%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU829^1 : TPTP v6.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n115.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:33:15 EDT 2014

% Result   : Timeout 300.03s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU829^1 : TPTP v6.1.0. Released v3.7.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n115.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 11:35:41 CDT 2014
% % CPUTime  : 300.03 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0xc441b8>, <kernel.DependentProduct object at 0xc44dd0>) of role type named subseteq_type
% Using role type
% Declaring subseteq:((fofType->Prop)->((fofType->Prop)->Prop))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) subseteq) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (forall (U:fofType), ((X U)->(Y U))))) of role definition named subseteq
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) subseteq) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (forall (U:fofType), ((X U)->(Y U)))))
% Defined: subseteq:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (forall (U:fofType), ((X U)->(Y U))))
% FOF formula (<kernel.Constant object at 0xc441b8>, <kernel.DependentProduct object at 0xc44dd0>) of role type named powerset_type
% Using role type
% Declaring powerset:((fofType->Prop)->((fofType->Prop)->Prop))
% FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) powerset) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> ((subseteq Y) X))) of role definition named poserset
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->Prop))) powerset) (fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> ((subseteq Y) X)))
% Defined: powerset:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> ((subseteq Y) X))
% FOF formula (<kernel.Constant object at 0xc44dd0>, <kernel.DependentProduct object at 0xc26908>) of role type named emptyset_type
% Using role type
% Declaring emptyset:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) emptyset) (fun (X:fofType)=> False)) of role definition named emptyset
% A new definition: (((eq (fofType->Prop)) emptyset) (fun (X:fofType)=> False))
% Defined: emptyset:=(fun (X:fofType)=> False)
% FOF formula (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) of role conjecture named conj
% Conjecture to prove = (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(((eq ((fofType->Prop)->Prop)) (powerset emptyset)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))']
% Parameter fofType:Type.
% Definition subseteq:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> (forall (U:fofType), ((X U)->(Y U)))):((fofType->Prop)->((fofType->Prop)->Prop)).
% Definition powerset:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop))=> ((subseteq Y) X)):((fofType->Prop)->((fofType->Prop)->Prop)).
% Definition emptyset:=(fun (X:fofType)=> False):(fofType->Prop).
% Trying to prove (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (powerset emptyset)):(((eq ((fofType->Prop)->Prop)) (powerset emptyset)) (fun (x:(fofType->Prop))=> ((powerset emptyset) x)))
% Found (eta_expansion_dep00 (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found eta_expansion000:=(eta_expansion00 b):(((eq ((fofType->Prop)->Prop)) b) (fun (x:(fofType->Prop))=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((eta_expansion0 Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found x2:(P (powerset emptyset))
% Found (fun (x2:(P (powerset emptyset)))=> x2) as proof of (P (powerset emptyset))
% Found (fun (x2:(P (powerset emptyset)))=> x2) as proof of (P0 (powerset emptyset))
% Found x2:(P (powerset emptyset))
% Found (fun (x2:(P (powerset emptyset)))=> x2) as proof of (P (powerset emptyset))
% Found (fun (x2:(P (powerset emptyset)))=> x2) as proof of (P0 (powerset emptyset))
% Found x2:(P (powerset emptyset))
% Found (fun (x2:(P (powerset emptyset)))=> x2) as proof of (P (powerset emptyset))
% Found (fun (x2:(P (powerset emptyset)))=> x2) as proof of (P0 (powerset emptyset))
% Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found eta_expansion000:=(eta_expansion00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))):(((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) (fun (x:(fofType->Prop))=> (((eq (fofType->Prop)) x) emptyset)))
% Found (eta_expansion00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found ((eta_expansion0 Prop) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion (fofType->Prop)) Prop) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion (fofType->Prop)) Prop) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion (fofType->Prop)) Prop) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))->(P (fun (x:(fofType->Prop))=> (((eq (fofType->Prop)) x) emptyset))))
% Found (eta_expansion000 P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((eta_expansion00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion0 Prop) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((((eta_expansion (fofType->Prop)) Prop) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((((eta_expansion (fofType->Prop)) Prop) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))->(P (fun (x:(fofType->Prop))=> (((eq (fofType->Prop)) x) emptyset))))
% Found (eta_expansion_dep000 P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found x01:(P ((powerset emptyset) x))
% Found (fun (x01:(P ((powerset emptyset) x)))=> x01) as proof of (P ((powerset emptyset) x))
% Found (fun (x01:(P ((powerset emptyset) x)))=> x01) as proof of (P0 ((powerset emptyset) x))
% Found x01:(P ((powerset emptyset) x))
% Found (fun (x01:(P ((powerset emptyset) x)))=> x01) as proof of (P ((powerset emptyset) x))
% Found (fun (x01:(P ((powerset emptyset) x)))=> x01) as proof of (P0 ((powerset emptyset) x))
% Found eq_ref000:=(eq_ref00 P):((P (((eq (fofType->Prop)) x) emptyset))->(P (((eq (fofType->Prop)) x) emptyset)))
% Found (eq_ref00 P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref0 (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P (((eq (fofType->Prop)) x) emptyset))->(P (((eq (fofType->Prop)) x) emptyset)))
% Found (eq_ref00 P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref0 (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found x:(P (powerset emptyset))
% Instantiate: b:=(powerset emptyset):((fofType->Prop)->Prop)
% Found x as proof of (P0 b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))):(((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) (fun (x:(fofType->Prop))=> (((eq (fofType->Prop)) x) emptyset)))
