TSTP Solution File: SEU610^2 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU610^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n103.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32286.75MB
% OS : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:32:36 EDT 2014
% Result : Timeout 300.11s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU610^2 : TPTP v6.1.0. Released v3.7.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n103.star.cs.uiowa.edu
% % Model : x86_64 x86_64
% % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory : 32286.75MB
% % OS : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 10:53:06 CDT 2014
% % CPUTime : 300.11
% 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 0x169b638>, <kernel.DependentProduct object at 0x169b8c0>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x169bb48>, <kernel.Single object at 0x169bab8>) of role type named emptyset_type
% Using role type
% Declaring emptyset:fofType
% FOF formula (<kernel.Constant object at 0x169b8c0>, <kernel.Sort object at 0x157b3f8>) of role type named emptysetE_type
% Using role type
% Declaring emptysetE:Prop
% FOF formula (((eq Prop) emptysetE) (forall (Xx:fofType), (((in Xx) emptyset)->(forall (Xphi:Prop), Xphi)))) of role definition named emptysetE
% A new definition: (((eq Prop) emptysetE) (forall (Xx:fofType), (((in Xx) emptyset)->(forall (Xphi:Prop), Xphi))))
% Defined: emptysetE:=(forall (Xx:fofType), (((in Xx) emptyset)->(forall (Xphi:Prop), Xphi)))
% FOF formula (<kernel.Constant object at 0x169b518>, <kernel.Sort object at 0x157b3f8>) of role type named in__Cong_type
% Using role type
% Declaring in__Cong:Prop
% FOF formula (((eq Prop) in__Cong) (forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((iff ((in Xx) A)) ((in Xy) B))))))) of role definition named in__Cong
% A new definition: (((eq Prop) in__Cong) (forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((iff ((in Xx) A)) ((in Xy) B)))))))
% Defined: in__Cong:=(forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((iff ((in Xx) A)) ((in Xy) B))))))
% FOF formula (<kernel.Constant object at 0x157bc20>, <kernel.DependentProduct object at 0x169bef0>) of role type named subset_type
% Using role type
% Declaring subset:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x157bc20>, <kernel.Sort object at 0x157b3f8>) of role type named subsetI2_type
% Using role type
% Declaring subsetI2:Prop
% FOF formula (((eq Prop) subsetI2) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((subset A) B)))) of role definition named subsetI2
% A new definition: (((eq Prop) subsetI2) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((subset A) B))))
% Defined: subsetI2:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((subset A) B)))
% FOF formula (<kernel.Constant object at 0x169ba28>, <kernel.DependentProduct object at 0x169bb48>) of role type named setminus_type
% Using role type
% Declaring setminus:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x169b4d0>, <kernel.Sort object at 0x157b3f8>) of role type named setminusI_type
% Using role type
% Declaring setminusI:Prop
% FOF formula (((eq Prop) setminusI) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((((in Xx) B)->False)->((in Xx) ((setminus A) B)))))) of role definition named setminusI
% A new definition: (((eq Prop) setminusI) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((((in Xx) B)->False)->((in Xx) ((setminus A) B))))))
% Defined: setminusI:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((((in Xx) B)->False)->((in Xx) ((setminus A) B)))))
% FOF formula (emptysetE->(in__Cong->(subsetI2->(setminusI->(forall (A:fofType) (B:fofType), ((((eq fofType) ((setminus A) B)) emptyset)->((subset A) B))))))) of role conjecture named setminusSubset1
% Conjecture to prove = (emptysetE->(in__Cong->(subsetI2->(setminusI->(forall (A:fofType) (B:fofType), ((((eq fofType) ((setminus A) B)) emptyset)->((subset A) B))))))):Prop
% We need to prove ['(emptysetE->(in__Cong->(subsetI2->(setminusI->(forall (A:fofType) (B:fofType), ((((eq fofType) ((setminus A) B)) emptyset)->((subset A) B)))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter emptyset:fofType.
% Definition emptysetE:=(forall (Xx:fofType), (((in Xx) emptyset)->(forall (Xphi:Prop), Xphi))):Prop.
% Definition in__Cong:=(forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((iff ((in Xx) A)) ((in Xy) B)))))):Prop.
