TSTP Solution File: SEU805^2 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU805^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n106.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 13:33:11 EDT 2014
% Result : Timeout 300.10s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU805^2 : TPTP v6.1.0. Released v3.7.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n106.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 11:31:31 CDT 2014
% % CPUTime : 300.10
% 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 0x26b8c20>, <kernel.DependentProduct object at 0x26b8dd0>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x2896488>, <kernel.Single object at 0x26b8b90>) of role type named emptyset_type
% Using role type
% Declaring emptyset:fofType
% FOF formula (<kernel.Constant object at 0x26b8dd0>, <kernel.Sort object at 0x259d128>) of role type named foundationAx_type
% Using role type
% Declaring foundationAx:Prop
% FOF formula (((eq Prop) foundationAx) (forall (A:fofType), (((ex fofType) (fun (Xx:fofType)=> ((in Xx) A)))->((ex fofType) (fun (B:fofType)=> ((and ((in B) A)) (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) B)) ((in Xx) A))))->False))))))) of role definition named foundationAx
% A new definition: (((eq Prop) foundationAx) (forall (A:fofType), (((ex fofType) (fun (Xx:fofType)=> ((in Xx) A)))->((ex fofType) (fun (B:fofType)=> ((and ((in B) A)) (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) B)) ((in Xx) A))))->False)))))))
% Defined: foundationAx:=(forall (A:fofType), (((ex fofType) (fun (Xx:fofType)=> ((in Xx) A)))->((ex fofType) (fun (B:fofType)=> ((and ((in B) A)) (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) B)) ((in Xx) A))))->False))))))
% FOF formula (<kernel.Constant object at 0x26b8d40>, <kernel.DependentProduct object at 0x26b8998>) of role type named nonempty_type
% Using role type
% Declaring nonempty:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) nonempty) (fun (Xx:fofType)=> (not (((eq fofType) Xx) emptyset)))) of role definition named nonempty
% A new definition: (((eq (fofType->Prop)) nonempty) (fun (Xx:fofType)=> (not (((eq fofType) Xx) emptyset))))
% Defined: nonempty:=(fun (Xx:fofType)=> (not (((eq fofType) Xx) emptyset)))
% FOF formula (<kernel.Constant object at 0x26b8998>, <kernel.Sort object at 0x259d128>) of role type named nonemptyE1_type
% Using role type
% Declaring nonemptyE1:Prop
% FOF formula (((eq Prop) nonemptyE1) (forall (A:fofType), ((nonempty A)->((ex fofType) (fun (Xx:fofType)=> ((in Xx) A)))))) of role definition named nonemptyE1
% A new definition: (((eq Prop) nonemptyE1) (forall (A:fofType), ((nonempty A)->((ex fofType) (fun (Xx:fofType)=> ((in Xx) A))))))
% Defined: nonemptyE1:=(forall (A:fofType), ((nonempty A)->((ex fofType) (fun (Xx:fofType)=> ((in Xx) A)))))
% FOF formula (<kernel.Constant object at 0x26b8638>, <kernel.DependentProduct object at 0x26b8368>) of role type named binintersect_type
% Using role type
% Declaring binintersect:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x26b8f38>, <kernel.Sort object at 0x259d128>) of role type named disjointsetsI1_type
% Using role type
% Declaring disjointsetsI1:Prop
% FOF formula (((eq Prop) disjointsetsI1) (forall (A:fofType) (B:fofType), ((((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((in Xx) B))))->False)->(((eq fofType) ((binintersect A) B)) emptyset)))) of role definition named disjointsetsI1
% A new definition: (((eq Prop) disjointsetsI1) (forall (A:fofType) (B:fofType), ((((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((in Xx) B))))->False)->(((eq fofType) ((binintersect A) B)) emptyset))))
% Defined: disjointsetsI1:=(forall (A:fofType) (B:fofType), ((((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((in Xx) B))))->False)->(((eq fofType) ((binintersect A) B)) emptyset)))
% FOF formula (foundationAx->(nonemptyE1->(disjointsetsI1->(forall (A:fofType), ((nonempty A)->((ex fofType) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset))))))))) of role conjecture named foundation2
% Conjecture to prove = (foundationAx->(nonemptyE1->(disjointsetsI1->(forall (A:fofType), ((nonempty A)->((ex fofType) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset))))))))):Prop
% We need to prove ['(foundationAx->(nonemptyE1->(disjointsetsI1->(forall (A:fofType), ((nonempty A)->((ex fofType) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset)))))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter emptyset:fofType.
