%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU762^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n092.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:33:03 EDT 2014

% Result   : Theorem 9.52s
% Output   : Proof 9.52s
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU762^2 : TPTP v6.1.0. Released v3.7.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n092.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 11:25:11 CDT 2014
% % CPUTime  : 9.52 
% 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 0x1fa4320>, <kernel.DependentProduct object at 0x1fa4f80>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1faec20>, <kernel.DependentProduct object at 0x22c2b48>) of role type named powerset_type
% Using role type
% Declaring powerset:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x1fa4488>, <kernel.DependentProduct object at 0x22c28c0>) of role type named subset_type
% Using role type
% Declaring subset:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1fa4f80>, <kernel.DependentProduct object at 0x22c2b90>) of role type named binintersect_type
% Using role type
% Declaring binintersect:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x1fa4cf8>, <kernel.Sort object at 0x1fab1b8>) 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 0x1fa4e60>, <kernel.Sort object at 0x1fab1b8>) of role type named woz13rule1_type
% Using role type
% Declaring woz13rule1:Prop
% FOF formula (((eq Prop) woz13rule1) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->(((subset X) Z)->((subset ((binintersect X) Y)) Z))))))))) of role definition named woz13rule1
% A new definition: (((eq Prop) woz13rule1) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->(((subset X) Z)->((subset ((binintersect X) Y)) Z)))))))))
% Defined: woz13rule1:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->(((subset X) Z)->((subset ((binintersect X) Y)) Z))))))))
% FOF formula (<kernel.Constant object at 0x1fa4e60>, <kernel.Sort object at 0x1fab1b8>) of role type named woz13rule2_type
% Using role type
% Declaring woz13rule2:Prop
% FOF formula (((eq Prop) woz13rule2) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->(((subset Y) Z)->((subset ((binintersect X) Y)) Z))))))))) of role definition named woz13rule2
% A new definition: (((eq Prop) woz13rule2) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->(((subset Y) Z)->((subset ((binintersect X) Y)) Z)))))))))
% Defined: woz13rule2:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->(((subset Y) Z)->((subset ((binintersect X) Y)) Z))))))))
% FOF formula (<kernel.Constant object at 0x1fa4f80>, <kernel.Sort object at 0x1fab1b8>) of role type named woz13rule3_type
% Using role type
% Declaring woz13rule3:Prop
% FOF formula (((eq Prop) woz13rule3) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->(((subset X) Y)->(((subset X) Z)->((subset X) ((binintersect Y) Z))))))))))) of role definition named woz13rule3
% A new definition: (((eq Prop) woz13rule3) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->(((subset X) Y)->(((subset X) Z)->((subset X) ((binintersect Y) Z)))))))))))
% Defined: woz13rule3:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->(((subset X) Y)->(((subset X) Z)->((subset X) ((binintersect Y) Z))))))))))
% FOF formula (binintersectT_lem->(woz13rule1->(woz13rule2->(woz13rule3->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->(forall (W:fofType), (((in W) (powerset A))->(((subset X) Z)->(((subset Y) W)->((subset ((binintersect X) Y)) ((binintersect Z) W)))))))))))))))) of role conjecture named woz13rule4
% Conjecture to prove = (binintersectT_lem->(woz13rule1->(woz13rule2->(woz13rule3->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->(forall (W:fofType), (((in W) (powerset A))->(((subset X) Z)->(((subset Y) W)->((subset ((binintersect X) Y)) ((binintersect Z) W)))))))))))))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(binintersectT_lem->(woz13rule1->(woz13rule2->(woz13rule3->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->(forall (W:fofType), (((in W) (powerset A))->(((subset X) Z)->(((subset Y) W)->((subset ((binintersect X) Y)) ((binintersect Z) W))))))))))))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter powerset:(fofType->fofType).
% Parameter subset:(fofType->(fofType->Prop)).
% 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 woz13rule1:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->(((subset X) Z)->((subset ((binintersect X) Y)) Z)))))))):Prop.
% Definition woz13rule2:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->(((subset Y) Z)->((subset ((binintersect X) Y)) Z)))))))):Prop.
% Definition woz13rule3:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->(((subset X) Y)->(((subset X) Z)->((subset X) ((binintersect Y) Z)))))))))):Prop.
