%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU743^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n103.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 13:32:59 EDT 2014

% Result   : Timeout 300.01s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU743^2 : TPTP v6.1.0. Released v3.7.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n103.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 11:21:21 CDT 2014
% % CPUTime  : 300.01 
% 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 0x1e84710>, <kernel.DependentProduct object at 0x1e84b90>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1d4cf38>, <kernel.DependentProduct object at 0x1e84ef0>) of role type named powerset_type
% Using role type
% Declaring powerset:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x1e843b0>, <kernel.DependentProduct object at 0x1e84680>) of role type named binunion_type
% Using role type
% Declaring binunion:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x1e84518>, <kernel.DependentProduct object at 0x1e84710>) of role type named binintersect_type
% Using role type
% Declaring binintersect:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x1e849e0>, <kernel.Sort object at 0x1d4a9e0>) of role type named binintersectT_lem_type
% Using role type
% Declaring binintersectT_lem:Prop
% FOF formula (((eq Prop) binintersectT_lem) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->((in ((binintersect X) Y)) (powerset A))))))) of role definition named binintersectT_lem
% A new definition: (((eq Prop) binintersectT_lem) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->((in ((binintersect X) Y)) (powerset A)))))))
% Defined: binintersectT_lem:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->((in ((binintersect X) Y)) (powerset A))))))
% FOF formula (<kernel.Constant object at 0x1d48200>, <kernel.Sort object at 0x1d4a9e0>) of role type named binunionT_lem_type
% Using role type
% Declaring binunionT_lem:Prop
% FOF formula (((eq Prop) binunionT_lem) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->((in ((binunion X) Y)) (powerset A))))))) of role definition named binunionT_lem
% A new definition: (((eq Prop) binunionT_lem) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->((in ((binunion X) Y)) (powerset A)))))))
% Defined: binunionT_lem:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->((in ((binunion X) Y)) (powerset A))))))
% FOF formula (<kernel.Constant object at 0x1e848c0>, <kernel.Sort object at 0x1d4a9e0>) of role type named powersetTI1_type
% Using role type
% Declaring powersetTI1:Prop
% FOF formula (((eq Prop) powersetTI1) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->((forall (Xx:fofType), (((in Xx) A)->(((in Xx) X)->((in Xx) Y))))->((in X) (powerset Y)))))))) of role definition named powersetTI1
% A new definition: (((eq Prop) powersetTI1) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->((forall (Xx:fofType), (((in Xx) A)->(((in Xx) X)->((in Xx) Y))))->((in X) (powerset Y))))))))
% Defined: powersetTI1:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->((forall (Xx:fofType), (((in Xx) A)->(((in Xx) X)->((in Xx) Y))))->((in X) (powerset Y)))))))
% FOF formula (<kernel.Constant object at 0x1e848c0>, <kernel.Sort object at 0x1d4a9e0>) of role type named inIntersectImpInIntersectUnions_type
% Using role type
% Declaring inIntersectImpInIntersectUnions:Prop
% FOF formula (((eq Prop) inIntersectImpInIntersectUnions) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((binintersect X) Y))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))))))))))) of role definition named inIntersectImpInIntersectUnions
% A new definition: (((eq Prop) inIntersectImpInIntersectUnions) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((binintersect X) Y))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))))))))))))
% Defined: inIntersectImpInIntersectUnions:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((binintersect X) Y))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))))))))))
% FOF formula (binintersectT_lem->(binunionT_lem->(powersetTI1->(inIntersectImpInIntersectUnions->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->((in ((binintersect X) Y)) (powerset ((binintersect ((binunion X) Z)) ((binunion Y) Z)))))))))))))) of role conjecture named intersectInPowersetIntersectUnions
% Conjecture to prove = (binintersectT_lem->(binunionT_lem->(powersetTI1->(inIntersectImpInIntersectUnions->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->((in ((binintersect X) Y)) (powerset ((binintersect ((binunion X) Z)) ((binunion Y) Z)))))))))))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(binintersectT_lem->(binunionT_lem->(powersetTI1->(inIntersectImpInIntersectUnions->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->((in ((binintersect X) Y)) (powerset ((binintersect ((binunion X) Z)) ((binunion Y) Z))))))))))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter powerset:(fofType->fofType).
% Parameter binunion:(fofType->(fofType->fofType)).
% Parameter binintersect:(fofType->(fofType->fofType)).
% Definition binintersectT_lem:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->((in ((binintersect X) Y)) (powerset A)))))):Prop.
% Definition binunionT_lem:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->((in ((binunion X) Y)) (powerset A)))))):Prop.
% Definition powersetTI1:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->((forall (Xx:fofType), (((in Xx) A)->(((in Xx) X)->((in Xx) Y))))->((in X) (powerset Y))))))):Prop.
% Definition inIntersectImpInIntersectUnions:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((binintersect X) Y))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))))))))))):Prop.
% Trying to prove (binintersectT_lem->(binunionT_lem->(powersetTI1->(inIntersectImpInIntersectUnions->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->((in ((binintersect X) Y)) (powerset ((binintersect ((binunion X) Z)) ((binunion Y) Z))))))))))))))
% Found x6:((in Xx) A0)
% Instantiate: A0:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x7:((in Xx) ((binintersect X) Y)))=> x6) as proof of ((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))
% Found (fun (x6:((in Xx) A0)) (x7:((in Xx) ((binintersect X) Y)))=> x6) as proof of (((in Xx) ((binintersect X) Y))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))
% Found (fun (Xx:fofType) (x6:((in Xx) A0)) (x7:((in Xx) ((binintersect X) Y)))=> x6) as proof of (((in Xx) A0)->(((in Xx) ((binintersect X) Y))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))))
% Found (fun (Xx:fofType) (x6:((in Xx) A0)) (x7:((in Xx) ((binintersect X) Y)))=> x6) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect X) Y))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))))
% Found x3:((in X) (powerset A))
% Instantiate: A0:=A:fofType
% Found x3 as proof of ((in X) (powerset A0))
% Found x4:((in Y) (powerset A))
% Instantiate: A0:=A:fofType
% Found x4 as proof of ((in Y) (powerset A0))
% Found ((x600 x3) x4) as proof of ((in ((binintersect X) Y)) (powerset A0))
% Found (((fun (x7:((in X) (powerset A0)))=> ((x60 x7) Y)) x3) x4) as proof of ((in ((binintersect X) Y)) (powerset A0))
% Found (((fun (x7:((in X) (powerset A0)))=> (((x6 X) x7) Y)) x3) x4) as proof of ((in ((binintersect X) Y)) (powerset A0))
% Found (((fun (x7:((in X) (powerset A0)))=> ((((x A0) X) x7) Y)) x3) x4) as proof of ((in ((binintersect X) Y)) (powerset A0))
% Found (((fun (x7:((in X) (powerset A0)))=> ((((x A0) X) x7) Y)) x3) x4) as proof of ((in ((binintersect X) Y)) (powerset A0))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Instantiate: A0:=A:fofType
% Found x4 as proof of ((in Y) (powerset A0))
% Found x5:((in Z) (powerset A))
% Instantiate: A0:=A:fofType
% Found x5 as proof of ((in Z) (powerset A0))
% Found ((x0000 x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A0))
% Found (((fun (x7:((in Y) (powerset A0)))=> ((x000 x7) Z)) x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A0))
% Found (((fun (x7:((in Y) (powerset A0)))=> (((x00 Y) x7) Z)) x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A0))
% Found (((fun (x7:((in Y) (powerset A0)))=> ((((x0 A0) Y) x7) Z)) x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A0))
% Found (((fun (x7:((in Y) (powerset A0)))=> ((((x0 A0) Y) x7) Z)) x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A0))
% Found x000000:=(x00000 x5):((in ((binunion X) Z)) (powerset A0))
% Found (x00000 x5) as proof of ((in ((binunion X) Z)) (powerset A0))
% Found ((x0000 Z) x5) as proof of ((in ((binunion X) Z)) (powerset A0))
% Found (((x000 x3) Z) x5) as proof of ((in ((binunion X) Z)) (powerset A0))
% Found ((((x00 X) x3) Z) x5) as proof of ((in ((binunion X) Z)) (powerset A0))
% Found (((((x0 A0) X) x3) Z) x5) as proof of ((in ((binunion X) Z)) (powerset A0))
% Found (((((x0 A0) X) x3) Z) x5) as proof of ((in ((binunion X) Z)) (powerset A0))
% Found ((x600 (((((x0 A0) X) x3) Z) x5)) (((fun (x7:((in Y) (powerset A0)))=> ((((x0 A0) Y) x7) Z)) x4) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A0))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A0)))=> ((x60 x7) ((binunion Y) Z))) (((((x0 A0) X) x3) Z) x5)) (((fun (x7:((in Y) (powerset A0)))=> ((((x0 A0) Y) x7) Z)) x4) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A0))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A0)))=> (((x6 ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A0) X) x3) Z) x5)) (((fun (x7:((in Y) (powerset A0)))=> ((((x0 A0) Y) x7) Z)) x4) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A0))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A0)))=> ((((x A0) ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A0) X) x3) Z) x5)) (((fun (x7:((in Y) (powerset A0)))=> ((((x0 A0) Y) x7) Z)) x4) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A0))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A0)))=> ((((x A0) ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A0) X) x3) Z) x5)) (((fun (x7:((in Y) (powerset A0)))=> ((((x0 A0) Y) x7) Z)) x4) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A0))
% Found x6:((in Xx) A00)
% Instantiate: A00:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x7:((in Xx) ((binintersect X) Y)))=> x6) as proof of ((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))
% Found (fun (x6:((in Xx) A00)) (x7:((in Xx) ((binintersect X) Y)))=> x6) as proof of (((in Xx) ((binintersect X) Y))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))
% Found (fun (Xx:fofType) (x6:((in Xx) A00)) (x7:((in Xx) ((binintersect X) Y)))=> x6) as proof of (((in Xx) A00)->(((in Xx) ((binintersect X) Y))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))))
% Found (fun (Xx:fofType) (x6:((in Xx) A00)) (x7:((in Xx) ((binintersect X) Y)))=> x6) as proof of (forall (Xx:fofType), (((in Xx) A00)->(((in Xx) ((binintersect X) Y))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))))
% Found x7:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))
% Found (fun (x7:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A0)
% Found (fun (x6:((in Xx) A1)) (x7:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A0))
% Found (fun (Xx:fofType) (x6:((in Xx) A1)) (x7:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A1)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A0)))
% Found (fun (Xx:fofType) (x6:((in Xx) A1)) (x7:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A0))))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Instantiate: A00:=A:fofType
% Found x4 as proof of ((in Y) (powerset A00))
% Found x3:((in X) (powerset A))
% Instantiate: A00:=A:fofType
% Found x3 as proof of ((in X) (powerset A00))
% Found ((x600 x3) x4) as proof of ((in ((binintersect X) Y)) (powerset A00))
% Found (((fun (x7:((in X) (powerset A00)))=> ((x60 x7) Y)) x3) x4) as proof of ((in ((binintersect X) Y)) (powerset A00))
% Found (((fun (x7:((in X) (powerset A00)))=> (((x6 X) x7) Y)) x3) x4) as proof of ((in ((binintersect X) Y)) (powerset A00))
% Found (((fun (x7:((in X) (powerset A00)))=> ((((x A00) X) x7) Y)) x3) x4) as proof of ((in ((binintersect X) Y)) (powerset A00))
% Found (((fun (x7:((in X) (powerset A00)))=> ((((x A00) X) x7) Y)) x3) x4) as proof of ((in ((binintersect X) Y)) (powerset A00))
% Found x7:((in Xx) A0)
% Instantiate: A0:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x7:((in Xx) A1)
% Instantiate: A1:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of ((in Xx) A0)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of (((in Xx) ((binunion X) Z))->((in Xx) A0))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of (((in Xx) A1)->(((in Xx) ((binunion X) Z))->((in Xx) A0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) ((binunion X) Z))->((in Xx) A0))))
% Found x7:((in Xx) A1)
% Instantiate: A1:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binunion Y) Z)))=> x7) as proof of ((in Xx) A0)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) ((binunion Y) Z)))=> x7) as proof of (((in Xx) ((binunion Y) Z))->((in Xx) A0))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) ((binunion Y) Z)))=> x7) as proof of (((in Xx) A1)->(((in Xx) ((binunion Y) Z))->((in Xx) A0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) ((binunion Y) Z)))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) ((binunion Y) Z))->((in Xx) A0))))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Instantiate: A00:=A:fofType
% Found x3 as proof of ((in X) (powerset A00))
% Found x5:((in Z) (powerset A))
% Instantiate: A00:=A:fofType
% Found x5 as proof of ((in Z) (powerset A00))
% Found ((x0000 x3) x5) as proof of ((in ((binunion X) Z)) (powerset A00))
% Found (((fun (x7:((in X) (powerset A00)))=> ((x000 x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A00))
% Found (((fun (x7:((in X) (powerset A00)))=> (((x00 X) x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A00))
% Found (((fun (x7:((in X) (powerset A00)))=> ((((x0 A00) X) x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A00))
% Found (((fun (x7:((in X) (powerset A00)))=> ((((x0 A00) X) x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A00))
% Found x000000:=(x00000 x5):((in ((binunion Y) Z)) (powerset A00))
% Found (x00000 x5) as proof of ((in ((binunion Y) Z)) (powerset A00))
% Found ((x0000 Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A00))
% Found (((x000 x4) Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A00))
% Found ((((x00 Y) x4) Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A00))
% Found (((((x0 A00) Y) x4) Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A00))
% Found (((((x0 A00) Y) x4) Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A00))
% Found ((x600 (((fun (x7:((in X) (powerset A00)))=> ((((x0 A00) X) x7) Z)) x3) x5)) (((((x0 A00) Y) x4) Z) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A00))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A00)))=> ((x60 x7) ((binunion Y) Z))) (((fun (x7:((in X) (powerset A00)))=> ((((x0 A00) X) x7) Z)) x3) x5)) (((((x0 A00) Y) x4) Z) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A00))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A00)))=> (((x6 ((binunion X) Z)) x7) ((binunion Y) Z))) (((fun (x7:((in X) (powerset A00)))=> ((((x0 A00) X) x7) Z)) x3) x5)) (((((x0 A00) Y) x4) Z) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A00))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A00)))=> ((((x A00) ((binunion X) Z)) x7) ((binunion Y) Z))) (((fun (x7:((in X) (powerset A00)))=> ((((x0 A00) X) x7) Z)) x3) x5)) (((((x0 A00) Y) x4) Z) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A00))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A00)))=> ((((x A00) ((binunion X) Z)) x7) ((binunion Y) Z))) (((fun (x7:((in X) (powerset A00)))=> ((((x0 A00) X) x7) Z)) x3) x5)) (((((x0 A00) Y) x4) Z) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A00))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x8:((in Xx) X)
% Found x8 as proof of ((in Xx) X)
% Found x8:((in Xx) Y)
% Found x8 as proof of ((in Xx) Y)
% Found x5:((in Z) (powerset A))
% Instantiate: A1:=A:fofType
% Found x5 as proof of ((in Z) (powerset A1))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=A:fofType
% Found x3 as proof of ((in X) (powerset A1))
% Found ((x0000 x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((fun (x7:((in X) (powerset A1)))=> ((x000 x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((fun (x7:((in X) (powerset A1)))=> (((x00 X) x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found x000000:=(x00000 x5):((in ((binunion Y) Z)) (powerset A1))
% Found (x00000 x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found ((x0000 Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((x000 x4) Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found ((((x00 Y) x4) Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((((x0 A1) Y) x4) Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((((x0 A1) Y) x4) Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found ((x600 (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5)) (((((x0 A1) Y) x4) Z) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A1))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A1)))=> ((x60 x7) ((binunion Y) Z))) (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5)) (((((x0 A1) Y) x4) Z) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A1))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A1)))=> (((x6 ((binunion X) Z)) x7) ((binunion Y) Z))) (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5)) (((((x0 A1) Y) x4) Z) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A1))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A1)))=> ((((x A1) ((binunion X) Z)) x7) ((binunion Y) Z))) (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5)) (((((x0 A1) Y) x4) Z) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A1))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A1)))=> ((((x A1) ((binunion X) Z)) x7) ((binunion Y) Z))) (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5)) (((((x0 A1) Y) x4) Z) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A1))