% Definition foundationAx:=(forall (A:fofType), (((ex fofType) (fun (Xx:fofType)=> ((in Xx) A)))->((ex fofType) (fun (B:fofType)=> ((and ((in B) A)) (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) B)) ((in Xx) A))))->False)))))):Prop.
% Definition nonempty:=(fun (Xx:fofType)=> (not (((eq fofType) Xx) emptyset))):(fofType->Prop).
% Definition nonemptyE1:=(forall (A:fofType), ((nonempty A)->((ex fofType) (fun (Xx:fofType)=> ((in Xx) A))))):Prop.
% Parameter binintersect:(fofType->(fofType->fofType)).
% Definition disjointsetsI1:=(forall (A:fofType) (B:fofType), ((((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((in Xx) B))))->False)->(((eq fofType) ((binintersect A) B)) emptyset))):Prop.
% Trying to prove (foundationAx->(nonemptyE1->(disjointsetsI1->(forall (A:fofType), ((nonempty A)->((ex fofType) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset)))))))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset)))):(((eq (fofType->Prop)) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset)))) (fun (x:fofType)=> ((and ((in x) A)) (((eq fofType) ((binintersect x) A)) emptyset))))
% Found (eta_expansion_dep00 (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset)))) b)
% Found ((eta_expansion_dep0 (fun (x4:fofType)=> Prop)) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset)))) b)
% Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset)))) b)
% Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset)))) b)
% Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset)))) b)
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) ((and ((in x3) A)) (((eq fofType) ((binintersect x3) A)) emptyset)))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((and ((in x3) A)) (((eq fofType) ((binintersect x3) A)) emptyset)))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((and ((in x3) A)) (((eq fofType) ((binintersect x3) A)) emptyset)))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) ((and ((in x3) A)) (((eq fofType) ((binintersect x3) A)) emptyset)))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((and ((in x) A)) (((eq fofType) ((binintersect x) A)) emptyset))))
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) ((and ((in x3) A)) (((eq fofType) ((binintersect x3) A)) emptyset)))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((and ((in x3) A)) (((eq fofType) ((binintersect x3) A)) emptyset)))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((and ((in x3) A)) (((eq fofType) ((binintersect x3) A)) emptyset)))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) ((and ((in x3) A)) (((eq fofType) ((binintersect x3) A)) emptyset)))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((and ((in x) A)) (((eq fofType) ((binintersect x) A)) emptyset))))
% Found eq_ref00:=(eq_ref0 (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset)))):(((eq (fofType->Prop)) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset)))) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset))))
% Found (eq_ref0 (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset)))) b)
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) ((and ((in x3) A)) (((eq fofType) ((binintersect x3) A)) emptyset)))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((and ((in x3) A)) (((eq fofType) ((binintersect x3) A)) emptyset)))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((and ((in x3) A)) (((eq fofType) ((binintersect x3) A)) emptyset)))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) ((and ((in x3) A)) (((eq fofType) ((binintersect x3) A)) emptyset)))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((and ((in x) A)) (((eq fofType) ((binintersect x) A)) emptyset))))
