%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU579^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n104.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 13:32:31 EDT 2014

% Result   : Timeout 300.09s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU579^2 : TPTP v6.1.0. Released v3.7.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n104.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 10:47:31 CDT 2014
% % CPUTime  : 300.09 
% 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 0x23d0dd0>, <kernel.DependentProduct object at 0x23d0560>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x23d0680>, <kernel.DependentProduct object at 0x23d0b90>) of role type named powerset_type
% Using role type
% Declaring powerset:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x23d0d88>, <kernel.Sort object at 0x20b3518>) of role type named powersetI_type
% Using role type
% Declaring powersetI:Prop
% FOF formula (((eq Prop) powersetI) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))->((in B) (powerset A))))) of role definition named powersetI
% A new definition: (((eq Prop) powersetI) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))->((in B) (powerset A)))))
% Defined: powersetI:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))->((in B) (powerset A))))
% FOF formula (<kernel.Constant object at 0x23d0050>, <kernel.Sort object at 0x20b3518>) of role type named powersetE_type
% Using role type
% Declaring powersetE:Prop
% FOF formula (((eq Prop) powersetE) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in B) (powerset A))->(((in Xx) B)->((in Xx) A))))) of role definition named powersetE
% A new definition: (((eq Prop) powersetE) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in B) (powerset A))->(((in Xx) B)->((in Xx) A)))))
% Defined: powersetE:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in B) (powerset A))->(((in Xx) B)->((in Xx) A))))
% FOF formula (<kernel.Constant object at 0x23d0f38>, <kernel.DependentProduct object at 0x21eed40>) of role type named subset_type
% Using role type
% Declaring subset:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x23d0290>, <kernel.Sort object at 0x20b3518>) of role type named subsetI2_type
% Using role type
% Declaring subsetI2:Prop
% FOF formula (((eq Prop) subsetI2) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((subset A) B)))) of role definition named subsetI2
% A new definition: (((eq Prop) subsetI2) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((subset A) B))))
% Defined: subsetI2:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((subset A) B)))
% FOF formula (<kernel.Constant object at 0x23d0680>, <kernel.Sort object at 0x20b3518>) of role type named subsetE_type
% Using role type
% Declaring subsetE:Prop
% FOF formula (((eq Prop) subsetE) (forall (A:fofType) (B:fofType) (Xx:fofType), (((subset A) B)->(((in Xx) A)->((in Xx) B))))) of role definition named subsetE
% A new definition: (((eq Prop) subsetE) (forall (A:fofType) (B:fofType) (Xx:fofType), (((subset A) B)->(((in Xx) A)->((in Xx) B)))))
% Defined: subsetE:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((subset A) B)->(((in Xx) A)->((in Xx) B))))
% FOF formula (powersetI->(powersetE->(subsetI2->(subsetE->(forall (A:fofType) (B:fofType), (((subset A) B)->((subset (powerset A)) (powerset B)))))))) of role conjecture named powersetsubset
% Conjecture to prove = (powersetI->(powersetE->(subsetI2->(subsetE->(forall (A:fofType) (B:fofType), (((subset A) B)->((subset (powerset A)) (powerset B)))))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(powersetI->(powersetE->(subsetI2->(subsetE->(forall (A:fofType) (B:fofType), (((subset A) B)->((subset (powerset A)) (powerset B))))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter powerset:(fofType->fofType).
% Definition powersetI:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))->((in B) (powerset A)))):Prop.
% Definition powersetE:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in B) (powerset A))->(((in Xx) B)->((in Xx) A)))):Prop.
% Parameter subset:(fofType->(fofType->Prop)).
% Definition subsetI2:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((subset A) B))):Prop.
% Definition subsetE:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((subset A) B)->(((in Xx) A)->((in Xx) B)))):Prop.
% Trying to prove (powersetI->(powersetE->(subsetI2->(subsetE->(forall (A:fofType) (B:fofType), (((subset A) B)->((subset (powerset A)) (powerset B))))))))
% Found x4:((in Xx) (powerset A))
% Found x4 as proof of ((in Xx) (powerset A))
% Found x6:((in Xx0) Xx)
% Found x6 as proof of ((in Xx0) Xx)
% Found x6:((in Xx0) Xx)
% Found x6 as proof of ((in Xx0) Xx)
% Found x6:((in Xx0) Xx)
% Found x6 as proof of ((in Xx0) Xx)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A0:=B:fofType
% Found x3 as proof of ((subset A1) A0)
% Found x7:((in Xx1) (powerset A))
% Found x7 as proof of ((in Xx1) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A0:=B:fofType
% Found x3 as proof of ((subset A1) A0)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A0:=B:fofType
% Found x3 as proof of ((subset A1) A0)
% Found x4:((in Xx) (powerset A))
% Found x4 as proof of ((in Xx) (powerset A))
% Found x4:((in Xx) (powerset A))
% Found x4 as proof of ((in Xx) (powerset A))
% Found x5:((in Xx0) B0)
% Instantiate: B0:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B0))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5) as proof of (((in Xx0) B0)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found ((x4 B0) (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found x6:((in Xx1) Xx0)
% Found x6 as proof of ((in Xx1) Xx0)
% Found x6:((in Xx0) B0)
% Instantiate: B0:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B0))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (((in Xx0) B0)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found ((x5 B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found x7:((in Xx1) (powerset A))
% Found x7 as proof of ((in Xx1) (powerset A))
% Found x6:((in Xx0) B0)
% Instantiate: B0:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B0))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (((in Xx0) B0)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found ((x5 B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found x7:((in Xx1) (powerset A))
% Found x7 as proof of ((in Xx1) (powerset A))
% Found x7:((in Xx1) Xx0)
% Found x7 as proof of ((in Xx1) Xx0)
% Found x7:((in Xx1) Xx0)
% Found x7 as proof of ((in Xx1) Xx0)
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A1) B0)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A0:=B:fofType
% Found x3 as proof of ((subset A1) A0)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A00:=B:fofType
% Found x3 as proof of ((subset A1) A00)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A1) B0)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A1) B0)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A00:=B:fofType
% Found x3 as proof of ((subset A1) A00)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A0:=B:fofType
% Found x3 as proof of ((subset A1) A0)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A00:=B:fofType
% Found x3 as proof of ((subset A1) A00)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A0:=B:fofType
% Found x3 as proof of ((subset A1) A0)
% Found x5:((in Xx0) B00)
% Instantiate: B00:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B00))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5) as proof of (((in Xx0) B00)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found ((x4 B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found x5:((in Xx0) B00)
% Instantiate: B00:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B00))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5) as proof of (((in Xx0) B00)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found ((x4 B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found x5:((in Xx0) B0)
% Instantiate: B0:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B0))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5) as proof of (((in Xx0) B0)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found ((x4 B0) (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found x7:((in Xx1) (powerset A))
% Found x7 as proof of ((in Xx1) (powerset A))
% Found x6:((in Xx0) B00)
% Instantiate: B00:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B00))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (((in Xx0) B00)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found ((x5 B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found x6:((in Xx1) Xx0)
% Found x6 as proof of ((in Xx1) Xx0)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x6:((in Xx0) B00)
% Instantiate: B00:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B00))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (((in Xx0) B00)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found ((x5 B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found x6:((in Xx0) B00)
% Instantiate: B00:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B00))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (((in Xx0) B00)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found ((x5 B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found x7:((in Xx1) (powerset A))
% Found x7 as proof of ((in Xx1) (powerset A))
% Found x7:((in Xx1) (powerset A))
% Found x7 as proof of ((in Xx1) (powerset A))
% Found x6:((in Xx0) B00)
% Instantiate: B00:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B00))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (((in Xx0) B00)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found ((x5 B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found x6:((in Xx0) B0)
% Instantiate: B0:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B0))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (((in Xx0) B0)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found ((x5 B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found x8:((in Xx00) (powerset A))
% Found x8 as proof of ((in Xx00) (powerset A))
% Found x6:((in Xx0) B0)
% Instantiate: B0:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B0))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (((in Xx0) B0)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found ((x5 B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found x7:((in Xx1) (powerset A))
% Found x7 as proof of ((in Xx1) (powerset A))
% Found x5:((in Xx0) B0)
% Instantiate: B0:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B0))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5) as proof of (((in Xx0) B0)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found ((x4 B0) (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found x8:((in Xx00) (powerset A))
% Found x8 as proof of ((in Xx00) (powerset A))
% Found x7:((in Xx2) B0)
% Instantiate: B0:=B:fofType
% Found (fun (x7:((in Xx2) B0))=> x7) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x7:((in Xx2) B0))=> x7) as proof of (((in Xx2) B0)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x7:((in Xx2) B0))=> x7) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x7:((in Xx2) B0))=> x7)) as proof of ((in B0) (powerset B))
% Found ((x5 B0) (fun (Xx2:fofType) (x7:((in Xx2) B0))=> x7)) as proof of ((in B0) (powerset B))