% Found (eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found x:(P (powerset emptyset))
% Instantiate: f:=(powerset emptyset):((fofType->Prop)->Prop)
% Found x as proof of (P0 f)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq (fofType->Prop)) x0) emptyset))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq (fofType->Prop)) x0) emptyset))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq (fofType->Prop)) x0) emptyset))
% Found (fun (x0:(fofType->Prop))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq (fofType->Prop)) x0) emptyset))
% Found (fun (x0:(fofType->Prop))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (((eq (fofType->Prop)) x) emptyset)))
% Found x:(P (powerset emptyset))
% Instantiate: f:=(powerset emptyset):((fofType->Prop)->Prop)
% Found x as proof of (P0 f)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq (fofType->Prop)) x0) emptyset))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq (fofType->Prop)) x0) emptyset))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq (fofType->Prop)) x0) emptyset))
% Found (fun (x0:(fofType->Prop))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq (fofType->Prop)) x0) emptyset))
% Found (fun (x0:(fofType->Prop))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (((eq (fofType->Prop)) x) emptyset)))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 (powerset emptyset)):(((eq ((fofType->Prop)->Prop)) (powerset emptyset)) (powerset emptyset))
% Found (eq_ref0 (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq ((fofType->Prop)->Prop)) b) (fun (x:(fofType->Prop))=> (b x)))
% Found (eta_expansion_dep00 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found x:(P (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Instantiate: b:=(fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)):((fofType->Prop)->Prop)
% Found x as proof of (P0 b)
% Found eta_expansion000:=(eta_expansion00 (powerset emptyset)):(((eq ((fofType->Prop)->Prop)) (powerset emptyset)) (fun (x:(fofType->Prop))=> ((powerset emptyset) x)))
% Found (eta_expansion00 (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found ((eta_expansion0 Prop) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found (((eta_expansion (fofType->Prop)) Prop) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found (((eta_expansion (fofType->Prop)) Prop) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found (((eta_expansion (fofType->Prop)) Prop) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))):(((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) (fun (x:(fofType->Prop))=> (((eq (fofType->Prop)) x) emptyset)))
% Found (eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found x:(P0 b)
% Instantiate: b:=(fun (Y:(fofType->Prop))=> (forall (U:fofType), ((Y U)->(emptyset U)))):((fofType->Prop)->Prop)
% Found (fun (x:(P0 b))=> x) as proof of (P0 (powerset emptyset))
% Found (fun (P0:(((fofType->Prop)->Prop)->Prop)) (x:(P0 b))=> x) as proof of ((P0 b)->(P0 (powerset emptyset)))
% Found (fun (P0:(((fofType->Prop)->Prop)->Prop)) (x:(P0 b))=> x) as proof of (P b)
% Found x3:(P (powerset emptyset))
% Found (fun (x3:(P (powerset emptyset)))=> x3) as proof of (P (powerset emptyset))
% Found (fun (x3:(P (powerset emptyset)))=> x3) as proof of (P0 (powerset emptyset))
% Found eq_ref00:=(eq_ref0 (powerset emptyset)):(((eq ((fofType->Prop)->Prop)) (powerset emptyset)) (powerset emptyset))
% Found (eq_ref0 (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq ((fofType->Prop)->Prop)) b) (fun (x:(fofType->Prop))=> (b x)))
% Found (eta_expansion_dep00 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found x:(P (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Instantiate: f:=(fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)):((fofType->Prop)->Prop)
% Found x as proof of (P0 f)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((powerset emptyset) x0))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((powerset emptyset) x0))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((powerset emptyset) x0))
% Found (fun (x0:(fofType->Prop))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((powerset emptyset) x0))
% Found (fun (x0:(fofType->Prop))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) ((powerset emptyset) x)))
% Found x:(P (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Instantiate: f:=(fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)):((fofType->Prop)->Prop)
% Found x as proof of (P0 f)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((powerset emptyset) x0))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((powerset emptyset) x0))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((powerset emptyset) x0))
% Found (fun (x0:(fofType->Prop))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((powerset emptyset) x0))
% Found (fun (x0:(fofType->Prop))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) ((powerset emptyset) x)))
% Found x0:(P ((powerset emptyset) x))
% Instantiate: b:=((powerset emptyset) x):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found x0:(P ((powerset emptyset) x))
% Instantiate: b:=((powerset emptyset) x):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eta_expansion000:=(eta_expansion00 (powerset emptyset)):(((eq ((fofType->Prop)->Prop)) (powerset emptyset)) (fun (x:(fofType->Prop))=> ((powerset emptyset) x)))
% Found (eta_expansion00 (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b0)
% Found ((eta_expansion0 Prop) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b0)
% Found (((eta_expansion (fofType->Prop)) Prop) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b0)
% Found (((eta_expansion (fofType->Prop)) Prop) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b0)
% Found (((eta_expansion (fofType->Prop)) Prop) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b0)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b0):(((eq ((fofType->Prop)->Prop)) b0) (fun (x:(fofType->Prop))=> (b0 x)))
% Found (eta_expansion_dep00 b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))):(((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) (fun (x:(fofType->Prop))=> (((eq (fofType->Prop)) x) emptyset)))
% Found (eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))):(((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) (fun (x:(fofType->Prop))=> (((eq (fofType->Prop)) x) emptyset)))