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) ((and ((in x3) A)) (((eq fofType) ((binintersect x3) A)) emptyset)))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((and ((in x3) A)) (((eq fofType) ((binintersect x3) A)) emptyset)))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) ((and ((in x3) A)) (((eq fofType) ((binintersect x3) A)) emptyset)))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) ((and ((in x3) A)) (((eq fofType) ((binintersect x3) A)) emptyset)))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((and ((in x) A)) (((eq fofType) ((binintersect x) A)) emptyset))))
% Found eq_ref000:=(eq_ref00 P):((P ((binintersect x3) A))->(P ((binintersect x3) A)))
% Found (eq_ref00 P) as proof of (P0 ((binintersect x3) A))
% Found ((eq_ref0 ((binintersect x3) A)) P) as proof of (P0 ((binintersect x3) A))
% Found (((eq_ref fofType) ((binintersect x3) A)) P) as proof of (P0 ((binintersect x3) A))
% Found (((eq_ref fofType) ((binintersect x3) A)) P) as proof of (P0 ((binintersect x3) A))
% Found x40:(P ((binintersect x3) A))
% Found (fun (x40:(P ((binintersect x3) A)))=> x40) as proof of (P ((binintersect x3) A))
% Found (fun (x40:(P ((binintersect x3) A)))=> x40) as proof of (P0 ((binintersect x3) A))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_ref00:=(eq_ref0 ((binintersect x3) A)):(((eq fofType) ((binintersect x3) A)) ((binintersect x3) A))
% Found (eq_ref0 ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found eq_ref000:=(eq_ref00 P):((P ((binintersect x3) A))->(P ((binintersect x3) A)))
% Found (eq_ref00 P) as proof of (P0 ((binintersect x3) A))
% Found ((eq_ref0 ((binintersect x3) A)) P) as proof of (P0 ((binintersect x3) A))
% Found (((eq_ref fofType) ((binintersect x3) A)) P) as proof of (P0 ((binintersect x3) A))
% Found (((eq_ref fofType) ((binintersect x3) A)) P) as proof of (P0 ((binintersect x3) A))
% Found x40:(P ((binintersect x3) A))
% Found (fun (x40:(P ((binintersect x3) A)))=> x40) as proof of (P ((binintersect x3) A))
% Found (fun (x40:(P ((binintersect x3) A)))=> x40) as proof of (P0 ((binintersect x3) A))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_ref00:=(eq_ref0 ((binintersect x3) A)):(((eq fofType) ((binintersect x3) A)) ((binintersect x3) A))
% Found (eq_ref0 ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found x2:(nonempty A)
% Instantiate: A0:=A:fofType
% Found x2 as proof of (nonempty A0)
% Found (x00 x2) as proof of (P b)
% Found (x00 x2) as proof of (P b)
% Found ((x0 A) x2) as proof of (P b)
% Found ((x0 A) x2) as proof of (P b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x2:(nonempty A)
% Instantiate: A0:=A:fofType
% Found x2 as proof of (nonempty A0)
% Found (x00 x2) as proof of (P f)
% Found (x00 x2) as proof of (P f)
% Found ((x0 A) x2) as proof of (P f)
% Found ((x0 A) x2) as proof of (P f)
% Found x2:(nonempty A)
% Instantiate: A0:=A:fofType
% Found x2 as proof of (nonempty A0)
% Found (x00 x2) as proof of (P f)
% Found (x00 x2) as proof of (P f)
% Found ((x0 A) x2) as proof of (P f)
% Found ((x0 A) x2) as proof of (P f)
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found x2:(not (((eq fofType) A) emptyset))
% Instantiate: A0:=A:fofType
% Found x2 as proof of (nonempty A0)
% Found (x00 x2) as proof of (P b)
% Found (x00 x2) as proof of (P b)
% Found ((x0 A) x2) as proof of (P b)
% Found ((x0 A) x2) as proof of (P b)
% Found eq_ref000:=(eq_ref00 P):((P A)->(P A))
% Found (eq_ref00 P) as proof of (P0 A)
% Found ((eq_ref0 A) P) as proof of (P0 A)
% Found (((eq_ref fofType) A) P) as proof of (P0 A)
% Found (((eq_ref fofType) A) P) as proof of (P0 A)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found x50:(P A)
% Found (fun (x50:(P A))=> x50) as proof of (P A)
% Found (fun (x50:(P A))=> x50) as proof of (P0 A)
% Found x2:(not (((eq fofType) A) emptyset))
% Instantiate: A0:=A:fofType
% Found x2 as proof of (nonempty A0)
% Found (x00 x2) as proof of (P f)
% Found (x00 x2) as proof of (P f)
% Found ((x0 A) x2) as proof of (P f)
% Found ((x0 A) x2) as proof of (P f)
% Found x2:(not (((eq fofType) A) emptyset))
% Instantiate: A0:=A:fofType
% Found x2 as proof of (nonempty A0)