% Found ((x5 B0) (fun (Xx2:fofType) (x7:((in Xx2) B0))=> x7)) as proof of ((in B0) (powerset B))
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x7:((in Xx1) Xx0)
% Found x7 as proof of ((in Xx1) Xx0)
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x7:((in Xx1) Xx0)
% Found x7 as proof of ((in Xx1) Xx0)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x6:((in Xx0) B0)
% Instantiate: B0:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B0))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (((in Xx0) B0)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found ((x5 B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) B0)
% Instantiate: B0:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B0))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (((in Xx0) B0)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found ((x5 B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found x8:((in Xx2) B0)
% Instantiate: B0:=B:fofType
% Found (fun (x8:((in Xx2) B0))=> x8) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x8:((in Xx2) B0))=> x8) as proof of (((in Xx2) B0)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x8:((in Xx2) B0))=> x8) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x8:((in Xx2) B0))=> x8)) as proof of ((in B0) (powerset B))
% Found ((x5 B0) (fun (Xx2:fofType) (x8:((in Xx2) B0))=> x8)) as proof of ((in B0) (powerset B))
% Found ((x5 B0) (fun (Xx2:fofType) (x8:((in Xx2) B0))=> x8)) as proof of ((in B0) (powerset B))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x8:((in Xx2) B0)
% Instantiate: B0:=B:fofType
% Found (fun (x8:((in Xx2) B0))=> x8) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x8:((in Xx2) B0))=> x8) as proof of (((in Xx2) B0)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x8:((in Xx2) B0))=> x8) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x8:((in Xx2) B0))=> x8)) as proof of ((in B0) (powerset B))
% Found ((x5 B0) (fun (Xx2:fofType) (x8:((in Xx2) B0))=> x8)) as proof of ((in B0) (powerset B))
% Found ((x5 B0) (fun (Xx2:fofType) (x8:((in Xx2) B0))=> x8)) as proof of ((in B0) (powerset B))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A0:=B:fofType
% Found x3 as proof of ((subset A1) A0)
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A0:=B:fofType
% Found x3 as proof of ((subset A1) A0)
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x3 as proof of ((subset A10) A0)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B00:=B:fofType
% Found x3 as proof of ((subset A1) B00)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B00:=B:fofType
% Found x3 as proof of ((subset A1) B00)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A1) B0)
% Found x4:((in Xx0) (powerset A))
% Found x4 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A00:=B:fofType
% Found x3 as proof of ((subset A1) A00)
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A2) B0)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;A10:=B:fofType
% Found x3 as proof of ((subset A2) A10)
% Found x3:((subset A) B)
% Instantiate: A00:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A00)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B00:=B:fofType
% Found x3 as proof of ((subset A1) B00)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x3 as proof of ((subset A10) A0)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B00:=B:fofType
% Found x3 as proof of ((subset A1) B00)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A00:=B:fofType
% Found x3 as proof of ((subset A1) A00)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B00:=B:fofType
% Found x3 as proof of ((subset A1) B00)
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A1) B0)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A2) B0)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B00:=B:fofType
% Found x3 as proof of ((subset A1) B00)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A00:=B:fofType
% Found x3 as proof of ((subset A1) A00)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x3 as proof of ((subset A10) A0)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;A10:=B:fofType
% Found x3 as proof of ((subset A2) A10)
% Found x3:((subset A) B)
% Instantiate: A00:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A00)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A2) B0)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A1) B0)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A00:=B:fofType
% Found x3 as proof of ((subset A1) A00)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A1) B0)
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;A10:=B:fofType
% Found x3 as proof of ((subset A2) A10)
% Found x3:((subset A) B)
% Instantiate: A00:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A00)
% Found x6:((in Xx1) Xx0)
% Found x6 as proof of ((in Xx1) Xx0)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x5:((in Xx0) B01)
% Instantiate: B01:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B01))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5) as proof of (((in Xx0) B01)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B01)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found ((x4 B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A01:=B:fofType
% Found x3 as proof of ((subset A1) A01)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x5:((in Xx0) B01)
% Instantiate: B01:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B01))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5) as proof of (((in Xx0) B01)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B01)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found ((x4 B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found x5:((in Xx0) B01)
% Instantiate: B01:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B01))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5) as proof of (((in Xx0) B01)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B01)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found ((x4 B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x5:((in Xx0) B01)
% Instantiate: B01:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B01))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5) as proof of (((in Xx0) B01)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B01)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found ((x4 B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found x5:((in Xx0) B00)
% Instantiate: B00:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B00))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5) as proof of (((in Xx0) B00)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found ((x4 B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A00:=B:fofType
% Found x3 as proof of ((subset A1) A00)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x5:((in Xx0) B00)
% Instantiate: B00:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B00))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5) as proof of (((in Xx0) B00)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found ((x4 B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found x5:((in Xx0) B00)
% Instantiate: B00:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B00))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5) as proof of (((in Xx0) B00)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found ((x4 B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A00:=B:fofType
% Found x3 as proof of ((subset A1) A00)
% Found x7:((in Xx2) B00)
% Instantiate: B00:=B:fofType
% Found (fun (x7:((in Xx2) B00))=> x7) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x7:((in Xx2) B00))=> x7) as proof of (((in Xx2) B00)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x7:((in Xx2) B00))=> x7) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x7:((in Xx2) B00))=> x7)) as proof of ((in B00) (powerset B))
% Found ((x5 B00) (fun (Xx2:fofType) (x7:((in Xx2) B00))=> x7)) as proof of ((in B00) (powerset B))
% Found ((x5 B00) (fun (Xx2:fofType) (x7:((in Xx2) B00))=> x7)) as proof of ((in B00) (powerset B))
% Found x6:((in Xx1) Xx0)
% Found x6 as proof of ((in Xx1) Xx0)
% Found x6:((in Xx1) Xx0)
% Found x6 as proof of ((in Xx1) Xx0)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x5:((in Xx0) B0)
% Instantiate: B0:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B0))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5) as proof of (((in Xx0) B0)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found ((x4 B0) (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found x7:((in Xx2) B00)
% Instantiate: B00:=B:fofType
% Found (fun (x7:((in Xx2) B00))=> x7) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x7:((in Xx2) B00))=> x7) as proof of (((in Xx2) B00)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x7:((in Xx2) B00))=> x7) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x7:((in Xx2) B00))=> x7)) as proof of ((in B00) (powerset B))
% Found ((x5 B00) (fun (Xx2:fofType) (x7:((in Xx2) B00))=> x7)) as proof of ((in B00) (powerset B))
% Found ((x5 B00) (fun (Xx2:fofType) (x7:((in Xx2) B00))=> x7)) as proof of ((in B00) (powerset B))
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A1) B0)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x7:((in Xx1) Xx0)
% Found x7 as proof of ((in Xx1) Xx0)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A01:=B:fofType
% Found x3 as proof of ((subset A1) A01)
% Found x6:((in Xx0) B01)
% Instantiate: B01:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B01))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6) as proof of (((in Xx0) B01)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B01)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found ((x5 B01) (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A1) B0)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A01:=B:fofType
% Found x3 as proof of ((subset A1) A01)
% Found x6:((in Xx0) B01)
% Instantiate: B01:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B01))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6) as proof of (((in Xx0) B01)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B01)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found ((x5 B01) (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found x6:((in Xx0) B01)
% Instantiate: B01:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B01))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6) as proof of (((in Xx0) B01)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B01)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found ((x5 B01) (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found x6:((in Xx0) B01)
% Instantiate: B01:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B01))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6) as proof of (((in Xx0) B01)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B01)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found ((x5 B01) (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found x7:((in Xx1) Xx0)
% Found x7 as proof of ((in Xx1) Xx0)
% Found x7:((in Xx2) B0)
% Instantiate: B0:=B:fofType
% Found (fun (x7:((in Xx2) B0))=> x7) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x7:((in Xx2) B0))=> x7) as proof of (((in Xx2) B0)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x7:((in Xx2) B0))=> x7) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x7:((in Xx2) B0))=> x7)) as proof of ((in B0) (powerset B))
