%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU757^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n109.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 13:33:02 EDT 2014

% Result   : Timeout 300.04s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU757^2 : TPTP v6.1.0. Released v3.7.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n109.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 11:24:06 CDT 2014
% % CPUTime  : 300.04 
% 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 0x1996128>, <kernel.DependentProduct object at 0x1996830>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x173fea8>, <kernel.DependentProduct object at 0x1996a70>) of role type named powerset_type
% Using role type
% Declaring powerset:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x1996680>, <kernel.DependentProduct object at 0x1996fc8>) of role type named binunion_type
% Using role type
% Declaring binunion:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x1996dd0>, <kernel.DependentProduct object at 0x1996128>) of role type named binintersect_type
% Using role type
% Declaring binintersect:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x1996cf8>, <kernel.DependentProduct object at 0x1996a70>) of role type named setminus_type
% Using role type
% Declaring setminus:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x1996fc8>, <kernel.Sort object at 0x1423368>) 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 0x1996128>, <kernel.Sort object at 0x1423368>) 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 0x1721488>, <kernel.Sort object at 0x1423368>) of role type named complementT_lem_type
% Using role type
% Declaring complementT_lem:Prop
% FOF formula (((eq Prop) complementT_lem) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->((in ((setminus A) X)) (powerset A))))) of role definition named complementT_lem
% A new definition: (((eq Prop) complementT_lem) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->((in ((setminus A) X)) (powerset A)))))
% Defined: complementT_lem:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->((in ((setminus A) X)) (powerset A))))
% FOF formula (<kernel.Constant object at 0x17211b8>, <kernel.Sort object at 0x1423368>) of role type named setextT_type
% Using role type
% Declaring setextT:Prop
% FOF formula (((eq Prop) setextT) (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))))->((forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) X))))->(((eq fofType) X) Y)))))))) of role definition named setextT
% A new definition: (((eq Prop) setextT) (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))))->((forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) X))))->(((eq fofType) X) Y))))))))
% Defined: setextT:=(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))))->((forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) X))))->(((eq fofType) X) Y)))))))
% FOF formula (<kernel.Constant object at 0x17213b0>, <kernel.Sort object at 0x1423368>) of role type named demorgan2a_type
% Using role type
% Declaring demorgan2a:Prop
% FOF formula (((eq Prop) demorgan2a) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))))))) of role definition named demorgan2a
% A new definition: (((eq Prop) demorgan2a) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))))))))
% Defined: demorgan2a:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))))))
% FOF formula (<kernel.Constant object at 0x17214d0>, <kernel.Sort object at 0x1423368>) of role type named demorgan2b_type
% Using role type
% Declaring demorgan2b:Prop
% FOF formula (((eq Prop) demorgan2b) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))))))))) of role definition named demorgan2b
% A new definition: (((eq Prop) demorgan2b) (forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y)))))))))))
% Defined: demorgan2b:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))))))))
% FOF formula (binintersectT_lem->(binunionT_lem->(complementT_lem->(setextT->(demorgan2a->(demorgan2b->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(((eq fofType) ((setminus A) ((binunion X) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y))))))))))))) of role conjecture named demorgan2
% Conjecture to prove = (binintersectT_lem->(binunionT_lem->(complementT_lem->(setextT->(demorgan2a->(demorgan2b->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(((eq fofType) ((setminus A) ((binunion X) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y))))))))))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(binintersectT_lem->(binunionT_lem->(complementT_lem->(setextT->(demorgan2a->(demorgan2b->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(((eq fofType) ((setminus A) ((binunion X) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))))))))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter powerset:(fofType->fofType).
% Parameter binunion:(fofType->(fofType->fofType)).
% Parameter binintersect:(fofType->(fofType->fofType)).
% Parameter setminus:(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 complementT_lem:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->((in ((setminus A) X)) (powerset A)))):Prop.
% Definition setextT:=(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))))->((forall (Xx:fofType), (((in Xx) A)->(((in Xx) Y)->((in Xx) X))))->(((eq fofType) X) Y))))))):Prop.
% Definition demorgan2a:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))))))):Prop.
% Definition demorgan2b:=(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(forall (Xx:fofType), (((in Xx) A)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y)))))))))):Prop.