% Found (eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))):(((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) (fun (x:(fofType->Prop))=> (((eq (fofType->Prop)) x) emptyset)))
% Found (eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))->(P (fun (x:(fofType->Prop))=> (((eq (fofType->Prop)) x) emptyset))))
% Found (eta_expansion_dep000 P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))):(((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) (fun (x:(fofType->Prop))=> (((eq (fofType->Prop)) x) emptyset)))
% Found (eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found eq_ref000:=(eq_ref00 P1):((P1 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))->(P1 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))))
% Found (eq_ref00 P1) as proof of (P2 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((eq_ref0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P1) as proof of (P2 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eq_ref ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P1) as proof of (P2 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eq_ref ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P1) as proof of (P2 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found eq_ref000:=(eq_ref00 P1):((P1 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))->(P1 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))))
% Found (eq_ref00 P1) as proof of (P2 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((eq_ref0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P1) as proof of (P2 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eq_ref ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P1) as proof of (P2 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eq_ref ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P1) as proof of (P2 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))->(P1 (fun (x:(fofType->Prop))=> (((eq (fofType->Prop)) x) emptyset))))
% Found (eta_expansion000 P1) as proof of (P2 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((eta_expansion00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P1) as proof of (P2 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion0 Prop) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P1) as proof of (P2 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((((eta_expansion (fofType->Prop)) Prop) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P1) as proof of (P2 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((((eta_expansion (fofType->Prop)) Prop) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P1) as proof of (P2 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found eta_expansion0000:=(eta_expansion000 P1):((P1 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))->(P1 (fun (x:(fofType->Prop))=> (((eq (fofType->Prop)) x) emptyset))))
% Found (eta_expansion000 P1) as proof of (P2 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((eta_expansion00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P1) as proof of (P2 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion0 Prop) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P1) as proof of (P2 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((((eta_expansion (fofType->Prop)) Prop) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P1) as proof of (P2 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((((eta_expansion (fofType->Prop)) Prop) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P1) as proof of (P2 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found x2:(P b)
% Found (fun (x2:(P b))=> x2) as proof of (P b)
% Found (fun (x2:(P b))=> x2) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found x2:(P b)
% Found (fun (x2:(P b))=> x2) as proof of (P b)
% Found (fun (x2:(P b))=> x2) as proof of (P0 b)
% Found x2:(P b)
% Found (fun (x2:(P b))=> x2) as proof of (P b)
% Found (fun (x2:(P b))=> x2) as proof of (P0 b)
% Found x01:(P1 ((powerset emptyset) x))
% Found (fun (x01:(P1 ((powerset emptyset) x)))=> x01) as proof of (P1 ((powerset emptyset) x))
% Found (fun (x01:(P1 ((powerset emptyset) x)))=> x01) as proof of (P2 ((powerset emptyset) x))
% Found x01:(P1 ((powerset emptyset) x))
% Found (fun (x01:(P1 ((powerset emptyset) x)))=> x01) as proof of (P1 ((powerset emptyset) x))
% Found (fun (x01:(P1 ((powerset emptyset) x)))=> x01) as proof of (P2 ((powerset emptyset) x))
% Found x01:(P1 ((powerset emptyset) x))
% Found (fun (x01:(P1 ((powerset emptyset) x)))=> x01) as proof of (P1 ((powerset emptyset) x))
% Found (fun (x01:(P1 ((powerset emptyset) x)))=> x01) as proof of (P2 ((powerset emptyset) x))
% Found x01:(P1 ((powerset emptyset) x))
% Found (fun (x01:(P1 ((powerset emptyset) x)))=> x01) as proof of (P1 ((powerset emptyset) x))
% Found (fun (x01:(P1 ((powerset emptyset) x)))=> x01) as proof of (P2 ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 b0):(((eq ((fofType->Prop)->Prop)) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))):(((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) (fun (x:(fofType->Prop))=> (((eq (fofType->Prop)) x) emptyset)))
% Found (eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b0)
% Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b0)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b0)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b0)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b0)
% Found eq_ref000:=(eq_ref00 P):((P (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))->(P (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))))
% Found (eq_ref00 P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((eq_ref0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eq_ref ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eq_ref ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found x0:(P0 b)
% Instantiate: b:=(forall (U:fofType), ((x U)->(emptyset U))):Prop
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 ((powerset emptyset) x))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 ((powerset emptyset) x)))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found x0:(P0 b)
% Instantiate: b:=(forall (U:fofType), ((x U)->(emptyset U))):Prop
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 ((powerset emptyset) x))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 ((powerset emptyset) x)))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% Found x02:(P ((powerset emptyset) x))
% Found (fun (x02:(P ((powerset emptyset) x)))=> x02) as proof of (P ((powerset emptyset) x))