% Found x000000:=(x00000 x5):((in ((binunion X) Z)) (powerset A1))
% Found (x00000 x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found ((x0000 Z) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((x000 x3) Z) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found ((((x00 X) x3) Z) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((((x0 A1) X) x3) Z) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((((x0 A1) X) x3) Z) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found x000000:=(x00000 x5):((in ((binunion Y) Z)) (powerset A1))
% Found (x00000 x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found ((x0000 Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((x000 x4) Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found ((((x00 Y) x4) Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((((x0 A1) Y) x4) Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((((x0 A1) Y) x4) Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found ((x600 (((((x0 A1) X) x3) Z) x5)) (((((x0 A1) Y) x4) Z) x5)) as proof of ((in A0) (powerset A1))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A1)))=> ((x60 x7) ((binunion Y) Z))) (((((x0 A1) X) x3) Z) x5)) (((((x0 A1) Y) x4) Z) x5)) as proof of ((in A0) (powerset A1))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A1)))=> (((x6 ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A1) X) x3) Z) x5)) (((((x0 A1) Y) x4) Z) x5)) as proof of ((in A0) (powerset A1))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A1)))=> ((((x A1) ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A1) X) x3) Z) x5)) (((((x0 A1) Y) x4) Z) x5)) as proof of ((in A0) (powerset A1))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A1)))=> ((((x A1) ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A1) X) x3) Z) x5)) (((((x0 A1) Y) x4) Z) x5)) as proof of ((in A0) (powerset A1))
% Found (((x1100 (((fun (x7:((in ((binunion X) Z)) (powerset A1)))=> ((((x A1) ((binunion X) Z)) x7) ((binunion Y) Z))) (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5)) (((((x0 A1) Y) x4) Z) x5))) (((fun (x7:((in ((binunion X) Z)) (powerset A1)))=> ((((x A1) ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A1) X) x3) Z) x5)) (((((x0 A1) Y) x4) Z) x5))) (fun (Xx:fofType) (x6:((in Xx) A1)) (x7:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A0))
% Found ((((x110 A) (((fun (x7:((in ((binunion X) Z)) (powerset A)))=> ((((x A) ((binunion X) Z)) x7) ((binunion Y) Z))) (((fun (x7:((in X) (powerset A)))=> ((((x0 A) X) x7) Z)) x3) x5)) (((((x0 A) Y) x4) Z) x5))) (((fun (x7:((in ((binunion X) Z)) (powerset A)))=> ((((x A) ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A) X) x3) Z) x5)) (((((x0 A) Y) x4) Z) x5))) (fun (Xx:fofType) (x6:((in Xx) A)) (x7:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A0))
% Found (((((fun (A1:fofType) (x6:((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A1)))=> (((x11 A1) x6) A0)) A) (((fun (x7:((in ((binunion X) Z)) (powerset A)))=> ((((x A) ((binunion X) Z)) x7) ((binunion Y) Z))) (((fun (x7:((in X) (powerset A)))=> ((((x0 A) X) x7) Z)) x3) x5)) (((((x0 A) Y) x4) Z) x5))) (((fun (x7:((in ((binunion X) Z)) (powerset A)))=> ((((x A) ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A) X) x3) Z) x5)) (((((x0 A) Y) x4) Z) x5))) (fun (Xx:fofType) (x6:((in Xx) A)) (x7:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A0))
% Found (((((fun (A1:fofType) (x6:((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A1)))=> ((((fun (A1:fofType)=> ((x1 A1) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))) A1) x6) A0)) A) (((fun (x7:((in ((binunion X) Z)) (powerset A)))=> ((((x A) ((binunion X) Z)) x7) ((binunion Y) Z))) (((fun (x7:((in X) (powerset A)))=> ((((x0 A) X) x7) Z)) x3) x5)) (((((x0 A) Y) x4) Z) x5))) (((fun (x7:((in ((binunion X) Z)) (powerset A)))=> ((((x A) ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A) X) x3) Z) x5)) (((((x0 A) Y) x4) Z) x5))) (fun (Xx:fofType) (x6:((in Xx) A)) (x7:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A0))
% Found (((((fun (A1:fofType) (x6:((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A1)))=> ((((fun (A1:fofType)=> ((x1 A1) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))) A1) x6) A0)) A) (((fun (x7:((in ((binunion X) Z)) (powerset A)))=> ((((x A) ((binunion X) Z)) x7) ((binunion Y) Z))) (((fun (x7:((in X) (powerset A)))=> ((((x0 A) X) x7) Z)) x3) x5)) (((((x0 A) Y) x4) Z) x5))) (((fun (x7:((in ((binunion X) Z)) (powerset A)))=> ((((x A) ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A) X) x3) Z) x5)) (((((x0 A) Y) x4) Z) x5))) (fun (Xx:fofType) (x6:((in Xx) A)) (x7:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A0))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x8:((in Xx) Y)
% Found x8 as proof of ((in Xx) Y)
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x8:((in Xx) X)
% Found x8 as proof of ((in Xx) X)
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x6:((in Xx) A01)
% Instantiate: A01:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x7:((in Xx) ((binintersect X) Y)))=> x6) as proof of ((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))
% Found (fun (x6:((in Xx) A01)) (x7:((in Xx) ((binintersect X) Y)))=> x6) as proof of (((in Xx) ((binintersect X) Y))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))
% Found (fun (Xx:fofType) (x6:((in Xx) A01)) (x7:((in Xx) ((binintersect X) Y)))=> x6) as proof of (((in Xx) A01)->(((in Xx) ((binintersect X) Y))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))))
% Found (fun (Xx:fofType) (x6:((in Xx) A01)) (x7:((in Xx) ((binintersect X) Y)))=> x6) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect X) Y))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))))
% Found x5:((in Z) (powerset A))
% Instantiate: A0:=Z:fofType;A00:=A:fofType
% Found x5 as proof of ((in A0) (powerset A00))
% Found x5:((in Z) (powerset A))
% Instantiate: A0:=Z:fofType;A00:=A:fofType
% Found x5 as proof of ((in A0) (powerset A00))
% Found x7:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))
% Found (fun (x7:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A00)
% Found (fun (x6:((in Xx) A1)) (x7:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00))
% Found (fun (Xx:fofType) (x6:((in Xx) A1)) (x7:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A1)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00)))
% Found (fun (Xx:fofType) (x6:((in Xx) A1)) (x7:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00))))
% Found x8:((in Xx) Y)
% Found x8 as proof of ((in Xx) Y)
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x8:((in Xx) X)
% Found x8 as proof of ((in Xx) X)
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Instantiate: A0:=Z:fofType;A00:=A:fofType
% Found x5 as proof of ((in A0) (powerset A00))
% Found x5:((in Z) (powerset A))
% Instantiate: A0:=Z:fofType;A00:=A:fofType
% Found x5 as proof of ((in A0) (powerset A00))
% Found x7:((in Xx) A1)
% Instantiate: A1:=A:fofType
% Found (fun (x8:((in Xx) A0))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A0))=> x7) as proof of (((in Xx) A0)->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A0))=> x7) as proof of (((in Xx) A1)->(((in Xx) A0)->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A0))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A0)->((in Xx) A))))
% Found x7:((in Xx) A1)
% Instantiate: A1:=A:fofType
% Found (fun (x8:((in Xx) A0))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A0))=> x7) as proof of (((in Xx) A0)->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A0))=> x7) as proof of (((in Xx) A1)->(((in Xx) A0)->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A0))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A0)->((in Xx) A))))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Instantiate: A01:=A:fofType
% Found x4 as proof of ((in Y) (powerset A01))
% Found x3:((in X) (powerset A))
% Instantiate: A01:=A:fofType
% Found x3 as proof of ((in X) (powerset A01))
% Found ((x600 x3) x4) as proof of ((in ((binintersect X) Y)) (powerset A01))
% Found (((fun (x7:((in X) (powerset A01)))=> ((x60 x7) Y)) x3) x4) as proof of ((in ((binintersect X) Y)) (powerset A01))
% Found (((fun (x7:((in X) (powerset A01)))=> (((x6 X) x7) Y)) x3) x4) as proof of ((in ((binintersect X) Y)) (powerset A01))
% Found (((fun (x7:((in X) (powerset A01)))=> ((((x A01) X) x7) Y)) x3) x4) as proof of ((in ((binintersect X) Y)) (powerset A01))
% Found (((fun (x7:((in X) (powerset A01)))=> ((((x A01) X) x7) Y)) x3) x4) as proof of ((in ((binintersect X) Y)) (powerset A01))
% Found x5:((in Z) (powerset A))
% Instantiate: A1:=A:fofType;A0:=Z:fofType
% Found x5 as proof of ((in A0) (powerset A1))
% Found x5:((in Z) (powerset A))
% Instantiate: A1:=A:fofType;A0:=Z:fofType
% Found x5 as proof of ((in A0) (powerset A1))
% Found x8:((in Xx) Y)
% Found x8 as proof of ((in Xx) Y)
% Found x8:((in Xx) X)
% Found x8 as proof of ((in Xx) X)
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x7:((in Xx) A1)
% Instantiate: A1:=A:fofType
% Found (fun (x8:((in Xx) A0))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A0))=> x7) as proof of (((in Xx) A0)->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A0))=> x7) as proof of (((in Xx) A1)->(((in Xx) A0)->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A0))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A0)->((in Xx) A))))
% Found x7:((in Xx) A1)
% Instantiate: A1:=A:fofType
% Found (fun (x8:((in Xx) A0))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A0))=> x7) as proof of (((in Xx) A0)->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A0))=> x7) as proof of (((in Xx) A1)->(((in Xx) A0)->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A0))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A0)->((in Xx) A))))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=A:fofType;A0:=X:fofType
% Found x3 as proof of ((in A0) (powerset A1))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=A:fofType;A0:=X:fofType
% Found x3 as proof of ((in A0) (powerset A1))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x7:((in Xx) A00)
% Instantiate: A00:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A00)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A00)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x7:((in Xx) A00)
% Instantiate: A00:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A00)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A00)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))
% Instantiate: A0:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of ((in Xx) A0)
% Found (fun (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A0))
% Found (fun (Xx:fofType) (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) A00)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A00)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A0))))
% Found x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))
% Instantiate: A0:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of ((in Xx) A0)
% Found (fun (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A0))
% Found (fun (Xx:fofType) (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) A00)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A00)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A0))))
% Found x7:((in Xx) A00)
% Instantiate: A00:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A00)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A00)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x7:((in Xx) A00)
% Instantiate: A00:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A00)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A00)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))
% Instantiate: A0:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of ((in Xx) A0)
% Found (fun (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A0))
% Found (fun (Xx:fofType) (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) A00)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A00)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A0))))
% Found x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))
% Instantiate: A0:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of ((in Xx) A0)
% Found (fun (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A0))
% Found (fun (Xx:fofType) (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) A00)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A00)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A0))))
% Found x7:((in Xx) A00)
% Instantiate: A00:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A00)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A00)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x7:((in Xx) A00)
% Instantiate: A00:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A00)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A00)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x8:((in Xx) A)
% Instantiate: A0:=A:fofType
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A0)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A0))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A1)->(((in Xx) A)->((in Xx) A0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A)->((in Xx) A0))))
% Found x8:((in Xx) A)
% Instantiate: A0:=A:fofType
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A0)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A0))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A1)->(((in Xx) A)->((in Xx) A0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A)->((in Xx) A0))))
% Found x7:((in Xx) A00)
% Instantiate: A00:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A00)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A00)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x7:((in Xx) A00)
% Instantiate: A00:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A00)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A00)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A00)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x8:((in Xx) A)
% Instantiate: A0:=A:fofType
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A0)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A0))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A1)->(((in Xx) A)->((in Xx) A0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A)->((in Xx) A0))))
% Found x8:((in Xx) A)
% Instantiate: A0:=A:fofType
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A0)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A0))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A1)->(((in Xx) A)->((in Xx) A0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A)->((in Xx) A0))))
% Found x8:((in Xx) A)
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A0)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A0))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A1)->(((in Xx) A)->((in Xx) A0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A)->((in Xx) A0))))
% Found x8:((in Xx) A)
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A0)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A0))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A1)->(((in Xx) A)->((in Xx) A0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A)->((in Xx) A0))))
% Found x7:((in Xx) A1)
% Instantiate: A1:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binunion Y) Z)))=> x7) as proof of ((in Xx) A00)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) ((binunion Y) Z)))=> x7) as proof of (((in Xx) ((binunion Y) Z))->((in Xx) A00))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) ((binunion Y) Z)))=> x7) as proof of (((in Xx) A1)->(((in Xx) ((binunion Y) Z))->((in Xx) A00)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) ((binunion Y) Z)))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) ((binunion Y) Z))->((in Xx) A00))))
% Found x7:((in Xx) A1)
% Instantiate: A1:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of ((in Xx) A00)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of (((in Xx) ((binunion X) Z))->((in Xx) A00))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of (((in Xx) A1)->(((in Xx) ((binunion X) Z))->((in Xx) A00)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) ((binunion X) Z))->((in Xx) A00))))
% Found x8:((in Xx) A)
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A0)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A0))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A1)->(((in Xx) A)->((in Xx) A0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A)->((in Xx) A0))))
% Found x8:((in Xx) A)
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A0)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A0))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A1)->(((in Xx) A)->((in Xx) A0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A)->((in Xx) A0))))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Instantiate: A01:=A:fofType
% Found x4 as proof of ((in Y) (powerset A01))
% Found x5:((in Z) (powerset A))
% Instantiate: A01:=A:fofType
% Found x5 as proof of ((in Z) (powerset A01))
% Found ((x0000 x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A01))
% Found (((fun (x7:((in Y) (powerset A01)))=> ((x000 x7) Z)) x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A01))