% Parameter subset:(fofType->(fofType->Prop)).
% Definition subsetI2:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((subset A) B))):Prop.
% Parameter setminus:(fofType->(fofType->fofType)).
% Definition setminusI:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((((in Xx) B)->False)->((in Xx) ((setminus A) B))))):Prop.
% Trying to prove (emptysetE->(in__Cong->(subsetI2->(setminusI->(forall (A:fofType) (B:fofType), ((((eq fofType) ((setminus A) B)) emptyset)->((subset A) B)))))))
% Found x30:=(x3 (fun (x4:fofType)=> ((in Xx) A))):(((in Xx) A)->((in Xx) A))
% Found (x3 (fun (x4:fofType)=> ((in Xx) A))) as proof of (P A)
% Found (x3 (fun (x4:fofType)=> ((in Xx) A))) 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) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found eq_ref000:=(eq_ref00 (in Xx)):(((in Xx) A)->((in Xx) A))
% Found (eq_ref00 (in Xx)) as proof of (((in Xx) A)->((in Xx) b))
% Found ((eq_ref0 A) (in Xx)) as proof of (((in Xx) A)->((in Xx) b))
% Found (((eq_ref fofType) A) (in Xx)) as proof of (((in Xx) A)->((in Xx) b))
% Found (((eq_ref fofType) A) (in Xx)) as proof of (((in Xx) A)->((in Xx) b))
% Found (fun (Xx:fofType)=> (((eq_ref fofType) A) (in Xx))) as proof of (((in Xx) A)->((in Xx) b))
% Found (fun (Xx:fofType)=> (((eq_ref fofType) A) (in Xx))) as proof of (forall (Xx:fofType), (((in Xx) A)->((in Xx) b)))
% Found (x100 (fun (Xx:fofType)=> (((eq_ref fofType) A) (in Xx)))) as proof of (P b)
% Found ((x10 b) (fun (Xx:fofType)=> (((eq_ref fofType) A) (in Xx)))) as proof of (P b)
% Found (((x1 A) b) (fun (Xx:fofType)=> (((eq_ref fofType) A) (in Xx)))) as proof of (P b)
% Found (((x1 A) b) (fun (Xx:fofType)=> (((eq_ref fofType) A) (in Xx)))) as proof of (P b)
% Found x4:((in Xx) A)
% Instantiate: b:=A:fofType
% Found x4 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) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found x4:((in Xx) A)
% Instantiate: Xx0:=Xx:fofType
% Found x4 as proof of ((in Xx0) A)
% Found x30:=(x3 (fun (x4:fofType)=> ((in Xx) A))):(((in Xx) A)->((in Xx) A))
% Found (x3 (fun (x4:fofType)=> ((in Xx) A))) as proof of (P A)
% Found (x3 (fun (x4:fofType)=> ((in Xx) A))) as proof of (P 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found x30:=(x3 (fun (x4:fofType)=> (P0 B))):((P0 B)->(P0 B))
% Found (x3 (fun (x4:fofType)=> (P0 B))) as proof of (P1 B)
% Found (x3 (fun (x4:fofType)=> (P0 B))) as proof of (P1 B)
% Found x30:=(x3 (fun (x4:fofType)=> (P0 B))):((P0 B)->(P0 B))
% Found (x3 (fun (x4:fofType)=> (P0 B))) as proof of (P1 B)
% Found (x3 (fun (x4:fofType)=> (P0 B))) as proof of (P1 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) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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 x3:(((eq fofType) ((setminus A) B)) emptyset)
% Instantiate: a:=((setminus A) B):fofType;b:=emptyset:fofType
% Found x3 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found x3:(((eq fofType) ((setminus A) B)) emptyset)
% Instantiate: a:=((setminus A) B):fofType;b:=emptyset:fofType
% Found x3 as proof of (((eq fofType) a) b)
% Found x4:((in Xx) A)
% Instantiate: a:=A:fofType
% Found x4 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found ((eq_ref fofType) b) 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) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found ((eq_ref fofType) b) 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) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found x4:(P0 B)
% Instantiate: b:=B:fofType
% Found x4 as proof of (P1 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:(P0 B)
% Instantiate: b:=B:fofType
% Found x4 as proof of (P1 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 x30:=(x3 (fun (x5:fofType)=> (P0 B))):((P0 B)->(P0 B))
% Found (x3 (fun (x5:fofType)=> (P0 B))) as proof of (P1 B)
% Found (x3 (fun (x5:fofType)=> (P0 B))) as proof of (P1 B)
% Found eq_ref000:=(eq_ref00 (in Xx)):(((in Xx) A)->((in Xx) A))
% Found (eq_ref00 (in Xx)) as proof of (((in Xx) A)->((in Xx) a))