% Found ((x5 B0) (fun (Xx2:fofType) (x7:((in Xx2) B0))=> x7)) as proof of ((in B0) (powerset B))
% Found ((x5 B0) (fun (Xx2:fofType) (x7:((in Xx2) B0))=> x7)) as proof of ((in B0) (powerset B))
% Found x6:((in Xx0) B01)
% Instantiate: B01:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B01))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6) as proof of (((in Xx0) B01)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B01)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found ((x5 B01) (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found x6:((in Xx0) B01)
% Instantiate: B01:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B01))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6) as proof of (((in Xx0) B01)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B01)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found ((x5 B01) (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found x6:((in Xx0) B01)
% Instantiate: B01:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B01))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6) as proof of (((in Xx0) B01)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B01)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found ((x5 B01) (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found x6:((in Xx0) B00)
% Instantiate: B00:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B00))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (((in Xx0) B00)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found ((x5 B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A0:=B:fofType
% Found x3 as proof of ((subset A1) A0)
% Found x6:((in Xx0) B01)
% Instantiate: B01:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B01))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6) as proof of (((in Xx0) B01)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B01)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found ((x5 B01) (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x6:((in Xx0) B01))=> x6)) as proof of ((in B01) (powerset (powerset B)))
% Found x6:((in Xx0) B00)
% Instantiate: B00:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B00))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (((in Xx0) B00)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found ((x5 B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found x6:((in Xx0) B00)
% Instantiate: B00:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B00))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (((in Xx0) B00)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found ((x5 B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found x6:((in Xx0) B00)
% Instantiate: B00:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B00))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (((in Xx0) B00)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found ((x5 B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found x7:((in Xx1) Xx0)
% Found x7 as proof of ((in Xx1) Xx0)
% Found x7:((in Xx1) Xx0)
% Found x7 as proof of ((in Xx1) Xx0)
% Found x6:((in Xx0) B00)
% Instantiate: B00:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B00))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (((in Xx0) B00)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found ((x5 B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found x6:((in Xx0) B00)
% Instantiate: B00:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B00))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (((in Xx0) B00)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found ((x5 B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found x6:((in Xx0) B0)
% Instantiate: B0:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B0))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (((in Xx0) B0)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found ((x5 B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found x5:((in Xx0) B00)
% Instantiate: B00:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B00))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5) as proof of (((in Xx0) B00)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found ((x4 B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found x8:((in Xx2) B00)
% Instantiate: B00:=B:fofType
% Found (fun (x8:((in Xx2) B00))=> x8) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x8:((in Xx2) B00))=> x8) as proof of (((in Xx2) B00)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x8:((in Xx2) B00))=> x8) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x8:((in Xx2) B00))=> x8)) as proof of ((in B00) (powerset B))
% Found ((x5 B00) (fun (Xx2:fofType) (x8:((in Xx2) B00))=> x8)) as proof of ((in B00) (powerset B))
% Found ((x5 B00) (fun (Xx2:fofType) (x8:((in Xx2) B00))=> x8)) as proof of ((in B00) (powerset B))
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) A0)
% Found x5:((in Xx0) B00)
% Instantiate: B00:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B00))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5) as proof of (((in Xx0) B00)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found ((x4 B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A0:=B:fofType
% Found x3 as proof of ((subset A1) A0)
% Found x7:((in Xx1) Xx0)
% Found x7 as proof of ((in Xx1) Xx0)
% Found x7:((in Xx1) Xx0)
% Found x7 as proof of ((in Xx1) Xx0)
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) B0)
% Instantiate: B0:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B0))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (((in Xx0) B0)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found ((x5 B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found x5:((in Xx0) B0)
% Instantiate: B0:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B0))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5) as proof of (((in Xx0) B0)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found ((x4 B0) (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found x5:((in Xx0) B00)
% Instantiate: B00:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B00))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5) as proof of (((in Xx0) B00)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found ((x4 B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found x8:((in Xx2) B00)
% Instantiate: B00:=B:fofType
% Found (fun (x8:((in Xx2) B00))=> x8) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x8:((in Xx2) B00))=> x8) as proof of (((in Xx2) B00)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x8:((in Xx2) B00))=> x8) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x8:((in Xx2) B00))=> x8)) as proof of ((in B00) (powerset B))
% Found ((x5 B00) (fun (Xx2:fofType) (x8:((in Xx2) B00))=> x8)) as proof of ((in B00) (powerset B))
% Found ((x5 B00) (fun (Xx2:fofType) (x8:((in Xx2) B00))=> x8)) as proof of ((in B00) (powerset B))
% Found x8:((in Xx2) B00)
% Instantiate: B00:=B:fofType
% Found (fun (x8:((in Xx2) B00))=> x8) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x8:((in Xx2) B00))=> x8) as proof of (((in Xx2) B00)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x8:((in Xx2) B00))=> x8) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x8:((in Xx2) B00))=> x8)) as proof of ((in B00) (powerset B))
% Found ((x5 B00) (fun (Xx2:fofType) (x8:((in Xx2) B00))=> x8)) as proof of ((in B00) (powerset B))
% Found ((x5 B00) (fun (Xx2:fofType) (x8:((in Xx2) B00))=> x8)) as proof of ((in B00) (powerset B))
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x5:((in Xx0) B0)
% Instantiate: B0:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B0))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5) as proof of (((in Xx0) B0)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found ((x4 B0) (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found x5:((in Xx0) B0)
% Instantiate: B0:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B0))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5) as proof of (((in Xx0) B0)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found ((x4 B0) (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx1) Xx0)
% Found x6 as proof of ((in Xx1) Xx0)
% Found x5:((in Xx0) B00)
% Instantiate: B00:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B00))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5) as proof of (((in Xx0) B00)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found ((x4 B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found x8:((in Xx2) B00)
% Instantiate: B00:=B:fofType
% Found (fun (x8:((in Xx2) B00))=> x8) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x8:((in Xx2) B00))=> x8) as proof of (((in Xx2) B00)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x8:((in Xx2) B00))=> x8) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x8:((in Xx2) B00))=> x8)) as proof of ((in B00) (powerset B))
% Found ((x5 B00) (fun (Xx2:fofType) (x8:((in Xx2) B00))=> x8)) as proof of ((in B00) (powerset B))
% Found ((x5 B00) (fun (Xx2:fofType) (x8:((in Xx2) B00))=> x8)) as proof of ((in B00) (powerset B))
% Found x8:((in Xx2) B0)
% Instantiate: B0:=B:fofType
% Found (fun (x8:((in Xx2) B0))=> x8) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x8:((in Xx2) B0))=> x8) as proof of (((in Xx2) B0)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x8:((in Xx2) B0))=> x8) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x8:((in Xx2) B0))=> x8)) as proof of ((in B0) (powerset B))
% Found ((x5 B0) (fun (Xx2:fofType) (x8:((in Xx2) B0))=> x8)) as proof of ((in B0) (powerset B))
% Found ((x5 B0) (fun (Xx2:fofType) (x8:((in Xx2) B0))=> x8)) as proof of ((in B0) (powerset B))
% Found x7:((in Xx2) B0)
% Instantiate: B0:=B:fofType
% Found (fun (x7:((in Xx2) B0))=> x7) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x7:((in Xx2) B0))=> x7) as proof of (((in Xx2) B0)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x7:((in Xx2) B0))=> x7) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x7:((in Xx2) B0))=> x7)) as proof of ((in B0) (powerset B))
% Found ((x5 B0) (fun (Xx2:fofType) (x7:((in Xx2) B0))=> x7)) as proof of ((in B0) (powerset B))
% Found ((x5 B0) (fun (Xx2:fofType) (x7:((in Xx2) B0))=> x7)) as proof of ((in B0) (powerset B))
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x5:((in Xx0) B0)
% Instantiate: B0:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B0))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5) as proof of (((in Xx0) B0)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found ((x4 B0) (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A0:=B:fofType
% Found x3 as proof of ((subset A1) A0)
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x8:((in Xx2) B0)
% Instantiate: B0:=B:fofType
% Found (fun (x8:((in Xx2) B0))=> x8) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x8:((in Xx2) B0))=> x8) as proof of (((in Xx2) B0)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x8:((in Xx2) B0))=> x8) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x8:((in Xx2) B0))=> x8)) as proof of ((in B0) (powerset B))
% Found ((x5 B0) (fun (Xx2:fofType) (x8:((in Xx2) B0))=> x8)) as proof of ((in B0) (powerset B))
% Found ((x5 B0) (fun (Xx2:fofType) (x8:((in Xx2) B0))=> x8)) as proof of ((in B0) (powerset B))
