259.81/260.25 Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (X:fofType)=> b))
% 259.81/260.25 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (X:fofType)=> b))
% 259.81/260.25 Found (fun (x00:(b->a))=> (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> b))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (X:fofType)=> b))
% 259.81/260.25 Found (fun (x00:(b->a))=> (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> b))) as proof of (P (fun (X:fofType)=> b))
% 259.81/260.25 Found fa0:=(fa (fun (x:(fofType->Prop))=> (P g))):((P g)->(P g))
% 259.81/260.25 Found (fa (fun (x:(fofType->Prop))=> (P g))) as proof of (P0 g)
% 259.81/260.25 Found (fa (fun (x:(fofType->Prop))=> (P g))) as proof of (P0 g)
% 259.81/260.25 Found fa0:=(fa (fun (x0:(fofType->Prop))=> (P b))):((P b)->(P b))
% 259.81/260.25 Found (fa (fun (x0:(fofType->Prop))=> (P b))) as proof of (P0 b)
% 259.81/260.25 Found (fa (fun (x0:(fofType->Prop))=> (P b))) as proof of (P0 b)
% 259.81/260.25 Found fa0:=(fa (fun (x0:(fofType->Prop))=> (P b))):((P b)->(P b))
% 259.81/260.25 Found (fa (fun (x0:(fofType->Prop))=> (P b))) as proof of (P0 b)
% 259.81/260.25 Found (fa (fun (x0:(fofType->Prop))=> (P b))) as proof of (P0 b)
% 259.81/260.25 Found fa0:=(fa (fun (x:(fofType->Prop))=> (P g))):((P g)->(P g))
% 259.81/260.25 Found (fa (fun (x:(fofType->Prop))=> (P g))) as proof of (P0 g)
% 259.81/260.25 Found (fa (fun (x:(fofType->Prop))=> (P g))) as proof of (P0 g)
% 259.81/260.25 Found fa0:=(fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))):((P (fun (X:fofType)=> b))->(P (fun (X:fofType)=> b)))
% 259.81/260.25 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 259.81/260.25 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 259.81/260.25 Found fa0:=(fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))):((P (fun (X:fofType)=> b))->(P (fun (X:fofType)=> b)))
% 259.81/260.25 Found (fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 259.81/260.25 Found (fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 259.81/260.25 Found fg0:=(fg (fun (x1:(fofType->Prop))=> (P (g x)))):((P (g x))->(P (g x)))
% 259.81/260.25 Found (fg (fun (x1:(fofType->Prop))=> (P (g x)))) as proof of (P0 (g x))
% 259.81/260.25 Found (fg (fun (x1:(fofType->Prop))=> (P (g x)))) as proof of (P0 (g x))
% 259.81/260.25 Found fg0:=(fg (fun (x1:(fofType->Prop))=> (P (g x)))):((P (g x))->(P (g x)))
% 259.81/260.25 Found (fg (fun (x1:(fofType->Prop))=> (P (g x)))) as proof of (P0 (g x))
% 259.81/260.25 Found (fg (fun (x1:(fofType->Prop))=> (P (g x)))) as proof of (P0 (g x))
% 259.81/260.25 Found fg__eq_sym:=((((eq_sym (fofType->Prop)) f) g) fg):(((eq (fofType->Prop)) g) f)
% 259.81/260.25 Instantiate: b0:=g:(fofType->Prop)
% 259.81/260.25 Found fg__eq_sym as proof of (((eq (fofType->Prop)) b0) f)
% 259.81/260.25 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> b)):(((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (x:fofType)=> b))
% 259.81/260.25 Found (eta_expansion_dep00 (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 259.81/260.25 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 259.81/260.25 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 259.81/260.25 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 259.81/260.25 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 259.81/260.25 Found fg__eq_sym:=((((eq_sym (fofType->Prop)) f) g) fg):(((eq (fofType->Prop)) g) f)
% 265.70/266.13 Instantiate: b0:=g:(fofType->Prop)
% 265.70/266.13 Found fg__eq_sym as proof of (((eq (fofType->Prop)) b0) f)
% 265.70/266.13 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> b)):(((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (x:fofType)=> b))
% 265.70/266.13 Found (eta_expansion_dep00 (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 265.70/266.13 Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 265.70/266.13 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 265.70/266.13 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 265.70/266.13 Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) b0)
% 265.70/266.13 Found fa0:=(fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))):((P (fun (X:fofType)=> b))->(P (fun (X:fofType)=> b)))
% 265.70/266.13 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 265.70/266.13 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 265.70/266.13 Found fa0:=(fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))):((P (fun (X:fofType)=> b))->(P (fun (X:fofType)=> b)))
% 265.70/266.13 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 265.70/266.13 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 265.70/266.13 Found fa0:=(fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))):((P (fun (X:fofType)=> b))->(P (fun (X:fofType)=> b)))
% 265.70/266.13 Found (fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 265.70/266.13 Found (fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 265.70/266.13 Found fa0:=(fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))):((P (fun (X:fofType)=> b))->(P (fun (X:fofType)=> b)))
% 265.70/266.13 Found (fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 265.70/266.13 Found (fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 265.70/266.13 Found fa0:=(fa (fun (x0:(fofType->Prop))=> (P (fun (X:fofType)=> b)))):((P (fun (X:fofType)=> b))->(P (fun (X:fofType)=> b)))