% Trying to prove (binintersectT_lem->(woz13rule1->(woz13rule2->(woz13rule3->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->(forall (W:fofType), (((in W) (powerset A))->(((subset X) Z)->(((subset Y) W)->((subset ((binintersect X) Y)) ((binintersect Z) W))))))))))))))))
% 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 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 x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x90000:=(x9000 x6):((in ((binintersect Z) W)) (powerset A))
% Found (x9000 x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found ((x900 W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((x90 x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found ((((x9 Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((((x A) Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((((x A) Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found x90000:=(x9000 x6):((in ((binintersect Z) W)) (powerset A))
% Found (x9000 x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found ((x900 W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((x90 x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found ((((x9 Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((((x A) Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((((x A) Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found x90000:=(x9000 x6):((in ((binintersect Z) W)) (powerset A))
% Found (x9000 x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found ((x900 W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((x90 x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found ((((x9 Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((((x A) Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((((x A) Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found x90000:=(x9000 x6):((in ((binintersect Z) W)) (powerset A))
% Found (x9000 x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found ((x900 W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((x90 x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found ((((x9 Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((((x A) Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((((x A) Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found x90000:=(x9000 x6):((in ((binintersect Z) W)) (powerset A))
% Found (x9000 x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found ((x900 W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((x90 x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found ((((x9 Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((((x A) Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((((x A) Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found x90000:=(x9000 x6):((in ((binintersect Z) W)) (powerset A))
% Found (x9000 x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found ((x900 W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((x90 x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found ((((x9 Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((((x A) Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((((x A) Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found x90000:=(x9000 x6):((in ((binintersect Z) W)) (powerset A))
% Found (x9000 x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found ((x900 W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((x90 x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found ((((x9 Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((((x A) Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((((x A) Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found x90000:=(x9000 x6):((in ((binintersect Z) W)) (powerset A))
% Found (x9000 x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found ((x900 W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((x90 x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found ((((x9 Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((((x A) Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((((x A) Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found x90000:=(x9000 x6):((in ((binintersect Z) W)) (powerset A))
% Found (x9000 x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found ((x900 W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((x90 x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found ((((x9 Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((((x A) Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((((x A) Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found x90000:=(x9000 x6):((in ((binintersect Z) W)) (powerset A))
% Found (x9000 x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found ((x900 W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((x90 x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found ((((x9 Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((((x A) Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((((x A) Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found x90000:=(x9000 x6):((in ((binintersect Z) W)) (powerset A))
% Found (x9000 x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found ((x900 W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((x90 x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found ((((x9 Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((((x A) Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((((x A) Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found x90000:=(x9000 x6):((in ((binintersect Z) W)) (powerset A))