% Found x6:((in Xx0) B00)
% Instantiate: B00:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B00))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (((in Xx0) B00)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found ((x5 B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found x6:((in Xx0) B00)
% Instantiate: B00:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B00))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (((in Xx0) B00)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found ((x5 B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) A0)
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) B00)
% Instantiate: B00:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B00))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (((in Xx0) B00)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found ((x5 B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x4:((in Xx0) (powerset A))
% Found x4 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) B00)
% Instantiate: B00:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B00))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (((in Xx0) B00)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found ((x5 B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found x6:((in Xx0) B0)
% Instantiate: B0:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B0))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (((in Xx0) B0)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found ((x5 B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found x6:((in Xx0) B00)
% Instantiate: B00:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B00))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (((in Xx0) B00)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found ((x5 B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A0:=B:fofType
% Found x3 as proof of ((subset A1) A0)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A0:=B:fofType
% Found x3 as proof of ((subset A1) A0)
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) B0)
% Instantiate: B0:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B0))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (((in Xx0) B0)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found ((x5 B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) B0)
% Instantiate: B0:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B0))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (((in Xx0) B0)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found ((x5 B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) B0)
% Instantiate: B0:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B0))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (((in Xx0) B0)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found ((x5 B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found x6:((in Xx0) B00)
% Instantiate: B00:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B00))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (((in Xx0) B00)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found ((x5 B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) A0)
% Found x6:((in Xx0) B0)
% Instantiate: B0:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B0))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (((in Xx0) B0)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found ((x5 B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) B0)
% Instantiate: B0:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B0))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (((in Xx0) B0)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found ((x5 B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) B00)
% Instantiate: B00:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B00))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (((in Xx0) B00)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found ((x5 B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found x7:((in Xx1) Xx0)
% Found x7 as proof of ((in Xx1) Xx0)
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) B00)
% Instantiate: B00:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B00))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (((in Xx0) B00)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found ((x5 B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x6:((in Xx0) B00))=> x6)) as proof of ((in B00) (powerset (powerset B)))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A0:=B:fofType
% Found x3 as proof of ((subset A1) A0)
% Found x7:((in Xx1) Xx0)
% Found x7 as proof of ((in Xx1) Xx0)
% Found x8:((in Xx2) B0)
% Instantiate: B0:=B:fofType
% Found (fun (x8:((in Xx2) B0))=> x8) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x8:((in Xx2) B0))=> x8) as proof of (((in Xx2) B0)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x8:((in Xx2) B0))=> x8) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x8:((in Xx2) B0))=> x8)) as proof of ((in B0) (powerset B))
% Found ((x5 B0) (fun (Xx2:fofType) (x8:((in Xx2) B0))=> x8)) as proof of ((in B0) (powerset B))
% Found ((x5 B0) (fun (Xx2:fofType) (x8:((in Xx2) B0))=> x8)) as proof of ((in B0) (powerset B))
% Found x6:((in Xx0) B0)
% Instantiate: B0:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B0))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (((in Xx0) B0)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found ((x5 B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) B0)
% Instantiate: B0:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B0))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (((in Xx0) B0)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found ((x5 B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found x8:((in Xx2) B0)
% Instantiate: B0:=B:fofType
% Found (fun (x8:((in Xx2) B0))=> x8) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x8:((in Xx2) B0))=> x8) as proof of (((in Xx2) B0)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x8:((in Xx2) B0))=> x8) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x8:((in Xx2) B0))=> x8)) as proof of ((in B0) (powerset B))
% Found ((x5 B0) (fun (Xx2:fofType) (x8:((in Xx2) B0))=> x8)) as proof of ((in B0) (powerset B))
% Found ((x5 B0) (fun (Xx2:fofType) (x8:((in Xx2) B0))=> x8)) as proof of ((in B0) (powerset B))
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x5:((in Xx0) B0)
% Instantiate: B0:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B0))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5) as proof of (((in Xx0) B0)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found ((x4 B0) (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x8:((in Xx00) (powerset A))
% Found x8 as proof of ((in Xx00) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x3 as proof of ((subset A10) A0)
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A00:=B:fofType
% Found x3 as proof of ((subset A1) A00)
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x8:((in Xx00) (powerset A))
% Found x8 as proof of ((in Xx00) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x3 as proof of ((subset A10) A0)
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A00:=B:fofType
% Found x3 as proof of ((subset A1) A00)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x4:((in Xx) (powerset A))
% Instantiate: A00:=(powerset A):fofType;B0:=Xx:fofType
% Found x4 as proof of ((in B0) A00)
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A1) B0)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x6:((in Xx0) B0)
% Instantiate: B0:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B0))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (((in Xx0) B0)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found ((x5 B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x7:((in Xx1) (powerset A))
% Instantiate: A00:=(powerset A):fofType;B0:=Xx1:fofType
% Found x7 as proof of ((in B0) A00)
% Found x6:((in Xx0) B0)
% Instantiate: B0:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B0))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (((in Xx0) B0)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found ((x5 B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x6:((in Xx0) B0))=> x6)) as proof of ((in B0) (powerset (powerset B)))
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A1) B0)
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x3:((subset A) B)
% Instantiate: A00:=A:fofType
% Found x3 as proof of ((subset A00) B)
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;A10:=B:fofType
% Found x3 as proof of ((subset A2) A10)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B00:=B:fofType
% Found x3 as proof of ((subset A1) B00)
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x4:((in Xx0) (powerset A))
% Found x4 as proof of ((in Xx0) (powerset A))
% Found x4:((in Xx0) (powerset A))
% Found x4 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B00:=B:fofType
% Found x3 as proof of ((subset A1) B00)
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A00:=A:fofType
% Found x3 as proof of ((subset A00) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x3 as proof of ((subset A10) A0)
% Found x3:((subset A) B)
% Instantiate: A20:=A:fofType
% Found x3 as proof of ((subset A20) A1)
% Found x3 as proof of ((subset A20) A1)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A11:=A:fofType
% Found x3 as proof of ((subset A11) A0)
% Found x3 as proof of ((subset A11) A0)
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A2) B0)
% Found x3:((subset A) B)
% Instantiate: A00:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A00)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x4:((in Xx0) (powerset A))
% Found x4 as proof of ((in Xx0) (powerset A))
% Found x4:((in Xx0) (powerset A))
% Found x4 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A3:=B:fofType;A4:=A:fofType
% Found x3 as proof of ((subset A4) A3)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B01:=B:fofType
% Found x3 as proof of ((subset A1) B01)
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x3:((subset A) B)
% Instantiate: A00:=A:fofType
% Found x3 as proof of ((subset A00) B)
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;A10:=B:fofType
% Found x3 as proof of ((subset A2) A10)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) B0)
% Found x3 as proof of ((subset A10) B0)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x3 as proof of ((subset A10) A0)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x3 as proof of ((subset A10) A0)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B00:=B:fofType
% Found x3 as proof of ((subset A1) B00)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B01:=B:fofType
% Found x3 as proof of ((subset A1) B01)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B01:=B:fofType
% Found x3 as proof of ((subset A1) B01)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A00:=B:fofType
% Found x3 as proof of ((subset A1) A00)
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B01:=B:fofType
% Found x3 as proof of ((subset A1) B01)
% Found x3:((subset A) B)
% Instantiate: B00:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) B00)
% Found x3:((subset A) B)
% Instantiate: A00:=A:fofType
% Found x3 as proof of ((subset A00) B)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;A10:=B:fofType