% Trying to prove (binintersectT_lem->(binunionT_lem->(complementT_lem->(setextT->(demorgan2a->(demorgan2b->(forall (A:fofType) (X:fofType), (((in X) (powerset A))->(forall (Y:fofType), (((in Y) (powerset A))->(((eq fofType) ((setminus A) ((binunion X) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))))))))))))
% Found x70:(P ((setminus A) ((binunion X) Y)))
% Found (fun (x70:(P ((setminus A) ((binunion X) Y))))=> x70) as proof of (P ((setminus A) ((binunion X) Y)))
% Found (fun (x70:(P ((setminus A) ((binunion X) Y))))=> x70) as proof of (P0 ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:(P ((setminus A) ((binunion X) Y)))
% Instantiate: b:=((setminus A) ((binunion X) Y)):fofType
% Found x7 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found x7:(P0 b)
% Instantiate: b:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x7:(P0 b))=> x7) as proof of (P0 ((setminus A) ((binunion X) Y)))
% Found (fun (P0:(fofType->Prop)) (x7:(P0 b))=> x7) as proof of ((P0 b)->(P0 ((setminus A) ((binunion X) Y))))
% Found (fun (P0:(fofType->Prop)) (x7:(P0 b))=> x7) as proof of (P b)
% Found x7:(P ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Instantiate: b:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found x7 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found x70:(P ((setminus A) ((binunion X) Y)))
% Found (fun (x70:(P ((setminus A) ((binunion X) Y))))=> x70) as proof of (P ((setminus A) ((binunion X) Y)))
% Found (fun (x70:(P ((setminus A) ((binunion X) Y))))=> x70) as proof of (P0 ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((setminus A) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((setminus A) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((setminus A) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((setminus A) Y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((setminus A) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((setminus A) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((setminus A) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((setminus A) Y))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found x70:(P b)
% Found (fun (x70:(P b))=> x70) as proof of (P b)
% Found (fun (x70:(P b))=> x70) as proof of (P0 b)
% Found x000000:=(x00000 x6):((in ((binunion X) Y)) (powerset A))
% Found (x00000 x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((x0000 Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((x000 x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((((x00 X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (x100 (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found ((x10 ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found x70:(P ((setminus A) ((binunion X) Y)))
% Found (fun (x70:(P ((setminus A) ((binunion X) Y))))=> x70) as proof of (P ((setminus A) ((binunion X) Y)))
% Found (fun (x70:(P ((setminus A) ((binunion X) Y))))=> x70) as proof of (P0 ((setminus A) ((binunion X) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x70:(P ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x70:(P ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x70) as proof of (P ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x70:(P ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x70) as proof of (P0 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found x70:(P ((setminus A) ((binunion X) Y)))
% Found (fun (x70:(P ((setminus A) ((binunion X) Y))))=> x70) as proof of (P ((setminus A) ((binunion X) Y)))
% Found (fun (x70:(P ((setminus A) ((binunion X) Y))))=> x70) as proof of (P0 ((setminus A) ((binunion X) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x1000:=(x100 x6):((in ((setminus A) Y)) (powerset A))
% Found (x100 x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found ((x10 Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found x1000:=(x100 x5):((in ((setminus A) X)) (powerset A))
% Found (x100 x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found ((x10 X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found ((x700 (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((x70 x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> (((x7 ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x70:(P b)
% Found (fun (x70:(P b))=> x70) as proof of (P b)
% Found (fun (x70:(P b))=> x70) as proof of (P0 b)
% Found x70:(P ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x70:(P ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x70) as proof of (P ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x70:(P ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x70) as proof of (P0 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x000000:=(x00000 x6):((in ((binunion X) Y)) (powerset A))
% Found (x00000 x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((x0000 Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((x000 x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((((x00 X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (x100 (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found ((x10 ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))))
% Found x1000:=(x100 x5):((in ((setminus A) X)) (powerset A))
% Found (x100 x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found ((x10 X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found x1000:=(x100 x6):((in ((setminus A) Y)) (powerset A))
% Found (x100 x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found ((x10 Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found ((x700 (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((x70 x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> (((x7 ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x7:(P ((setminus A) ((binunion X) Y)))
% Instantiate: b:=((setminus A) ((binunion X) Y)):fofType
% Found x7 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b))))
% Found x000000:=(x00000 x6):((in ((binunion X) Y)) (powerset A))
% Found (x00000 x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((x0000 Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((x000 x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((((x00 X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (x100 (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found ((x10 ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found x000000:=(x00000 x6):((in ((binunion X) Y)) (powerset A))
% Found (x00000 x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((x0000 Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((x000 x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((((x00 X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (x100 (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found ((x10 ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found x7:(P0 b)
% Instantiate: b:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x7:(P0 b))=> x7) as proof of (P0 ((setminus A) ((binunion X) Y)))
% Found (fun (P0:(fofType->Prop)) (x7:(P0 b))=> x7) as proof of ((P0 b)->(P0 ((setminus A) ((binunion X) Y))))
% Found (fun (P0:(fofType->Prop)) (x7:(P0 b))=> x7) as proof of (P b)
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:(P ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Instantiate: b:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found x7 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found x1000:=(x100 x6):((in ((setminus A) Y)) (powerset A))
% Found (x100 x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found ((x10 Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found x1000:=(x100 x5):((in ((setminus A) X)) (powerset A))