% Found (x00 x2) as proof of (P f)
% Found (x00 x2) as proof of (P f)
% Found ((x0 A) x2) as proof of (P f)
% Found ((x0 A) x2) as proof of (P f)
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset))))
% Found ((eta_expansion_dep0 (fun (x4:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset))))
% Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset))))
% Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset))))
% Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset))))
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_ref00:=(eq_ref0 (((eq fofType) ((binintersect x3) A)) emptyset)):(((eq Prop) (((eq fofType) ((binintersect x3) A)) emptyset)) (((eq fofType) ((binintersect x3) A)) emptyset))
% Found (eq_ref0 (((eq fofType) ((binintersect x3) A)) emptyset)) as proof of (((eq Prop) (((eq fofType) ((binintersect x3) A)) emptyset)) b)
% Found ((eq_ref Prop) (((eq fofType) ((binintersect x3) A)) emptyset)) as proof of (((eq Prop) (((eq fofType) ((binintersect x3) A)) emptyset)) b)
% Found ((eq_ref Prop) (((eq fofType) ((binintersect x3) A)) emptyset)) as proof of (((eq Prop) (((eq fofType) ((binintersect x3) A)) emptyset)) b)
% Found ((eq_ref Prop) (((eq fofType) ((binintersect x3) A)) emptyset)) as proof of (((eq Prop) (((eq fofType) ((binintersect x3) A)) emptyset)) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eta_expansion_dep0 (fun (x4:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset))))
% Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset))))
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (X:fofType)=> ((and ((in X) A)) (((eq fofType) ((binintersect X) A)) emptyset))))
% Found eq_ref00:=(eq_ref0 (((eq fofType) ((binintersect x3) A)) emptyset)):(((eq Prop) (((eq fofType) ((binintersect x3) A)) emptyset)) (((eq fofType) ((binintersect x3) A)) emptyset))
% Found (eq_ref0 (((eq fofType) ((binintersect x3) A)) emptyset)) as proof of (((eq Prop) (((eq fofType) ((binintersect x3) A)) emptyset)) b)
% Found ((eq_ref Prop) (((eq fofType) ((binintersect x3) A)) emptyset)) as proof of (((eq Prop) (((eq fofType) ((binintersect x3) A)) emptyset)) b)
% Found ((eq_ref Prop) (((eq fofType) ((binintersect x3) A)) emptyset)) as proof of (((eq Prop) (((eq fofType) ((binintersect x3) A)) emptyset)) b)
% Found ((eq_ref Prop) (((eq fofType) ((binintersect x3) A)) emptyset)) as proof of (((eq Prop) (((eq fofType) ((binintersect x3) A)) emptyset)) 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found x70:(P A)
% Found (fun (x70:(P A))=> x70) as proof of (P A)
% Found (fun (x70:(P A))=> x70) as proof of (P0 A)
% Found eq_ref000:=(eq_ref00 P):((P A)->(P A))
% Found (eq_ref00 P) as proof of (P0 A)
% Found ((eq_ref0 A) P) as proof of (P0 A)
% Found (((eq_ref fofType) A) P) as proof of (P0 A)
% Found (((eq_ref fofType) A) P) as proof of (P0 A)
% Found x70:(P A)
% Found (fun (x70:(P A))=> x70) as proof of (P A)
% Found (fun (x70:(P A))=> x70) as proof of (P0 A)
% Found eq_ref000:=(eq_ref00 P):((P A)->(P A))
% Found (eq_ref00 P) as proof of (P0 A)
% Found ((eq_ref0 A) P) as proof of (P0 A)
% Found (((eq_ref fofType) A) P) as proof of (P0 A)
% Found (((eq_ref fofType) A) P) as proof of (P0 A)
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref000:=(eq_ref00 P):((P ((binintersect x3) A))->(P ((binintersect x3) A)))
% Found (eq_ref00 P) as proof of (P0 ((binintersect x3) A))
% Found ((eq_ref0 ((binintersect x3) A)) P) as proof of (P0 ((binintersect x3) A))
% Found (((eq_ref fofType) ((binintersect x3) A)) P) as proof of (P0 ((binintersect x3) A))
% Found (((eq_ref fofType) ((binintersect x3) A)) P) as proof of (P0 ((binintersect x3) A))
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found x40:(P ((binintersect x3) A))
% Found (fun (x40:(P ((binintersect x3) A)))=> x40) as proof of (P ((binintersect x3) A))
% Found (fun (x40:(P ((binintersect x3) A)))=> x40) as proof of (P0 ((binintersect x3) A))