% Found (x9000 x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found ((x900 W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((x90 x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found ((((x9 Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((((x A) Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found (((((x A) Z) x5) W) x6) as proof of ((in ((binintersect Z) W)) (powerset A))
% Found x90000:=(x9000 x4):((in ((binintersect X) Y)) (powerset A))
% Found (x9000 x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found ((x900 Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((x90 x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found ((((x9 X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((((x A) X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((((x A) X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found x90000:=(x9000 x4):((in ((binintersect X) Y)) (powerset A))
% Found (x9000 x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found ((x900 Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((x90 x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found ((((x9 X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((((x A) X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((((x A) X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found x90000:=(x9000 x4):((in ((binintersect X) Y)) (powerset A))
% Found (x9000 x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found ((x900 Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((x90 x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found ((((x9 X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((((x A) X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((((x A) X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found x90000:=(x9000 x4):((in ((binintersect X) Y)) (powerset A))
% Found (x9000 x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found ((x900 Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((x90 x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found ((((x9 X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((((x A) X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((((x A) X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found x90000:=(x9000 x4):((in ((binintersect X) Y)) (powerset A))
% Found (x9000 x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found ((x900 Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((x90 x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found ((((x9 X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((((x A) X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((((x A) X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found x90000:=(x9000 x4):((in ((binintersect X) Y)) (powerset A))
% Found (x9000 x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found ((x900 Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((x90 x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found ((((x9 X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((((x A) X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((((x A) X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found x90000:=(x9000 x4):((in ((binintersect X) Y)) (powerset A))
% Found (x9000 x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found ((x900 Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((x90 x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found ((((x9 X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((((x A) X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((((x A) X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found x90000:=(x9000 x4):((in ((binintersect X) Y)) (powerset A))
% Found (x9000 x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found ((x900 Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((x90 x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found ((((x9 X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((((x A) X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((((x A) X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found x90000:=(x9000 x4):((in ((binintersect X) Y)) (powerset A))
% Found (x9000 x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found ((x900 Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((x90 x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found ((((x9 X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((((x A) X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((((x A) X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found x90000:=(x9000 x4):((in ((binintersect X) Y)) (powerset A))
% Found (x9000 x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found ((x900 Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((x90 x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found ((((x9 X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((((x A) X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((((x A) X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found x90000:=(x9000 x4):((in ((binintersect X) Y)) (powerset A))
% Found (x9000 x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found ((x900 Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((x90 x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found ((((x9 X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((((x A) X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((((x A) X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found x90000:=(x9000 x4):((in ((binintersect X) Y)) (powerset A))