% Found (x100 x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found ((x10 X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found ((x700 (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((x70 x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> (((x7 ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found x1000:=(x100 x6):((in ((setminus A) Y)) (powerset A))
% Found (x100 x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found ((x10 Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found x1000:=(x100 x5):((in ((setminus A) X)) (powerset A))
% Found (x100 x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found ((x10 X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found ((x700 (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((x70 x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> (((x7 ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:(P ((setminus A) ((binunion X) Y)))
% Instantiate: a:=((setminus A) ((binunion X) Y)):fofType
% Found x7 as proof of (P0 a)
% Found x70:(P ((setminus A) ((binunion X) Y)))
% Found (fun (x70:(P ((setminus A) ((binunion X) Y))))=> x70) as proof of (P ((setminus A) ((binunion X) Y)))
% Found (fun (x70:(P ((setminus A) ((binunion X) Y))))=> x70) as proof of (P0 ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x5:((in X) (powerset A))
% Instantiate: A0:=A:fofType;X0:=X:fofType
% Found x5 as proof of ((in X0) (powerset A0))
% Found x7:(P ((setminus A) ((binunion X) Y)))
% Instantiate: X0:=((setminus A) ((binunion X) Y)):fofType
% Found x7 as proof of (P0 X0)
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((setminus A) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((setminus A) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((setminus A) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((setminus A) Y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((setminus A) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((setminus A) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((setminus A) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((setminus A) Y))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found x7:(P2 b)
% Instantiate: b:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x7:(P2 b))=> x7) as proof of (P2 ((setminus A) ((binunion X) Y)))
% Found (fun (P2:(fofType->Prop)) (x7:(P2 b))=> x7) as proof of ((P2 b)->(P2 ((setminus A) ((binunion X) Y))))
% Found (fun (P2:(fofType->Prop)) (x7:(P2 b))=> x7) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found x7:(P2 b)
% Instantiate: b:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x7:(P2 b))=> x7) as proof of (P2 ((setminus A) ((binunion X) Y)))
% Found (fun (P2:(fofType->Prop)) (x7:(P2 b))=> x7) as proof of ((P2 b)->(P2 ((setminus A) ((binunion X) Y))))
% Found (fun (P2:(fofType->Prop)) (x7:(P2 b))=> x7) as proof of (P1 b)
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x000000:=(x00000 x6):((in ((binunion X) Y)) (powerset A))
% Found (x00000 x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((x0000 Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((x000 x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((((x00 X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (x100 (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found ((x10 ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found x000000:=(x00000 x6):((in ((binunion X) Y)) (powerset A))
% Found (x00000 x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((x0000 Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((x000 x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((((x00 X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (x100 (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found ((x10 ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found x000000:=(x00000 x6):((in ((binunion X) Y)) (powerset A))
% Found (x00000 x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((x0000 Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((x000 x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((((x00 X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (x100 (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found ((x10 ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found x000000:=(x00000 x6):((in ((binunion X) Y)) (powerset A))
% Found (x00000 x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((x0000 Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((x000 x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((((x00 X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (x100 (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found ((x10 ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found x7:(P1 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Instantiate: b:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found x7 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found x7:(P1 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Instantiate: b:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found x7 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x000000:=(x00000 x6):((in ((binunion X) Y)) (powerset A))
% Found (x00000 x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((x0000 Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((x000 x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((((x00 X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (x100 (((((x0 A) X) x5) Y) x6)) as proof of ((in b) (powerset A0))
% Found ((x10 ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in b) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in b) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in b) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in b) (powerset A0))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x70:(P b)
% Found (fun (x70:(P b))=> x70) as proof of (P b)
% Found (fun (x70:(P b))=> x70) as proof of (P0 b)
% Found x70:(P b)
% Found (fun (x70:(P b))=> x70) as proof of (P b)
% Found (fun (x70:(P b))=> x70) as proof of (P0 b)
% Found x70:(P ((setminus A) ((binunion X) Y)))
% Found (fun (x70:(P ((setminus A) ((binunion X) Y))))=> x70) as proof of (P ((setminus A) ((binunion X) Y)))
% Found (fun (x70:(P ((setminus A) ((binunion X) Y))))=> x70) as proof of (P0 ((setminus A) ((binunion X) Y)))
% Found x000000:=(x00000 x6):((in ((binunion X) Y)) (powerset A))
% Found (x00000 x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((x0000 Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((x000 x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((((x00 X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (x100 (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found ((x10 ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:(P b)
% Instantiate: b0:=b:fofType
% Found x7 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:(P ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Instantiate: b:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found x7 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found x7:(P b)
% Found x7 as proof of (P0 ((setminus A) ((binunion X) Y)))
% Found x80:(P1 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x80:(P1 ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x80) as proof of (P1 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x80:(P1 ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x80) as proof of (P2 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:(P ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Instantiate: a:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found x7 as proof of (P0 a)