% Found (((fun (x7:((in Y) (powerset A01)))=> (((x00 Y) x7) Z)) x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A01))
% Found (((fun (x7:((in Y) (powerset A01)))=> ((((x0 A01) Y) x7) Z)) x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A01))
% Found (((fun (x7:((in Y) (powerset A01)))=> ((((x0 A01) Y) x7) Z)) x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A01))
% Found x000000:=(x00000 x5):((in ((binunion X) Z)) (powerset A01))
% Found (x00000 x5) as proof of ((in ((binunion X) Z)) (powerset A01))
% Found ((x0000 Z) x5) as proof of ((in ((binunion X) Z)) (powerset A01))
% Found (((x000 x3) Z) x5) as proof of ((in ((binunion X) Z)) (powerset A01))
% Found ((((x00 X) x3) Z) x5) as proof of ((in ((binunion X) Z)) (powerset A01))
% Found (((((x0 A01) X) x3) Z) x5) as proof of ((in ((binunion X) Z)) (powerset A01))
% Found (((((x0 A01) X) x3) Z) x5) as proof of ((in ((binunion X) Z)) (powerset A01))
% Found ((x600 (((((x0 A01) X) x3) Z) x5)) (((fun (x7:((in Y) (powerset A01)))=> ((((x0 A01) Y) x7) Z)) x4) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A01))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A01)))=> ((x60 x7) ((binunion Y) Z))) (((((x0 A01) X) x3) Z) x5)) (((fun (x7:((in Y) (powerset A01)))=> ((((x0 A01) Y) x7) Z)) x4) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A01))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A01)))=> (((x6 ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A01) X) x3) Z) x5)) (((fun (x7:((in Y) (powerset A01)))=> ((((x0 A01) Y) x7) Z)) x4) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A01))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A01)))=> ((((x A01) ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A01) X) x3) Z) x5)) (((fun (x7:((in Y) (powerset A01)))=> ((((x0 A01) Y) x7) Z)) x4) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A01))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A01)))=> ((((x A01) ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A01) X) x3) Z) x5)) (((fun (x7:((in Y) (powerset A01)))=> ((((x0 A01) Y) x7) Z)) x4) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A01))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x5:((in Z) (powerset A))
% Instantiate: A1:=A:fofType
% Found x5 as proof of ((in Z) (powerset A1))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=A:fofType
% Found x3 as proof of ((in X) (powerset A1))
% Found ((x0000 x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((fun (x7:((in X) (powerset A1)))=> ((x000 x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((fun (x7:((in X) (powerset A1)))=> (((x00 X) x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found x000000:=(x00000 x5):((in ((binunion Y) Z)) (powerset A1))
% Found (x00000 x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found ((x0000 Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((x000 x4) Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found ((((x00 Y) x4) Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((((x0 A1) Y) x4) Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((((x0 A1) Y) x4) Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found ((x600 (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5)) (((((x0 A1) Y) x4) Z) x5)) as proof of ((in A00) (powerset A1))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A1)))=> ((x60 x7) ((binunion Y) Z))) (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5)) (((((x0 A1) Y) x4) Z) x5)) as proof of ((in A00) (powerset A1))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A1)))=> (((x6 ((binunion X) Z)) x7) ((binunion Y) Z))) (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5)) (((((x0 A1) Y) x4) Z) x5)) as proof of ((in A00) (powerset A1))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A1)))=> ((((x A1) ((binunion X) Z)) x7) ((binunion Y) Z))) (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5)) (((((x0 A1) Y) x4) Z) x5)) as proof of ((in A00) (powerset A1))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A1)))=> ((((x A1) ((binunion X) Z)) x7) ((binunion Y) Z))) (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5)) (((((x0 A1) Y) x4) Z) x5)) as proof of ((in A00) (powerset A1))
% Found x000000:=(x00000 x5):((in ((binunion X) Z)) (powerset A1))
% Found (x00000 x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found ((x0000 Z) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((x000 x3) Z) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found ((((x00 X) x3) Z) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((((x0 A1) X) x3) Z) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((((x0 A1) X) x3) Z) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found x000000:=(x00000 x5):((in ((binunion Y) Z)) (powerset A1))
% Found (x00000 x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found ((x0000 Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((x000 x4) Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found ((((x00 Y) x4) Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((((x0 A1) Y) x4) Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((((x0 A1) Y) x4) Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found ((x600 (((((x0 A1) X) x3) Z) x5)) (((((x0 A1) Y) x4) Z) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A1))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A1)))=> ((x60 x7) ((binunion Y) Z))) (((((x0 A1) X) x3) Z) x5)) (((((x0 A1) Y) x4) Z) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A1))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A1)))=> (((x6 ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A1) X) x3) Z) x5)) (((((x0 A1) Y) x4) Z) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A1))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A1)))=> ((((x A1) ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A1) X) x3) Z) x5)) (((((x0 A1) Y) x4) Z) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A1))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A1)))=> ((((x A1) ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A1) X) x3) Z) x5)) (((((x0 A1) Y) x4) Z) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A1))
% Found (((x1100 (((fun (x7:((in ((binunion X) Z)) (powerset A1)))=> ((((x A1) ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A1) X) x3) Z) x5)) (((((x0 A1) Y) x4) Z) x5))) (((fun (x7:((in ((binunion X) Z)) (powerset A1)))=> ((((x A1) ((binunion X) Z)) x7) ((binunion Y) Z))) (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5)) (((((x0 A1) Y) x4) Z) x5))) (fun (Xx:fofType) (x6:((in Xx) A1)) (x7:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A00))
% Found ((((x110 A) (((fun (x7:((in ((binunion X) Z)) (powerset A)))=> ((((x A) ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A) X) x3) Z) x5)) (((((x0 A) Y) x4) Z) x5))) (((fun (x7:((in ((binunion X) Z)) (powerset A)))=> ((((x A) ((binunion X) Z)) x7) ((binunion Y) Z))) (((fun (x7:((in X) (powerset A)))=> ((((x0 A) X) x7) Z)) x3) x5)) (((((x0 A) Y) x4) Z) x5))) (fun (Xx:fofType) (x6:((in Xx) A)) (x7:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A00))
% Found (((((fun (A1:fofType) (x6:((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A1)))=> (((x11 A1) x6) A00)) A) (((fun (x7:((in ((binunion X) Z)) (powerset A)))=> ((((x A) ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A) X) x3) Z) x5)) (((((x0 A) Y) x4) Z) x5))) (((fun (x7:((in ((binunion X) Z)) (powerset A)))=> ((((x A) ((binunion X) Z)) x7) ((binunion Y) Z))) (((fun (x7:((in X) (powerset A)))=> ((((x0 A) X) x7) Z)) x3) x5)) (((((x0 A) Y) x4) Z) x5))) (fun (Xx:fofType) (x6:((in Xx) A)) (x7:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A00))
% Found (((((fun (A1:fofType) (x6:((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A1)))=> ((((fun (A1:fofType)=> ((x1 A1) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))) A1) x6) A00)) A) (((fun (x7:((in ((binunion X) Z)) (powerset A)))=> ((((x A) ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A) X) x3) Z) x5)) (((((x0 A) Y) x4) Z) x5))) (((fun (x7:((in ((binunion X) Z)) (powerset A)))=> ((((x A) ((binunion X) Z)) x7) ((binunion Y) Z))) (((fun (x7:((in X) (powerset A)))=> ((((x0 A) X) x7) Z)) x3) x5)) (((((x0 A) Y) x4) Z) x5))) (fun (Xx:fofType) (x6:((in Xx) A)) (x7:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A00))
% Found (((((fun (A1:fofType) (x6:((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A1)))=> ((((fun (A1:fofType)=> ((x1 A1) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))) A1) x6) A00)) A) (((fun (x7:((in ((binunion X) Z)) (powerset A)))=> ((((x A) ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A) X) x3) Z) x5)) (((((x0 A) Y) x4) Z) x5))) (((fun (x7:((in ((binunion X) Z)) (powerset A)))=> ((((x A) ((binunion X) Z)) x7) ((binunion Y) Z))) (((fun (x7:((in X) (powerset A)))=> ((((x0 A) X) x7) Z)) x3) x5)) (((((x0 A) Y) x4) Z) x5))) (fun (Xx:fofType) (x6:((in Xx) A)) (x7:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A00))
% Found x8:((in Xx) X)
% Found x8 as proof of ((in Xx) X)
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x8:((in Xx) Y)
% Found x8 as proof of ((in Xx) Y)
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x8:((in Xx) X)
% Found x8 as proof of ((in Xx) X)
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x8:((in Xx) Y)
% Found x8 as proof of ((in Xx) Y)
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x11:((in Xx0) Y)
% Found (fun (x11:((in Xx0) Y))=> x11) as proof of ((in Xx0) Y)
% Found (fun (x9:((in Xx0) A)) (x11:((in Xx0) Y))=> x11) as proof of (((in Xx0) Y)->((in Xx0) Y))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) Y))=> x11) as proof of (((in Xx0) A)->(((in Xx0) Y)->((in Xx0) Y)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) Y))=> x11) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) Y))))
% Found (((x1010 x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) Y))=> x11)) as proof of ((in Y) (powerset Y))
% Found ((((x101 A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) Y))=> x11)) as proof of ((in Y) (powerset Y))
% Found (((((fun (A0:fofType) (x9:((in Y) (powerset A0)))=> (((x10 A0) x9) Y)) A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) Y))=> x11)) as proof of ((in Y) (powerset Y))
% Found (((((fun (A0:fofType) (x9:((in Y) (powerset A0)))=> (((x10 A0) x9) Y)) A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) Y))=> x11)) as proof of ((in Y) (powerset Y))
% Found x11:((in Xx0) X)
% Found (fun (x11:((in Xx0) X))=> x11) as proof of ((in Xx0) X)
% Found (fun (x9:((in Xx0) A)) (x11:((in Xx0) X))=> x11) as proof of (((in Xx0) X)->((in Xx0) X))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) X))=> x11) as proof of (((in Xx0) A)->(((in Xx0) X)->((in Xx0) X)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) X))=> x11) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) X)->((in Xx) X))))
% Found (((x1010 x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) X))=> x11)) as proof of ((in X) (powerset X))
% Found ((((x101 A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) X))=> x11)) as proof of ((in X) (powerset X))
% Found (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> (((x10 A0) x9) X)) A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) X))=> x11)) as proof of ((in X) (powerset X))
% Found (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> (((x10 A0) x9) X)) A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) X))=> x11)) as proof of ((in X) (powerset X))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x11:((in Xx0) X)
% Found (fun (x11:((in Xx0) X))=> x11) as proof of ((in Xx0) X)
% Found (fun (x9:((in Xx0) A)) (x11:((in Xx0) X))=> x11) as proof of (((in Xx0) X)->((in Xx0) X))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) X))=> x11) as proof of (((in Xx0) A)->(((in Xx0) X)->((in Xx0) X)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) X))=> x11) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) X)->((in Xx) X))))
% Found (((x1010 x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) X))=> x11)) as proof of ((in X) (powerset X))
% Found ((((x101 A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) X))=> x11)) as proof of ((in X) (powerset X))
% Found (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> (((x10 A0) x9) X)) A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) X))=> x11)) as proof of ((in X) (powerset X))
% Found (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> (((x10 A0) x9) X)) A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) X))=> x11)) as proof of ((in X) (powerset X))
% Found x11:((in Xx0) Y)
% Found (fun (x11:((in Xx0) Y))=> x11) as proof of ((in Xx0) Y)
% Found (fun (x9:((in Xx0) A)) (x11:((in Xx0) Y))=> x11) as proof of (((in Xx0) Y)->((in Xx0) Y))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) Y))=> x11) as proof of (((in Xx0) A)->(((in Xx0) Y)->((in Xx0) Y)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) Y))=> x11) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) Y))))
% Found (((x1010 x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) Y))=> x11)) as proof of ((in Y) (powerset Y))
% Found ((((x101 A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) Y))=> x11)) as proof of ((in Y) (powerset Y))
% Found (((((fun (A0:fofType) (x9:((in Y) (powerset A0)))=> (((x10 A0) x9) Y)) A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) Y))=> x11)) as proof of ((in Y) (powerset Y))
% Found (((((fun (A0:fofType) (x9:((in Y) (powerset A0)))=> (((x10 A0) x9) Y)) A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) Y))=> x11)) as proof of ((in Y) (powerset Y))
% Found x11:((in Xx0) Y)
% Found (fun (x11:((in Xx0) Y))=> x11) as proof of ((in Xx0) Y)
% Found (fun (x9:((in Xx0) A)) (x11:((in Xx0) Y))=> x11) as proof of (((in Xx0) Y)->((in Xx0) Y))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) Y))=> x11) as proof of (((in Xx0) A)->(((in Xx0) Y)->((in Xx0) Y)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) Y))=> x11) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) Y))))
% Found (((x1010 x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) Y))=> x11)) as proof of ((in Y) (powerset Y))
% Found ((((x101 A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) Y))=> x11)) as proof of ((in Y) (powerset Y))
% Found (((((fun (A0:fofType) (x9:((in Y) (powerset A0)))=> (((x10 A0) x9) Y)) A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) Y))=> x11)) as proof of ((in Y) (powerset Y))
% Found (((((fun (A0:fofType) (x9:((in Y) (powerset A0)))=> (((x10 A0) x9) Y)) A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) Y))=> x11)) as proof of ((in Y) (powerset Y))
% Found x11:((in Xx0) X)
% Found (fun (x11:((in Xx0) X))=> x11) as proof of ((in Xx0) X)
% Found (fun (x9:((in Xx0) A)) (x11:((in Xx0) X))=> x11) as proof of (((in Xx0) X)->((in Xx0) X))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) X))=> x11) as proof of (((in Xx0) A)->(((in Xx0) X)->((in Xx0) X)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) X))=> x11) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) X)->((in Xx) X))))
% Found (((x1010 x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) X))=> x11)) as proof of ((in X) (powerset X))
% Found ((((x101 A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) X))=> x11)) as proof of ((in X) (powerset X))
% Found (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> (((x10 A0) x9) X)) A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) X))=> x11)) as proof of ((in X) (powerset X))
% Found (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> (((x10 A0) x9) X)) A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) X))=> x11)) as proof of ((in X) (powerset X))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x11:((in Xx0) X)
% Found (fun (x11:((in Xx0) X))=> x11) as proof of ((in Xx0) X)
% Found (fun (x9:((in Xx0) A)) (x11:((in Xx0) X))=> x11) as proof of (((in Xx0) X)->((in Xx0) X))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) X))=> x11) as proof of (((in Xx0) A)->(((in Xx0) X)->((in Xx0) X)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) X))=> x11) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) X)->((in Xx) X))))
% Found (((x1010 x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) X))=> x11)) as proof of ((in X) (powerset X))
% Found ((((x101 A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) X))=> x11)) as proof of ((in X) (powerset X))
% Found (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> (((x10 A0) x9) X)) A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) X))=> x11)) as proof of ((in X) (powerset X))
% Found (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> (((x10 A0) x9) X)) A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) X))=> x11)) as proof of ((in X) (powerset X))
% Found x11:((in Xx0) Y)
% Found (fun (x11:((in Xx0) Y))=> x11) as proof of ((in Xx0) Y)
% Found (fun (x9:((in Xx0) A)) (x11:((in Xx0) Y))=> x11) as proof of (((in Xx0) Y)->((in Xx0) Y))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) Y))=> x11) as proof of (((in Xx0) A)->(((in Xx0) Y)->((in Xx0) Y)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) Y))=> x11) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) Y))))
% Found (((x1010 x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) Y))=> x11)) as proof of ((in Y) (powerset Y))
% Found ((((x101 A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) Y))=> x11)) as proof of ((in Y) (powerset Y))
% Found (((((fun (A0:fofType) (x9:((in Y) (powerset A0)))=> (((x10 A0) x9) Y)) A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) Y))=> x11)) as proof of ((in Y) (powerset Y))