% 265.70/266.13 Found (fa (fun (x0:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 265.70/266.13 Found (fa (fun (x0:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 265.70/266.13 Found fa0:=(fa (fun (x0:(fofType->Prop))=> (P (fun (X:fofType)=> b)))):((P (fun (X:fofType)=> b))->(P (fun (X:fofType)=> b)))
% 265.70/266.13 Found (fa (fun (x0:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 265.70/266.13 Found (fa (fun (x0:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 265.70/266.13 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 265.70/266.13 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 265.70/266.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 265.70/266.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 265.70/266.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 265.70/266.13 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 265.70/266.13 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x))
% 265.70/266.13 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x))
% 265.70/266.13 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x))
% 265.70/266.13 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x))
% 265.70/266.13 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 265.70/266.13 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 265.70/266.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 265.70/266.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 265.70/266.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 265.70/266.13 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 265.70/266.13 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x))
% 265.70/266.13 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x))
% 265.70/266.13 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x))
% 265.70/266.13 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x))
% 282.31/282.72 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 282.31/282.72 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x))
% 282.31/282.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x))
% 282.31/282.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x))
% 282.31/282.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x))
% 282.31/282.72 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 282.31/282.72 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 282.31/282.72 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 282.31/282.72 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 282.31/282.72 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 282.31/282.72 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 282.31/282.72 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 282.31/282.72 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 282.31/282.72 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 282.31/282.72 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 282.31/282.72 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 282.31/282.72 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (g x))
% 282.31/282.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x))
% 282.31/282.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x))
% 282.31/282.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (g x))
% 282.31/282.72 Found fa0:=(fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))):((P (fun (X:fofType)=> b))->(P (fun (X:fofType)=> b)))
% 282.31/282.72 Found (fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 282.31/282.72 Found (fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 282.31/282.72 Found fa0:=(fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))):((P (fun (X:fofType)=> b))->(P (fun (X:fofType)=> b)))
% 282.31/282.72 Found (fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 282.31/282.72 Found (fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 282.31/282.72 Found eq_ref000:=(eq_ref00 P):((P f)->(P f))
% 282.31/282.72 Found (eq_ref00 P) as proof of (P0 f)
% 282.31/282.72 Found ((eq_ref0 f) P) as proof of (P0 f)
% 282.31/282.72 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 282.31/282.72 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 282.31/282.72 Found eq_ref00:=(eq_ref0 f):(((eq (fofType->Prop)) f) f)
% 282.31/282.72 Found (eq_ref0 f) as proof of (((eq (fofType->Prop)) f) f)
% 282.31/282.72 Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) f)
% 282.31/282.72 Found (fun (x00:(b->a))=> ((eq_ref (fofType->Prop)) f)) as proof of (((eq (fofType->Prop)) f) f)
% 282.31/282.72 Found (fun (x00:(b->a))=> ((eq_ref (fofType->Prop)) f)) as proof of (P f)
% 282.31/282.72 Found eq_ref00:=(eq_ref0 (g x)):(((eq Prop) (g x)) (g x))
% 282.31/282.72 Found (eq_ref0 (g x)) as proof of (((eq Prop) (g x)) b0)
% 282.31/282.72 Found ((eq_ref Prop) (g x)) as proof of (((eq Prop) (g x)) b0)
% 282.31/282.72 Found ((eq_ref Prop) (g x)) as proof of (((eq Prop) (g x)) b0)
% 282.31/282.72 Found ((eq_ref Prop) (g x)) as proof of (((eq Prop) (g x)) b0)
% 282.31/282.72 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 282.31/282.72 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 282.31/282.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 282.31/282.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 282.31/282.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 282.31/282.72 Found eq_ref00:=(eq_ref0 (g x)):(((eq Prop) (g x)) (g x))
% 282.31/282.72 Found (eq_ref0 (g x)) as proof of (((eq Prop) (g x)) b0)