% Found eq_ref00:=(eq_ref0 ((binintersect x3) A)):(((eq fofType) ((binintersect x3) A)) ((binintersect x3) A))
% Found (eq_ref0 ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found x4:(P ((binintersect x3) A))
% Instantiate: b:=((binintersect x3) A):fofType
% Found x4 as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P ((binintersect x3) A))->(P ((binintersect x3) A)))
% Found (eq_ref00 P) as proof of (P0 ((binintersect x3) A))
% Found ((eq_ref0 ((binintersect x3) A)) P) as proof of (P0 ((binintersect x3) A))
% Found (((eq_ref fofType) ((binintersect x3) A)) P) as proof of (P0 ((binintersect x3) A))
% Found (((eq_ref fofType) ((binintersect x3) A)) P) as proof of (P0 ((binintersect x3) A))
% Found x40:(P ((binintersect x3) A))
% Found (fun (x40:(P ((binintersect x3) A)))=> x40) as proof of (P ((binintersect x3) A))
% Found (fun (x40:(P ((binintersect x3) A)))=> x40) as proof of (P0 ((binintersect x3) A))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_ref00:=(eq_ref0 ((binintersect x3) A)):(((eq fofType) ((binintersect x3) A)) ((binintersect x3) A))
% Found (eq_ref0 ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) 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 x4:(P ((binintersect x3) A))
% Instantiate: b:=((binintersect x3) A):fofType
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_ref00:=(eq_ref0 ((binintersect x3) A)):(((eq fofType) ((binintersect x3) A)) ((binintersect x3) A))
% Found (eq_ref0 ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x4:(P0 b)
% Instantiate: b:=((binintersect x3) A):fofType
% Found (fun (x4:(P0 b))=> x4) as proof of (P0 ((binintersect x3) A))
% Found (fun (P0:(fofType->Prop)) (x4:(P0 b))=> x4) as proof of ((P0 b)->(P0 ((binintersect x3) A)))
% Found (fun (P0:(fofType->Prop)) (x4:(P0 b))=> x4) as proof of (P b)
% Found x90:(P A)
% Found (fun (x90:(P A))=> x90) as proof of (P A)
% Found (fun (x90:(P A))=> x90) as proof of (P0 A)
% Found eq_ref000:=(eq_ref00 P):((P A)->(P A))
% Found (eq_ref00 P) as proof of (P0 A)
% Found ((eq_ref0 A) P) as proof of (P0 A)
% Found (((eq_ref fofType) A) P) as proof of (P0 A)
% Found (((eq_ref fofType) A) P) as proof of (P0 A)
% Found x40:(P ((binintersect x3) A))
% Found (fun (x40:(P ((binintersect x3) A)))=> x40) as proof of (P ((binintersect x3) A))
% Found (fun (x40:(P ((binintersect x3) A)))=> x40) as proof of (P0 ((binintersect x3) A))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_ref00:=(eq_ref0 ((binintersect x3) A)):(((eq fofType) ((binintersect x3) A)) ((binintersect x3) A))
% Found (eq_ref0 ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_ref00:=(eq_ref0 ((binintersect x3) A)):(((eq fofType) ((binintersect x3) A)) ((binintersect x3) A))
% Found (eq_ref0 ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found x90:(P A)
% Found (fun (x90:(P A))=> x90) as proof of (P A)
% Found (fun (x90:(P A))=> x90) as proof of (P0 A)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x90:(P A)
% Found (fun (x90:(P A))=> x90) as proof of (P A)
% Found (fun (x90:(P A))=> x90) as proof of (P0 A)
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_ref000:=(eq_ref00 P):((P ((binintersect x3) A))->(P ((binintersect x3) A)))
% Found (eq_ref00 P) as proof of (P0 ((binintersect x3) A))
% Found ((eq_ref0 ((binintersect x3) A)) P) as proof of (P0 ((binintersect x3) A))
% Found (((eq_ref fofType) ((binintersect x3) A)) P) as proof of (P0 ((binintersect x3) A))
% Found (((eq_ref fofType) ((binintersect x3) A)) P) as proof of (P0 ((binintersect x3) A))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_ref00:=(eq_ref0 ((binintersect x3) A)):(((eq fofType) ((binintersect x3) A)) ((binintersect x3) A))
% Found (eq_ref0 ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found eq_ref000:=(eq_ref00 P):((P A)->(P A))
% Found (eq_ref00 P) as proof of (P0 A)
% Found ((eq_ref0 A) P) as proof of (P0 A)
% Found (((eq_ref fofType) A) P) as proof of (P0 A)