% Found (((((fun (A0:fofType) (x9:((in Y) (powerset A0)))=> (((x10 A0) x9) Y)) A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x11:((in Xx0) Y))=> x11)) as proof of ((in Y) (powerset Y))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=X:fofType;A10:=A:fofType
% Found x3 as proof of ((in A1) (powerset A10))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=X:fofType;A10:=A:fofType
% Found x3 as proof of ((in A1) (powerset A10))
% Found x7:((in Xx) A1)
% Instantiate: A1:=A:fofType
% Found (fun (x8:((in Xx) A00))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A00))=> x7) as proof of (((in Xx) A00)->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A00))=> x7) as proof of (((in Xx) A1)->(((in Xx) A00)->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A00))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A00)->((in Xx) A))))
% Found x7:((in Xx) A1)
% Instantiate: A1:=A:fofType
% Found (fun (x8:((in Xx) A00))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A00))=> x7) as proof of (((in Xx) A00)->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A00))=> x7) as proof of (((in Xx) A1)->(((in Xx) A00)->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A00))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A00)->((in Xx) A))))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Instantiate: A1:=Z:fofType;A10:=A:fofType
% Found x5 as proof of ((in A1) (powerset A10))
% Found x5:((in Z) (powerset A))
% Instantiate: A1:=Z:fofType;A10:=A:fofType
% Found x5 as proof of ((in A1) (powerset A10))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x7:((in Xx) A1)
% Instantiate: A1:=A:fofType
% Found (fun (x8:((in Xx) A00))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A00))=> x7) as proof of (((in Xx) A00)->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A00))=> x7) as proof of (((in Xx) A1)->(((in Xx) A00)->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A00))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A00)->((in Xx) A))))
% Found x7:((in Xx) A1)
% Instantiate: A1:=A:fofType
% Found (fun (x8:((in Xx) A00))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A00))=> x7) as proof of (((in Xx) A00)->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A00))=> x7) as proof of (((in Xx) A1)->(((in Xx) A00)->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A00))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A00)->((in Xx) A))))
% Found x5:((in Z) (powerset A))
% Instantiate: A1:=Z:fofType;A2:=A:fofType
% Found x5 as proof of ((in A1) (powerset A2))
% Found x5:((in Z) (powerset A))
% Instantiate: A1:=Z:fofType;A2:=A:fofType
% Found x5 as proof of ((in A1) (powerset A2))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=X:fofType;A2:=A:fofType
% Found x3 as proof of ((in A1) (powerset A2))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=X:fofType;A2:=A:fofType
% Found x3 as proof of ((in A1) (powerset A2))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Instantiate: A00:=X:fofType;A01:=A:fofType
% Found x3 as proof of ((in A00) (powerset A01))
% Found x3:((in X) (powerset A))
% Instantiate: A00:=X:fofType;A01:=A:fofType
% Found x3 as proof of ((in A00) (powerset A01))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x7:((in Xx) A1)
% Instantiate: A1:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binunion Y) Z)))=> x7) as proof of ((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) ((binunion Y) Z)))=> x7) as proof of (((in Xx) ((binunion Y) Z))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) ((binunion Y) Z)))=> x7) as proof of (((in Xx) A1)->(((in Xx) ((binunion Y) Z))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) ((binunion Y) Z)))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) ((binunion Y) Z))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))))
% Found x7:((in Xx) A1)
% Instantiate: A1:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of ((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of (((in Xx) ((binunion X) Z))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of (((in Xx) A1)->(((in Xx) ((binunion X) Z))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) ((binunion X) Z))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))))
% Found x7:((in Xx) A1)
% Instantiate: A1:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of ((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of (((in Xx) ((binunion X) Z))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of (((in Xx) A1)->(((in Xx) ((binunion X) Z))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) ((binunion X) Z))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))))
% Found x7:((in Xx) A1)
% Instantiate: A1:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binunion Y) Z)))=> x7) as proof of ((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) ((binunion Y) Z)))=> x7) as proof of (((in Xx) ((binunion Y) Z))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) ((binunion Y) Z)))=> x7) as proof of (((in Xx) A1)->(((in Xx) ((binunion Y) Z))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) ((binunion Y) Z)))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) ((binunion Y) Z))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))))
% Found x12:((in Xx0) X)
% Found (fun (x12:((in Xx0) X))=> x12) as proof of ((in Xx0) X)
% Found (fun (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12) as proof of (((in Xx0) X)->((in Xx0) X))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12) as proof of (((in Xx0) A)->(((in Xx0) X)->((in Xx0) X)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) X)->((in Xx) X))))
% Found (((x1110 x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found ((((x111 A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found (((((fun (A1:fofType) (x9:((in X) (powerset A1)))=> (((x11 A1) x9) X)) A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found (((((fun (A1:fofType) (x9:((in X) (powerset A1)))=> (((x11 A1) x9) X)) A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found x12:((in Xx0) Y)
% Found (fun (x12:((in Xx0) Y))=> x12) as proof of ((in Xx0) Y)
% Found (fun (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12) as proof of (((in Xx0) Y)->((in Xx0) Y))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12) as proof of (((in Xx0) A)->(((in Xx0) Y)->((in Xx0) Y)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) Y))))
% Found (((x1110 x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found ((((x111 A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found (((((fun (A1:fofType) (x9:((in Y) (powerset A1)))=> (((x11 A1) x9) Y)) A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found (((((fun (A1:fofType) (x9:((in Y) (powerset A1)))=> (((x11 A1) x9) Y)) A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found x6:((in Xx) A02)
% Instantiate: A02:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x7:((in Xx) ((binintersect X) Y)))=> x6) as proof of ((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))
% Found (fun (x6:((in Xx) A02)) (x7:((in Xx) ((binintersect X) Y)))=> x6) as proof of (((in Xx) ((binintersect X) Y))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))
% Found (fun (Xx:fofType) (x6:((in Xx) A02)) (x7:((in Xx) ((binintersect X) Y)))=> x6) as proof of (((in Xx) A02)->(((in Xx) ((binintersect X) Y))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))))
% Found (fun (Xx:fofType) (x6:((in Xx) A02)) (x7:((in Xx) ((binintersect X) Y)))=> x6) as proof of (forall (Xx:fofType), (((in Xx) A02)->(((in Xx) ((binintersect X) Y))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Instantiate: A00:=Y:fofType;A01:=A:fofType
% Found x4 as proof of ((in A00) (powerset A01))
% Found x4:((in Y) (powerset A))
% Instantiate: A00:=Y:fofType;A01:=A:fofType
% Found x4 as proof of ((in A00) (powerset A01))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Instantiate: A00:=X:fofType;A01:=A:fofType
% Found x3 as proof of ((in A00) (powerset A01))
% Found x3:((in X) (powerset A))
% Instantiate: A00:=X:fofType;A01:=A:fofType
% Found x3 as proof of ((in A00) (powerset A01))
% Found x7:((in Xx) A1)
% Instantiate: A1:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of ((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of (((in Xx) ((binunion X) Z))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of (((in Xx) A1)->(((in Xx) ((binunion X) Z))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) ((binunion X) Z))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))))
% Found x7:((in Xx) A1)
% Instantiate: A1:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binunion Y) Z)))=> x7) as proof of ((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) ((binunion Y) Z)))=> x7) as proof of (((in Xx) ((binunion Y) Z))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) ((binunion Y) Z)))=> x7) as proof of (((in Xx) A1)->(((in Xx) ((binunion Y) Z))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) ((binunion Y) Z)))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) ((binunion Y) Z))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))))
% Found x7:((in Xx) A1)
% Instantiate: A1:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of ((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of (((in Xx) ((binunion X) Z))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of (((in Xx) A1)->(((in Xx) ((binunion X) Z))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) ((binunion X) Z))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))))
% Found x7:((in Xx) A1)
% Instantiate: A1:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binunion Y) Z)))=> x7) as proof of ((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) ((binunion Y) Z)))=> x7) as proof of (((in Xx) ((binunion Y) Z))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) ((binunion Y) Z)))=> x7) as proof of (((in Xx) A1)->(((in Xx) ((binunion Y) Z))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) ((binunion Y) Z)))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) ((binunion Y) Z))->((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))))
% Found x12:((in Xx0) Y)
% Found (fun (x12:((in Xx0) Y))=> x12) as proof of ((in Xx0) Y)
% Found (fun (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12) as proof of (((in Xx0) Y)->((in Xx0) Y))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12) as proof of (((in Xx0) A)->(((in Xx0) Y)->((in Xx0) Y)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) Y))))
% Found (((x1110 x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found ((((x111 A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found (((((fun (A1:fofType) (x9:((in Y) (powerset A1)))=> (((x11 A1) x9) Y)) A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found (((((fun (A1:fofType) (x9:((in Y) (powerset A1)))=> (((x11 A1) x9) Y)) A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found x12:((in Xx0) X)
% Found (fun (x12:((in Xx0) X))=> x12) as proof of ((in Xx0) X)
% Found (fun (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12) as proof of (((in Xx0) X)->((in Xx0) X))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12) as proof of (((in Xx0) A)->(((in Xx0) X)->((in Xx0) X)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) X)->((in Xx) X))))
% Found (((x1110 x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found ((((x111 A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found (((((fun (A1:fofType) (x9:((in X) (powerset A1)))=> (((x11 A1) x9) X)) A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found (((((fun (A1:fofType) (x9:((in X) (powerset A1)))=> (((x11 A1) x9) X)) A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found x9:((in Xx0) A0)
% Instantiate: A0:=A:fofType
% Found (fun (x12:((in Xx0) Xx))=> x9) as proof of ((in Xx0) A)
% Found (fun (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (((in Xx0) Xx)->((in Xx0) A))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (((in Xx0) A0)->(((in Xx0) Xx)->((in Xx0) A)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (forall (Xx0:fofType), (((in Xx0) A0)->(((in Xx0) Xx)->((in Xx0) A))))
% Found x9:((in Xx0) A0)
% Instantiate: A0:=A:fofType
% Found (fun (x12:((in Xx0) Xx))=> x9) as proof of ((in Xx0) A)
% Found (fun (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (((in Xx0) Xx)->((in Xx0) A))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (((in Xx0) A0)->(((in Xx0) Xx)->((in Xx0) A)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (forall (Xx0:fofType), (((in Xx0) A0)->(((in Xx0) Xx)->((in Xx0) A))))
% Found x9:((in Xx0) A0)
% Instantiate: A0:=A:fofType
% Found (fun (x12:((in Xx0) Xx))=> x9) as proof of ((in Xx0) A)
% Found (fun (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (((in Xx0) Xx)->((in Xx0) A))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (((in Xx0) A0)->(((in Xx0) Xx)->((in Xx0) A)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (forall (Xx0:fofType), (((in Xx0) A0)->(((in Xx0) Xx)->((in Xx0) A))))
% Found x9:((in Xx0) A0)
% Instantiate: A0:=A:fofType
% Found (fun (x12:((in Xx0) Xx))=> x9) as proof of ((in Xx0) A)
% Found (fun (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (((in Xx0) Xx)->((in Xx0) A))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (((in Xx0) A0)->(((in Xx0) Xx)->((in Xx0) A)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (forall (Xx0:fofType), (((in Xx0) A0)->(((in Xx0) Xx)->((in Xx0) A))))
% Found x9:((in Xx0) A0)
% Instantiate: A0:=A:fofType
% Found (fun (x12:((in Xx0) Xx))=> x9) as proof of ((in Xx0) A)
% Found (fun (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (((in Xx0) Xx)->((in Xx0) A))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (((in Xx0) A0)->(((in Xx0) Xx)->((in Xx0) A)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (forall (Xx0:fofType), (((in Xx0) A0)->(((in Xx0) Xx)->((in Xx0) A))))
% Found x9:((in Xx0) A0)
% Instantiate: A0:=A:fofType
% Found (fun (x12:((in Xx0) Xx))=> x9) as proof of ((in Xx0) A)
% Found (fun (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (((in Xx0) Xx)->((in Xx0) A))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (((in Xx0) A0)->(((in Xx0) Xx)->((in Xx0) A)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (forall (Xx0:fofType), (((in Xx0) A0)->(((in Xx0) Xx)->((in Xx0) A))))
% Found x7:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))
% Found (fun (x7:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A01)
% Found (fun (x6:((in Xx) A1)) (x7:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A01))
% Found (fun (Xx:fofType) (x6:((in Xx) A1)) (x7:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A1)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A01)))
% Found (fun (Xx:fofType) (x6:((in Xx) A1)) (x7:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A01))))
% Found x12:((in Xx0) Y)
% Found (fun (x12:((in Xx0) Y))=> x12) as proof of ((in Xx0) Y)
% Found (fun (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12) as proof of (((in Xx0) Y)->((in Xx0) Y))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12) as proof of (((in Xx0) A)->(((in Xx0) Y)->((in Xx0) Y)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) Y))))
% Found (((x1110 x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found ((((x111 A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found (((((fun (A1:fofType) (x9:((in Y) (powerset A1)))=> (((x11 A1) x9) Y)) A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found (((((fun (A1:fofType) (x9:((in Y) (powerset A1)))=> (((x11 A1) x9) Y)) A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found x12:((in Xx0) X)
% Found (fun (x12:((in Xx0) X))=> x12) as proof of ((in Xx0) X)
% Found (fun (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12) as proof of (((in Xx0) X)->((in Xx0) X))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12) as proof of (((in Xx0) A)->(((in Xx0) X)->((in Xx0) X)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) X)->((in Xx) X))))
% Found (((x1110 x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found ((((x111 A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found (((((fun (A1:fofType) (x9:((in X) (powerset A1)))=> (((x11 A1) x9) X)) A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found (((((fun (A1:fofType) (x9:((in X) (powerset A1)))=> (((x11 A1) x9) X)) A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found x8:((in Xx) A0)
% Instantiate: A1:=A0:fofType
% Found (fun (x8:((in Xx) A0))=> x8) as proof of ((in Xx) A1)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x8) as proof of (((in Xx) A0)->((in Xx) A1))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x8) as proof of (((in Xx) A10)->(((in Xx) A0)->((in Xx) A1)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A0)->((in Xx) A1))))
% Found x8:((in Xx) A0)
% Instantiate: A1:=A0:fofType
% Found (fun (x8:((in Xx) A0))=> x8) as proof of ((in Xx) A1)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x8) as proof of (((in Xx) A0)->((in Xx) A1))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x8) as proof of (((in Xx) A10)->(((in Xx) A0)->((in Xx) A1)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A0)->((in Xx) A1))))
% Found x4:((in Y) (powerset A))
% Instantiate: A1:=A:fofType;A00:=Y:fofType
% Found x4 as proof of ((in A00) (powerset A1))
% Found x4:((in Y) (powerset A))
% Instantiate: A1:=A:fofType;A00:=Y:fofType
% Found x4 as proof of ((in A00) (powerset A1))
% Found x4:((in Y) (powerset A))
% Instantiate: A00:=Y:fofType;A01:=A:fofType
% Found x4 as proof of ((in A00) (powerset A01))
% Found x4:((in Y) (powerset A))
% Instantiate: A00:=Y:fofType;A01:=A:fofType
% Found x4 as proof of ((in A00) (powerset A01))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A10)
% Instantiate: A10:=A:fofType