% Found (fun (x02:(P ((powerset emptyset) x)))=> x02) as proof of (P0 ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found x02:(P ((powerset emptyset) x))
% Found (fun (x02:(P ((powerset emptyset) x)))=> x02) as proof of (P ((powerset emptyset) x))
% Found (fun (x02:(P ((powerset emptyset) x)))=> x02) as proof of (P0 ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found x0:(P (((eq (fofType->Prop)) x) emptyset))
% Instantiate: b:=(((eq (fofType->Prop)) x) emptyset):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found x0:(P (((eq (fofType->Prop)) x) emptyset))
% Instantiate: b:=(((eq (fofType->Prop)) x) emptyset):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eta_expansion000:=(eta_expansion00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))):(((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) (fun (x:(fofType->Prop))=> (((eq (fofType->Prop)) x) emptyset)))
% Found (eta_expansion00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b0)
% Found ((eta_expansion0 Prop) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b0)
% Found (((eta_expansion (fofType->Prop)) Prop) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b0)
% Found (((eta_expansion (fofType->Prop)) Prop) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b0)
% Found (((eta_expansion (fofType->Prop)) Prop) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq ((fofType->Prop)->Prop)) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) b)
% Found x0:(P (((eq (fofType->Prop)) x) emptyset))
% Instantiate: b:=(((eq (fofType->Prop)) x) emptyset):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found x0:(P (((eq (fofType->Prop)) x) emptyset))
% Instantiate: b:=(((eq (fofType->Prop)) x) emptyset):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))->(P (fun (x:(fofType->Prop))=> (((eq (fofType->Prop)) x) emptyset))))
% Found (eta_expansion_dep000 P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found eq_ref000:=(eq_ref00 P):((P (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))->(P (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))))
% Found (eq_ref00 P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((eq_ref0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eq_ref ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eq_ref ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))->(P (fun (x:(fofType->Prop))=> (((eq (fofType->Prop)) x) emptyset))))
% Found (eta_expansion_dep000 P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found eq_ref000:=(eq_ref00 P):((P (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))->(P (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))))
% Found (eq_ref00 P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((eq_ref0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eq_ref ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eq_ref ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found eq_ref00:=(eq_ref0 (powerset emptyset)):(((eq ((fofType->Prop)->Prop)) (powerset emptyset)) (powerset emptyset))
% Found (eq_ref0 (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found eta_expansion000:=(eta_expansion00 b):(((eq ((fofType->Prop)->Prop)) b) (fun (x:(fofType->Prop))=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((eta_expansion0 Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b0)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b0)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b0)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b0)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b0)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b0)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found x2:(P (powerset emptyset))
% Found (fun (x2:(P (powerset emptyset)))=> x2) as proof of (P (powerset emptyset))
% Found (fun (x2:(P (powerset emptyset)))=> x2) as proof of (P0 (powerset emptyset))
% Found eq_ref00:=(eq_ref0 (b x)):(((eq Prop) (b x)) (b x))
% Found (eq_ref0 (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 (b x)):(((eq Prop) (b x)) (b x))
% Found (eq_ref0 (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref000:=(eq_ref00 P1):((P1 (((eq (fofType->Prop)) x) emptyset))->(P1 (((eq (fofType->Prop)) x) emptyset)))
% Found (eq_ref00 P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref0 (((eq (fofType->Prop)) x) emptyset)) P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref000:=(eq_ref00 P1):((P1 (((eq (fofType->Prop)) x) emptyset))->(P1 (((eq (fofType->Prop)) x) emptyset)))
% Found (eq_ref00 P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref0 (((eq (fofType->Prop)) x) emptyset)) P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref000:=(eq_ref00 P1):((P1 (((eq (fofType->Prop)) x) emptyset))->(P1 (((eq (fofType->Prop)) x) emptyset)))
% Found (eq_ref00 P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref0 (((eq (fofType->Prop)) x) emptyset)) P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref000:=(eq_ref00 P1):((P1 (((eq (fofType->Prop)) x) emptyset))->(P1 (((eq (fofType->Prop)) x) emptyset)))
% Found (eq_ref00 P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref0 (((eq (fofType->Prop)) x) emptyset)) P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref000:=(eq_ref00 P1):((P1 (((eq (fofType->Prop)) x) emptyset))->(P1 (((eq (fofType->Prop)) x) emptyset)))
% Found (eq_ref00 P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref0 (((eq (fofType->Prop)) x) emptyset)) P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref000:=(eq_ref00 P1):((P1 (((eq (fofType->Prop)) x) emptyset))->(P1 (((eq (fofType->Prop)) x) emptyset)))
% Found (eq_ref00 P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref0 (((eq (fofType->Prop)) x) emptyset)) P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref000:=(eq_ref00 P1):((P1 (((eq (fofType->Prop)) x) emptyset))->(P1 (((eq (fofType->Prop)) x) emptyset)))
% Found (eq_ref00 P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref0 (((eq (fofType->Prop)) x) emptyset)) P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref000:=(eq_ref00 P1):((P1 (((eq (fofType->Prop)) x) emptyset))->(P1 (((eq (fofType->Prop)) x) emptyset)))
% Found (eq_ref00 P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref0 (((eq (fofType->Prop)) x) emptyset)) P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P1) as proof of (P2 (((eq (fofType->Prop)) x) emptyset))
% Found x2:(P (powerset emptyset))
% Found (fun (x2:(P (powerset emptyset)))=> x2) as proof of (P (powerset emptyset))