% Found (((eq_ref fofType) A) P) as proof of (P0 A)
% Found eq_ref000:=(eq_ref00 P):((P A)->(P A))
% Found (eq_ref00 P) as proof of (P0 A)
% Found ((eq_ref0 A) P) as proof of (P0 A)
% Found (((eq_ref fofType) A) P) as proof of (P0 A)
% Found (((eq_ref fofType) A) P) as proof of (P0 A)
% Found eq_ref00:=(eq_ref0 ((binintersect x3) A)):(((eq fofType) ((binintersect x3) A)) ((binintersect x3) A))
% Found (eq_ref0 ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b0)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b0)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b0)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x4:(P emptyset)
% Instantiate: b:=emptyset:fofType
% Found x4 as proof of (P0 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_ref00:=(eq_ref0 ((binintersect x3) A)):(((eq fofType) ((binintersect x3) A)) ((binintersect x3) A))
% Found (eq_ref0 ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 ((binintersect x3) A)):(((eq fofType) ((binintersect x3) A)) ((binintersect x3) A))
% Found (eq_ref0 ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b0)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b0)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b0)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b0)
% Found x4:(P emptyset)
% Instantiate: b:=emptyset:fofType
% Found x4 as proof of (P0 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_ref00:=(eq_ref0 ((binintersect x3) A)):(((eq fofType) ((binintersect x3) A)) ((binintersect x3) A))
% Found (eq_ref0 ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found ((eq_ref fofType) ((binintersect x3) A)) as proof of (((eq fofType) ((binintersect x3) A)) b)
% Found x5:(P A)
% Instantiate: b:=A:fofType
% Found x5 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref000:=(eq_ref00 P):((P A)->(P A))
% Found (eq_ref00 P) as proof of (P0 A)
% Found ((eq_ref0 A) P) as proof of (P0 A)
% Found (((eq_ref fofType) A) P) as proof of (P0 A)
% Found (((eq_ref fofType) A) P) as proof of (P0 A)
% Found eq_ref000:=(eq_ref00 P):((P A)->(P A))
% Found (eq_ref00 P) as proof of (P0 A)
% Found ((eq_ref0 A) P) as proof of (P0 A)
% Found (((eq_ref fofType) A) P) as proof of (P0 A)
% Found (((eq_ref fofType) A) P) as proof of (P0 A)
% Found eq_ref000:=(eq_ref00 P):((P ((binintersect x3) A))->(P ((binintersect x3) A)))
% Found (eq_ref00 P) as proof of (P0 ((binintersect x3) A))
% Found ((eq_ref0 ((binintersect x3) A)) P) as proof of (P0 ((binintersect x3) A))
% Found (((eq_ref fofType) ((binintersect x3) A)) P) as proof of (P0 ((binintersect x3) A))
% Found (((eq_ref fofType) ((binintersect x3) A)) P) as proof of (P0 ((binintersect x3) A))
% Found x50:(P A)
% Found (fun (x50:(P A))=> x50) as proof of (P A)
% Found (fun (x50:(P A))=> x50) as proof of (P0 A)
% Found x50:(P A)
% Found (fun (x50:(P A))=> x50) as proof of (P A)
% Found (fun (x50:(P A))=> x50) as proof of (P0 A)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x40:(P ((binintersect x3) A))
% Found (fun (x40:(P ((binintersect x3) A)))=> x40) as proof of (P ((binintersect x3) A))
% Found (fun (x40:(P ((binintersect x3) A)))=> x40) as proof of (P0 ((binintersect x3) A))
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found x5:(P A)
% Instantiate: b:=A:fofType
% Found x5 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found eq_ref000:=(eq_ref00 P):((P ((binintersect x3) A))->(P ((binintersect x3) A)))
% Found (eq_ref00 P) as proof of (P0 ((binintersect x3) A))
% Found ((eq_ref0 ((binintersect x3) A)) P) as proof of (P0 ((binintersect x3) A))
% Found (((eq_ref fofType) ((binintersect x3) A)) P) as proof of (P0 ((binintersect x3) A))
% Found (((eq_ref fofType) ((binintersect x3) A)) P) as proof of (P0 ((binintersect x3) A))
% Found x40:(P ((binintersect x3) A))
% Found (fun (x40:(P ((binintersect x3) A)))=> x40) as proof of (P ((binintersect x3) A))