% Found (fun (x8:((in Xx) A0))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x7) as proof of (((in Xx) A0)->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x7) as proof of (((in Xx) A10)->(((in Xx) A0)->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A0)->((in Xx) A))))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x7:((in Xx) A10)
% Instantiate: A10:=A:fofType
% Found (fun (x8:((in Xx) A0))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x7) as proof of (((in Xx) A0)->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x7) as proof of (((in Xx) A10)->(((in Xx) A0)->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A0)->((in Xx) A))))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Instantiate: A00:=Y:fofType;A01:=A:fofType
% Found x4 as proof of ((in A00) (powerset A01))
% Found x4:((in Y) (powerset A))
% Instantiate: A00:=Y:fofType;A01:=A:fofType
% Found x4 as proof of ((in A00) (powerset A01))
% Found x9:((in Xx0) A0)
% Instantiate: A0:=A:fofType
% Found (fun (x12:((in Xx0) Xx))=> x9) as proof of ((in Xx0) A)
% Found (fun (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (((in Xx0) Xx)->((in Xx0) A))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (((in Xx0) A0)->(((in Xx0) Xx)->((in Xx0) A)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (forall (Xx0:fofType), (((in Xx0) A0)->(((in Xx0) Xx)->((in Xx0) A))))
% Found x9:((in Xx0) A0)
% Instantiate: A0:=A:fofType
% Found (fun (x12:((in Xx0) Xx))=> x9) as proof of ((in Xx0) A)
% Found (fun (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (((in Xx0) Xx)->((in Xx0) A))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (((in Xx0) A0)->(((in Xx0) Xx)->((in Xx0) A)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (forall (Xx0:fofType), (((in Xx0) A0)->(((in Xx0) Xx)->((in Xx0) A))))
% Found x9:((in Xx0) A0)
% Instantiate: A0:=A:fofType
% Found (fun (x12:((in Xx0) Xx))=> x9) as proof of ((in Xx0) A)
% Found (fun (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (((in Xx0) Xx)->((in Xx0) A))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (((in Xx0) A0)->(((in Xx0) Xx)->((in Xx0) A)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (forall (Xx0:fofType), (((in Xx0) A0)->(((in Xx0) Xx)->((in Xx0) A))))
% Found x9:((in Xx0) A0)
% Instantiate: A0:=A:fofType
% Found (fun (x12:((in Xx0) Xx))=> x9) as proof of ((in Xx0) A)
% Found (fun (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (((in Xx0) Xx)->((in Xx0) A))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (((in Xx0) A0)->(((in Xx0) Xx)->((in Xx0) A)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (forall (Xx0:fofType), (((in Xx0) A0)->(((in Xx0) Xx)->((in Xx0) A))))
% Found x9:((in Xx0) A0)
% Instantiate: A0:=A:fofType
% Found (fun (x12:((in Xx0) Xx))=> x9) as proof of ((in Xx0) A)
% Found (fun (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (((in Xx0) Xx)->((in Xx0) A))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (((in Xx0) A0)->(((in Xx0) Xx)->((in Xx0) A)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (forall (Xx0:fofType), (((in Xx0) A0)->(((in Xx0) Xx)->((in Xx0) A))))
% Found x9:((in Xx0) A0)
% Instantiate: A0:=A:fofType
% Found (fun (x12:((in Xx0) Xx))=> x9) as proof of ((in Xx0) A)
% Found (fun (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (((in Xx0) Xx)->((in Xx0) A))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (((in Xx0) A0)->(((in Xx0) Xx)->((in Xx0) A)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A0)) (x12:((in Xx0) Xx))=> x9) as proof of (forall (Xx0:fofType), (((in Xx0) A0)->(((in Xx0) Xx)->((in Xx0) A))))
% Found x8:((in Xx) A0)
% Instantiate: A1:=A0:fofType
% Found (fun (x8:((in Xx) A0))=> x8) as proof of ((in Xx) A1)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x8) as proof of (((in Xx) A0)->((in Xx) A1))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x8) as proof of (((in Xx) A10)->(((in Xx) A0)->((in Xx) A1)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A0)->((in Xx) A1))))
% Found x8:((in Xx) A0)
% Instantiate: A1:=A0:fofType
% Found (fun (x8:((in Xx) A0))=> x8) as proof of ((in Xx) A1)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x8) as proof of (((in Xx) A0)->((in Xx) A1))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x8) as proof of (((in Xx) A10)->(((in Xx) A0)->((in Xx) A1)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A0)->((in Xx) A1))))
% Found x12:((in Xx0) X)
% Found (fun (x12:((in Xx0) X))=> x12) as proof of ((in Xx0) X)
% Found (fun (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12) as proof of (((in Xx0) X)->((in Xx0) X))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12) as proof of (((in Xx0) A)->(((in Xx0) X)->((in Xx0) X)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) X)->((in Xx) X))))
% Found (((x1110 x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found ((((x111 A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found (((((fun (A1:fofType) (x9:((in X) (powerset A1)))=> (((x11 A1) x9) X)) A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found (((((fun (A1:fofType) (x9:((in X) (powerset A1)))=> (((x11 A1) x9) X)) A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found x12:((in Xx0) Y)
% Found (fun (x12:((in Xx0) Y))=> x12) as proof of ((in Xx0) Y)
% Found (fun (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12) as proof of (((in Xx0) Y)->((in Xx0) Y))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12) as proof of (((in Xx0) A)->(((in Xx0) Y)->((in Xx0) Y)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) Y))))
% Found (((x1110 x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found ((((x111 A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found (((((fun (A1:fofType) (x9:((in Y) (powerset A1)))=> (((x11 A1) x9) Y)) A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found (((((fun (A1:fofType) (x9:((in Y) (powerset A1)))=> (((x11 A1) x9) Y)) A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found x4:((in Y) (powerset A))
% Instantiate: A02:=A:fofType
% Found x4 as proof of ((in Y) (powerset A02))
% Found x3:((in X) (powerset A))
% Instantiate: A02:=A:fofType
% Found x3 as proof of ((in X) (powerset A02))
% Found ((x600 x3) x4) as proof of ((in ((binintersect X) Y)) (powerset A02))
% Found (((fun (x7:((in X) (powerset A02)))=> ((x60 x7) Y)) x3) x4) as proof of ((in ((binintersect X) Y)) (powerset A02))
% Found (((fun (x7:((in X) (powerset A02)))=> (((x6 X) x7) Y)) x3) x4) as proof of ((in ((binintersect X) Y)) (powerset A02))
% Found (((fun (x7:((in X) (powerset A02)))=> ((((x A02) X) x7) Y)) x3) x4) as proof of ((in ((binintersect X) Y)) (powerset A02))
% Found (((fun (x7:((in X) (powerset A02)))=> ((((x A02) X) x7) Y)) x3) x4) as proof of ((in ((binintersect X) Y)) (powerset A02))
% Found x8:((in Xx) A)
% Instantiate: A1:=A:fofType
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A1)
% Found (fun (x7:((in Xx) A2)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A1))
% Found (fun (Xx:fofType) (x7:((in Xx) A2)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A2)->(((in Xx) A)->((in Xx) A1)))
% Found (fun (Xx:fofType) (x7:((in Xx) A2)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A2)->(((in Xx) A)->((in Xx) A1))))
% Found x8:((in Xx) A)
% Instantiate: A1:=A:fofType
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A1)
% Found (fun (x7:((in Xx) A2)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A1))
% Found (fun (Xx:fofType) (x7:((in Xx) A2)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A2)->(((in Xx) A)->((in Xx) A1)))
% Found (fun (Xx:fofType) (x7:((in Xx) A2)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A2)->(((in Xx) A)->((in Xx) A1))))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=A:fofType;A00:=X:fofType
% Found x3 as proof of ((in A00) (powerset A1))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=A:fofType;A00:=X:fofType
% Found x3 as proof of ((in A00) (powerset A1))
% Found x3:((in X) (powerset A))
% Instantiate: A00:=X:fofType;A01:=A:fofType
% Found x3 as proof of ((in A00) (powerset A01))
% Found x3:((in X) (powerset A))
% Instantiate: A00:=X:fofType;A01:=A:fofType
% Found x3 as proof of ((in A00) (powerset A01))
% Found x7:((in Xx) A10)
% Instantiate: A10:=A:fofType
% Found (fun (x8:((in Xx) A0))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x7) as proof of (((in Xx) A0)->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x7) as proof of (((in Xx) A10)->(((in Xx) A0)->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A0)->((in Xx) A))))
% Found x7:((in Xx) A10)
% Instantiate: A10:=A:fofType
% Found (fun (x8:((in Xx) A0))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x7) as proof of (((in Xx) A0)->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x7) as proof of (((in Xx) A10)->(((in Xx) A0)->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A0)->((in Xx) A))))
% Found x4:((in Y) (powerset A))
% Instantiate: A1:=A:fofType;A00:=Y:fofType
% Found x4 as proof of ((in A00) (powerset A1))
% Found x4:((in Y) (powerset A))
% Instantiate: A1:=A:fofType;A00:=Y:fofType
% Found x4 as proof of ((in A00) (powerset A1))
% Found x7:((in Xx) A10)
% Instantiate: A10:=A:fofType
% Found (fun (x8:((in Xx) A0))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x7) as proof of (((in Xx) A0)->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x7) as proof of (((in Xx) A10)->(((in Xx) A0)->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A0)->((in Xx) A))))
% Found x7:((in Xx) A10)
% Instantiate: A10:=A:fofType
% Found (fun (x8:((in Xx) A0))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x7) as proof of (((in Xx) A0)->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x7) as proof of (((in Xx) A10)->(((in Xx) A0)->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A0)->((in Xx) A))))
% Found x8:((in Xx) A)
% Instantiate: A1:=A:fofType
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A1)
% Found (fun (x7:((in Xx) A2)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A1))
% Found (fun (Xx:fofType) (x7:((in Xx) A2)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A2)->(((in Xx) A)->((in Xx) A1)))
% Found (fun (Xx:fofType) (x7:((in Xx) A2)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A2)->(((in Xx) A)->((in Xx) A1))))
% Found x8:((in Xx) A)
% Instantiate: A1:=A:fofType
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A1)
% Found (fun (x7:((in Xx) A2)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A1))
% Found (fun (Xx:fofType) (x7:((in Xx) A2)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A2)->(((in Xx) A)->((in Xx) A1)))
% Found (fun (Xx:fofType) (x7:((in Xx) A2)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A2)->(((in Xx) A)->((in Xx) A1))))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=X:fofType;A10:=A:fofType
% Found x3 as proof of ((in A1) (powerset A10))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=X:fofType;A10:=A:fofType
% Found x3 as proof of ((in A1) (powerset A10))
% Found x3:((in X) (powerset A))
% Instantiate: A000:=A:fofType
% Found x3 as proof of ((in A0) (powerset A000))
% Found x3 as proof of ((in A0) (powerset A000))
% Found x4:((in Y) (powerset A))
% Instantiate: A000:=A:fofType
% Found x4 as proof of ((in A0) (powerset A000))
% Found x4 as proof of ((in A0) (powerset A000))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=A:fofType;A00:=X:fofType
% Found x3 as proof of ((in A00) (powerset A1))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=A:fofType;A00:=X:fofType
% Found x3 as proof of ((in A00) (powerset A1))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=X:fofType;A10:=A:fofType
% Found x3 as proof of ((in A1) (powerset A10))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=X:fofType;A10:=A:fofType
% Found x3 as proof of ((in A1) (powerset A10))
% Found x7:((in Xx) A10)
% Instantiate: A10:=A:fofType
% Found (fun (x8:((in Xx) A0))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x7) as proof of (((in Xx) A0)->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x7) as proof of (((in Xx) A10)->(((in Xx) A0)->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A0)->((in Xx) A))))
% Found x7:((in Xx) A10)
% Instantiate: A10:=A:fofType
% Found (fun (x8:((in Xx) A0))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x7) as proof of (((in Xx) A0)->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x7) as proof of (((in Xx) A10)->(((in Xx) A0)->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A0))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A0)->((in Xx) A))))
% Found x8:((in Xx) A)
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A1)
% Found (fun (x7:((in Xx) A2)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A1))
% Found (fun (Xx:fofType) (x7:((in Xx) A2)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A2)->(((in Xx) A)->((in Xx) A1)))
% Found (fun (Xx:fofType) (x7:((in Xx) A2)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A2)->(((in Xx) A)->((in Xx) A1))))
% Found x8:((in Xx) A)
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A1)
% Found (fun (x7:((in Xx) A2)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A1))
% Found (fun (Xx:fofType) (x7:((in Xx) A2)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A2)->(((in Xx) A)->((in Xx) A1)))
% Found (fun (Xx:fofType) (x7:((in Xx) A2)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A2)->(((in Xx) A)->((in Xx) A1))))
% Found x5:((in Z) (powerset A))
% Instantiate: A1:=Z:fofType;A10:=A:fofType
% Found x5 as proof of ((in A1) (powerset A10))
% Found x5:((in Z) (powerset A))
% Instantiate: A1:=Z:fofType;A10:=A:fofType
% Found x5 as proof of ((in A1) (powerset A10))
% Found x4:((in Y) (powerset A))
% Instantiate: A000:=A:fofType
% Found x4 as proof of ((in A0) (powerset A000))
% Found x4 as proof of ((in A0) (powerset A000))
% Found x3:((in X) (powerset A))
% Instantiate: A000:=A:fofType
% Found x3 as proof of ((in A0) (powerset A000))
% Found x3 as proof of ((in A0) (powerset A000))
% Found x5:((in Z) (powerset A))
% Instantiate: A1:=Z:fofType;A10:=A:fofType
% Found x5 as proof of ((in A1) (powerset A10))
% Found x5:((in Z) (powerset A))
% Instantiate: A1:=Z:fofType;A10:=A:fofType
% Found x5 as proof of ((in A1) (powerset A10))
% Found x5:((in Z) (powerset A))
% Instantiate: A1:=A:fofType
% Found x5 as proof of ((in Z) (powerset A1))
% Found x4:((in Y) (powerset A))
% Instantiate: A1:=A:fofType
% Found x4 as proof of ((in Y) (powerset A1))
% Found ((x0000 x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((fun (x7:((in Y) (powerset A1)))=> ((x000 x7) Z)) x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((fun (x7:((in Y) (powerset A1)))=> (((x00 Y) x7) Z)) x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((fun (x7:((in Y) (powerset A1)))=> ((((x0 A1) Y) x7) Z)) x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((fun (x7:((in Y) (powerset A1)))=> ((((x0 A1) Y) x7) Z)) x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=A:fofType
% Found x3 as proof of ((in X) (powerset A1))
% Found x5:((in Z) (powerset A))
% Instantiate: A1:=A:fofType
% Found x5 as proof of ((in Z) (powerset A1))
% Found ((x0000 x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((fun (x7:((in X) (powerset A1)))=> ((x000 x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((fun (x7:((in X) (powerset A1)))=> (((x00 X) x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found x5:((in Z) (powerset A))
% Instantiate: A1:=A:fofType
% Found x5 as proof of ((in Z) (powerset A1))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=A:fofType
% Found x3 as proof of ((in X) (powerset A1))
% Found ((x0000 x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((fun (x7:((in X) (powerset A1)))=> ((x000 x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((fun (x7:((in X) (powerset A1)))=> (((x00 X) x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found x5:((in Z) (powerset A))
% Instantiate: A1:=A:fofType
% Found x5 as proof of ((in Z) (powerset A1))
% Found x4:((in Y) (powerset A))
% Instantiate: A1:=A:fofType
% Found x4 as proof of ((in Y) (powerset A1))
% Found ((x0000 x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((fun (x7:((in Y) (powerset A1)))=> ((x000 x7) Z)) x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((fun (x7:((in Y) (powerset A1)))=> (((x00 Y) x7) Z)) x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((fun (x7:((in Y) (powerset A1)))=> ((((x0 A1) Y) x7) Z)) x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((fun (x7:((in Y) (powerset A1)))=> ((((x0 A1) Y) x7) Z)) x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found x7:((in Xx) A01)
% Instantiate: A01:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x7:((in Xx) A01)
% Instantiate: A01:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x8:((in Xx) A)
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A1)
% Found (fun (x7:((in Xx) A2)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A1))
% Found (fun (Xx:fofType) (x7:((in Xx) A2)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A2)->(((in Xx) A)->((in Xx) A1)))
% Found (fun (Xx:fofType) (x7:((in Xx) A2)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A2)->(((in Xx) A)->((in Xx) A1))))
% Found x8:((in Xx) A)
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A1)
% Found (fun (x7:((in Xx) A2)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A1))
% Found (fun (Xx:fofType) (x7:((in Xx) A2)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A2)->(((in Xx) A)->((in Xx) A1)))
% Found (fun (Xx:fofType) (x7:((in Xx) A2)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A2)->(((in Xx) A)->((in Xx) A1))))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))