% Found (fun (x2:(P (powerset emptyset)))=> x2) as proof of (P0 (powerset emptyset))
% Found x2:(P (powerset emptyset))
% Found (fun (x2:(P (powerset emptyset)))=> x2) as proof of (P (powerset emptyset))
% Found (fun (x2:(P (powerset emptyset)))=> x2) as proof of (P0 (powerset emptyset))
% Found eq_ref000:=(eq_ref00 P):((P (((eq (fofType->Prop)) x) emptyset))->(P (((eq (fofType->Prop)) x) emptyset)))
% Found (eq_ref00 P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref0 (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P (((eq (fofType->Prop)) x) emptyset))->(P (((eq (fofType->Prop)) x) emptyset)))
% Found (eq_ref00 P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref0 (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref000:=(eq_ref00 P):((P (((eq (fofType->Prop)) x) emptyset))->(P (((eq (fofType->Prop)) x) emptyset)))
% Found (eq_ref00 P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref0 (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P (((eq (fofType->Prop)) x) emptyset))->(P (((eq (fofType->Prop)) x) emptyset)))
% Found (eq_ref00 P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref0 (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found x01:(P b)
% Found (fun (x01:(P b))=> x01) as proof of (P b)
% Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% Found x01:(P b)
% Found (fun (x01:(P b))=> x01) as proof of (P b)
% Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% Found x01:(P (b x))
% Found (fun (x01:(P (b x)))=> x01) as proof of (P (b x))
% Found (fun (x01:(P (b x)))=> x01) as proof of (P0 (b x))
% Found x01:(P (b x))
% Found (fun (x01:(P (b x)))=> x01) as proof of (P (b x))
% Found (fun (x01:(P (b x)))=> x01) as proof of (P0 (b x))
% Found eta_expansion000:=(eta_expansion00 b0):(((eq ((fofType->Prop)->Prop)) b0) (fun (x:(fofType->Prop))=> (b0 x)))
% Found (eta_expansion00 b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((eta_expansion0 Prop) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion (fofType->Prop)) Prop) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion (fofType->Prop)) Prop) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion (fofType->Prop)) Prop) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found eta_expansion000:=(eta_expansion00 b):(((eq ((fofType->Prop)->Prop)) b) (fun (x:(fofType->Prop))=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0)
% Found ((eta_expansion0 Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0)
% Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0)
% Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0)
% Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) b0)
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found x0:(P0 b)
% Instantiate: b:=(forall (P:((fofType->Prop)->Prop)), ((P x)->(P emptyset))):Prop
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (((eq (fofType->Prop)) x) emptyset)))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found x0:(P0 b)
% Instantiate: b:=(forall (P:((fofType->Prop)->Prop)), ((P x)->(P emptyset))):Prop
% Found (fun (x0:(P0 b))=> x0) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (((eq (fofType->Prop)) x) emptyset)))
% Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% Found x0:(P ((powerset emptyset) x))
% Instantiate: b:=((powerset emptyset) x):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found eq_ref00:=(eq_ref0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))):(((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (eq_ref0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found x0:(P ((powerset emptyset) x))
% Instantiate: b:=((powerset emptyset) x):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found eta_expansion000:=(eta_expansion00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))):(((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) (fun (x:(fofType->Prop))=> (((eq (fofType->Prop)) x) emptyset)))
% Found (eta_expansion00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found ((eta_expansion0 Prop) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion (fofType->Prop)) Prop) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion (fofType->Prop)) Prop) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion (fofType->Prop)) Prop) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))->(P (fun (x:(fofType->Prop))=> (((eq (fofType->Prop)) x) emptyset))))
% Found (eta_expansion_dep000 P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))->(P (fun (x:(fofType->Prop))=> (((eq (fofType->Prop)) x) emptyset))))
% Found (eta_expansion000 P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((eta_expansion00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion0 Prop) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((((eta_expansion (fofType->Prop)) Prop) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((((eta_expansion (fofType->Prop)) Prop) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))->(P (fun (x:(fofType->Prop))=> (((eq (fofType->Prop)) x) emptyset))))
% Found (eta_expansion000 P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((eta_expansion00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion0 Prop) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((((eta_expansion (fofType->Prop)) Prop) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((((eta_expansion (fofType->Prop)) Prop) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))->(P (fun (x:(fofType->Prop))=> (((eq (fofType->Prop)) x) emptyset))))
% Found (eta_expansion_dep000 P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) P) as proof of (P0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found eq_ref000:=(eq_ref00 P):((P (((eq (fofType->Prop)) x) emptyset))->(P (((eq (fofType->Prop)) x) emptyset)))
% Found (eq_ref00 P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref0 (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found x01:(P ((powerset emptyset) x))
% Found (fun (x01:(P ((powerset emptyset) x)))=> x01) as proof of (P ((powerset emptyset) x))
% Found (fun (x01:(P ((powerset emptyset) x)))=> x01) as proof of (P0 ((powerset emptyset) x))
% Found x01:(P ((powerset emptyset) x))
% Found (fun (x01:(P ((powerset emptyset) x)))=> x01) as proof of (P ((powerset emptyset) x))
% Found (fun (x01:(P ((powerset emptyset) x)))=> x01) as proof of (P0 ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((powerset emptyset) x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((powerset emptyset) x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((powerset emptyset) x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((powerset emptyset) x))