% Found (fun (x40:(P ((binintersect x3) A)))=> x40) as proof of (P0 ((binintersect x3) A))
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found x40:(P emptyset)
% Found (fun (x40:(P emptyset))=> x40) as proof of (P emptyset)
% Found (fun (x40:(P emptyset))=> x40) as proof of (P0 emptyset)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Instantiate: b:=(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b)))):Prop
% Found eq_substitution as proof of b
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref000:=(eq_ref00 P1):((P1 A)->(P1 A))
% Found (eq_ref00 P1) as proof of (P2 A)
% Found ((eq_ref0 A) P1) as proof of (P2 A)
% Found (((eq_ref fofType) A) P1) as proof of (P2 A)
% Found (((eq_ref fofType) A) P1) as proof of (P2 A)
% Found eq_ref000:=(eq_ref00 P1):((P1 A)->(P1 A))
% Found (eq_ref00 P1) as proof of (P2 A)
% Found ((eq_ref0 A) P1) as proof of (P2 A)
% Found (((eq_ref fofType) A) P1) as proof of (P2 A)
% Found (((eq_ref fofType) A) P1) as proof of (P2 A)
% Found x50:(P1 A)
% Found (fun (x50:(P1 A))=> x50) as proof of (P1 A)
% Found (fun (x50:(P1 A))=> x50) as proof of (P2 A)
% Found x50:(P1 A)
% Found (fun (x50:(P1 A))=> x50) as proof of (P1 A)
% Found (fun (x50:(P1 A))=> x50) as proof of (P2 A)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x5:(P0 b)
% Instantiate: b:=A:fofType
% Found (fun (x5:(P0 b))=> x5) as proof of (P0 A)
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b))=> x5) as proof of ((P0 b)->(P0 A))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b))=> x5) as proof of (P b)
% Found eq_ref000:=(eq_ref00 P):((P emptyset)->(P emptyset))
% Found (eq_ref00 P) as proof of (P0 emptyset)
% Found ((eq_ref0 emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found (((eq_ref fofType) emptyset) P) as proof of (P0 emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((binintersect x3) A))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x50:(P A)
% Found (fun (x50:(P A))=> x50) as proof of (P A)
% Found (fun (x50:(P A))=> x50) as proof of (P0 A)
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Instantiate: b:=(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b)))):Prop
% Found eq_substitution as proof of b
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref000:=(eq_ref00 P):((P A)->(P A))
% Found (eq_ref00 P) as proof of (P0 A)
% Found ((eq_ref0 A) P) as proof of (P0 A)
% Found (((eq_ref fofType) A) P) as proof of (P0 A)
% Found (((eq_ref fofType) A) P) as proof of (P0 A)
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 A):(((eq fofType) A) A)
% Found (eq_ref0 A) as proof of (((eq fofType) A) b0)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) b0)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) b0)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x5:(P emptyset)
% Instantiate: b:=emptyset:fofType
% Found x5 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) A)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) A)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) A)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) A)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) A)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) A)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) A)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) A)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((binintersect x3) A))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect x3) A))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect x3) A))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect x3) A))
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found x7:(P A)
% Instantiate: b:=A:fofType
% Found x7 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x70:(P A)
% Found (fun (x70:(P A))=> x70) as proof of (P A)
% Found (fun (x70:(P A))=> x70) as proof of (P0 A)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found x70:(P A)
% Found (fun (x70:(P A))=> x70) as proof of (P A)