% Found ((eq_ref0 A) (in Xx)) as proof of (((in Xx) A)->((in Xx) a))
% Found (((eq_ref fofType) A) (in Xx)) as proof of (((in Xx) A)->((in Xx) a))
% Found (((eq_ref fofType) A) (in Xx)) as proof of (((in Xx) A)->((in Xx) a))
% Found (fun (Xx:fofType)=> (((eq_ref fofType) A) (in Xx))) as proof of (((in Xx) A)->((in Xx) a))
% Found (fun (Xx:fofType)=> (((eq_ref fofType) A) (in Xx))) as proof of (forall (Xx:fofType), (((in Xx) A)->((in Xx) a)))
% Found (x100 (fun (Xx:fofType)=> (((eq_ref fofType) A) (in Xx)))) as proof of (P a)
% Found ((x10 a) (fun (Xx:fofType)=> (((eq_ref fofType) A) (in Xx)))) as proof of (P a)
% Found (((x1 A) a) (fun (Xx:fofType)=> (((eq_ref fofType) A) (in Xx)))) as proof of (P a)
% Found (((x1 A) a) (fun (Xx:fofType)=> (((eq_ref fofType) A) (in Xx)))) 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 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) 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) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) 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) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 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) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found x30:=(x3 (fun (x4:fofType)=> (P0 b))):((P0 b)->(P0 b))
% Found (x3 (fun (x4:fofType)=> (P0 b))) as proof of (P1 b)
% Found (x3 (fun (x4:fofType)=> (P0 b))) as proof of (P1 b)
% Found x30:=(x3 (fun (x4:fofType)=> (P0 b))):((P0 b)->(P0 b))
% Found (x3 (fun (x4:fofType)=> (P0 b))) as proof of (P1 b)
% Found (x3 (fun (x4:fofType)=> (P0 b))) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 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 x30:=(x3 (fun (x4:fofType)=> (P0 B))):((P0 B)->(P0 B))
% Found (x3 (fun (x4:fofType)=> (P0 B))) as proof of (P1 B)
% Found (x3 (fun (x4:fofType)=> (P0 B))) as proof of (P1 B)
% Found x30:=(x3 (fun (x4:fofType)=> (P0 B))):((P0 B)->(P0 B))
% Found (x3 (fun (x4:fofType)=> (P0 B))) as proof of (P1 B)
% Found (x3 (fun (x4:fofType)=> (P0 B))) as proof of (P1 B)
% Found x4:(P0 A)
% Instantiate: b:=A:fofType
% Found x4 as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found x4:(P0 A)
% Instantiate: b:=A:fofType
% Found x4 as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found ((eq_ref fofType) b) 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 (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found ((eq_ref fofType) b) 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) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found eq_ref00:=(eq_ref0 A):(((eq fofType) A) A)
% Found (eq_ref0 A) as proof of (P0 b)
% Found ((eq_ref fofType) A) as proof of (P0 b)
% Found ((eq_ref fofType) A) as proof of (P0 b)
% Found ((eq_ref fofType) A) 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) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found eq_ref00:=(eq_ref0 A):(((eq fofType) A) A)
% Found (eq_ref0 A) as proof of (P0 b)
% Found ((eq_ref fofType) A) as proof of (P0 b)
% Found ((eq_ref fofType) A) as proof of (P0 b)
% Found ((eq_ref fofType) A) as proof of (P0 b)
% Found x30:=(x3 (fun (x4:fofType)=> (P0 B))):((P0 B)->(P0 B))
% Found (x3 (fun (x4:fofType)=> (P0 B))) as proof of (P1 B)
% Found (x3 (fun (x4:fofType)=> (P0 B))) as proof of (P1 B)
% Found eq_ref000:=(eq_ref00 P0):((P0 B)->(P0 B))
% Found (eq_ref00 P0) as proof of (P1 B)
% Found ((eq_ref0 B) P0) as proof of (P1 B)
% Found (((eq_ref fofType) B) P0) as proof of (P1 B)
% Found (((eq_ref fofType) B) P0) as proof of (P1 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) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) 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) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) 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 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found x4:((in Xx) A)
% Found x4 as proof of ((in Xx) A)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) 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) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) 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 x30:=(x3 (fun (x4:fofType)=> (P0 b))):((P0 b)->(P0 b))