% Instantiate: A00:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of ((in Xx) A00)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00))))
% Found x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))
% Instantiate: A00:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of ((in Xx) A00)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00))))
% Found x5:((in Z) (powerset A))
% Instantiate: A1:=A:fofType
% Found x5 as proof of ((in Z) (powerset A1))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=A:fofType
% Found x3 as proof of ((in X) (powerset A1))
% Found ((x0000 x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((fun (x7:((in X) (powerset A1)))=> ((x000 x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((fun (x7:((in X) (powerset A1)))=> (((x00 X) x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found x4:((in Y) (powerset A))
% Instantiate: A1:=A:fofType
% Found x4 as proof of ((in Y) (powerset A1))
% Found x5:((in Z) (powerset A))
% Instantiate: A1:=A:fofType
% Found x5 as proof of ((in Z) (powerset A1))
% Found ((x0000 x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((fun (x7:((in Y) (powerset A1)))=> ((x000 x7) Z)) x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((fun (x7:((in Y) (powerset A1)))=> (((x00 Y) x7) Z)) x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((fun (x7:((in Y) (powerset A1)))=> ((((x0 A1) Y) x7) Z)) x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((fun (x7:((in Y) (powerset A1)))=> ((((x0 A1) Y) x7) Z)) x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found x5:((in Z) (powerset A))
% Instantiate: A1:=A:fofType
% Found x5 as proof of ((in Z) (powerset A1))
% Found x4:((in Y) (powerset A))
% Instantiate: A1:=A:fofType
% Found x4 as proof of ((in Y) (powerset A1))
% Found ((x0000 x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((fun (x7:((in Y) (powerset A1)))=> ((x000 x7) Z)) x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((fun (x7:((in Y) (powerset A1)))=> (((x00 Y) x7) Z)) x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((fun (x7:((in Y) (powerset A1)))=> ((((x0 A1) Y) x7) Z)) x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((fun (x7:((in Y) (powerset A1)))=> ((((x0 A1) Y) x7) Z)) x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found x5:((in Z) (powerset A))
% Instantiate: A1:=A:fofType
% Found x5 as proof of ((in Z) (powerset A1))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=A:fofType
% Found x3 as proof of ((in X) (powerset A1))
% Found ((x0000 x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((fun (x7:((in X) (powerset A1)))=> ((x000 x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((fun (x7:((in X) (powerset A1)))=> (((x00 X) x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found x7:((in Xx) A01)
% Instantiate: A01:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x7:((in Xx) A01)
% Instantiate: A01:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=X:fofType;A10:=A:fofType
% Found x3 as proof of ((in A1) (powerset A10))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=X:fofType;A10:=A:fofType
% Found x3 as proof of ((in A1) (powerset A10))
% Found x7:((in Xx) A01)
% Instantiate: A01:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x7:((in Xx) A01)
% Instantiate: A01:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x4:((in Y) (powerset A))
% Instantiate: A10:=A:fofType
% Found x4 as proof of ((in A0) (powerset A10))
% Found x4 as proof of ((in A0) (powerset A10))
% Found x3:((in X) (powerset A))
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((in A0) (powerset A10))
% Found x3 as proof of ((in A0) (powerset A10))
% Found x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))
% Instantiate: A00:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of ((in Xx) A00)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00))))
% Found x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))
% Instantiate: A00:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of ((in Xx) A00)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00))))
% Found x7:((in Xx) A01)
% Instantiate: A01:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A01)
% Instantiate: A01:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x7:((in Xx) A000)
% Instantiate: A000:=A00:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A0)
% Found (fun (x7:((in Xx) A000)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A0))
% Found (fun (Xx:fofType) (x7:((in Xx) A000)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A000)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A000)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A000)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A0))))
% Found x7:((in Xx) A000)
% Instantiate: A000:=A00:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A0)
% Found (fun (x7:((in Xx) A000)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A0))
% Found (fun (Xx:fofType) (x7:((in Xx) A000)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A000)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A000)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A000)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A0))))
% Found x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))
% Instantiate: A00:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of ((in Xx) A00)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00))))
% Found x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))
% Instantiate: A00:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of ((in Xx) A00)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00))))
% Found x5:((in Z) (powerset A))
% Instantiate: A1:=Z:fofType;A10:=A:fofType
% Found x5 as proof of ((in A1) (powerset A10))
% Found x5:((in Z) (powerset A))
% Instantiate: A1:=Z:fofType;A10:=A:fofType
% Found x5 as proof of ((in A1) (powerset A10))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A01)
% Instantiate: A01:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x7:((in Xx) A01)
% Instantiate: A01:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x7:((in Xx) A01)
% Instantiate: A01:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x7:((in Xx) A01)
% Instantiate: A01:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x4:((in Y) (powerset A))
% Instantiate: A10:=A:fofType
% Found x4 as proof of ((in A0) (powerset A10))
% Found x4 as proof of ((in A0) (powerset A10))
% Found x3:((in X) (powerset A))
% Instantiate: A10:=A:fofType
% Found x3 as proof of ((in A0) (powerset A10))
% Found x3 as proof of ((in A0) (powerset A10))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x8:((in Xx) A)
% Instantiate: A00:=A:fofType
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A00)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A00))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A1)->(((in Xx) A)->((in Xx) A00)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A)->((in Xx) A00))))
% Found x8:((in Xx) A)
% Instantiate: A00:=A:fofType
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A00)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A00))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A1)->(((in Xx) A)->((in Xx) A00)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A)->((in Xx) A00))))
% Found x7:((in Xx) A01)
% Instantiate: A01:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x7:((in Xx) A01)
% Instantiate: A01:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))
% Instantiate: A00:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of ((in Xx) A00)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00))))
% Found x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))
% Instantiate: A00:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of ((in Xx) A00)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00))))
% Found x7:((in Xx) A000)
% Instantiate: A000:=A00:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A0)
% Found (fun (x7:((in Xx) A000)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A0))
% Found (fun (Xx:fofType) (x7:((in Xx) A000)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A000)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A000)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A000)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A0))))
% Found x7:((in Xx) A000)
% Instantiate: A000:=A00:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A0)
% Found (fun (x7:((in Xx) A000)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A0))
% Found (fun (Xx:fofType) (x7:((in Xx) A000)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A000)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A000)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A000)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A0))))
% Found x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))
% Instantiate: A00:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of ((in Xx) A00)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00))))
% Found x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))
% Instantiate: A00:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of ((in Xx) A00)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00))))
% Found x7:((in Xx) A01)
% Instantiate: A01:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x7:((in Xx) A01)
% Instantiate: A01:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x7:((in Xx) A01)
% Instantiate: A01:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x7:((in Xx) A01)
% Instantiate: A01:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x8:((in Xx) A)
% Instantiate: A00:=A:fofType
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A00)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A00))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A1)->(((in Xx) A)->((in Xx) A00)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A)->((in Xx) A00))))
% Found x8:((in Xx) A)
% Instantiate: A00:=A:fofType
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A00)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A00))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A1)->(((in Xx) A)->((in Xx) A00)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A)->((in Xx) A00))))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))
% Instantiate: A00:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of ((in Xx) A00)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00))))
% Found x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))
% Instantiate: A00:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of ((in Xx) A00)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A00))))
% Found x7:((in Xx) A01)
% Instantiate: A01:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x7:((in Xx) A01)
% Instantiate: A01:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x8:((in Xx) A)
% Instantiate: A00:=A:fofType
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A00)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A00))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A1)->(((in Xx) A)->((in Xx) A00)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A)->((in Xx) A00))))
% Found x8:((in Xx) A)
% Instantiate: A00:=A:fofType
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A00)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A00))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A1)->(((in Xx) A)->((in Xx) A00)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A)->((in Xx) A00))))
% Found x7:((in Xx) A01)
% Instantiate: A01:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x7:((in Xx) A01)
% Instantiate: A01:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A10)
% Instantiate: A10:=A1:fofType
% Found (fun (x8:((in Xx) A))=> x7) as proof of ((in Xx) A0)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A))=> x7) as proof of (((in Xx) A)->((in Xx) A0))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x7) as proof of (((in Xx) A10)->(((in Xx) A)->((in Xx) A0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A)->((in Xx) A0))))
% Found x7:((in Xx) A10)
% Instantiate: A10:=A1:fofType
% Found (fun (x8:((in Xx) A))=> x7) as proof of ((in Xx) A0)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A))=> x7) as proof of (((in Xx) A)->((in Xx) A0))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x7) as proof of (((in Xx) A10)->(((in Xx) A)->((in Xx) A0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A)->((in Xx) A0))))
% Found x8:((in Xx) A)
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A00)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A00))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A1)->(((in Xx) A)->((in Xx) A00)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A)->((in Xx) A00))))
% Found x8:((in Xx) A)
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A00)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A00))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A1)->(((in Xx) A)->((in Xx) A00)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A)->((in Xx) A00))))
% Found x7:((in Xx) A01)
% Instantiate: A01:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x7:((in Xx) A01)
% Instantiate: A01:=A:fofType
% Found (fun (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A01)) (x8:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A01)->(((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))->((in Xx) A))))
% Found x8:((in Xx) A)
% Instantiate: A1:=A:fofType
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A1)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A1))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A10)->(((in Xx) A)->((in Xx) A1)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A)->((in Xx) A1))))
% Found x8:((in Xx) A)
% Instantiate: A1:=A:fofType
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A1)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A1))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A10)->(((in Xx) A)->((in Xx) A1)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A)->((in Xx) A1))))
% Found x8:((in Xx) A)
% Instantiate: A00:=A:fofType
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A00)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A00))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A1)->(((in Xx) A)->((in Xx) A00)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A)->((in Xx) A00))))
% Found x8:((in Xx) A)
% Instantiate: A00:=A:fofType
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A00)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A00))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A1)->(((in Xx) A)->((in Xx) A00)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A)->((in Xx) A00))))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x8:((in Xx) A)
% Instantiate: A1:=A:fofType
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A1)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A1))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A10)->(((in Xx) A)->((in Xx) A1)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A)->((in Xx) A1))))
% Found x8:((in Xx) A)
% Instantiate: A1:=A:fofType
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A1)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A1))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A10)->(((in Xx) A)->((in Xx) A1)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A)->((in Xx) A1))))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A1)
% Instantiate: A1:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binunion Y) Z)))=> x7) as proof of ((in Xx) A01)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) ((binunion Y) Z)))=> x7) as proof of (((in Xx) ((binunion Y) Z))->((in Xx) A01))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) ((binunion Y) Z)))=> x7) as proof of (((in Xx) A1)->(((in Xx) ((binunion Y) Z))->((in Xx) A01)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) ((binunion Y) Z)))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) ((binunion Y) Z))->((in Xx) A01))))
% Found x7:((in Xx) A1)
% Instantiate: A1:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of ((in Xx) A01)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of (((in Xx) ((binunion X) Z))->((in Xx) A01))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of (((in Xx) A1)->(((in Xx) ((binunion X) Z))->((in Xx) A01)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) ((binunion X) Z))->((in Xx) A01))))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A10)
% Instantiate: A10:=A1:fofType
% Found (fun (x8:((in Xx) A))=> x7) as proof of ((in Xx) A0)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A))=> x7) as proof of (((in Xx) A)->((in Xx) A0))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x7) as proof of (((in Xx) A10)->(((in Xx) A)->((in Xx) A0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A)->((in Xx) A0))))
% Found x8:((in Xx) A)
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A00)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A00))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A1)->(((in Xx) A)->((in Xx) A00)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A)->((in Xx) A00))))
% Found x8:((in Xx) A)
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A00)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A00))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A1)->(((in Xx) A)->((in Xx) A00)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A)->((in Xx) A00))))
% Found x7:((in Xx) A10)
% Instantiate: A10:=A1:fofType
% Found (fun (x8:((in Xx) A))=> x7) as proof of ((in Xx) A0)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A))=> x7) as proof of (((in Xx) A)->((in Xx) A0))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x7) as proof of (((in Xx) A10)->(((in Xx) A)->((in Xx) A0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A)->((in Xx) A0))))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x8:((in Xx) A)