% Found x3 as proof of ((subset A2) A10)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B00:=B:fofType
% Found x3 as proof of ((subset A1) B00)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B00:=B:fofType
% Found x3 as proof of ((subset A1) B00)
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A00:=A:fofType
% Found x3 as proof of ((subset A00) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: B00:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) B00)
% Found x3:((subset A) B)
% Instantiate: B00:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) B00)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x3 as proof of ((subset A10) A0)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A20:=A:fofType
% Found x3 as proof of ((subset A20) A1)
% Found x3 as proof of ((subset A20) A1)
% Found x3:((subset A) B)
% Instantiate: A11:=A:fofType
% Found x3 as proof of ((subset A11) A0)
% Found x3 as proof of ((subset A11) A0)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A00)
% Found x3 as proof of ((subset A10) A00)
% Found x6:((in Xx1) Xx0)
% Found x6 as proof of ((in Xx1) Xx0)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A01:=B:fofType
% Found x3 as proof of ((subset A1) A01)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A3) B0)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A2) B0)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B00:=B:fofType
% Found x3 as proof of ((subset A1) B00)
% Found x3:((subset A) B)
% Instantiate: A00:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A00)
% Found x3:((subset A) B)
% Instantiate: A3:=B:fofType;A4:=A:fofType
% Found x3 as proof of ((subset A4) A3)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A1) B0)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x4:((in Xx0) (powerset A))
% Found x4 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A00:=A:fofType
% Found x3 as proof of ((subset A00) B)
% Found x3:((subset A) B)
% Instantiate: A20:=A:fofType
% Found x3 as proof of ((subset A20) A1)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A10:=B:fofType
% Found x3 as proof of ((subset A3) A10)
% Found x6:((in Xx1) Xx0)
% Found x6 as proof of ((in Xx1) Xx0)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A00:=B:fofType
% Found x3 as proof of ((subset A3) A00)
% Found x3:((subset A) B)
% Instantiate: A20:=B:fofType;A3:=A:fofType
% Found x3 as proof of ((subset A3) A20)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x3 as proof of ((subset A10) A0)
% Found x3:((subset A) B)
% Instantiate: A20:=A:fofType
% Found x3 as proof of ((subset A20) A1)
% Found x3 as proof of ((subset A20) A1)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A11:=A:fofType
% Found x3 as proof of ((subset A11) A0)
% Found x3 as proof of ((subset A11) A0)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A10:=B:fofType
% Found x3 as proof of ((subset A3) A10)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A20:=A:fofType
% Found x3 as proof of ((subset A20) A1)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B01:=B:fofType
% Found x3 as proof of ((subset A1) B01)
% Found x3:((subset A) B)
% Instantiate: A3:=B:fofType;A4:=A:fofType
% Found x3 as proof of ((subset A4) A3)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x6:((in Xx1) Xx0)
% Found x6 as proof of ((in Xx1) Xx0)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A2) B0)
% Found x3:((subset A) B)
% Instantiate: A00:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A00)
% Found x5:((in Xx1) (powerset A))
% Found x5 as proof of ((in Xx1) (powerset A))
% Found x5:((in Xx1) (powerset A))
% Found x5 as proof of ((in Xx1) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x7:((in Xx2) B01)
% Instantiate: B01:=B:fofType
% Found (fun (x7:((in Xx2) B01))=> x7) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x7:((in Xx2) B01))=> x7) as proof of (((in Xx2) B01)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x7:((in Xx2) B01))=> x7) as proof of (forall (Xx:fofType), (((in Xx) B01)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x7:((in Xx2) B01))=> x7)) as proof of ((in B01) (powerset B))
% Found ((x5 B01) (fun (Xx2:fofType) (x7:((in Xx2) B01))=> x7)) as proof of ((in B01) (powerset B))
% Found ((x5 B01) (fun (Xx2:fofType) (x7:((in Xx2) B01))=> x7)) as proof of ((in B01) (powerset B))
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A00:=B:fofType
% Found x3 as proof of ((subset A1) A00)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B01:=B:fofType
% Found x3 as proof of ((subset A1) B01)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B01:=B:fofType
% Found x3 as proof of ((subset A1) B01)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B01:=B:fofType
% Found x3 as proof of ((subset A1) B01)
% Found x3:((subset A) B)
% Instantiate: A3:=B:fofType;A4:=A:fofType
% Found x3 as proof of ((subset A4) A3)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A3:=B:fofType;A4:=A:fofType
% Found x3 as proof of ((subset A4) A3)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) B0)
% Found x3 as proof of ((subset A10) B0)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x3 as proof of ((subset A10) A0)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x3 as proof of ((subset A10) A0)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x6:((in Xx1) Xx0)
% Found x6 as proof of ((in Xx1) Xx0)
% Found x6:((in Xx1) Xx0)
% Found x6 as proof of ((in Xx1) Xx0)
% Found x6:((in Xx1) Xx0)
% Found x6 as proof of ((in Xx1) Xx0)
% Found x6:((in Xx1) Xx0)
% Found x6 as proof of ((in Xx1) Xx0)
% Found x4:((in Xx0) (powerset A))
% Found x4 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A10:=B:fofType
% Found x3 as proof of ((subset A3) A10)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A11:=A:fofType
% Found x3 as proof of ((subset A11) A0)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A00:=B:fofType
% Found x3 as proof of ((subset A1) A00)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: B00:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) B00)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B01:=B:fofType
% Found x3 as proof of ((subset A1) B01)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B01:=B:fofType
% Found x3 as proof of ((subset A1) B01)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B01:=B:fofType
% Found x3 as proof of ((subset A1) B01)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A00:=B:fofType
% Found x3 as proof of ((subset A1) A00)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) B0)
% Found x7:((in Xx2) B01)
% Instantiate: B01:=B:fofType
% Found (fun (x7:((in Xx2) B01))=> x7) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x7:((in Xx2) B01))=> x7) as proof of (((in Xx2) B01)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x7:((in Xx2) B01))=> x7) as proof of (forall (Xx:fofType), (((in Xx) B01)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x7:((in Xx2) B01))=> x7)) as proof of ((in B01) (powerset B))
% Found ((x5 B01) (fun (Xx2:fofType) (x7:((in Xx2) B01))=> x7)) as proof of ((in B01) (powerset B))
% Found ((x5 B01) (fun (Xx2:fofType) (x7:((in Xx2) B01))=> x7)) as proof of ((in B01) (powerset B))
% Found x7:((in Xx2) B01)
% Instantiate: B01:=B:fofType
% Found (fun (x7:((in Xx2) B01))=> x7) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x7:((in Xx2) B01))=> x7) as proof of (((in Xx2) B01)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x7:((in Xx2) B01))=> x7) as proof of (forall (Xx:fofType), (((in Xx) B01)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x7:((in Xx2) B01))=> x7)) as proof of ((in B01) (powerset B))
% Found ((x5 B01) (fun (Xx2:fofType) (x7:((in Xx2) B01))=> x7)) as proof of ((in B01) (powerset B))
% Found ((x5 B01) (fun (Xx2:fofType) (x7:((in Xx2) B01))=> x7)) as proof of ((in B01) (powerset B))
% Found x3:((subset A) B)
% Instantiate: A00:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A00)
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;A10:=B:fofType
% Found x3 as proof of ((subset A2) A10)
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;A10:=B:fofType
% Found x3 as proof of ((subset A2) A10)
% Found x3:((subset A) B)
% Instantiate: A00:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A00)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: B00:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) B00)
% Found x3:((subset A) B)
% Instantiate: B00:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) B00)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B01:=B:fofType
% Found x3 as proof of ((subset A1) B01)
% Found x3:((subset A) B)
% Instantiate: B00:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) B00)
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x6:((in Xx0) (powerset A))
% Found x6 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) B0)
% Found x3 as proof of ((subset A10) B0)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x3 as proof of ((subset A10) A0)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x3 as proof of ((subset A10) A0)
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;A10:=B:fofType
% Found x3 as proof of ((subset A2) A10)
% Found x3:((subset A) B)
% Instantiate: B00:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) B00)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x7:((in Xx1) Xx0)
% Found x7 as proof of ((in Xx1) Xx0)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A3) B0)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: B00:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) B00)
% Found x3:((subset A) B)
% Instantiate: B00:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) B00)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A00)
% Found x3 as proof of ((subset A10) A00)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B00:=B:fofType
% Found x3 as proof of ((subset A1) B00)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A00:=B:fofType
% Found x3 as proof of ((subset A1) A00)
% Found x5:((in Xx0) B02)
% Instantiate: B02:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B02))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5) as proof of (((in Xx0) B02)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B02)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found ((x4 B02) (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found (((x (powerset B)) B02) (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found (((x (powerset B)) B02) (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found x3:((subset A) B)
% Instantiate: A3:=B:fofType;A4:=A:fofType
% Found x3 as proof of ((subset A4) A3)
% Found x7:((in Xx2) B01)
% Instantiate: B01:=B:fofType
% Found (fun (x7:((in Xx2) B01))=> x7) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x7:((in Xx2) B01))=> x7) as proof of (((in Xx2) B01)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x7:((in Xx2) B01))=> x7) as proof of (forall (Xx:fofType), (((in Xx) B01)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x7:((in Xx2) B01))=> x7)) as proof of ((in B01) (powerset B))
% Found ((x5 B01) (fun (Xx2:fofType) (x7:((in Xx2) B01))=> x7)) as proof of ((in B01) (powerset B))
% Found ((x5 B01) (fun (Xx2:fofType) (x7:((in Xx2) B01))=> x7)) as proof of ((in B01) (powerset B))
% Found x7:((in Xx2) B00)