% Found (x3 (fun (x4:fofType)=> (P0 b))) as proof of (P1 b)
% Found (x3 (fun (x4:fofType)=> (P0 b))) as proof of (P1 b)
% Found x30:=(x3 (fun (x4:fofType)=> (P0 B))):((P0 B)->(P0 B))
% Found (x3 (fun (x4:fofType)=> (P0 B))) as proof of (P1 B)
% Found (x3 (fun (x4:fofType)=> (P0 B))) as proof of (P1 B)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 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 x30:=(x3 (fun (x4:fofType)=> (P0 A))):((P0 A)->(P0 A))
% Found (x3 (fun (x4:fofType)=> (P0 A))) as proof of (P1 A)
% Found (x3 (fun (x4:fofType)=> (P0 A))) as proof of (P1 A)
% Found eq_ref000:=(eq_ref00 P0):((P0 A)->(P0 A))
% Found (eq_ref00 P0) as proof of (P1 A)
% Found ((eq_ref0 A) P0) as proof of (P1 A)
% Found (((eq_ref fofType) A) P0) as proof of (P1 A)
% Found (((eq_ref fofType) A) P0) as proof of (P1 A)
% Found x4:((in Xx) A)
% Found x4 as proof of ((in Xx) A)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 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 x30:=(x3 (fun (x4:fofType)=> ((in Xx) A))):(((in Xx) A)->((in Xx) A))
% Found (x3 (fun (x4:fofType)=> ((in Xx) A))) as proof of (P0 A)
% Found (x3 (fun (x4:fofType)=> ((in Xx) A))) as proof of (P0 A)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 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) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 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) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 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) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 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 x3:(((eq fofType) ((setminus A) B)) emptyset)
% Found x3 as proof of (((eq fofType) ((setminus A) B)) b)
% Found x3:(((eq fofType) ((setminus A) B)) emptyset)
% Found x3 as proof of (((eq fofType) ((setminus A) B)) b)
% Found x30:=(x3 (fun (x4:fofType)=> (P0 b))):((P0 b)->(P0 b))
% Found (x3 (fun (x4:fofType)=> (P0 b))) as proof of (P1 b)
% Found (x3 (fun (x4:fofType)=> (P0 b))) as proof of (P1 b)
% Found x30:=(x3 (fun (x4:fofType)=> (P0 b))):((P0 b)->(P0 b))
% Found (x3 (fun (x4:fofType)=> (P0 b))) as proof of (P1 b)
% Found (x3 (fun (x4:fofType)=> (P0 b))) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x30:=(x3 (fun (x4:fofType)=> (P0 B))):((P0 B)->(P0 B))
% Found (x3 (fun (x4:fofType)=> (P0 B))) as proof of (P1 B)
% Found (x3 (fun (x4:fofType)=> (P0 B))) as proof of (P1 B)
% Found eq_ref000:=(eq_ref00 P0):((P0 B)->(P0 B))
% Found (eq_ref00 P0) as proof of (P1 B)
% Found ((eq_ref0 B) P0) as proof of (P1 B)
% Found (((eq_ref fofType) B) P0) as proof of (P1 B)
% Found (((eq_ref fofType) B) P0) as proof of (P1 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) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) 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) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) 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) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) 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) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found x4:(P0 B)
% Instantiate: b:=B:fofType
% Found x4 as proof of (P1 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:(P0 B)
% Instantiate: b:=B:fofType
% Found x4 as proof of (P1 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 x30:=(x3 (fun (x5:fofType)=> (P0 B))):((P0 B)->(P0 B))
% Found (x3 (fun (x5:fofType)=> (P0 B))) as proof of (P1 B)
% Found (x3 (fun (x5:fofType)=> (P0 B))) as proof of (P1 B)
% Found x4:(P0 A)
% Instantiate: b:=A:fofType
% Found x4 as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found x4:((in Xx) A)
% Found x4 as proof of ((in Xx) A)
% Found x4:(P0 A)
% Instantiate: b:=A:fofType
% Found x4 as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) 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 x3:(((eq fofType) ((setminus A) B)) emptyset)