% Found (x9000 x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found ((x900 Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((x90 x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found ((((x9 X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((((x A) X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found (((((x A) X) x3) Y) x4) as proof of ((in ((binintersect X) Y)) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (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 x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (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 x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (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 x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (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 x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (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 x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (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 x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (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 x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (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 x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (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 x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (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 x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (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 x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (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 x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (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 x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (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 x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (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 x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x5:((in Z) (powerset A))
% Found x5 as proof of ((in Z) (powerset A))
% Found x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (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 x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (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 x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (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 x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (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 x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (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 x6:((in W) (powerset A))
% Found x6 as proof of ((in W) (powerset A))
% Found x3:((in X) (powerset A))
% Found x3 as proof of ((in X) (powerset A))
% Found x100000000:=(x10000000 x6):((subset ((binintersect X) Y)) W)
% Found (x10000000 x6) as proof of ((subset ((binintersect X) Y)) W)
% Found ((x1000000 x4) x6) as proof of ((subset ((binintersect X) Y)) W)
% Found (((x100000 x3) x4) x6) as proof of ((subset ((binintersect X) Y)) W)
% Found ((((x10000 A) x3) x4) x6) as proof of ((subset ((binintersect X) Y)) W)
% Found (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0))) (x12:((in W) (powerset A0)))=> (((((x1000 A0) x9) x11) x12) x8)) A) x3) x4) x6) as proof of ((subset ((binintersect X) Y)) W)
% Found (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0))) (x12:((in W) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0)))=> ((((x100 A0) x9) x11) W)) A0) x9) x11) x12) x8)) A) x3) x4) x6) as proof of ((subset ((binintersect X) Y)) W)
% Found (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0))) (x12:((in W) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> (((x10 A0) x9) Y)) A0) x9) x11) W)) A0) x9) x11) x12) x8)) A) x3) x4) x6) as proof of ((subset ((binintersect X) Y)) W)
% Found (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0))) (x12:((in W) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x1 A0) X)) A0) x9) Y)) A0) x9) x11) W)) A0) x9) x11) x12) x8)) A) x3) x4) x6) as proof of ((subset ((binintersect X) Y)) W)
% Found (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0))) (x12:((in W) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x1 A0) X)) A0) x9) Y)) A0) x9) x11) W)) A0) x9) x11) x12) x8)) A) x3) x4) x6) as proof of ((subset ((binintersect X) Y)) W)
% Found x000000000:=(x00000000 x5):((subset ((binintersect X) Y)) Z)
% Found (x00000000 x5) as proof of ((subset ((binintersect X) Y)) Z)
% Found ((x0000000 x4) x5) as proof of ((subset ((binintersect X) Y)) Z)
% Found (((x000000 x3) x4) x5) as proof of ((subset ((binintersect X) Y)) Z)
% Found ((((x00000 A) x3) x4) x5) as proof of ((subset ((binintersect X) Y)) Z)
% Found (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0))) (x11:((in Z) (powerset A0)))=> (((((x0000 A0) x9) x10) x11) x7)) A) x3) x4) x5) as proof of ((subset ((binintersect X) Y)) Z)
% Found (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0))) (x11:((in Z) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> ((((x000 A0) x9) x10) Z)) A0) x9) x10) x11) x7)) A) x3) x4) x5) as proof of ((subset ((binintersect X) Y)) Z)
% Found (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0))) (x11:((in Z) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> (((x00 A0) x9) Y)) A0) x9) x10) Z)) A0) x9) x10) x11) x7)) A) x3) x4) x5) as proof of ((subset ((binintersect X) Y)) Z)