% Instantiate: B00:=B:fofType
% Found (fun (x7:((in Xx2) B00))=> x7) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x7:((in Xx2) B00))=> x7) as proof of (((in Xx2) B00)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x7:((in Xx2) B00))=> x7) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x7:((in Xx2) B00))=> x7)) as proof of ((in B00) (powerset B))
% Found ((x5 B00) (fun (Xx2:fofType) (x7:((in Xx2) B00))=> x7)) as proof of ((in B00) (powerset B))
% Found ((x5 B00) (fun (Xx2:fofType) (x7:((in Xx2) B00))=> x7)) as proof of ((in B00) (powerset B))
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x3:((subset A) B)
% Instantiate: A20:=A:fofType
% Found x3 as proof of ((subset A20) A1)
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A01:=B:fofType
% Found x3 as proof of ((subset A1) A01)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A10:=B:fofType
% Found x3 as proof of ((subset A3) A10)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A00:=B:fofType
% Found x3 as proof of ((subset A3) A00)
% Found x3:((subset A) B)
% Instantiate: A20:=B:fofType;A3:=A:fofType
% Found x3 as proof of ((subset A3) A20)
% Found x7:((in Xx1) Xx0)
% Found x7 as proof of ((in Xx1) Xx0)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x7:((in Xx1) Xx0)
% Found x7 as proof of ((in Xx1) Xx0)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A3) B0)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A1) B0)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A10:=B:fofType
% Found x3 as proof of ((subset A3) A10)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A3) B0)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x5:((in Xx0) B02)
% Instantiate: B02:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B02))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5) as proof of (((in Xx0) B02)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B02)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found ((x4 B02) (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found (((x (powerset B)) B02) (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found (((x (powerset B)) B02) (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found x5:((in Xx0) B02)
% Instantiate: B02:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B02))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5) as proof of (((in Xx0) B02)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B02)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found ((x4 B02) (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found (((x (powerset B)) B02) (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found (((x (powerset B)) B02) (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found x5:((in Xx0) B02)
% Instantiate: B02:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B02))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5) as proof of (((in Xx0) B02)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B02)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found ((x4 B02) (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found (((x (powerset B)) B02) (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found (((x (powerset B)) B02) (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found x6:((in Xx1) Xx0)
% Found x6 as proof of ((in Xx1) Xx0)
% Found x6:((in Xx1) Xx0)
% Found x6 as proof of ((in Xx1) Xx0)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B00:=B:fofType
% Found x3 as proof of ((subset A1) B00)
% Found x3:((subset A) B)
% Instantiate: A3:=B:fofType;A4:=A:fofType
% Found x3 as proof of ((subset A4) A3)
% Found x3:((subset A) B)
% Instantiate: A20:=A:fofType
% Found x3 as proof of ((subset A20) A1)
% Found x3:((subset A) B)
% Instantiate: A20:=B:fofType;A3:=A:fofType
% Found x3 as proof of ((subset A3) A20)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A00:=B:fofType
% Found x3 as proof of ((subset A3) A00)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A2) B0)
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A2) B0)
% Found x3:((subset A) B)
% Instantiate: A20:=A:fofType
% Found x3 as proof of ((subset A20) A1)
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A00:=B:fofType
% Found x3 as proof of ((subset A3) A00)
% Found x3:((subset A) B)
% Instantiate: A20:=B:fofType;A3:=A:fofType
% Found x3 as proof of ((subset A3) A20)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A10:=B:fofType
% Found x3 as proof of ((subset A3) A10)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A00)
% Found x3 as proof of ((subset A10) A00)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x3 as proof of ((subset A10) A0)
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;A10:=B:fofType
% Found x3 as proof of ((subset A2) A10)
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;A01:=B:fofType
% Found x3 as proof of ((subset A2) A01)
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;A11:=B:fofType
% Found x3 as proof of ((subset A2) A11)
% Found x3:((subset A) B)
% Instantiate: A00:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A00)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A10:=B:fofType
% Found x3 as proof of ((subset A3) A10)
% Found x7:((in Xx1) Xx0)
% Found x7 as proof of ((in Xx1) Xx0)
% Found x7:((in Xx1) Xx0)
% Found x7 as proof of ((in Xx1) Xx0)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A00:=B:fofType
% Found x3 as proof of ((subset A1) A00)
% Found x5:((in Xx0) B02)
% Instantiate: B02:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B02))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5) as proof of (((in Xx0) B02)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B02)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found ((x4 B02) (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found (((x (powerset B)) B02) (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found (((x (powerset B)) B02) (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found x5:((in Xx0) B02)
% Instantiate: B02:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B02))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5) as proof of (((in Xx0) B02)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B02)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found ((x4 B02) (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found (((x (powerset B)) B02) (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found (((x (powerset B)) B02) (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found x5:((in Xx0) B02)
% Instantiate: B02:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B02))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5) as proof of (((in Xx0) B02)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B02)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found ((x4 B02) (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found (((x (powerset B)) B02) (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found (((x (powerset B)) B02) (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found x7:((in Xx2) B00)
% Instantiate: B00:=B:fofType
% Found (fun (x7:((in Xx2) B00))=> x7) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x7:((in Xx2) B00))=> x7) as proof of (((in Xx2) B00)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x7:((in Xx2) B00))=> x7) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x7:((in Xx2) B00))=> x7)) as proof of ((in B00) (powerset B))
% Found ((x5 B00) (fun (Xx2:fofType) (x7:((in Xx2) B00))=> x7)) as proof of ((in B00) (powerset B))
% Found ((x5 B00) (fun (Xx2:fofType) (x7:((in Xx2) B00))=> x7)) as proof of ((in B00) (powerset B))
% Found x6:((in Xx1) (powerset A))
% Found x6 as proof of ((in Xx1) (powerset A))
% Found x6:((in Xx1) (powerset A))
% Found x6 as proof of ((in Xx1) (powerset A))
% Found x7:((in Xx2) B00)
% Instantiate: B00:=B:fofType
% Found (fun (x7:((in Xx2) B00))=> x7) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x7:((in Xx2) B00))=> x7) as proof of (((in Xx2) B00)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x7:((in Xx2) B00))=> x7) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x7:((in Xx2) B00))=> x7)) as proof of ((in B00) (powerset B))
% Found ((x5 B00) (fun (Xx2:fofType) (x7:((in Xx2) B00))=> x7)) as proof of ((in B00) (powerset B))
% Found ((x5 B00) (fun (Xx2:fofType) (x7:((in Xx2) B00))=> x7)) as proof of ((in B00) (powerset B))
% Found x5:((in Xx0) B01)
% Instantiate: B01:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B01))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5) as proof of (((in Xx0) B01)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B01)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found ((x4 B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A01:=B:fofType
% Found x3 as proof of ((subset A1) A01)
% Found x3:((subset A) B)
% Instantiate: A20:=A:fofType
% Found x3 as proof of ((subset A20) A1)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A00:=B:fofType
% Found x3 as proof of ((subset A1) A00)
% Found x6:((in Xx1) (powerset A))
% Found x6 as proof of ((in Xx1) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B00:=B:fofType
% Found x3 as proof of ((subset A1) B00)
% Found x6:((in Xx1) (powerset A))
% Found x6 as proof of ((in Xx1) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A1) B0)
% Found x3:((subset A) B)
% Instantiate: A3:=B:fofType;A4:=A:fofType
% Found x3 as proof of ((subset A4) A3)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A10:=B:fofType
% Found x3 as proof of ((subset A3) A10)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x5:((in Xx0) B02)
% Instantiate: B02:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B02))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5) as proof of (((in Xx0) B02)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B02)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found ((x4 B02) (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found (((x (powerset B)) B02) (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found (((x (powerset B)) B02) (fun (Xx0:fofType) (x5:((in Xx0) B02))=> x5)) as proof of ((in B02) (powerset (powerset B)))
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x5:((in Xx0) B01)
% Instantiate: B01:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B01))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5) as proof of (((in Xx0) B01)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B01)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found ((x4 B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found x8:((in Xx2) B01)
% Instantiate: B01:=B:fofType
% Found (fun (x8:((in Xx2) B01))=> x8) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8) as proof of (((in Xx2) B01)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8) as proof of (forall (Xx:fofType), (((in Xx) B01)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8)) as proof of ((in B01) (powerset B))
% Found ((x5 B01) (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8)) as proof of ((in B01) (powerset B))
% Found ((x5 B01) (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8)) as proof of ((in B01) (powerset B))
% Found x5:((in Xx0) B01)
% Instantiate: B01:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B01))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5) as proof of (((in Xx0) B01)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B01)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found ((x4 B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found x7:((in Xx1) Xx0)