% Instantiate: b:=emptyset:fofType
% Found x3 as proof of (((eq fofType) ((setminus A) B)) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) 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 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) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 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 x30:=(x3 (fun (x4:fofType)=> (P0 B))):((P0 B)->(P0 B))
% Found (x3 (fun (x4:fofType)=> (P0 B))) as proof of (P1 B)
% Found (x3 (fun (x4:fofType)=> (P0 B))) as proof of (P1 B)
% Found x30:=(x3 (fun (x4:fofType)=> (P0 B))):((P0 B)->(P0 B))
% Found (x3 (fun (x4:fofType)=> (P0 B))) as proof of (P1 B)
% Found (x3 (fun (x4:fofType)=> (P0 B))) as proof of (P1 B)
% Found x4:(P0 A)
% Instantiate: b:=A:fofType
% Found x4 as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found x4:(P0 A)
% Instantiate: b:=A:fofType
% Found x4 as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found x30:=(x3 (fun (x4:fofType)=> (P0 A))):((P0 A)->(P0 A))
% Found (x3 (fun (x4:fofType)=> (P0 A))) as proof of (P1 A)
% Found (x3 (fun (x4:fofType)=> (P0 A))) as proof of (P1 A)
% Found x4:((in Xx) A)
% Instantiate: Xx0:=Xx:fofType;b:=A:fofType
% Found x4 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_ref000:=(eq_ref00 P0):((P0 A)->(P0 A))
% Found (eq_ref00 P0) as proof of (P1 A)
% Found ((eq_ref0 A) P0) as proof of (P1 A)
% Found (((eq_ref fofType) A) P0) as proof of (P1 A)
% Found (((eq_ref fofType) A) P0) as proof of (P1 A)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found ((eq_ref fofType) b) 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 (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found ((eq_ref fofType) b) 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) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found eq_ref00:=(eq_ref0 A):(((eq fofType) A) A)
% Found (eq_ref0 A) as proof of (P0 b)
% Found ((eq_ref fofType) A) as proof of (P0 b)
% Found ((eq_ref fofType) A) as proof of (P0 b)
% Found ((eq_ref fofType) A) 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) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found eq_ref00:=(eq_ref0 A):(((eq fofType) A) A)
% Found (eq_ref0 A) as proof of (P0 b)
% Found ((eq_ref fofType) A) as proof of (P0 b)
% Found ((eq_ref fofType) A) as proof of (P0 b)
% Found ((eq_ref fofType) A) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x4:((in Xx) A)
% Found x4 as proof of ((in Xx) A)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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:((in Xx) A)
% Instantiate: Xx0:=Xx:fofType;b:=A:fofType
% Found x4 as proof of (P b)
% Found x3:(((eq fofType) ((setminus A) B)) emptyset)
% Instantiate: b:=emptyset:fofType
% Found x3 as proof of (((eq fofType) ((setminus A) B)) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 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 x30:=(x3 (fun (x4:fofType)=> ((in Xx) A))):(((in Xx) A)->((in Xx) A))
% Found (x3 (fun (x4:fofType)=> ((in Xx) A))) as proof of (P0 A)
% Found (x3 (fun (x4:fofType)=> ((in Xx) A))) as proof of (P0 A)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found x4:((in Xx) A)
% Instantiate: Xx1:=Xx:fofType
% Found x4 as proof of ((in Xx1) A)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 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) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 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 x5:(P0 B)
% Instantiate: b0:=B:fofType
% Found x5 as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x30:=(x3 (fun (x4:fofType)=> (P0 B))):((P0 B)->(P0 B))
% Found (x3 (fun (x4:fofType)=> (P0 B))) as proof of (P1 B)
% Found (x3 (fun (x4:fofType)=> (P0 B))) as proof of (P1 B)
% Found x30:=(x3 (fun (x4:fofType)=> (P0 b))):((P0 b)->(P0 b))
% Found (x3 (fun (x4:fofType)=> (P0 b))) as proof of (P1 b)
% Found (x3 (fun (x4:fofType)=> (P0 b))) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 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 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 x30:=(x3 (fun (x4:fofType)=> (P0 A))):((P0 A)->(P0 A))