% Found x70:(P ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x70:(P ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x70) as proof of (P ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x70:(P ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x70) as proof of (P0 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found x70:(P ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x70:(P ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x70) as proof of (P ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x70:(P ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x70) as proof of (P0 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Instantiate: A0:=A:fofType;X0:=Y:fofType
% Found x6 as proof of ((in X0) (powerset A0))
% Found x7:(P ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Instantiate: X0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found x7 as proof of (P0 X0)
% Found x1000:=(x100 x5):((in ((setminus A) X)) (powerset A))
% Found (x100 x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found ((x10 X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found x1000:=(x100 x6):((in ((setminus A) Y)) (powerset A))
% Found (x100 x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found ((x10 Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found ((x700 (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((x70 x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> (((x7 ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found x1000:=(x100 x6):((in ((setminus A) Y)) (powerset A))
% Found (x100 x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found ((x10 Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found x1000:=(x100 x5):((in ((setminus A) X)) (powerset A))
% Found (x100 x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found ((x10 X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found ((x700 (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((x70 x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> (((x7 ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found x1000:=(x100 x6):((in ((setminus A) Y)) (powerset A))
% Found (x100 x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found ((x10 Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found x1000:=(x100 x5):((in ((setminus A) X)) (powerset A))
% Found (x100 x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found ((x10 X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found ((x700 (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((x70 x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> (((x7 ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found x1000:=(x100 x6):((in ((setminus A) Y)) (powerset A))
% Found (x100 x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found ((x10 Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found x1000:=(x100 x5):((in ((setminus A) X)) (powerset A))
% Found (x100 x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found ((x10 X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found ((x700 (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((x70 x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> (((x7 ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found x8:((in Xx) ((setminus A) ((binunion X) Y)))
% Found x8 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x1000:=(x100 x6):((in ((setminus A) Y)) (powerset A))
% Found (x100 x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found ((x10 Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found x1000:=(x100 x5):((in ((setminus A) X)) (powerset A))
% Found (x100 x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found ((x10 X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found ((x700 (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((x70 x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> (((x7 ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b1)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b1)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b1)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found x9:((in Xx) X0)
% Instantiate: X0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x9:((in Xx) X0))=> x9) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x8:((in Xx) A0)) (x9:((in Xx) X0))=> x9) as proof of (((in Xx) X0)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x8:((in Xx) A0)) (x9:((in Xx) X0))=> x9) as proof of (((in Xx) A0)->(((in Xx) X0)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x8:((in Xx) A0)) (x9:((in Xx) X0))=> x9) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) X0)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x9:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Instantiate: X0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x9:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x9) as proof of ((in Xx) X0)
% Found (fun (x8:((in Xx) A0)) (x9:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x9) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) X0))
% Found (fun (Xx:fofType) (x8:((in Xx) A0)) (x9:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x9) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) X0)))
% Found (fun (Xx:fofType) (x8:((in Xx) A0)) (x9:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x9) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) X0))))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x1000:=(x100 x5):((in ((setminus A) X)) (powerset A))
% Found (x100 x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found ((x10 X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found x1000:=(x100 x6):((in ((setminus A) Y)) (powerset A))
% Found (x100 x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found ((x10 Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found ((x700 (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((x70 x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> (((x7 ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found x70:(P1 b)
% Found (fun (x70:(P1 b))=> x70) as proof of (P1 b)
% Found (fun (x70:(P1 b))=> x70) as proof of (P2 b)
% Found x70:(P1 b)
% Found (fun (x70:(P1 b))=> x70) as proof of (P1 b)
% Found (fun (x70:(P1 b))=> x70) as proof of (P2 b)
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8:((in Xx) ((setminus A) ((binunion X) Y)))
% Found x8 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8:((in Xx) ((setminus A) ((binunion X) Y)))
% Found x8 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found x7:(P0 b0)
% Instantiate: b0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x7:(P0 b0))=> x7) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x7:(P0 b0))=> x7) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x7:(P0 b0))=> x7) as proof of (P b0)
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x70:(P ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x70:(P ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x70) as proof of (P ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x70:(P ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x70) as proof of (P0 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x70:(P b)
% Found (fun (x70:(P b))=> x70) as proof of (P b)
% Found (fun (x70:(P b))=> x70) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found x7:(P0 b0)
% Instantiate: b0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x7:(P0 b0))=> x7) as proof of (P0 ((setminus A) ((binunion X) Y)))
% Found (fun (P0:(fofType->Prop)) (x7:(P0 b0))=> x7) as proof of ((P0 b0)->(P0 ((setminus A) ((binunion X) Y))))
% Found (fun (P0:(fofType->Prop)) (x7:(P0 b0))=> x7) as proof of (P b0)