% Found (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0))) (x11:((in Z) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) X)) A0) x9) Y)) A0) x9) x10) Z)) A0) x9) x10) x11) x7)) A) x3) x4) x5) as proof of ((subset ((binintersect X) Y)) Z)
% Found (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0))) (x11:((in Z) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) X)) A0) x9) Y)) A0) x9) x10) Z)) A0) x9) x10) x11) x7)) A) x3) x4) x5) as proof of ((subset ((binintersect X) Y)) Z)
% Found (((((x20000 (((((x A) X) x3) Y) x4)) x5) x6) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0))) (x11:((in Z) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) X)) A0) x9) Y)) A0) x9) x10) Z)) A0) x9) x10) x11) x7)) A) x3) x4) x5)) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0))) (x12:((in W) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x1 A0) X)) A0) x9) Y)) A0) x9) x11) W)) A0) x9) x11) x12) x8)) A) x3) x4) x6)) as proof of ((subset ((binintersect X) Y)) ((binintersect Z) W))
% Found ((((((x2000 A) (((((x A) X) x3) Y) x4)) x5) x6) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0))) (x11:((in Z) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) X)) A0) x9) Y)) A0) x9) x10) Z)) A0) x9) x10) x11) x7)) A) x3) x4) x5)) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0))) (x12:((in W) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x1 A0) X)) A0) x9) Y)) A0) x9) x11) W)) A0) x9) x11) x12) x8)) A) x3) x4) x6)) as proof of ((subset ((binintersect X) Y)) ((binintersect Z) W))
% Found (((((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0))) (x10:((in Z) (powerset A0)))=> ((((x200 A0) x9) x10) W)) A) (((((x A) X) x3) Y) x4)) x5) x6) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0))) (x11:((in Z) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) X)) A0) x9) Y)) A0) x9) x10) Z)) A0) x9) x10) x11) x7)) A) x3) x4) x5)) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0))) (x12:((in W) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x1 A0) X)) A0) x9) Y)) A0) x9) x11) W)) A0) x9) x11) x12) x8)) A) x3) x4) x6)) as proof of ((subset ((binintersect X) Y)) ((binintersect Z) W))
% Found (((((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0))) (x10:((in Z) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0)))=> (((x20 A0) x9) Z)) A0) x9) x10) W)) A) (((((x A) X) x3) Y) x4)) x5) x6) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0))) (x11:((in Z) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) X)) A0) x9) Y)) A0) x9) x10) Z)) A0) x9) x10) x11) x7)) A) x3) x4) x5)) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0))) (x12:((in W) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x1 A0) X)) A0) x9) Y)) A0) x9) x11) W)) A0) x9) x11) x12) x8)) A) x3) x4) x6)) as proof of ((subset ((binintersect X) Y)) ((binintersect Z) W))
% Found (((((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0))) (x10:((in Z) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0)))=> ((((fun (A0:fofType)=> ((x2 A0) ((binintersect X) Y))) A0) x9) Z)) A0) x9) x10) W)) A) (((((x A) X) x3) Y) x4)) x5) x6) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0))) (x11:((in Z) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) X)) A0) x9) Y)) A0) x9) x10) Z)) A0) x9) x10) x11) x7)) A) x3) x4) x5)) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0))) (x12:((in W) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x1 A0) X)) A0) x9) Y)) A0) x9) x11) W)) A0) x9) x11) x12) x8)) A) x3) x4) x6)) as proof of ((subset ((binintersect X) Y)) ((binintersect Z) W))
% Found (fun (x8:((subset Y) W))=> (((((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0))) (x10:((in Z) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0)))=> ((((fun (A0:fofType)=> ((x2 A0) ((binintersect X) Y))) A0) x9) Z)) A0) x9) x10) W)) A) (((((x A) X) x3) Y) x4)) x5) x6) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0))) (x11:((in Z) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) X)) A0) x9) Y)) A0) x9) x10) Z)) A0) x9) x10) x11) x7)) A) x3) x4) x5)) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0))) (x12:((in W) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x1 A0) X)) A0) x9) Y)) A0) x9) x11) W)) A0) x9) x11) x12) x8)) A) x3) x4) x6))) as proof of ((subset ((binintersect X) Y)) ((binintersect Z) W))
% Found (fun (x7:((subset X) Z)) (x8:((subset Y) W))=> (((((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0))) (x10:((in Z) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0)))=> ((((fun (A0:fofType)=> ((x2 A0) ((binintersect X) Y))) A0) x9) Z)) A0) x9) x10) W)) A) (((((x A) X) x3) Y) x4)) x5) x6) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0))) (x11:((in Z) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) X)) A0) x9) Y)) A0) x9) x10) Z)) A0) x9) x10) x11) x7)) A) x3) x4) x5)) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0))) (x12:((in W) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x1 A0) X)) A0) x9) Y)) A0) x9) x11) W)) A0) x9) x11) x12) x8)) A) x3) x4) x6))) as proof of (((subset Y) W)->((subset ((binintersect X) Y)) ((binintersect Z) W)))
% Found (fun (x6:((in W) (powerset A))) (x7:((subset X) Z)) (x8:((subset Y) W))=> (((((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0))) (x10:((in Z) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0)))=> ((((fun (A0:fofType)=> ((x2 A0) ((binintersect X) Y))) A0) x9) Z)) A0) x9) x10) W)) A) (((((x A) X) x3) Y) x4)) x5) x6) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0))) (x11:((in Z) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) X)) A0) x9) Y)) A0) x9) x10) Z)) A0) x9) x10) x11) x7)) A) x3) x4) x5)) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0))) (x12:((in W) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x1 A0) X)) A0) x9) Y)) A0) x9) x11) W)) A0) x9) x11) x12) x8)) A) x3) x4) x6))) as proof of (((subset X) Z)->(((subset Y) W)->((subset ((binintersect X) Y)) ((binintersect Z) W))))