% Found (x3 (fun (x4:fofType)=> (P0 A))) as proof of (P1 A)
% Found (x3 (fun (x4:fofType)=> (P0 A))) as proof of (P1 A)
% Found x30:=(x3 (fun (x4:fofType)=> (P0 A))):((P0 A)->(P0 A))
% Found (x3 (fun (x4:fofType)=> (P0 A))) as proof of (P1 A)
% Found (x3 (fun (x4:fofType)=> (P0 A))) as proof of (P1 A)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 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 x30:=(x3 (fun (x4:fofType)=> ((in Xx) A))):(((in Xx) A)->((in Xx) A))
% Found (x3 (fun (x4:fofType)=> ((in Xx) A))) as proof of (P0 A)
% Found (x3 (fun (x4:fofType)=> ((in Xx) A))) as proof of (P0 A)
% Found x4:(P0 b)
% Instantiate: b0:=b:fofType
% Found x4 as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found x4:(P0 b)
% Instantiate: b0:=b:fofType
% Found x4 as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 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 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) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x4:((in Xx) A)
% Instantiate: Xx0:=Xx:fofType
% Found x4 as proof of ((in Xx0) A)
% Found x4:((in Xx) A)
% Instantiate: Xx0:=Xx:fofType
% Found x4 as proof of ((in Xx0) A)
% Found x4:(P0 b)
% Found x4 as proof of (P1 A)
% Found x4:(P0 b)
% Found x4 as proof of (P1 A)
% Found x3:(((eq fofType) ((setminus A) B)) emptyset)
% Instantiate: a:=((setminus A) B):fofType;b:=emptyset:fofType
% Found x3 as proof of (((eq fofType) a) b)
% Found x4:(P0 B)
% Instantiate: a:=B:fofType
% Found x4 as proof of (P1 a)
% Found x3:(((eq fofType) ((setminus A) B)) emptyset)
% Instantiate: a:=((setminus A) B):fofType;b:=emptyset:fofType
% Found x3 as proof of (((eq fofType) a) b)
% Found x4:(P0 B)
% Instantiate: a:=B:fofType
% Found x4 as proof of (P1 a)
% Found x5:(P0 b)
% Instantiate: b0:=b:fofType
% Found x5 as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 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 x3:(((eq fofType) ((setminus A) B)) emptyset)
% Instantiate: b0:=emptyset:fofType
% Found x3 as proof of (((eq fofType) a) b0)
% 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) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 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) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x3:(((eq fofType) ((setminus A) B)) emptyset)
% Found x3 as proof of (((eq fofType) ((setminus A) B)) b)
% Found x30:=(x3 (fun (x4:fofType)=> (P1 B))):((P1 B)->(P1 B))
% Found (x3 (fun (x4:fofType)=> (P1 B))) as proof of (P2 B)
% Found (x3 (fun (x4:fofType)=> (P1 B))) as proof of (P2 B)
% Found x30:=(x3 (fun (x4:fofType)=> (P1 B))):((P1 B)->(P1 B))
% Found (x3 (fun (x4:fofType)=> (P1 B))) as proof of (P2 B)
% Found (x3 (fun (x4:fofType)=> (P1 B))) as proof of (P2 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P0 b0)
% Found ((eq_ref fofType) b) as proof of (P0 b0)
% Found ((eq_ref fofType) b) as proof of (P0 b0)
% Found ((eq_ref fofType) b) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found x30:=(x3 (fun (x5:fofType)=> (P0 B))):((P0 B)->(P0 B))
% Found (x3 (fun (x5:fofType)=> (P0 B))) as proof of (P1 B)
% Found (x3 (fun (x5:fofType)=> (P0 B))) as proof of (P1 B)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 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) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 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 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) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 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) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found x4:((in Xx) A)
% Instantiate: Xx0:=Xx:fofType
% Found x4 as proof of ((in Xx0) 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 x4:(P2 A)
% Instantiate: b:=A:fofType
% Found x4 as proof of (P3 b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found x4:(P2 A)
% Instantiate: b:=A:fofType