% Found x70:(P ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x70:(P ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x70) as proof of (P ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x70:(P ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x70) as proof of (P0 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x70:(P ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x70:(P ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x70) as proof of (P ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x70:(P ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x70) as proof of (P0 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x70:(P1 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x70:(P1 ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x70) as proof of (P1 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x70:(P1 ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x70) as proof of (P2 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found x70:(P1 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x70:(P1 ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x70) as proof of (P1 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x70:(P1 ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x70) as proof of (P2 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:(P ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Instantiate: b0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found x7 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:(P b)
% Instantiate: b0:=b:fofType
% Found x7 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8:((in Xx) ((setminus A) ((binunion X) Y)))
% Found x8 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x8:((in Xx) ((setminus A) ((binunion X) Y)))
% Found x8 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found x000000:=(x00000 x6):((in ((binunion X) Y)) (powerset A))
% Found (x00000 x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((x0000 Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((x000 x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((((x00 X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (x100 (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found ((x10 ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found x000000:=(x00000 x6):((in ((binunion X) Y)) (powerset A))
% Found (x00000 x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((x0000 Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((x000 x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((((x00 X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (x100 (((((x0 A) X) x5) Y) x6)) as proof of ((in b) (powerset A0))
% Found ((x10 ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in b) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in b) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in b) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in b) (powerset A0))
% Found x000000:=(x00000 x6):((in ((binunion X) Y)) (powerset A))
% Found (x00000 x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((x0000 Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((x000 x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((((x00 X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (x100 (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found ((x10 ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found x000000:=(x00000 x6):((in ((binunion X) Y)) (powerset A))
% Found (x00000 x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((x0000 Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((x000 x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((((x00 X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (x100 (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found ((x10 ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found x70:(P b0)
% Found (fun (x70:(P b0))=> x70) as proof of (P b0)
% Found (fun (x70:(P b0))=> x70) as proof of (P0 b0)
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:(P b)
% Found x7 as proof of (P0 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found x7:(P0 ((setminus A) ((binunion X) Y)))
% Found (fun (x7:(P0 ((setminus A) ((binunion X) Y))))=> x7) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x7:(P0 ((setminus A) ((binunion X) Y))))=> x7) as proof of ((P0 ((setminus A) ((binunion X) Y)))->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x7:(P0 ((setminus A) ((binunion X) Y))))=> x7) as proof of (P ((setminus A) ((binunion X) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((setminus A) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((setminus A) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((setminus A) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((setminus A) Y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((setminus A) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((setminus A) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((setminus A) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((setminus A) Y))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b1)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b1)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b1)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b1)
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x70:(P0 b)
% Found (fun (x70:(P0 b))=> x70) as proof of (P0 b)
% Found (fun (x70:(P0 b))=> x70) as proof of (P1 b)
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x70:(P1 b)
% Found (fun (x70:(P1 b))=> x70) as proof of (P1 b)
% Found (fun (x70:(P1 b))=> x70) as proof of (P2 b)
% Found x70:(P1 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x70:(P1 ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x70) as proof of (P1 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x70:(P1 ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x70) as proof of (P2 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x70:(P1 b)
% Found (fun (x70:(P1 b))=> x70) as proof of (P1 b)
% Found (fun (x70:(P1 b))=> x70) as proof of (P2 b)
% Found x70:(P1 b)
% Found (fun (x70:(P1 b))=> x70) as proof of (P1 b)
% Found (fun (x70:(P1 b))=> x70) as proof of (P2 b)
% Found x9:((in Xx) X0)
% Instantiate: X0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x9:((in Xx) X0))=> x9) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x8:((in Xx) A0)) (x9:((in Xx) X0))=> x9) as proof of (((in Xx) X0)->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x8:((in Xx) A0)) (x9:((in Xx) X0))=> x9) as proof of (((in Xx) A0)->(((in Xx) X0)->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x8:((in Xx) A0)) (x9:((in Xx) X0))=> x9) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) X0)->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x70:(P1 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x70:(P1 ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x70) as proof of (P1 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x70:(P1 ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x70) as proof of (P2 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x70:(P1 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x70:(P1 ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x70) as proof of (P1 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x70:(P1 ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x70) as proof of (P2 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x9:((in Xx) ((setminus A) ((binunion X) Y)))
% Instantiate: X0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x9:((in Xx) ((setminus A) ((binunion X) Y))))=> x9) as proof of ((in Xx) X0)
% Found (fun (x8:((in Xx) A0)) (x9:((in Xx) ((setminus A) ((binunion X) Y))))=> x9) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) X0))
% Found (fun (Xx:fofType) (x8:((in Xx) A0)) (x9:((in Xx) ((setminus A) ((binunion X) Y))))=> x9) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) X0)))