% Found (fun (W:fofType) (x6:((in W) (powerset A))) (x7:((subset X) Z)) (x8:((subset Y) W))=> (((((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0))) (x10:((in Z) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0)))=> ((((fun (A0:fofType)=> ((x2 A0) ((binintersect X) Y))) A0) x9) Z)) A0) x9) x10) W)) A) (((((x A) X) x3) Y) x4)) x5) x6) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0))) (x11:((in Z) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) X)) A0) x9) Y)) A0) x9) x10) Z)) A0) x9) x10) x11) x7)) A) x3) x4) x5)) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0))) (x12:((in W) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x1 A0) X)) A0) x9) Y)) A0) x9) x11) W)) A0) x9) x11) x12) x8)) A) x3) x4) x6))) as proof of (((in W) (powerset A))->(((subset X) Z)->(((subset Y) W)->((subset ((binintersect X) Y)) ((binintersect Z) W)))))
% Found (fun (x5:((in Z) (powerset A))) (W:fofType) (x6:((in W) (powerset A))) (x7:((subset X) Z)) (x8:((subset Y) W))=> (((((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0))) (x10:((in Z) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0)))=> ((((fun (A0:fofType)=> ((x2 A0) ((binintersect X) Y))) A0) x9) Z)) A0) x9) x10) W)) A) (((((x A) X) x3) Y) x4)) x5) x6) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0))) (x11:((in Z) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) X)) A0) x9) Y)) A0) x9) x10) Z)) A0) x9) x10) x11) x7)) A) x3) x4) x5)) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0))) (x12:((in W) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x1 A0) X)) A0) x9) Y)) A0) x9) x11) W)) A0) x9) x11) x12) x8)) A) x3) x4) x6))) as proof of (forall (W:fofType), (((in W) (powerset A))->(((subset X) Z)->(((subset Y) W)->((subset ((binintersect X) Y)) ((binintersect Z) W))))))
% Found (fun (Z:fofType) (x5:((in Z) (powerset A))) (W:fofType) (x6:((in W) (powerset A))) (x7:((subset X) Z)) (x8:((subset Y) W))=> (((((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0))) (x10:((in Z) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0)))=> ((((fun (A0:fofType)=> ((x2 A0) ((binintersect X) Y))) A0) x9) Z)) A0) x9) x10) W)) A) (((((x A) X) x3) Y) x4)) x5) x6) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0))) (x11:((in Z) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) X)) A0) x9) Y)) A0) x9) x10) Z)) A0) x9) x10) x11) x7)) A) x3) x4) x5)) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0))) (x12:((in W) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x1 A0) X)) A0) x9) Y)) A0) x9) x11) W)) A0) x9) x11) x12) x8)) A) x3) x4) x6))) as proof of (((in Z) (powerset A))->(forall (W:fofType), (((in W) (powerset A))->(((subset X) Z)->(((subset Y) W)->((subset ((binintersect X) Y)) ((binintersect Z) W)))))))
% Found (fun (x4:((in Y) (powerset A))) (Z:fofType) (x5:((in Z) (powerset A))) (W:fofType) (x6:((in W) (powerset A))) (x7:((subset X) Z)) (x8:((subset Y) W))=> (((((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0))) (x10:((in Z) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0)))=> ((((fun (A0:fofType)=> ((x2 A0) ((binintersect X) Y))) A0) x9) Z)) A0) x9) x10) W)) A) (((((x A) X) x3) Y) x4)) x5) x6) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0))) (x11:((in Z) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) X)) A0) x9) Y)) A0) x9) x10) Z)) A0) x9) x10) x11) x7)) A) x3) x4) x5)) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0))) (x12:((in W) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x1 A0) X)) A0) x9) Y)) A0) x9) x11) W)) A0) x9) x11) x12) x8)) A) x3) x4) x6))) as proof of (forall (Z:fofType), (((in Z) (powerset A))->(forall (W:fofType), (((in W) (powerset A))->(((subset X) Z)->(((subset Y) W)->((subset ((binintersect X) Y)) ((binintersect Z) W))))))))
% Found (fun (Y:fofType) (x4:((in Y) (powerset A))) (Z:fofType) (x5:((in Z) (powerset A))) (W:fofType) (x6:((in W) (powerset A))) (x7:((subset X) Z)) (x8:((subset Y) W))=> (((((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0))) (x10:((in Z) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0)))=> ((((fun (A0:fofType)=> ((x2 A0) ((binintersect X) Y))) A0) x9) Z)) A0) x9) x10) W)) A) (((((x A) X) x3) Y) x4)) x5) x6) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0))) (x11:((in Z) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) X)) A0) x9) Y)) A0) x9) x10) Z)) A0) x9) x10) x11) x7)) A) x3) x4) x5)) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0))) (x12:((in W) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x1 A0) X)) A0) x9) Y)) A0) x9) x11) W)) A0) x9) x11) x12) x8)) A) x3) x4) x6))) as proof of (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->(forall (W:fofType), (((in W) (powerset A))->(((subset X) Z)->(((subset Y) W)->((subset ((binintersect X) Y)) ((binintersect Z) W)))))))))