% Instantiate: A1:=A:fofType
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A1)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A1))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A10)->(((in Xx) A)->((in Xx) A1)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A)->((in Xx) A1))))
% Found x8:((in Xx) A)
% Instantiate: A1:=A:fofType
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A1)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A1))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A10)->(((in Xx) A)->((in Xx) A1)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A)->((in Xx) A1))))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x8:((in Xx) A)
% Instantiate: A1:=A:fofType
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A1)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A1))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A10)->(((in Xx) A)->((in Xx) A1)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A)->((in Xx) A1))))
% Found x8:((in Xx) A)
% Instantiate: A1:=A:fofType
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A1)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A1))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A10)->(((in Xx) A)->((in Xx) A1)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A)->((in Xx) A1))))
% Found x8:((in Xx) A)
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A00)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A00))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A1)->(((in Xx) A)->((in Xx) A00)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A)->((in Xx) A00))))
% Found x8:((in Xx) A)
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A00)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A00))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A1)->(((in Xx) A)->((in Xx) A00)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A)->((in Xx) A00))))
% Found x12:((in Xx0) Y)
% Found (fun (x12:((in Xx0) Y))=> x12) as proof of ((in Xx0) Y)
% Found (fun (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12) as proof of (((in Xx0) Y)->((in Xx0) Y))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12) as proof of (((in Xx0) A)->(((in Xx0) Y)->((in Xx0) Y)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) Y))))
% Found (((x1110 x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found ((((x111 A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found (((((fun (A1:fofType) (x9:((in Y) (powerset A1)))=> (((x11 A1) x9) Y)) A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found (((((fun (A1:fofType) (x9:((in Y) (powerset A1)))=> (((x11 A1) x9) Y)) A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found x12:((in Xx0) X)
% Found (fun (x12:((in Xx0) X))=> x12) as proof of ((in Xx0) X)
% Found (fun (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12) as proof of (((in Xx0) X)->((in Xx0) X))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12) as proof of (((in Xx0) A)->(((in Xx0) X)->((in Xx0) X)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) X)->((in Xx) X))))
% Found (((x1110 x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found ((((x111 A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found (((((fun (A1:fofType) (x9:((in X) (powerset A1)))=> (((x11 A1) x9) X)) A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found (((((fun (A1:fofType) (x9:((in X) (powerset A1)))=> (((x11 A1) x9) X)) A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found x8:((in Xx) A)
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A0)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A0))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A10)->(((in Xx) A)->((in Xx) A0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A)->((in Xx) A0))))
% Found x8:((in Xx) A)
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A0)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A0))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A10)->(((in Xx) A)->((in Xx) A0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A)->((in Xx) A0))))
% Found x8:((in Xx) A)
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A0)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A0))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A10)->(((in Xx) A)->((in Xx) A0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A)->((in Xx) A0))))
% Found x8:((in Xx) A)
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A0)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A0))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A10)->(((in Xx) A)->((in Xx) A0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A)->((in Xx) A0))))
% Found x8:((in Xx) A)
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A1)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A1))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A10)->(((in Xx) A)->((in Xx) A1)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A)->((in Xx) A1))))
% Found x8:((in Xx) A)
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A1)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A1))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A10)->(((in Xx) A)->((in Xx) A1)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A)->((in Xx) A1))))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x8:((in Xx) A)
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A00)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A00))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A1)->(((in Xx) A)->((in Xx) A00)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A)->((in Xx) A00))))
% Found x8:((in Xx) A)
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A00)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A00))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A1)->(((in Xx) A)->((in Xx) A00)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A)->((in Xx) A00))))
% Found x4:((in Y) (powerset A))
% Instantiate: A02:=A:fofType
% Found x4 as proof of ((in Y) (powerset A02))
% Found x5:((in Z) (powerset A))
% Instantiate: A02:=A:fofType
% Found x5 as proof of ((in Z) (powerset A02))
% Found ((x0000 x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A02))
% Found (((fun (x7:((in Y) (powerset A02)))=> ((x000 x7) Z)) x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A02))
% Found (((fun (x7:((in Y) (powerset A02)))=> (((x00 Y) x7) Z)) x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A02))
% Found (((fun (x7:((in Y) (powerset A02)))=> ((((x0 A02) Y) x7) Z)) x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A02))
% Found (((fun (x7:((in Y) (powerset A02)))=> ((((x0 A02) Y) x7) Z)) x4) x5) as proof of ((in ((binunion Y) Z)) (powerset A02))
% Found x000000:=(x00000 x5):((in ((binunion X) Z)) (powerset A02))
% Found (x00000 x5) as proof of ((in ((binunion X) Z)) (powerset A02))
% Found ((x0000 Z) x5) as proof of ((in ((binunion X) Z)) (powerset A02))
% Found (((x000 x3) Z) x5) as proof of ((in ((binunion X) Z)) (powerset A02))
% Found ((((x00 X) x3) Z) x5) as proof of ((in ((binunion X) Z)) (powerset A02))
% Found (((((x0 A02) X) x3) Z) x5) as proof of ((in ((binunion X) Z)) (powerset A02))
% Found (((((x0 A02) X) x3) Z) x5) as proof of ((in ((binunion X) Z)) (powerset A02))
% Found ((x600 (((((x0 A02) X) x3) Z) x5)) (((fun (x7:((in Y) (powerset A02)))=> ((((x0 A02) Y) x7) Z)) x4) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A02))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A02)))=> ((x60 x7) ((binunion Y) Z))) (((((x0 A02) X) x3) Z) x5)) (((fun (x7:((in Y) (powerset A02)))=> ((((x0 A02) Y) x7) Z)) x4) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A02))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A02)))=> (((x6 ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A02) X) x3) Z) x5)) (((fun (x7:((in Y) (powerset A02)))=> ((((x0 A02) Y) x7) Z)) x4) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A02))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A02)))=> ((((x A02) ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A02) X) x3) Z) x5)) (((fun (x7:((in Y) (powerset A02)))=> ((((x0 A02) Y) x7) Z)) x4) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A02))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A02)))=> ((((x A02) ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A02) X) x3) Z) x5)) (((fun (x7:((in Y) (powerset A02)))=> ((((x0 A02) Y) x7) Z)) x4) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A02))
% Found x8:((in Xx) A)
% Instantiate: A1:=A:fofType
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A1)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A1))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A10)->(((in Xx) A)->((in Xx) A1)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A)->((in Xx) A1))))
% Found x8:((in Xx) A)
% Instantiate: A1:=A:fofType
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A1)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A1))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A10)->(((in Xx) A)->((in Xx) A1)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A)->((in Xx) A1))))
% Found x12:((in Xx0) X)
% Found (fun (x12:((in Xx0) X))=> x12) as proof of ((in Xx0) X)
% Found (fun (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12) as proof of (((in Xx0) X)->((in Xx0) X))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12) as proof of (((in Xx0) A)->(((in Xx0) X)->((in Xx0) X)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) X)->((in Xx) X))))
% Found (((x1110 x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found ((((x111 A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found (((((fun (A1:fofType) (x9:((in X) (powerset A1)))=> (((x11 A1) x9) X)) A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found (((((fun (A1:fofType) (x9:((in X) (powerset A1)))=> (((x11 A1) x9) X)) A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found x12:((in Xx0) Y)
% Found (fun (x12:((in Xx0) Y))=> x12) as proof of ((in Xx0) Y)
% Found (fun (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12) as proof of (((in Xx0) Y)->((in Xx0) Y))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12) as proof of (((in Xx0) A)->(((in Xx0) Y)->((in Xx0) Y)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) Y))))
% Found (((x1110 x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found ((((x111 A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found (((((fun (A1:fofType) (x9:((in Y) (powerset A1)))=> (((x11 A1) x9) Y)) A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found (((((fun (A1:fofType) (x9:((in Y) (powerset A1)))=> (((x11 A1) x9) Y)) A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found x8:((in Xx) A)
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A0)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A0))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A10)->(((in Xx) A)->((in Xx) A0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A)->((in Xx) A0))))
% Found x8:((in Xx) A)
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A0)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A0))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A10)->(((in Xx) A)->((in Xx) A0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A)->((in Xx) A0))))
% Found x8:((in Xx) A)
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A0)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A0))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A10)->(((in Xx) A)->((in Xx) A0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A)->((in Xx) A0))))
% Found x8:((in Xx) A)
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A0)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A0))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A10)->(((in Xx) A)->((in Xx) A0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A)->((in Xx) A0))))
% Found x12:((in Xx0) Y)
% Found (fun (x12:((in Xx0) Y))=> x12) as proof of ((in Xx0) Y)
% Found (fun (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12) as proof of (((in Xx0) Y)->((in Xx0) Y))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12) as proof of (((in Xx0) A)->(((in Xx0) Y)->((in Xx0) Y)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) Y))))
% Found (((x1110 x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found ((((x111 A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found (((((fun (A1:fofType) (x9:((in Y) (powerset A1)))=> (((x11 A1) x9) Y)) A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found (((((fun (A1:fofType) (x9:((in Y) (powerset A1)))=> (((x11 A1) x9) Y)) A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found x12:((in Xx0) X)
% Found (fun (x12:((in Xx0) X))=> x12) as proof of ((in Xx0) X)
% Found (fun (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12) as proof of (((in Xx0) X)->((in Xx0) X))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12) as proof of (((in Xx0) A)->(((in Xx0) X)->((in Xx0) X)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) X)->((in Xx) X))))
% Found (((x1110 x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found ((((x111 A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found (((((fun (A1:fofType) (x9:((in X) (powerset A1)))=> (((x11 A1) x9) X)) A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found (((((fun (A1:fofType) (x9:((in X) (powerset A1)))=> (((x11 A1) x9) X)) A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found x8:((in Xx) A)
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A1)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A1))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A10)->(((in Xx) A)->((in Xx) A1)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A)->((in Xx) A1))))
% Found x8:((in Xx) A)
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A1)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A1))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A10)->(((in Xx) A)->((in Xx) A1)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A)->((in Xx) A1))))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x8:((in Xx) A)
% Instantiate: A1:=A:fofType
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A1)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A1))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A10)->(((in Xx) A)->((in Xx) A1)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A)->((in Xx) A1))))
% Found x8:((in Xx) A)
% Instantiate: A1:=A:fofType
% Found (fun (x8:((in Xx) A))=> x8) as proof of ((in Xx) A1)
% Found (fun (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A)->((in Xx) A1))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (((in Xx) A10)->(((in Xx) A)->((in Xx) A1)))
% Found (fun (Xx:fofType) (x7:((in Xx) A10)) (x8:((in Xx) A))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A10)->(((in Xx) A)->((in Xx) A1))))
% Found x9:((in Xx0) A1)
% Instantiate: A1:=A:fofType
% Found (fun (x13:((in Xx0) Xx))=> x9) as proof of ((in Xx0) A)
% Found (fun (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (((in Xx0) Xx)->((in Xx0) A))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (((in Xx0) A1)->(((in Xx0) Xx)->((in Xx0) A)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (forall (Xx0:fofType), (((in Xx0) A1)->(((in Xx0) Xx)->((in Xx0) A))))
% Found x9:((in Xx0) A1)
% Instantiate: A1:=A:fofType
% Found (fun (x13:((in Xx0) Xx))=> x9) as proof of ((in Xx0) A)
% Found (fun (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (((in Xx0) Xx)->((in Xx0) A))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (((in Xx0) A1)->(((in Xx0) Xx)->((in Xx0) A)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (forall (Xx0:fofType), (((in Xx0) A1)->(((in Xx0) Xx)->((in Xx0) A))))
% Found x9:((in Xx0) A1)
% Instantiate: A1:=A:fofType
% Found (fun (x13:((in Xx0) Xx))=> x9) as proof of ((in Xx0) A)
% Found (fun (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (((in Xx0) Xx)->((in Xx0) A))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (((in Xx0) A1)->(((in Xx0) Xx)->((in Xx0) A)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (forall (Xx0:fofType), (((in Xx0) A1)->(((in Xx0) Xx)->((in Xx0) A))))
% Found x9:((in Xx0) A1)
% Instantiate: A1:=A:fofType
% Found (fun (x13:((in Xx0) Xx))=> x9) as proof of ((in Xx0) A)
% Found (fun (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (((in Xx0) Xx)->((in Xx0) A))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (((in Xx0) A1)->(((in Xx0) Xx)->((in Xx0) A)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (forall (Xx0:fofType), (((in Xx0) A1)->(((in Xx0) Xx)->((in Xx0) A))))
% Found x9:((in Xx0) A1)
% Instantiate: A1:=A:fofType
% Found (fun (x13:((in Xx0) Xx))=> x9) as proof of ((in Xx0) A)
% Found (fun (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (((in Xx0) Xx)->((in Xx0) A))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (((in Xx0) A1)->(((in Xx0) Xx)->((in Xx0) A)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (forall (Xx0:fofType), (((in Xx0) A1)->(((in Xx0) Xx)->((in Xx0) A))))
% Found x9:((in Xx0) A1)
% Instantiate: A1:=A:fofType
% Found (fun (x13:((in Xx0) Xx))=> x9) as proof of ((in Xx0) A)
% Found (fun (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (((in Xx0) Xx)->((in Xx0) A))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (((in Xx0) A1)->(((in Xx0) Xx)->((in Xx0) A)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (forall (Xx0:fofType), (((in Xx0) A1)->(((in Xx0) Xx)->((in Xx0) A))))
% Found x5:((in Z) (powerset A))
% Instantiate: A0:=Z:fofType;A00:=A:fofType
% Found x5 as proof of ((in A0) (powerset A00))
% Found x5:((in Z) (powerset A))