% Found x01:(P ((powerset emptyset) x))
% Found (fun (x01:(P ((powerset emptyset) x)))=> x01) as proof of (P ((powerset emptyset) x))
% Found (fun (x01:(P ((powerset emptyset) x)))=> x01) as proof of (P0 ((powerset emptyset) x))
% Found x01:(P ((powerset emptyset) x))
% Found (fun (x01:(P ((powerset emptyset) x)))=> x01) as proof of (P ((powerset emptyset) x))
% Found (fun (x01:(P ((powerset emptyset) x)))=> x01) as proof of (P0 ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((powerset emptyset) x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((powerset emptyset) x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((powerset emptyset) x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((powerset emptyset) x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((powerset emptyset) x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((powerset emptyset) x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((powerset emptyset) x))
% Found eq_ref000:=(eq_ref00 P):((P (((eq (fofType->Prop)) x) emptyset))->(P (((eq (fofType->Prop)) x) emptyset)))
% Found (eq_ref00 P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref0 (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P (((eq (fofType->Prop)) x) emptyset))->(P (((eq (fofType->Prop)) x) emptyset)))
% Found (eq_ref00 P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref0 (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P (((eq (fofType->Prop)) x) emptyset))->(P (((eq (fofType->Prop)) x) emptyset)))
% Found (eq_ref00 P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref0 (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P (((eq (fofType->Prop)) x) emptyset))->(P (((eq (fofType->Prop)) x) emptyset)))
% Found (eq_ref00 P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref0 (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found x2:(P b)
% Found (fun (x2:(P b))=> x2) as proof of (P b)
% Found (fun (x2:(P b))=> x2) as proof of (P0 b)
% Found x2:(P b)
% Found (fun (x2:(P b))=> x2) as proof of (P b)
% Found (fun (x2:(P b))=> x2) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found x01:(P b)
% Found (fun (x01:(P b))=> x01) as proof of (P b)
% Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found x01:(P b)
% Found (fun (x01:(P b))=> x01) as proof of (P b)
% Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% Found x01:(P b)
% Found (fun (x01:(P b))=> x01) as proof of (P b)
% Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% Found x02:(P ((powerset emptyset) x))
% Found (fun (x02:(P ((powerset emptyset) x)))=> x02) as proof of (P ((powerset emptyset) x))
% Found (fun (x02:(P ((powerset emptyset) x)))=> x02) as proof of (P0 ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found x02:(P ((powerset emptyset) x))
% Found (fun (x02:(P ((powerset emptyset) x)))=> x02) as proof of (P ((powerset emptyset) x))
% Found (fun (x02:(P ((powerset emptyset) x)))=> x02) as proof of (P0 ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref000:=(eq_ref00 P):((P (((eq (fofType->Prop)) x) emptyset))->(P (((eq (fofType->Prop)) x) emptyset)))
% Found (eq_ref00 P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref0 (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P (((eq (fofType->Prop)) x) emptyset))->(P (((eq (fofType->Prop)) x) emptyset)))
% Found (eq_ref00 P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref0 (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P (((eq (fofType->Prop)) x) emptyset))->(P (((eq (fofType->Prop)) x) emptyset)))
% Found (eq_ref00 P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref0 (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P (((eq (fofType->Prop)) x) emptyset))->(P (((eq (fofType->Prop)) x) emptyset)))
% Found (eq_ref00 P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref0 (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P (((eq (fofType->Prop)) x) emptyset))->(P (((eq (fofType->Prop)) x) emptyset)))
% Found (eq_ref00 P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref0 (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P (((eq (fofType->Prop)) x) emptyset))->(P (((eq (fofType->Prop)) x) emptyset)))
% Found (eq_ref00 P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref0 (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found (((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) P) as proof of (P0 (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b0)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b0)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b0)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b0)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b0)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b0)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b0)
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b0)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b0)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b0)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b0)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b0)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b0)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 (b x)):(((eq Prop) (b x)) (b x))
% Found (eq_ref0 (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 (b x)):(((eq Prop) (b x)) (b x))
% Found (eq_ref0 (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b0)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b0)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b0)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 (b x)):(((eq Prop) (b x)) (b x))
% Found (eq_ref0 (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 (b x)):(((eq Prop) (b x)) (b x))
% Found (eq_ref0 (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 (b x)):(((eq Prop) (b x)) (b x))
% Found (eq_ref0 (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 (b x)):(((eq Prop) (b x)) (b x))
% Found (eq_ref0 (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found ((eq_ref Prop) (b x)) as proof of (((eq Prop) (b x)) b0)
% Found x01:(P b)
% Found (fun (x01:(P b))=> x01) as proof of (P b)
% Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% Found x01:(P ((powerset emptyset) x))
% Found (fun (x01:(P ((powerset emptyset) x)))=> x01) as proof of (P ((powerset emptyset) x))
% Found (fun (x01:(P ((powerset emptyset) x)))=> x01) as proof of (P0 ((powerset emptyset) x))