% Found x7 as proof of ((in Xx1) Xx0)
% Found x5:((in Xx0) B01)
% Instantiate: B01:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B01))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5) as proof of (((in Xx0) B01)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B01)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found ((x4 B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found x5:((in Xx0) B01)
% Instantiate: B01:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B01))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5) as proof of (((in Xx0) B01)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B01)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found ((x4 B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found x7:((in Xx1) Xx0)
% Found x7 as proof of ((in Xx1) Xx0)
% Found x7:((in Xx1) Xx0)
% Found x7 as proof of ((in Xx1) Xx0)
% Found x7:((in Xx1) Xx0)
% Found x7 as proof of ((in Xx1) Xx0)
% Found x7:((in Xx1) Xx0)
% Found x7 as proof of ((in Xx1) Xx0)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) A0)
% Found x3:((subset A) B)
% Instantiate: A11:=A:fofType
% Found x3 as proof of ((subset A11) A0)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A00:=B:fofType
% Found x3 as proof of ((subset A1) A00)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A00:=B:fofType
% Found x3 as proof of ((subset A1) A00)
% Found x6:((in Xx1) (powerset A))
% Found x6 as proof of ((in Xx1) (powerset A))
% Found x6:((in Xx1) (powerset A))
% Found x6 as proof of ((in Xx1) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x7:((in Xx2) B0)
% Instantiate: B0:=B:fofType
% Found (fun (x7:((in Xx2) B0))=> x7) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x7:((in Xx2) B0))=> x7) as proof of (((in Xx2) B0)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x7:((in Xx2) B0))=> x7) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x7:((in Xx2) B0))=> x7)) as proof of ((in B0) (powerset B))
% Found ((x5 B0) (fun (Xx2:fofType) (x7:((in Xx2) B0))=> x7)) as proof of ((in B0) (powerset B))
% Found ((x5 B0) (fun (Xx2:fofType) (x7:((in Xx2) B0))=> x7)) as proof of ((in B0) (powerset B))
% Found x3:((subset A) B)
% Instantiate: A3:=B:fofType;A4:=A:fofType
% Found x3 as proof of ((subset A4) A3)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x7:((in Xx2) B0)
% Instantiate: B0:=B:fofType
% Found (fun (x7:((in Xx2) B0))=> x7) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x7:((in Xx2) B0))=> x7) as proof of (((in Xx2) B0)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x7:((in Xx2) B0))=> x7) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x7:((in Xx2) B0))=> x7)) as proof of ((in B0) (powerset B))
% Found ((x5 B0) (fun (Xx2:fofType) (x7:((in Xx2) B0))=> x7)) as proof of ((in B0) (powerset B))
% Found ((x5 B0) (fun (Xx2:fofType) (x7:((in Xx2) B0))=> x7)) as proof of ((in B0) (powerset B))
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A10:=B:fofType
% Found x3 as proof of ((subset A3) A10)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A2) B0)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) B0)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x3 as proof of ((subset A10) A0)
% Found x5:((in Xx0) B01)
% Instantiate: B01:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B01))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5) as proof of (((in Xx0) B01)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B01)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found ((x4 B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found x5:((in Xx0) B01)
% Instantiate: B01:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B01))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5) as proof of (((in Xx0) B01)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B01)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found ((x4 B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A00)
% Found x5:((in Xx0) B01)
% Instantiate: B01:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B01))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5) as proof of (((in Xx0) B01)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B01)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found ((x4 B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found (((x (powerset B)) B01) (fun (Xx0:fofType) (x5:((in Xx0) B01))=> x5)) as proof of ((in B01) (powerset (powerset B)))
% Found x5:((in Xx0) (powerset A))
% Found x5 as proof of ((in Xx0) (powerset A))
% Found x5:((in Xx0) B00)
% Instantiate: B00:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B00))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5) as proof of (((in Xx0) B00)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found ((x4 B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x3:((subset A) B)
% Instantiate: A00:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A00)
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;A10:=B:fofType
% Found x3 as proof of ((subset A2) A10)
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;A10:=B:fofType
% Found x3 as proof of ((subset A2) A10)
% Found x3:((subset A) B)
% Instantiate: A00:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A00)
% Found x7:((in Xx1) Xx0)
% Found x7 as proof of ((in Xx1) Xx0)
% Found x3:((subset A) B)
% Instantiate: A11:=A:fofType
% Found x3 as proof of ((subset A11) A0)
% Found x7:((in Xx1) Xx0)
% Found x7 as proof of ((in Xx1) Xx0)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A00:=B:fofType
% Found x3 as proof of ((subset A1) A00)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;A01:=B:fofType
% Found x3 as proof of ((subset A2) A01)
% Found x7:((in Xx1) Xx0)
% Found x7 as proof of ((in Xx1) Xx0)
% Found x7:((in Xx1) Xx0)
% Found x7 as proof of ((in Xx1) Xx0)
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;A10:=B:fofType
% Found x3 as proof of ((subset A2) A10)
% Found x6:((in Xx1) (powerset A))
% Found x6 as proof of ((in Xx1) (powerset A))
% Found x6:((in Xx1) (powerset A))
% Found x6 as proof of ((in Xx1) (powerset A))
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A00:=B:fofType
% Found x3 as proof of ((subset A1) A00)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;A10:=B:fofType
% Found x3 as proof of ((subset A2) A10)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x8:((in Xx2) B01)
% Instantiate: B01:=B:fofType
% Found (fun (x8:((in Xx2) B01))=> x8) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8) as proof of (((in Xx2) B01)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8) as proof of (forall (Xx:fofType), (((in Xx) B01)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8)) as proof of ((in B01) (powerset B))
% Found ((x5 B01) (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8)) as proof of ((in B01) (powerset B))
% Found ((x5 B01) (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8)) as proof of ((in B01) (powerset B))
% Found x8:((in Xx2) B01)
% Instantiate: B01:=B:fofType
% Found (fun (x8:((in Xx2) B01))=> x8) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8) as proof of (((in Xx2) B01)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8) as proof of (forall (Xx:fofType), (((in Xx) B01)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8)) as proof of ((in B01) (powerset B))
% Found ((x5 B01) (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8)) as proof of ((in B01) (powerset B))
% Found ((x5 B01) (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8)) as proof of ((in B01) (powerset B))
% Found x8:((in Xx2) B01)
% Instantiate: B01:=B:fofType
% Found (fun (x8:((in Xx2) B01))=> x8) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8) as proof of (((in Xx2) B01)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8) as proof of (forall (Xx:fofType), (((in Xx) B01)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8)) as proof of ((in B01) (powerset B))
% Found ((x5 B01) (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8)) as proof of ((in B01) (powerset B))
% Found ((x5 B01) (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8)) as proof of ((in B01) (powerset B))
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;A10:=B:fofType
% Found x3 as proof of ((subset A2) A10)
% Found x3:((subset A) B)
% Instantiate: A00:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A00)
% Found x3:((subset A) B)
% Instantiate: B00:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) B00)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B0)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) A0)
% Found x6:((in Xx0) Xx)
% Instantiate: A00:=Xx:fofType;B0:=Xx0:fofType
% Found x6 as proof of ((in B0) A00)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) B0)
% Found x5:((in Xx0) B00)
% Instantiate: B00:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B00))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5) as proof of (((in Xx0) B00)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found ((x4 B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found x5:((in Xx0) B00)
% Instantiate: B00:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B00))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5) as proof of (((in Xx0) B00)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found ((x4 B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found x5:((in Xx0) B00)
% Instantiate: B00:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B00))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5) as proof of (((in Xx0) B00)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found ((x4 B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found (((x (powerset B)) B00) (fun (Xx0:fofType) (x5:((in Xx0) B00))=> x5)) as proof of ((in B00) (powerset (powerset B)))
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;A10:=B:fofType
% Found x3 as proof of ((subset A2) A10)
% Found x3:((subset A) B)
% Instantiate: A00:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A00)
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;A10:=B:fofType
% Found x3 as proof of ((subset A2) A10)
% Found x3:((subset A) B)
% Instantiate: A00:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A00)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;A01:=B:fofType
% Found x3 as proof of ((subset A1) A01)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B00:=B:fofType
% Found x3 as proof of ((subset A1) B00)
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;A10:=B:fofType
% Found x3 as proof of ((subset A2) A10)
% Found x6:((in Xx0) B02)
% Instantiate: B02:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B02))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6) as proof of (((in Xx0) B02)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B02)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6)) as proof of ((in B02) (powerset (powerset B)))
% Found ((x5 B02) (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6)) as proof of ((in B02) (powerset (powerset B)))
% Found (((x (powerset B)) B02) (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6)) as proof of ((in B02) (powerset (powerset B)))