% Found (fun (x3:((in X) (powerset A))) (Y:fofType) (x4:((in Y) (powerset A))) (Z:fofType) (x5:((in Z) (powerset A))) (W:fofType) (x6:((in W) (powerset A))) (x7:((subset X) Z)) (x8:((subset Y) W))=> (((((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0))) (x10:((in Z) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0)))=> ((((fun (A0:fofType)=> ((x2 A0) ((binintersect X) Y))) A0) x9) Z)) A0) x9) x10) W)) A) (((((x A) X) x3) Y) x4)) x5) x6) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0))) (x11:((in Z) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) X)) A0) x9) Y)) A0) x9) x10) Z)) A0) x9) x10) x11) x7)) A) x3) x4) x5)) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0))) (x12:((in W) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x1 A0) X)) A0) x9) Y)) A0) x9) x11) W)) A0) x9) x11) x12) x8)) A) x3) x4) x6))) as proof of (forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->(forall (W:fofType), (((in W) (powerset A))->(((subset X) Z)->(((subset Y) W)->((subset ((binintersect X) Y)) ((binintersect Z) W))))))))))
% Found (fun (X:fofType) (x3:((in X) (powerset A))) (Y:fofType) (x4:((in Y) (powerset A))) (Z:fofType) (x5:((in Z) (powerset A))) (W:fofType) (x6:((in W) (powerset A))) (x7:((subset X) Z)) (x8:((subset Y) W))=> (((((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0))) (x10:((in Z) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0)))=> ((((fun (A0:fofType)=> ((x2 A0) ((binintersect X) Y))) A0) x9) Z)) A0) x9) x10) W)) A) (((((x A) X) x3) Y) x4)) x5) x6) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0))) (x11:((in Z) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) X)) A0) x9) Y)) A0) x9) x10) Z)) A0) x9) x10) x11) x7)) A) x3) x4) x5)) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0))) (x12:((in W) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x1 A0) X)) A0) x9) Y)) A0) x9) x11) W)) A0) x9) x11) x12) x8)) A) x3) x4) x6))) as proof of (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->(forall (W:fofType), (((in W) (powerset A))->(((subset X) Z)->(((subset Y) W)->((subset ((binintersect X) Y)) ((binintersect Z) W)))))))))))
% Found (fun (A:fofType) (X:fofType) (x3:((in X) (powerset A))) (Y:fofType) (x4:((in Y) (powerset A))) (Z:fofType) (x5:((in Z) (powerset A))) (W:fofType) (x6:((in W) (powerset A))) (x7:((subset X) Z)) (x8:((subset Y) W))=> (((((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0))) (x10:((in Z) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0)))=> ((((fun (A0:fofType)=> ((x2 A0) ((binintersect X) Y))) A0) x9) Z)) A0) x9) x10) W)) A) (((((x A) X) x3) Y) x4)) x5) x6) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0))) (x11:((in Z) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) X)) A0) x9) Y)) A0) x9) x10) Z)) A0) x9) x10) x11) x7)) A) x3) x4) x5)) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0))) (x12:((in W) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x1 A0) X)) A0) x9) Y)) A0) x9) x11) W)) A0) x9) x11) x12) x8)) A) x3) x4) x6))) as proof of (forall (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->(forall (W:fofType), (((in W) (powerset A))->(((subset X) Z)->(((subset Y) W)->((subset ((binintersect X) Y)) ((binintersect Z) W))))))))))))
% Found (fun (x2:woz13rule3) (A:fofType) (X:fofType) (x3:((in X) (powerset A))) (Y:fofType) (x4:((in Y) (powerset A))) (Z:fofType) (x5:((in Z) (powerset A))) (W:fofType) (x6:((in W) (powerset A))) (x7:((subset X) Z)) (x8:((subset Y) W))=> (((((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0))) (x10:((in Z) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0)))=> ((((fun (A0:fofType)=> ((x2 A0) ((binintersect X) Y))) A0) x9) Z)) A0) x9) x10) W)) A) (((((x A) X) x3) Y) x4)) x5) x6) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0))) (x11:((in Z) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) X)) A0) x9) Y)) A0) x9) x10) Z)) A0) x9) x10) x11) x7)) A) x3) x4) x5)) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0))) (x12:((in W) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x1 A0) X)) A0) x9) Y)) A0) x9) x11) W)) A0) x9) x11) x12) x8)) A) x3) x4) x6))) as proof of (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->(forall (W:fofType), (((in W) (powerset A))->(((subset X) Z)->(((subset Y) W)->((subset ((binintersect X) Y)) ((binintersect Z) W))))))))))))
% Found (fun (x1:woz13rule2) (x2:woz13rule3) (A:fofType) (X:fofType) (x3:((in X) (powerset A))) (Y:fofType) (x4:((in Y) (powerset A))) (Z:fofType) (x5:((in Z) (powerset A))) (W:fofType) (x6:((in W) (powerset A))) (x7:((subset X) Z)) (x8:((subset Y) W))=> (((((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0))) (x10:((in Z) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0)))=> ((((fun (A0:fofType)=> ((x2 A0) ((binintersect X) Y))) A0) x9) Z)) A0) x9) x10) W)) A) (((((x A) X) x3) Y) x4)) x5) x6) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0))) (x11:((in Z) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) X)) A0) x9) Y)) A0) x9) x10) Z)) A0) x9) x10) x11) x7)) A) x3) x4) x5)) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0))) (x12:((in W) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x1 A0) X)) A0) x9) Y)) A0) x9) x11) W)) A0) x9) x11) x12) x8)) A) x3) x4) x6))) as proof of (woz13rule3->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->(forall (W:fofType), (((in W) (powerset A))->(((subset X) Z)->(((subset Y) W)->((subset ((binintersect X) Y)) ((binintersect Z) W)))))))))))))