% Found (fun (x70:(P A))=> x70) as proof of (P0 A)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 A):(((eq fofType) A) A)
% Found (eq_ref0 A) as proof of (((eq fofType) A) b0)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) b0)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) b0)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) emptyset)
% Found eq_ref000:=(eq_ref00 P):((P A)->(P A))
% Found (eq_ref00 P) as proof of (P0 A)
% Found ((eq_ref0 A) P) as proof of (P0 A)
% Found (((eq_ref fofType) A) P) as proof of (P0 A)
% Found (((eq_ref fofType) A) P) as proof of (P0 A)
% Found x7:(P A)
% Instantiate: b:=A:fofType
% Found x7 as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P A)->(P A))
% Found (eq_ref00 P) as proof of (P0 A)
% Found ((eq_ref0 A) P) as proof of (P0 A)
% Found (((eq_ref fofType) A) P) as proof of (P0 A)
% Found (((eq_ref fofType) A) P) as proof of (P0 A)
% Found x5:(P emptyset)
% Instantiate: b:=emptyset:fofType
% Found x5 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) A)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) A)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) A)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) A)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) A)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) A)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) A)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) A)
% 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 x3) A))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect x3) A))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect x3) A))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect x3) A))
% Found x70:(P A)
% Found (fun (x70:(P A))=> x70) as proof of (P A)
% Found (fun (x70:(P A))=> x70) as proof of (P0 A)
% Found x70:(P A)
% Found (fun (x70:(P A))=> x70) as proof of (P A)
% Found (fun (x70:(P A))=> x70) as proof of (P0 A)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref000:=(eq_ref00 P):((P A)->(P A))
% Found (eq_ref00 P) as proof of (P0 A)
% Found ((eq_ref0 A) P) as proof of (P0 A)
% Found (((eq_ref fofType) A) P) as proof of (P0 A)
% Found (((eq_ref fofType) A) P) as proof of (P0 A)
% Found x2:(nonempty A)
% Instantiate: A0:=A:fofType
% Found x2 as proof of (nonempty A0)
% Found (x00 x2) as proof of (P a)
% Found (x00 x2) as proof of (P a)
% Found ((x0 A) x2) as proof of (P a)
% Found ((x0 A) x2) as proof of (P a)
% Found eq_ref000:=(eq_ref00 P):((P A)->(P A))
% Found (eq_ref00 P) as proof of (P0 A)
% Found ((eq_ref0 A) P) as proof of (P0 A)
% Found (((eq_ref fofType) A) P) as proof of (P0 A)
% Found (((eq_ref fofType) A) P) as proof of (P0 A)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((binintersect x3) A))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect x3) A))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect x3) A))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((binintersect x3) A))
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found x2:(nonempty A)
% Instantiate: A0:=A:fofType
% Found x2 as proof of (nonempty A0)
% Found (x00 x2) as proof of (P a)
% Found (x00 x2) as proof of (P a)
% Found ((x0 A) x2) as proof of (P a)
% Found ((x0 A) x2) as proof of (P a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) A)
% Found eq_ref00:=(eq_ref0 emptyset):(((eq fofType) emptyset) emptyset)
% Found (eq_ref0 emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found ((eq_ref fofType) emptyset) as proof of (((eq fofType) emptyset) b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found x40:(P emptyset)
% Found (fun (x40:(P emptyset))=> x40) as proof of (P emptyset)
% Found (fun (x40:(P emptyset))=> x40) as proof of (P0 emptyset)
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) emptyset)
% Found eq_ref00:=(eq_r
% EOF
%------------------------------------------------------------------------------