% Found (((x (powerset B)) B02) (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6)) as proof of ((in B02) (powerset (powerset B)))
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x3:((subset A) B)
% Instantiate: B00:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) B00)
% Found x6:((in Xx1) Xx0)
% Found x6 as proof of ((in Xx1) Xx0)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A1) B0)
% Found x5:((in Xx0) B0)
% Instantiate: B0:=(powerset B):fofType
% Found (fun (x5:((in Xx0) B0))=> x5) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5) as proof of (((in Xx0) B0)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) (powerset B))))
% Found (x40 (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found ((x4 B0) (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found (((x (powerset B)) B0) (fun (Xx0:fofType) (x5:((in Xx0) B0))=> x5)) as proof of ((in B0) (powerset (powerset B)))
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A3) B0)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B00:=B:fofType
% Found x3 as proof of ((subset A1) B00)
% Found x6:((in Xx1) Xx0)
% Found x6 as proof of ((in Xx1) Xx0)
% Found x6:((in Xx1) Xx0)
% Found x6 as proof of ((in Xx1) Xx0)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x6:((in Xx0) B02)
% Instantiate: B02:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B02))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6) as proof of (((in Xx0) B02)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B02)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6)) as proof of ((in B02) (powerset (powerset B)))
% Found ((x5 B02) (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6)) as proof of ((in B02) (powerset (powerset B)))
% Found (((x (powerset B)) B02) (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6)) as proof of ((in B02) (powerset (powerset B)))
% Found (((x (powerset B)) B02) (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6)) as proof of ((in B02) (powerset (powerset B)))
% Found x6:((in Xx0) B02)
% Instantiate: B02:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B02))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6) as proof of (((in Xx0) B02)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B02)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6)) as proof of ((in B02) (powerset (powerset B)))
% Found ((x5 B02) (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6)) as proof of ((in B02) (powerset (powerset B)))
% Found (((x (powerset B)) B02) (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6)) as proof of ((in B02) (powerset (powerset B)))
% Found (((x (powerset B)) B02) (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6)) as proof of ((in B02) (powerset (powerset B)))
% Found x6:((in Xx0) B02)
% Instantiate: B02:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B02))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6) as proof of (((in Xx0) B02)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B02)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6)) as proof of ((in B02) (powerset (powerset B)))
% Found ((x5 B02) (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6)) as proof of ((in B02) (powerset (powerset B)))
% Found (((x (powerset B)) B02) (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6)) as proof of ((in B02) (powerset (powerset B)))
% Found (((x (powerset B)) B02) (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6)) as proof of ((in B02) (powerset (powerset B)))
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B00:=B:fofType
% Found x3 as proof of ((subset A1) B00)
% Found x8:((in Xx2) B01)
% Instantiate: B01:=B:fofType
% Found (fun (x8:((in Xx2) B01))=> x8) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8) as proof of (((in Xx2) B01)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8) as proof of (forall (Xx:fofType), (((in Xx) B01)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8)) as proof of ((in B01) (powerset B))
% Found ((x5 B01) (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8)) as proof of ((in B01) (powerset B))
% Found ((x5 B01) (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8)) as proof of ((in B01) (powerset B))
% Found x8:((in Xx2) B01)
% Instantiate: B01:=B:fofType
% Found (fun (x8:((in Xx2) B01))=> x8) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8) as proof of (((in Xx2) B01)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8) as proof of (forall (Xx:fofType), (((in Xx) B01)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8)) as proof of ((in B01) (powerset B))
% Found ((x5 B01) (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8)) as proof of ((in B01) (powerset B))
% Found ((x5 B01) (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8)) as proof of ((in B01) (powerset B))
% Found x6:((in Xx0) B02)
% Instantiate: B02:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B02))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6) as proof of (((in Xx0) B02)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B02)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6)) as proof of ((in B02) (powerset (powerset B)))
% Found ((x5 B02) (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6)) as proof of ((in B02) (powerset (powerset B)))
% Found (((x (powerset B)) B02) (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6)) as proof of ((in B02) (powerset (powerset B)))
% Found (((x (powerset B)) B02) (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6)) as proof of ((in B02) (powerset (powerset B)))
% Found x8:((in Xx2) B01)
% Instantiate: B01:=B:fofType
% Found (fun (x8:((in Xx2) B01))=> x8) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8) as proof of (((in Xx2) B01)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8) as proof of (forall (Xx:fofType), (((in Xx) B01)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8)) as proof of ((in B01) (powerset B))
% Found ((x5 B01) (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8)) as proof of ((in B01) (powerset B))
% Found ((x5 B01) (fun (Xx2:fofType) (x8:((in Xx2) B01))=> x8)) as proof of ((in B01) (powerset B))
% Found x8:((in Xx2) B00)
% Instantiate: B00:=B:fofType
% Found (fun (x8:((in Xx2) B00))=> x8) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x8:((in Xx2) B00))=> x8) as proof of (((in Xx2) B00)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x8:((in Xx2) B00))=> x8) as proof of (forall (Xx:fofType), (((in Xx) B00)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x8:((in Xx2) B00))=> x8)) as proof of ((in B00) (powerset B))
% Found ((x5 B00) (fun (Xx2:fofType) (x8:((in Xx2) B00))=> x8)) as proof of ((in B00) (powerset B))
% Found ((x5 B00) (fun (Xx2:fofType) (x8:((in Xx2) B00))=> x8)) as proof of ((in B00) (powerset B))
% Found x3:((subset A) B)
% Instantiate: A20:=B:fofType;A3:=A:fofType
% Found x3 as proof of ((subset A3) A20)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) A0)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A00:=B:fofType
% Found x3 as proof of ((subset A3) A00)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) A1)
% Found x7:((in Xx1) Xx0)
% Found x7 as proof of ((in Xx1) Xx0)
% Found x7:((in Xx1) Xx0)
% Found x7 as proof of ((in Xx1) Xx0)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x7:((in Xx2) B0)
% Instantiate: B0:=B:fofType
% Found (fun (x7:((in Xx2) B0))=> x7) as proof of ((in Xx2) B)
% Found (fun (Xx2:fofType) (x7:((in Xx2) B0))=> x7) as proof of (((in Xx2) B0)->((in Xx2) B))
% Found (fun (Xx2:fofType) (x7:((in Xx2) B0))=> x7) as proof of (forall (Xx:fofType), (((in Xx) B0)->((in Xx) B)))
% Found (x51 (fun (Xx2:fofType) (x7:((in Xx2) B0))=> x7)) as proof of ((in B0) (powerset B))
% Found ((x5 B0) (fun (Xx2:fofType) (x7:((in Xx2) B0))=> x7)) as proof of ((in B0) (powerset B))
% Found ((x5 B0) (fun (Xx2:fofType) (x7:((in Xx2) B0))=> x7)) as proof of ((in B0) (powerset B))
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A2) B0)
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A2) B0)
% Found x3:((subset A) B)
% Instantiate: A1:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A1)
% Found x3:((subset A) B)
% Found x3 as proof of ((subset A) B)
% Found x3:((subset A) B)
% Instantiate: A00:=B:fofType;A2:=A:fofType
% Found x3 as proof of ((subset A2) A00)
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;A11:=B:fofType
% Found x3 as proof of ((subset A2) A11)
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;A10:=B:fofType
% Found x3 as proof of ((subset A2) A10)
% Found x3:((subset A) B)
% Instantiate: A2:=A:fofType;A01:=B:fofType
% Found x3 as proof of ((subset A2) A01)
% Found x4:((in Xx) (powerset A))
% Instantiate: A00:=(powerset A):fofType;B0:=Xx:fofType
% Found x4 as proof of ((in B0) A00)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;A2:=B:fofType
% Found x3 as proof of ((subset A3) A2)
% Found x3:((subset A) B)
% Instantiate: A3:=A:fofType;B0:=B:fofType
% Found x3 as proof of ((subset A3) B0)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x3:((subset A) B)
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((subset A10) A0)
% Found x3:((subset A) B)
% Instantiate: A1:=A:fofType;B00:=B:fofType
% Found x3 as proof of ((subset A1) B00)
% Found x6:((in Xx0) B02)
% Instantiate: B02:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B02))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6) as proof of (((in Xx0) B02)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B02)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6)) as proof of ((in B02) (powerset (powerset B)))
% Found ((x5 B02) (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6)) as proof of ((in B02) (powerset (powerset B)))
% Found (((x (powerset B)) B02) (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6)) as proof of ((in B02) (powerset (powerset B)))
% Found (((x (powerset B)) B02) (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6)) as proof of ((in B02) (powerset (powerset B)))
% Found x6:((in Xx0) B02)
% Instantiate: B02:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B02))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6) as proof of (((in Xx0) B02)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B02)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6)) as proof of ((in B02) (powerset (powerset B)))
% Found ((x5 B02) (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6)) as proof of ((in B02) (powerset (powerset B)))
% Found (((x (powerset B)) B02) (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6)) as proof of ((in B02) (powerset (powerset B)))
% Found (((x (powerset B)) B02) (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6)) as proof of ((in B02) (powerset (powerset B)))
% Found x6:((in Xx0) B02)
% Instantiate: B02:=(powerset B):fofType
% Found (fun (x6:((in Xx0) B02))=> x6) as proof of ((in Xx0) (powerset B))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6) as proof of (((in Xx0) B02)->((in Xx0) (powerset B)))
% Found (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6) as proof of (forall (Xx:fofType), (((in Xx) B02)->((in Xx) (powerset B))))
% Found (x50 (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6)) as proof of ((in B02) (powerset (powerset B)))
% Found ((x5 B02) (fun (Xx0:fofType) (x6:((in Xx0) B02))=> x6)) as pr
% EOF
%------------------------------------------------------------------------------