% Found x01:(P (b x))
% Found (fun (x01:(P (b x)))=> x01) as proof of (P (b x))
% Found (fun (x01:(P (b x)))=> x01) as proof of (P0 (b x))
% Found x01:(P (b x))
% Found (fun (x01:(P (b x)))=> x01) as proof of (P (b x))
% Found (fun (x01:(P (b x)))=> x01) as proof of (P0 (b x))
% Found x:(P (powerset emptyset))
% Instantiate: b:=(powerset emptyset):((fofType->Prop)->Prop)
% Found x as proof of (P0 b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))):(((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) (fun (x:(fofType->Prop))=> (((eq (fofType->Prop)) x) emptyset)))
% Found (eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found x:(P (powerset emptyset))
% Instantiate: f:=(powerset emptyset):((fofType->Prop)->Prop)
% Found x as proof of (P0 f)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq (fofType->Prop)) x0) emptyset))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq (fofType->Prop)) x0) emptyset))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq (fofType->Prop)) x0) emptyset))
% Found (fun (x0:(fofType->Prop))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq (fofType->Prop)) x0) emptyset))
% Found (fun (x0:(fofType->Prop))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (((eq (fofType->Prop)) x) emptyset)))
% Found x:(P (powerset emptyset))
% Instantiate: f:=(powerset emptyset):((fofType->Prop)->Prop)
% Found x as proof of (P0 f)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq (fofType->Prop)) x0) emptyset))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq (fofType->Prop)) x0) emptyset))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq (fofType->Prop)) x0) emptyset))
% Found (fun (x0:(fofType->Prop))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq (fofType->Prop)) x0) emptyset))
% Found (fun (x0:(fofType->Prop))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) (((eq (fofType->Prop)) x) emptyset)))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq (fofType->Prop)) x) emptyset))
% Found eq_ref00:=(eq_ref0 ((powerset emptyset) x)):(((eq Prop) ((powerset emptyset) x)) ((powerset emptyset) x))
% Found (eq_ref0 ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found ((eq_ref Prop) ((powerset emptyset) x)) as proof of (((eq Prop) ((powerset emptyset) x)) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (powerset emptyset)):(((eq ((fofType->Prop)->Prop)) (powerset emptyset)) (fun (x:(fofType->Prop))=> ((powerset emptyset) x)))
% Found (eta_expansion_dep00 (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq ((fofType->Prop)->Prop)) b) (fun (x:(fofType->Prop))=> (b x)))
% Found (eta_expansion_dep00 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((powerset emptyset) x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((powerset emptyset) x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((powerset emptyset) x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((powerset emptyset) x))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found eq_ref00:=(eq_ref0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))):(((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (eq_ref0 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found x:(P0 b)
% Instantiate: b:=(fun (Y:(fofType->Prop))=> (forall (U:fofType), ((Y U)->(emptyset U)))):((fofType->Prop)->Prop)
% Found (fun (x:(P0 b))=> x) as proof of (P0 (powerset emptyset))
% Found (fun (P0:(((fofType->Prop)->Prop)->Prop)) (x:(P0 b))=> x) as proof of ((P0 b)->(P0 (powerset emptyset)))
% Found (fun (P0:(((fofType->Prop)->Prop)->Prop)) (x:(P0 b))=> x) as proof of (P b)
% Found x:(P (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Instantiate: b:=(fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)):((fofType->Prop)->Prop)
% Found x as proof of (P0 b)
% Found eta_expansion000:=(eta_expansion00 (powerset emptyset)):(((eq ((fofType->Prop)->Prop)) (powerset emptyset)) (fun (x:(fofType->Prop))=> ((powerset emptyset) x)))
% Found (eta_expansion00 (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found ((eta_expansion0 Prop) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found (((eta_expansion (fofType->Prop)) Prop) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found (((eta_expansion (fofType->Prop)) Prop) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found (((eta_expansion (fofType->Prop)) Prop) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found x:(P (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Instantiate: b:=(fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)):((fofType->Prop)->Prop)
% Found x as proof of (P0 b)
% Found eta_expansion000:=(eta_expansion00 (powerset emptyset)):(((eq ((fofType->Prop)->Prop)) (powerset emptyset)) (fun (x:(fofType->Prop))=> ((powerset emptyset) x)))
% Found (eta_expansion00 (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found ((eta_expansion0 Prop) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found (((eta_expansion (fofType->Prop)) Prop) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found (((eta_expansion (fofType->Prop)) Prop) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found (((eta_expansion (fofType->Prop)) Prop) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found x3:(P (powerset emptyset))
% Found (fun (x3:(P (powerset emptyset)))=> x3) as proof of (P (powerset emptyset))
% Found (fun (x3:(P (powerset emptyset)))=> x3) as proof of (P0 (powerset emptyset))
% Found eq_ref00:=(eq_ref0 (powerset emptyset)):(((eq ((fofType->Prop)->Prop)) (powerset emptyset)) (powerset emptyset))
% Found (eq_ref0 (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found ((eq_ref ((fofType->Prop)->Prop)) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq ((fofType->Prop)->Prop)) b) (fun (x:(fofType->Prop))=> (b x)))
% Found (eta_expansion_dep00 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found x:(P (powerset emptyset))
% Instantiate: a:=(powerset emptyset):((fofType->Prop)->Prop)
% Found x as proof of (P0 a)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq ((fofType->Prop)->Prop)) a) (fun (x:(fofType->Prop))=> (a x)))
% Found (eta_expansion_dep00 a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) a) as proof of (((eq ((fofType->Prop)->Prop)) a) b)
% Found eta_expansion000:=(eta_expansion00 b):(((eq ((fofType->Prop)->Prop)) b) (fun (x:(fofType->Prop))=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((eta_expansion0 Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion (fofType->Prop)) Prop) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq ((fofType->Prop)->Prop)) b) (fun (x:(fofType->Prop))=> (b x)))