% Found (fun (Xx:fofType) (x8:((in Xx) A0)) (x9:((in Xx) ((setminus A) ((binunion X) Y))))=> x9) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) X0))))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x1000:=(x100 x6):((in ((setminus A) Y)) (powerset A))
% Found (x100 x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found ((x10 Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found x1000:=(x100 x5):((in ((setminus A) X)) (powerset A))
% Found (x100 x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found ((x10 X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found ((x700 (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((x70 x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> (((x7 ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found x1000:=(x100 x5):((in ((setminus A) X)) (powerset A))
% Found (x100 x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found ((x10 X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found x1000:=(x100 x6):((in ((setminus A) Y)) (powerset A))
% Found (x100 x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found ((x10 Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found ((x700 (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in b) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((x70 x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in b) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> (((x7 ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in b) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in b) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in b) (powerset A0))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))))
% Found x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8:((in Xx) ((setminus A) ((binunion X) Y)))
% Found x8 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x1000:=(x100 x6):((in ((setminus A) Y)) (powerset A))
% Found (x100 x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found ((x10 Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found x1000:=(x100 x5):((in ((setminus A) X)) (powerset A))
% Found (x100 x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found ((x10 X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found ((x700 (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((x70 x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> (((x7 ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found x1000:=(x100 x5):((in ((setminus A) X)) (powerset A))
% Found (x100 x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found ((x10 X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found x1000:=(x100 x6):((in ((setminus A) Y)) (powerset A))
% Found (x100 x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found ((x10 Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found ((x700 (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((x70 x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> (((x7 ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found x7:(P0 b0)
% Instantiate: b0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x7:(P0 b0))=> x7) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x7:(P0 b0))=> x7) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x7:(P0 b0))=> x7) as proof of (P b0)
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x70:(P b)
% Found (fun (x70:(P b))=> x70) as proof of (P b)
% Found (fun (x70:(P b))=> x70) as proof of (P0 b)
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x8:((in Xx) ((setminus A) ((binunion X) Y)))
% Found x8 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:(P ((setminus A) ((binunion X) Y)))
% Instantiate: b0:=((setminus A) ((binunion X) Y)):fofType
% Found x7 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found x7:(P0 ((setminus A) ((binunion X) Y)))
% Instantiate: b0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x7:(P0 ((setminus A) ((binunion X) Y))))=> x7) as proof of (P0 b0)
% Found (fun (P0:(fofType->Prop)) (x7:(P0 ((setminus A) ((binunion X) Y))))=> x7) as proof of ((P0 ((setminus A) ((binunion X) Y)))->(P0 b0))
% Found (fun (P0:(fofType->Prop)) (x7:(P0 ((setminus A) ((binunion X) Y))))=> x7) as proof of (P b0)
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x70:(P b)
% Found (fun (x70:(P b))=> x70) as proof of (P b)
% Found (fun (x70:(P b))=> x70) as proof of (P0 b)
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found x8:((in Xx) ((setminus A) ((binunion X) Y)))
% Found x8 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x8:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x9:((in Xx) b))=> x8) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x8:((in Xx) A0)) (x9:((in Xx) b))=> x8) as proof of (((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x8:((in Xx) A0)) (x9:((in Xx) b))=> x8) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x8:((in Xx) A0)) (x9:((in Xx) b))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x8:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x9:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x8) as proof of ((in Xx) b)
% Found (fun (x8:((in Xx) A0)) (x9:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x8) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x8:((in Xx) A0)) (x9:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x8) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x8:((in Xx) A0)) (x9:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))))
% Found x70:(P ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x70:(P ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x70) as proof of (P ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x70:(P ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x70) as proof of (P0 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8:((in Xx) ((setminus A) ((binunion X) Y)))
% Found x8 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x8:((in Xx) ((setminus A) ((binunion X) Y)))
% Found x8 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x70:(P b0)
% Found (fun (x70:(P b0))=> x70) as proof of (P b0)
% Found (fun (x70:(P b0))=> x70) as proof of (P0 b0)
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b1)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b1)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b1)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found x000000:=(x00000 x6):((in ((binunion X) Y)) (powerset A))
% Found (x00000 x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((x0000 Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((x000 x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((((x00 X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (x100 (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found ((x10 ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x8:((in Xx) ((setminus A) ((binunion X) Y)))
% Found x8 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x8:((in Xx) ((setminus A) ((binunion X) Y)))
% Found x8 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b0)
% Found x7:(P0 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:(P0 ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x7:(P0 ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((P0 ((binintersect ((setminus A) X)) ((setminus A) Y)))->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x7:(P0 ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (P ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))))
% Found x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8:((in Xx) ((setminus A) ((binunion X) Y)))
% Found x8 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8:((in Xx) ((setminus A) ((binunion X) Y)))
% Found x8 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((binunion X) Y))