% Instantiate: A0:=Z:fofType;A00:=A:fofType
% Found x5 as proof of ((in A0) (powerset A00))
% Found x5:((in Z) (powerset A))
% Instantiate: A0:=Z:fofType;A00:=A:fofType
% Found x5 as proof of ((in A0) (powerset A00))
% Found x5:((in Z) (powerset A))
% Instantiate: A0:=Z:fofType;A00:=A:fofType
% Found x5 as proof of ((in A0) (powerset A00))
% Found x5:((in Z) (powerset A))
% Instantiate: A0:=Z:fofType;A00:=A:fofType
% Found x5 as proof of ((in A0) (powerset A00))
% Found x5:((in Z) (powerset A))
% Instantiate: A0:=Z:fofType;A00:=A:fofType
% Found x5 as proof of ((in A0) (powerset A00))
% Found x5:((in Z) (powerset A))
% Instantiate: A1:=A:fofType
% Found x5 as proof of ((in Z) (powerset A1))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=A:fofType
% Found x3 as proof of ((in X) (powerset A1))
% Found ((x0000 x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((fun (x7:((in X) (powerset A1)))=> ((x000 x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((fun (x7:((in X) (powerset A1)))=> (((x00 X) x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found x000000:=(x00000 x5):((in ((binunion Y) Z)) (powerset A1))
% Found (x00000 x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found ((x0000 Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((x000 x4) Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found ((((x00 Y) x4) Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((((x0 A1) Y) x4) Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((((x0 A1) Y) x4) Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found ((x600 (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5)) (((((x0 A1) Y) x4) Z) x5)) as proof of ((in A01) (powerset A1))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A1)))=> ((x60 x7) ((binunion Y) Z))) (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5)) (((((x0 A1) Y) x4) Z) x5)) as proof of ((in A01) (powerset A1))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A1)))=> (((x6 ((binunion X) Z)) x7) ((binunion Y) Z))) (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5)) (((((x0 A1) Y) x4) Z) x5)) as proof of ((in A01) (powerset A1))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A1)))=> ((((x A1) ((binunion X) Z)) x7) ((binunion Y) Z))) (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5)) (((((x0 A1) Y) x4) Z) x5)) as proof of ((in A01) (powerset A1))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A1)))=> ((((x A1) ((binunion X) Z)) x7) ((binunion Y) Z))) (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5)) (((((x0 A1) Y) x4) Z) x5)) as proof of ((in A01) (powerset A1))
% Found x000000:=(x00000 x5):((in ((binunion X) Z)) (powerset A1))
% Found (x00000 x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found ((x0000 Z) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((x000 x3) Z) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found ((((x00 X) x3) Z) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((((x0 A1) X) x3) Z) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found (((((x0 A1) X) x3) Z) x5) as proof of ((in ((binunion X) Z)) (powerset A1))
% Found x000000:=(x00000 x5):((in ((binunion Y) Z)) (powerset A1))
% Found (x00000 x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found ((x0000 Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((x000 x4) Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found ((((x00 Y) x4) Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((((x0 A1) Y) x4) Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found (((((x0 A1) Y) x4) Z) x5) as proof of ((in ((binunion Y) Z)) (powerset A1))
% Found ((x600 (((((x0 A1) X) x3) Z) x5)) (((((x0 A1) Y) x4) Z) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A1))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A1)))=> ((x60 x7) ((binunion Y) Z))) (((((x0 A1) X) x3) Z) x5)) (((((x0 A1) Y) x4) Z) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A1))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A1)))=> (((x6 ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A1) X) x3) Z) x5)) (((((x0 A1) Y) x4) Z) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A1))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A1)))=> ((((x A1) ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A1) X) x3) Z) x5)) (((((x0 A1) Y) x4) Z) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A1))
% Found (((fun (x7:((in ((binunion X) Z)) (powerset A1)))=> ((((x A1) ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A1) X) x3) Z) x5)) (((((x0 A1) Y) x4) Z) x5)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A1))
% Found (((x1100 (((fun (x7:((in ((binunion X) Z)) (powerset A1)))=> ((((x A1) ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A1) X) x3) Z) x5)) (((((x0 A1) Y) x4) Z) x5))) (((fun (x7:((in ((binunion X) Z)) (powerset A1)))=> ((((x A1) ((binunion X) Z)) x7) ((binunion Y) Z))) (((fun (x7:((in X) (powerset A1)))=> ((((x0 A1) X) x7) Z)) x3) x5)) (((((x0 A1) Y) x4) Z) x5))) (fun (Xx:fofType) (x6:((in Xx) A1)) (x7:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A01))
% Found ((((x110 A) (((fun (x7:((in ((binunion X) Z)) (powerset A)))=> ((((x A) ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A) X) x3) Z) x5)) (((((x0 A) Y) x4) Z) x5))) (((fun (x7:((in ((binunion X) Z)) (powerset A)))=> ((((x A) ((binunion X) Z)) x7) ((binunion Y) Z))) (((fun (x7:((in X) (powerset A)))=> ((((x0 A) X) x7) Z)) x3) x5)) (((((x0 A) Y) x4) Z) x5))) (fun (Xx:fofType) (x6:((in Xx) A)) (x7:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A01))
% Found (((((fun (A1:fofType) (x6:((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A1)))=> (((x11 A1) x6) A01)) A) (((fun (x7:((in ((binunion X) Z)) (powerset A)))=> ((((x A) ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A) X) x3) Z) x5)) (((((x0 A) Y) x4) Z) x5))) (((fun (x7:((in ((binunion X) Z)) (powerset A)))=> ((((x A) ((binunion X) Z)) x7) ((binunion Y) Z))) (((fun (x7:((in X) (powerset A)))=> ((((x0 A) X) x7) Z)) x3) x5)) (((((x0 A) Y) x4) Z) x5))) (fun (Xx:fofType) (x6:((in Xx) A)) (x7:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A01))
% Found (((((fun (A1:fofType) (x6:((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A1)))=> ((((fun (A1:fofType)=> ((x1 A1) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))) A1) x6) A01)) A) (((fun (x7:((in ((binunion X) Z)) (powerset A)))=> ((((x A) ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A) X) x3) Z) x5)) (((((x0 A) Y) x4) Z) x5))) (((fun (x7:((in ((binunion X) Z)) (powerset A)))=> ((((x A) ((binunion X) Z)) x7) ((binunion Y) Z))) (((fun (x7:((in X) (powerset A)))=> ((((x0 A) X) x7) Z)) x3) x5)) (((((x0 A) Y) x4) Z) x5))) (fun (Xx:fofType) (x6:((in Xx) A)) (x7:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A01))
% Found (((((fun (A1:fofType) (x6:((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A1)))=> ((((fun (A1:fofType)=> ((x1 A1) ((binintersect ((binunion X) Z)) ((binunion Y) Z)))) A1) x6) A01)) A) (((fun (x7:((in ((binunion X) Z)) (powerset A)))=> ((((x A) ((binunion X) Z)) x7) ((binunion Y) Z))) (((((x0 A) X) x3) Z) x5)) (((((x0 A) Y) x4) Z) x5))) (((fun (x7:((in ((binunion X) Z)) (powerset A)))=> ((((x A) ((binunion X) Z)) x7) ((binunion Y) Z))) (((fun (x7:((in X) (powerset A)))=> ((((x0 A) X) x7) Z)) x3) x5)) (((((x0 A) Y) x4) Z) x5))) (fun (Xx:fofType) (x6:((in Xx) A)) (x7:((in Xx) ((binintersect ((binunion X) Z)) ((binunion Y) Z))))=> x7)) as proof of ((in ((binintersect ((binunion X) Z)) ((binunion Y) Z))) (powerset A01))
% Found x8:((in Xx) Y)
% Found x8 as proof of ((in Xx) Y)
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x8:((in Xx) X)
% Found x8 as proof of ((in Xx) X)
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x8:((in Xx) Y)
% Found x8 as proof of ((in Xx) Y)
% Found x8:((in Xx) X)
% Found x8 as proof of ((in Xx) X)
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x7:((in Xx) A)
% Found x7 as proof of ((in Xx) A)
% Found x4:((in Y) (powerset A))
% Found x4 as proof of ((in Y) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x12:((in Xx0) X)
% Found (fun (x12:((in Xx0) X))=> x12) as proof of ((in Xx0) X)
% Found (fun (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12) as proof of (((in Xx0) X)->((in Xx0) X))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12) as proof of (((in Xx0) A)->(((in Xx0) X)->((in Xx0) X)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) X)->((in Xx) X))))
% Found (((x1110 x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found ((((x111 A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found (((((fun (A1:fofType) (x9:((in X) (powerset A1)))=> (((x11 A1) x9) X)) A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found (((((fun (A1:fofType) (x9:((in X) (powerset A1)))=> (((x11 A1) x9) X)) A) x3) x3) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) X))=> x12)) as proof of ((in X) (powerset X))
% Found x12:((in Xx0) Y)
% Found (fun (x12:((in Xx0) Y))=> x12) as proof of ((in Xx0) Y)
% Found (fun (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12) as proof of (((in Xx0) Y)->((in Xx0) Y))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12) as proof of (((in Xx0) A)->(((in Xx0) Y)->((in Xx0) Y)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12) as proof of (forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) Y))))
% Found (((x1110 x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found ((((x111 A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found (((((fun (A1:fofType) (x9:((in Y) (powerset A1)))=> (((x11 A1) x9) Y)) A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found (((((fun (A1:fofType) (x9:((in Y) (powerset A1)))=> (((x11 A1) x9) Y)) A) x4) x4) (fun (Xx0:fofType) (x9:((in Xx0) A)) (x12:((in Xx0) Y))=> x12)) as proof of ((in Y) (powerset Y))
% Found x9:((in Xx0) A1)
% Instantiate: A1:=A:fofType
% Found (fun (x13:((in Xx0) Xx))=> x9) as proof of ((in Xx0) A)
% Found (fun (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (((in Xx0) Xx)->((in Xx0) A))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (((in Xx0) A1)->(((in Xx0) Xx)->((in Xx0) A)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (forall (Xx0:fofType), (((in Xx0) A1)->(((in Xx0) Xx)->((in Xx0) A))))
% Found x9:((in Xx0) A1)
% Instantiate: A1:=A:fofType
% Found (fun (x13:((in Xx0) Xx))=> x9) as proof of ((in Xx0) A)
% Found (fun (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (((in Xx0) Xx)->((in Xx0) A))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (((in Xx0) A1)->(((in Xx0) Xx)->((in Xx0) A)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (forall (Xx0:fofType), (((in Xx0) A1)->(((in Xx0) Xx)->((in Xx0) A))))
% Found x9:((in Xx0) A1)
% Instantiate: A1:=A:fofType
% Found (fun (x13:((in Xx0) Xx))=> x9) as proof of ((in Xx0) A)
% Found (fun (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (((in Xx0) Xx)->((in Xx0) A))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (((in Xx0) A1)->(((in Xx0) Xx)->((in Xx0) A)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (forall (Xx0:fofType), (((in Xx0) A1)->(((in Xx0) Xx)->((in Xx0) A))))
% Found x9:((in Xx0) A1)
% Instantiate: A1:=A:fofType
% Found (fun (x13:((in Xx0) Xx))=> x9) as proof of ((in Xx0) A)
% Found (fun (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (((in Xx0) Xx)->((in Xx0) A))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (((in Xx0) A1)->(((in Xx0) Xx)->((in Xx0) A)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (forall (Xx0:fofType), (((in Xx0) A1)->(((in Xx0) Xx)->((in Xx0) A))))
% Found x9:((in Xx0) A1)
% Instantiate: A1:=A:fofType
% Found (fun (x13:((in Xx0) Xx))=> x9) as proof of ((in Xx0) A)
% Found (fun (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (((in Xx0) Xx)->((in Xx0) A))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (((in Xx0) A1)->(((in Xx0) Xx)->((in Xx0) A)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (forall (Xx0:fofType), (((in Xx0) A1)->(((in Xx0) Xx)->((in Xx0) A))))
% Found x9:((in Xx0) A1)
% Instantiate: A1:=A:fofType
% Found (fun (x13:((in Xx0) Xx))=> x9) as proof of ((in Xx0) A)
% Found (fun (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (((in Xx0) Xx)->((in Xx0) A))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (((in Xx0) A1)->(((in Xx0) Xx)->((in Xx0) A)))
% Found (fun (Xx0:fofType) (x9:((in Xx0) A1)) (x13:((in Xx0) Xx))=> x9) as proof of (forall (Xx0:fofType), (((in Xx0) A1)->(((in Xx0) Xx)->((in Xx0) A))))
% Found x3:((in X) (powerset A))
% Instantiate: A0:=X:fofType;A00:=A:fofType
% Found x3 as proof of ((in A0) (powerset A00))
% Found x3:((in X) (powerset A))
% Instantiate: A0:=X:fofType;A00:=A:fofType
% Found x3 as proof of ((in A0) (powerset A00))
% Found x3:((in X) (powerset A))
% Instantiate: A0:=X:fofType;A00:=A:fofType
% Found x3 as proof of ((in A0) (powerset A00))
% Found x3:((in X) (powerset A))
% Instantiate: A0:=X:fofType;A00:=A:fofType
% Found x3 as proof of ((in A0) (powerset A00))
% Found x3:((in X) (powerset A))
% Instantiate: A0:=X:fofType;A00:=A:fofType
% Found x3 as proof of ((in A0) (powerset A00))
% Found x3:((in X) (powerset A))
% Instantiate: A0:=X:fofType;A00:=A:fofType
% Found x3 as proof of ((in A0) (powerset A00))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=A:fofType;A0:=X:fofType
% Found x3 as proof of ((in A0) (powerset A1))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=A:fofType;A0:=X:fofType
% Found x3 as proof of ((in A0) (powerset A1))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=A:fofType;A0:=X:fofType
% Found x3 as proof of ((in A0) (powerset A1))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=A:fofType;A0:=X:fofType
% Found x3 as proof of ((in A0) (powerset A1))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=A:fofType;A0:=X:fofType
% Found x3 as proof of ((in A0) (powerset A1))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=A:fofType;A0:=X:fofType
% Found x3 as proof of ((in A0) (powerset A1))
% Found x4:((in Y) (powerset A))
% Instantiate: A1:=A:fofType;A0:=Y:fofType
% Found x4 as proof of ((in A0) (powerset A1))
% Found x4:((in Y) (powerset A))
% Instantiate: A1:=A:fofType;A0:=Y:fofType
% Found x4 as proof of ((in A0) (powerset A1))
% Found x4:((in Y) (powerset A))
% Instantiate: A1:=A:fofType;A0:=Y:fofType
% Found x4 as proof of ((in A0) (powerset A1))
% Found x4:((in Y) (powerset A))
% Instantiate: A1:=A:fofType;A0:=Y:fofType
% Found x4 as proof of ((in A0) (powerset A1))
% Found x4:((in Y) (powerset A))
% Instantiate: A1:=A:fofType;A0:=Y:fofType
% Found x4 as proof of ((in A0) (powerset A1))
% Found x4:((in Y) (powerset A))
% Instantiate: A1:=A:fofType;A0:=Y:fofType
% Found x4 as proof of ((in A0) (powerset A1))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=X:fofType;A00:=A:fofType
% Found x3 as proof of ((in A1) (powerset A00))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=X:fofType;A00:=A:fofType
% Found x3 as proof of ((in A1) (powerset A00))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=X:fofType;A00:=A:fofType
% Found x3 as proof of ((in A1) (powerset A00))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=X:fofType;A00:=A:fofType
% Found x3 as proof of ((in A1) (powerset A00))
% Found x5:((in Z) (powerset A))
% Instantiate: A1:=Z:fofType;A00:=A:fofType
% Found x5 as proof of ((in A1) (powerset A00))
% Found x5:((in Z) (powerset A))
% Instantiate: A1:=Z:fofType;A00:=A:fofType
% Found x5 as proof of ((in A1) (powerset A00))
% Found x5:((in Z) (powerset A))
% Instantiate: A1:=Z:fofType;A00:=A:fofType
% Found x5 as proof of ((in A1) (powerset A00))
% Found x5:((in Z) (powerset A))
% Instantiate: A1:=Z:fofType;A00:=A:fofType
% Found x5 as proof of ((in A1) (powerset A00))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=X:fofType;A10:=A:fofType
% Found x3 as proof of ((in A1) (powerset A10))
% Found x3:((in X) (powerset A))
% Instantiate: A1:=X:fofType;A10:=A:fofType
% Found x3 as proof of ((in A1) (powerset A10))
% Found x7:((in Xx) A1)
% Instantiate: A1:=A:fofType
% Found (fun (x8:((in Xx) A01))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A01))=> x7) as proof of (((in Xx) A01)->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A01))=> x7) as proof of (((in Xx) A1)->(((in Xx) A01)->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A01))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A01)->((in Xx) A))))
% Found x7:((in Xx) A1)
% Instantiate: A1:=A:fofType
% Found (fun (x8:((in Xx) A01))=> x7) as proof of ((in Xx) A)
% Found (fun (x7:((in Xx) A1)) (x8:((in Xx) A01))=> x7) as proof of (((in Xx) A01)->((in Xx) A))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A01))=> x7) as proof of (((in Xx) A1)->(((in Xx) A01)->((in Xx) A)))
% Found (fun (Xx:fofType) (x7:((in Xx) A1)) (x8:((in Xx) A01))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A1)->(((in Xx) A01)->((in Xx) A))))
% Found x7:((in Xx) A2)
% Instantiate: A2:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of ((in Xx) A0)
% Found (fun (x7:((in Xx) A2)) (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of (((in Xx) ((binunion X) Z))->((in Xx) A0))
% Found (fun (Xx:fofType) (x7:((in Xx) A2)) (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of (((in Xx) A2)->(((in Xx) ((binunion X) Z))->((in Xx) A0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A2)) (x8:((in Xx) ((binunion X) Z)))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A2)->(((in Xx) ((binunion X) Z))->((in Xx) A0))))
% Found x7:((in Xx) A2)
% Instantiate: A2:=((binintersect ((binunion X) Z)) ((binunion Y) Z)):fofType
% Found (fun (x8:((in Xx) ((binunion Y) Z)))=> x7) as proof of ((in Xx) A0)
% EOF
%------------------------------------------------------------------------------