% Found (eta_expansion_dep00 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (b x))
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b0)
% Found x:(P (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Instantiate: f:=(fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)):((fofType->Prop)->Prop)
% Found x as proof of (P0 f)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((powerset emptyset) x0))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((powerset emptyset) x0))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((powerset emptyset) x0))
% Found (fun (x0:(fofType->Prop))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((powerset emptyset) x0))
% Found (fun (x0:(fofType->Prop))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) ((powerset emptyset) x)))
% Found x:(P (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Instantiate: f:=(fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)):((fofType->Prop)->Prop)
% Found x as proof of (P0 f)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((powerset emptyset) x0))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((powerset emptyset) x0))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((powerset emptyset) x0))
% Found (fun (x0:(fofType->Prop))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((powerset emptyset) x0))
% Found (fun (x0:(fofType->Prop))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) ((powerset emptyset) x)))
% Found x:(P (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Instantiate: f:=(fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)):((fofType->Prop)->Prop)
% Found x as proof of (P0 f)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((powerset emptyset) x0))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((powerset emptyset) x0))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((powerset emptyset) x0))
% Found (fun (x0:(fofType->Prop))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((powerset emptyset) x0))
% Found (fun (x0:(fofType->Prop))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) ((powerset emptyset) x)))
% Found x:(P (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Instantiate: f:=(fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)):((fofType->Prop)->Prop)
% Found x as proof of (P0 f)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((powerset emptyset) x0))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((powerset emptyset) x0))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((powerset emptyset) x0))
% Found (fun (x0:(fofType->Prop))=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((powerset emptyset) x0))
% Found (fun (x0:(fofType->Prop))=> ((eq_ref Prop) (f x0))) as proof of (forall (x:(fofType->Prop)), (((eq Prop) (f x)) ((powerset emptyset) x)))
% Found x0:(P ((powerset emptyset) x))
% Instantiate: b:=((powerset emptyset) x):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found x0:(P ((powerset emptyset) x))
% Instantiate: b:=((powerset emptyset) x):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found x0:(P ((powerset emptyset) x))
% Instantiate: b:=((powerset emptyset) x):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found x0:(P ((powerset emptyset) x))
% Instantiate: b:=((powerset emptyset) x):Prop
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (((eq (fofType->Prop)) x) emptyset)):(((eq Prop) (((eq (fofType->Prop)) x) emptyset)) (((eq (fofType->Prop)) x) emptyset))
% Found (eq_ref0 (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found ((eq_ref Prop) (((eq (fofType->Prop)) x) emptyset)) as proof of (((eq Prop) (((eq (fofType->Prop)) x) emptyset)) b)
% Found eta_expansion000:=(eta_expansion00 (powerset emptyset)):(((eq ((fofType->Prop)->Prop)) (powerset emptyset)) (fun (x:(fofType->Prop))=> ((powerset emptyset) x)))
% Found (eta_expansion00 (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b0)
% Found ((eta_expansion0 Prop) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b0)
% Found (((eta_expansion (fofType->Prop)) Prop) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b0)
% Found (((eta_expansion (fofType->Prop)) Prop) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b0)
% Found (((eta_expansion (fofType->Prop)) Prop) (powerset emptyset)) as proof of (((eq ((fofType->Prop)->Prop)) (powerset emptyset)) b0)
% Found eta_expansion000:=(eta_expansion00 b0):(((eq ((fofType->Prop)->Prop)) b0) (fun (x:(fofType->Prop))=> (b0 x)))
% Found (eta_expansion00 b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found ((eta_expansion0 Prop) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion (fofType->Prop)) Prop) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion (fofType->Prop)) Prop) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found (((eta_expansion (fofType->Prop)) Prop) b0) as proof of (((eq ((fofType->Prop)->Prop)) b0) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset)))
% Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))):(((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) (fun (x:(fofType->Prop))=> (((eq (fofType->Prop)) x) emptyset)))
% Found (eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))):(((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) (fun (x:(fofType->Prop))=> (((eq (fofType->Prop)) x) emptyset)))
% Found (eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))):(((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) (fun (x:(fofType->Prop))=> (((eq (fofType->Prop)) x) emptyset)))
% Found (eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))):(((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) (fun (x:(fofType->Prop))=> (((eq (fofType->Prop)) x) emptyset)))
% Found (eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found ((eq_ref ((fofType->Prop)->Prop)) b) as proof of (((eq ((fofType->Prop)->Prop)) b) (powerset emptyset))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))):(((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) (fun (x:(fofType->Prop))=> (((eq (fofType->Prop)) x) emptyset)))
% Found (eta_expansion_dep00 (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) as proof of (((eq ((fofType->Prop)->Prop)) (fun (X:(fofType->Prop))=> (((eq (fofType->Prop)) X) emptyset))) b)
% Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> Prop)) (fun (X:(fo
% EOF
%------------------------------------------------------------------------------