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((setminus A) ((binunion X) Y)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b1)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b1)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b1)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found x70:(P b0)
% Found (fun (x70:(P b0))=> x70) as proof of (P b0)
% Found (fun (x70:(P b0))=> x70) as proof of (P0 b0)
% Found x1000:=(x100 x6):((in ((setminus A) Y)) (powerset A))
% Found (x100 x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found ((x10 Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found x1000:=(x100 x5):((in ((setminus A) X)) (powerset A))
% Found (x100 x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found ((x10 X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found ((x700 (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in b) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((x70 x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in b) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> (((x7 ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in b) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in b) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in b) (powerset A0))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) b0))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b0))=> x7) as proof of (((in Xx) b0)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b0))=> x7) as proof of (((in Xx) A0)->(((in Xx) b0)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b0))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b0)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) b0)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b0))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b0))))
% Found x8:((in Xx) b)
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x70:(P b)
% Found (fun (x70:(P b))=> x70) as proof of (P b)
% Found (fun (x70:(P b))=> x70) as proof of (P0 b)
% Found x70:(P ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x70:(P ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x70) as proof of (P ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x70:(P ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x70) as proof of (P0 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x000000:=(x00000 x6):((in ((binunion X) Y)) (powerset A))
% Found (x00000 x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((x0000 Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((x000 x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((((x00 X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (x100 (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found ((x10 ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found x000000:=(x00000 x6):((in ((binunion X) Y)) (powerset A))
% Found (x00000 x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((x0000 Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((x000 x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((((x00 X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (x100 (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found ((x10 ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x8:((in Xx) b)
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found x8:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x9:((in Xx) ((setminus A) ((binunion X) Y))))=> x8) as proof of ((in Xx) b)
% Found (fun (x8:((in Xx) A0)) (x9:((in Xx) ((setminus A) ((binunion X) Y))))=> x8) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x8:((in Xx) A0)) (x9:((in Xx) ((setminus A) ((binunion X) Y))))=> x8) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x8:((in Xx) A0)) (x9:((in Xx) ((setminus A) ((binunion X) Y))))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b))))
% Found x8:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x9:((in Xx) b))=> x8) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x8:((in Xx) A0)) (x9:((in Xx) b))=> x8) as proof of (((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x8:((in Xx) A0)) (x9:((in Xx) b))=> x8) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x8:((in Xx) A0)) (x9:((in Xx) b))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x8:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x9:((in Xx) b))=> x8) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x8:((in Xx) A0)) (x9:((in Xx) b))=> x8) as proof of (((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x8:((in Xx) A0)) (x9:((in Xx) b))=> x8) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x8:((in Xx) A0)) (x9:((in Xx) b))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x8:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x9:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x8) as proof of ((in Xx) b)
% Found (fun (x8:((in Xx) A0)) (x9:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x8) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x8:((in Xx) A0)) (x9:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x8) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x8:((in Xx) A0)) (x9:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x8) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x70:(P ((setminus A) ((binunion X) Y)))
% Found (fun (x70:(P ((setminus A) ((binunion X) Y))))=> x70) as proof of (P ((setminus A) ((binunion X) Y)))
% Found (fun (x70:(P ((setminus A) ((binunion X) Y))))=> x70) as proof of (P0 ((setminus A) ((binunion X) Y)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b0)
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found x8:((in Xx) b)
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b1)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b1)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b1)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b00)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b00)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b00)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b00)
% Found x8:((in Xx) b)
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8:((in Xx) b)
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x8:((in Xx) b)
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x8:((in Xx) b)
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Instantiate: b:=A0:fofType
% Found x7 as proof of (P b)
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))))
% Found x8:((in Xx) b)
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x8:((in Xx) b)
% Found x8 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x1000:=(x100 x5):((in ((setminus A) X)) (powerset A))
% Found (x100 x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found ((x10 X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found x1000:=(x100 x6):((in ((setminus A) Y)) (powerset A))
% Found (x100 x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found ((x10 Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found ((x700 (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((x70 x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> (((x7 ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found x1000:=(x100 x6):((in ((setminus A) Y)) (powerset A))
% Found (x100 x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found ((x10 Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found (((x1 A) Y) x6) as proof of ((in ((setminus A) Y)) (powerset A0))
% Found x1000:=(x100 x5):((in ((setminus A) X)) (powerset A))
% Found (x100 x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found ((x10 X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found (((x1 A) X) x5) as proof of ((in ((setminus A) X)) (powerset A0))