% Found (fun (x0:woz13rule1) (x1:woz13rule2) (x2:woz13rule3) (A:fofType) (X:fofType) (x3:((in X) (powerset A))) (Y:fofType) (x4:((in Y) (powerset A))) (Z:fofType) (x5:((in Z) (powerset A))) (W:fofType) (x6:((in W) (powerset A))) (x7:((subset X) Z)) (x8:((subset Y) W))=> (((((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0))) (x10:((in Z) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0)))=> ((((fun (A0:fofType)=> ((x2 A0) ((binintersect X) Y))) A0) x9) Z)) A0) x9) x10) W)) A) (((((x A) X) x3) Y) x4)) x5) x6) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0))) (x11:((in Z) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) X)) A0) x9) Y)) A0) x9) x10) Z)) A0) x9) x10) x11) x7)) A) x3) x4) x5)) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0))) (x12:((in W) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x1 A0) X)) A0) x9) Y)) A0) x9) x11) W)) A0) x9) x11) x12) x8)) A) x3) x4) x6))) as proof of (woz13rule2->(woz13rule3->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->(forall (W:fofType), (((in W) (powerset A))->(((subset X) Z)->(((subset Y) W)->((subset ((binintersect X) Y)) ((binintersect Z) W))))))))))))))
% Found (fun (x:binintersectT_lem) (x0:woz13rule1) (x1:woz13rule2) (x2:woz13rule3) (A:fofType) (X:fofType) (x3:((in X) (powerset A))) (Y:fofType) (x4:((in Y) (powerset A))) (Z:fofType) (x5:((in Z) (powerset A))) (W:fofType) (x6:((in W) (powerset A))) (x7:((subset X) Z)) (x8:((subset Y) W))=> (((((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0))) (x10:((in Z) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0)))=> ((((fun (A0:fofType)=> ((x2 A0) ((binintersect X) Y))) A0) x9) Z)) A0) x9) x10) W)) A) (((((x A) X) x3) Y) x4)) x5) x6) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0))) (x11:((in Z) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) X)) A0) x9) Y)) A0) x9) x10) Z)) A0) x9) x10) x11) x7)) A) x3) x4) x5)) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0))) (x12:((in W) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x1 A0) X)) A0) x9) Y)) A0) x9) x11) W)) A0) x9) x11) x12) x8)) A) x3) x4) x6))) as proof of (woz13rule1->(woz13rule2->(woz13rule3->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->(forall (W:fofType), (((in W) (powerset A))->(((subset X) Z)->(((subset Y) W)->((subset ((binintersect X) Y)) ((binintersect Z) W)))))))))))))))
% Found (fun (x:binintersectT_lem) (x0:woz13rule1) (x1:woz13rule2) (x2:woz13rule3) (A:fofType) (X:fofType) (x3:((in X) (powerset A))) (Y:fofType) (x4:((in Y) (powerset A))) (Z:fofType) (x5:((in Z) (powerset A))) (W:fofType) (x6:((in W) (powerset A))) (x7:((subset X) Z)) (x8:((subset Y) W))=> (((((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0))) (x10:((in Z) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0)))=> ((((fun (A0:fofType)=> ((x2 A0) ((binintersect X) Y))) A0) x9) Z)) A0) x9) x10) W)) A) (((((x A) X) x3) Y) x4)) x5) x6) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0))) (x11:((in Z) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) X)) A0) x9) Y)) A0) x9) x10) Z)) A0) x9) x10) x11) x7)) A) x3) x4) x5)) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0))) (x12:((in W) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x1 A0) X)) A0) x9) Y)) A0) x9) x11) W)) A0) x9) x11) x12) x8)) A) x3) x4) x6))) as proof of (binintersectT_lem->(woz13rule1->(woz13rule2->(woz13rule3->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Z:fofType), (((in Z) (powerset A))->(forall (W:fofType), (((in W) (powerset A))->(((subset X) Z)->(((subset Y) W)->((subset ((binintersect X) Y)) ((binintersect Z) W))))))))))))))))
% Got proof (fun (x:binintersectT_lem) (x0:woz13rule1) (x1:woz13rule2) (x2:woz13rule3) (A:fofType) (X:fofType) (x3:((in X) (powerset A))) (Y:fofType) (x4:((in Y) (powerset A))) (Z:fofType) (x5:((in Z) (powerset A))) (W:fofType) (x6:((in W) (powerset A))) (x7:((subset X) Z)) (x8:((subset Y) W))=> (((((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0))) (x10:((in Z) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0)))=> ((((fun (A0:fofType)=> ((x2 A0) ((binintersect X) Y))) A0) x9) Z)) A0) x9) x10) W)) A) (((((x A) X) x3) Y) x4)) x5) x6) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0))) (x11:((in Z) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) X)) A0) x9) Y)) A0) x9) x10) Z)) A0) x9) x10) x11) x7)) A) x3) x4) x5)) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0))) (x12:((in W) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x1 A0) X)) A0) x9) Y)) A0) x9) x11) W)) A0) x9) x11) x12) x8)) A) x3) x4) x6)))
% Time elapsed = 9.044915s
% node=1649 cost=1672.000000 depth=29
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (x:binintersectT_lem) (x0:woz13rule1) (x1:woz13rule2) (x2:woz13rule3) (A:fofType) (X:fofType) (x3:((in X) (powerset A))) (Y:fofType) (x4:((in Y) (powerset A))) (Z:fofType) (x5:((in Z) (powerset A))) (W:fofType) (x6:((in W) (powerset A))) (x7:((subset X) Z)) (x8:((subset Y) W))=> (((((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0))) (x10:((in Z) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in ((binintersect X) Y)) (powerset A0)))=> ((((fun (A0:fofType)=> ((x2 A0) ((binintersect X) Y))) A0) x9) Z)) A0) x9) x10) W)) A) (((((x A) X) x3) Y) x4)) x5) x6) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0))) (x11:((in Z) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x10:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x0 A0) X)) A0) x9) Y)) A0) x9) x10) Z)) A0) x9) x10) x11) x7)) A) x3) x4) x5)) (((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0))) (x12:((in W) (powerset A0)))=> ((((((fun (A0:fofType) (x9:((in X) (powerset A0))) (x11:((in Y) (powerset A0)))=> (((((fun (A0:fofType) (x9:((in X) (powerset A0)))=> ((((fun (A0:fofType)=> ((x1 A0) X)) A0) x9) Y)) A0) x9) x11) W)) A0) x9) x11) x12) x8)) A) x3) x4) x6)))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
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