% 282.31/282.72 Found ((eq_ref Prop) (g x)) as proof of (((eq Prop) (g x)) b0)
% 282.31/282.72 Found ((eq_ref Prop) (g x)) as proof of (((eq Prop) (g x)) b0)
% 282.31/282.72 Found ((eq_ref Prop) (g x)) as proof of (((eq Prop) (g x)) b0)
% 282.31/282.72 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 282.31/282.72 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 282.31/282.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 282.31/282.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 282.31/282.72 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 282.31/282.72 Found fa0:=(fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))):((P (fun (X:fofType)=> b))->(P (fun (X:fofType)=> b)))
% 282.31/282.72 Found (fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 282.31/282.72 Found (fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 282.31/282.72 Found fa0:=(fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))):((P (fun (X:fofType)=> b))->(P (fun (X:fofType)=> b)))
% 282.31/282.72 Found (fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 282.31/282.72 Found (fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 299.20/299.67 Found eta_expansion000:=(eta_expansion00 b0):(((eq (fofType->Prop)) b0) (fun (x:fofType)=> (b0 x)))
% 299.20/299.67 Found (eta_expansion00 b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 299.20/299.67 Found ((eta_expansion0 Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 299.20/299.67 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 299.20/299.67 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 299.20/299.67 Found (((eta_expansion fofType) Prop) b0) as proof of (((eq (fofType->Prop)) b0) (fun (X:fofType)=> b))
% 299.20/299.67 Found eta_expansion000:=(eta_expansion00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% 299.20/299.67 Found (eta_expansion00 f) as proof of (((eq (fofType->Prop)) f) b0)
% 299.20/299.67 Found ((eta_expansion0 Prop) f) as proof of (((eq (fofType->Prop)) f) b0)
% 299.20/299.67 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b0)
% 299.20/299.67 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b0)
% 299.20/299.67 Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b0)
% 299.20/299.67 Found fa0:=(fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))):((P (fun (X:fofType)=> b))->(P (fun (X:fofType)=> b)))
% 299.20/299.67 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 299.20/299.67 Found (fa (fun (x:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 299.20/299.67 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> b)):(((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (x:fofType)=> b))
% 299.20/299.67 Found (eta_expansion_dep00 (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (X:fofType)=> b))
% 299.20/299.67 Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (X:fofType)=> b))
% 299.20/299.67 Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> b)) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (X:fofType)=> b))
% 299.20/299.67 Found (fun (x00:(b->a))=> (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> b))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> b)) (fun (X:fofType)=> b))
% 299.20/299.67 Found (fun (x00:(b->a))=> (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> b))) as proof of (P (fun (X:fofType)=> b))
% 299.20/299.67 Found fa0:=(fa (fun (x0:(fofType->Prop))=> (P g))):((P g)->(P g))
% 299.20/299.67 Found (fa (fun (x0:(fofType->Prop))=> (P g))) as proof of (P0 g)
% 299.20/299.67 Found (fa (fun (x0:(fofType->Prop))=> (P g))) as proof of (P0 g)
% 299.20/299.67 Found fa0:=(fa (fun (x0:(fofType->Prop))=> (P g))):((P g)->(P g))
% 299.20/299.67 Found (fa (fun (x0:(fofType->Prop))=> (P g))) as proof of (P0 g)
% 299.20/299.67 Found (fa (fun (x0:(fofType->Prop))=> (P g))) as proof of (P0 g)
% 299.20/299.67 Found fa0:=(fa (fun (x:(fofType->Prop))=> (P g))):((P g)->(P g))
% 299.20/299.67 Found (fa (fun (x:(fofType->Prop))=> (P g))) as proof of (P0 g)
% 299.20/299.67 Found (fa (fun (x:(fofType->Prop))=> (P g))) as proof of (P0 g)
% 299.20/299.67 Found fa0:=(fa (fun (x:(fofType->Prop))=> (P g))):((P g)->(P g))
% 299.20/299.67 Found (fa (fun (x:(fofType->Prop))=> (P g))) as proof of (P0 g)
% 299.20/299.67 Found (fa (fun (x:(fofType->Prop))=> (P g))) as proof of (P0 g)
% 299.20/299.67 Found eq_ref000:=(eq_ref00 P):((P f)->(P f))
% 299.20/299.67 Found (eq_ref00 P) as proof of (P0 f)
% 299.20/299.67 Found ((eq_ref0 f) P) as proof of (P0 f)
% 299.20/299.67 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 299.20/299.67 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 299.20/299.67 Found eq_ref000:=(eq_ref00 P):((P f)->(P f))
% 299.20/299.67 Found (eq_ref00 P) as proof of (P0 f)
% 299.20/299.67 Found ((eq_ref0 f) P) as proof of (P0 f)
% 299.20/299.67 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 299.20/299.67 Found (((eq_ref (fofType->Prop)) f) P) as proof of (P0 f)
% 299.20/299.67 Found fa0:=(fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))):((P (fun (X:fofType)=> b))->(P (fun (X:fofType)=> b)))
% 299.20/299.67 Found (fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 299.20/299.67 Found (fa (fun (x1:(fofType->Prop))=> (P (fun (X:fofType)=> b)))) as proof of (P0 (fun (X:fofType)=> b))
% 299.20/299.67 Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=>
%------------------------------------------------------------------------------