% Found ((x700 (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((x70 x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> (((x7 ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found (((fun (x8:((in ((setminus A) X)) (powerset A0)))=> ((((x A0) ((setminus A) X)) x8) ((setminus A) Y))) (((x1 A) X) x5)) (((x1 A) Y) x6)) as proof of ((in ((binintersect ((setminus A) X)) ((setminus A) Y))) (powerset A0))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:(P ((setminus A) ((binunion X) Y)))
% Instantiate: a:=((setminus A) ((binunion X) Y)):fofType
% Found x7 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found x5:((in X) (powerset A))
% Instantiate: A0:=A:fofType;X0:=X:fofType
% Found x5 as proof of ((in X0) (powerset A0))
% Found x7:(P ((setminus A) ((binunion X) Y)))
% Instantiate: X0:=((setminus A) ((binunion X) Y)):fofType
% Found x7 as proof of (P0 X0)
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) b))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) b)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b))))
% Found x70:(P ((setminus A) ((binunion X) Y)))
% Found (fun (x70:(P ((setminus A) ((binunion X) Y))))=> x70) as proof of (P ((setminus A) ((binunion X) Y)))
% Found (fun (x70:(P ((setminus A) ((binunion X) Y))))=> x70) as proof of (P0 ((setminus A) ((binunion X) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x5:((in X) (powerset A))
% Found x5 as proof of ((in X) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found x7:(P2 b)
% Instantiate: b:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x7:(P2 b))=> x7) as proof of (P2 ((setminus A) ((binunion X) Y)))
% Found (fun (P2:(fofType->Prop)) (x7:(P2 b))=> x7) as proof of ((P2 b)->(P2 ((setminus A) ((binunion X) Y))))
% Found (fun (P2:(fofType->Prop)) (x7:(P2 b))=> x7) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b)
% Found x7:(P2 b)
% Instantiate: b:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x7:(P2 b))=> x7) as proof of (P2 ((setminus A) ((binunion X) Y)))
% Found (fun (P2:(fofType->Prop)) (x7:(P2 b))=> x7) as proof of ((P2 b)->(P2 ((setminus A) ((binunion X) Y))))
% Found (fun (P2:(fofType->Prop)) (x7:(P2 b))=> x7) as proof of (P1 b)
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) b0))=> x7) as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b0))=> x7) as proof of (((in Xx) b0)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b0))=> x7) as proof of (((in Xx) A0)->(((in Xx) b0)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b0))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b0)->((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of ((in Xx) b0)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b0))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))->((in Xx) b0))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((setminus A) ((binunion X) Y)):fofType
% Found (fun (x8:((in Xx) b0))=> x7) as proof of ((in Xx) ((setminus A) ((binunion X) Y)))
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) b0))=> x7) as proof of (((in Xx) b0)->((in Xx) ((setminus A) ((binunion X) Y))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b0))=> x7) as proof of (((in Xx) A0)->(((in Xx) b0)->((in Xx) ((setminus A) ((binunion X) Y)))))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) b0))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) b0)->((in Xx) ((setminus A) ((binunion X) Y))))))
% Found x7:((in Xx) A0)
% Instantiate: A0:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found (fun (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of ((in Xx) b0)
% Found (fun (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b0))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b0)))
% Found (fun (Xx:fofType) (x7:((in Xx) A0)) (x8:((in Xx) ((setminus A) ((binunion X) Y))))=> x7) as proof of (forall (Xx:fofType), (((in Xx) A0)->(((in Xx) ((setminus A) ((binunion X) Y)))->((in Xx) b0))))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found x6:((in Y) (powerset A))
% Found x6 as proof of ((in Y) (powerset A))
% Found x7:((in Xx) A0)
% Found x7 as proof of ((in Xx) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found eq_ref00:=(eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))):(((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Found (eq_ref0 ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b00)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b00)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b00)
% Found ((eq_ref fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) as proof of (((eq fofType) ((binintersect ((setminus A) X)) ((setminus A) Y))) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found x7:(P1 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Instantiate: b:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found x7 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found x7:(P1 ((binintersect ((setminus A) X)) ((setminus A) Y)))
% Instantiate: b:=((binintersect ((setminus A) X)) ((setminus A) Y)):fofType
% Found x7 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 ((setminus A) ((binunion X) Y))):(((eq fofType) ((setminus A) ((binunion X) Y))) ((setminus A) ((binunion X) Y)))
% Found (eq_ref0 ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found ((eq_ref fofType) ((setminus A) ((binunion X) Y))) as proof of (((eq fofType) ((setminus A) ((binunion X) Y))) b)
% Found x000000:=(x00000 x6):((in ((binunion X) Y)) (powerset A))
% Found (x00000 x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((x0000 Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((x000 x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((((x00 X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (x100 (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found ((x10 ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found x000000:=(x00000 x6):((in ((binunion X) Y)) (powerset A))
% Found (x00000 x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((x0000 Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((x000 x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((((x00 X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (x100 (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found ((x10 ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found x000000:=(x00000 x6):((in ((binunion X) Y)) (powerset A))
% Found (x00000 x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((x0000 Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((x000 x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((((x00 X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (x100 (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found ((x10 ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found x000000:=(x00000 x6):((in ((binunion X) Y)) (powerset A))
% Found (x00000 x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((x0000 Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((x000 x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((((x00 X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (x100 (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found ((x10 ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found (((x1 A) ((binunion X) Y)) (((((x0 A) X) x5) Y) x6)) as proof of ((in ((setminus A) ((binunion X) Y))) (powerset A0))
% Found x000000:=(x00000 x6):((in ((binunion X) Y)) (powerset A))
% Found (x00000 x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((x0000 Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((x000 x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found ((((x00 X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion X) Y)) (powerset A))
% Found (((((x0 A) X) x5) Y) x6) as proof of ((in ((binunion
% EOF
%------------------------------------------------------------------------------