% Found x4 as proof of (P3 b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found x4:(P2 A)
% Instantiate: b:=A:fofType
% Found x4 as proof of (P3 b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found x4:(P2 A)
% Instantiate: b:=A:fofType
% Found x4 as proof of (P3 b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found x30:=(x3 (fun (x4:fofType)=> (P0 b))):((P0 b)->(P0 b))
% Found (x3 (fun (x4:fofType)=> (P0 b))) as proof of (P1 b)
% Found (x3 (fun (x4:fofType)=> (P0 b))) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P2 b)
% Found ((eq_ref fofType) b) as proof of (P2 b)
% Found ((eq_ref fofType) b) as proof of (P2 b)
% Found ((eq_ref fofType) b) as proof of (P2 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 (P2 b)
% Found ((eq_ref fofType) b) as proof of (P2 b)
% Found ((eq_ref fofType) b) as proof of (P2 b)
% Found ((eq_ref fofType) b) as proof of (P2 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 (P2 b)
% Found ((eq_ref fofType) b) as proof of (P2 b)
% Found ((eq_ref fofType) b) as proof of (P2 b)
% Found ((eq_ref fofType) b) as proof of (P2 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 (P2 b)
% Found ((eq_ref fofType) b) as proof of (P2 b)
% Found ((eq_ref fofType) b) as proof of (P2 b)
% Found ((eq_ref fofType) b) as proof of (P2 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) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found eq_ref00:=(eq_ref0 A):(((eq fofType) A) A)
% Found (eq_ref0 A) as proof of (P2 b)
% Found ((eq_ref fofType) A) as proof of (P2 b)
% Found ((eq_ref fofType) A) as proof of (P2 b)
% Found ((eq_ref fofType) A) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found eq_ref00:=(eq_ref0 A):(((eq fofType) A) A)
% Found (eq_ref0 A) as proof of (P2 b)
% Found ((eq_ref fofType) A) as proof of (P2 b)
% Found ((eq_ref fofType) A) as proof of (P2 b)
% Found ((eq_ref fofType) A) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 A):(((eq fofType) A) A)
% Found (eq_ref0 A) as proof of (P2 b)
% Found ((eq_ref fofType) A) as proof of (P2 b)
% Found ((eq_ref fofType) A) as proof of (P2 b)
% Found ((eq_ref fofType) A) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b)
% Found eq_ref00:=(eq_ref0 A):(((eq fofType) A) A)
% Found (eq_ref0 A) as proof of (P2 b)
% Found ((eq_ref fofType) A) as proof of (P2 b)
% Found ((eq_ref fofType) A) as proof of (P2 b)
% Found ((eq_ref fofType) A) as proof of (P2 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 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 A):(((eq fofType) A) A)
% Found (eq_ref0 A) as proof of (((eq fofType) A) b1)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) b1)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) b1)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) B)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) B)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) B)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) B)
% Found eq_ref00:=(eq_ref0 A):(((eq fofType) A) A)
% Found (eq_ref0 A) as proof of (((eq fofType) A) b1)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) b1)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) b1)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) B)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) B)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) B)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) B)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 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) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 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 (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found x30:=(x3 (fun (x4:fofType)=> (P0 b0))):((P0 b0)->(P0 b0))
% Found (x3 (fun (x4:fofType)=> (P0 b0))) as proof of (P1 b0)
% Found (x3 (fun (x4:fofType)=> (P0 b0))) as proof of (P1 b0)
% Found x30:=(x3 (fun (x4:fofType)=> (P0 b0))):((P0 b0)->(P0 b0))
% Found (x3 (fun (x4:fofType)=> (P0 b0))) as proof of (P1 b0)
% Found (x3 (fun (x4:fofType)=> (P0 b0))) as proof of (P1 b0)
% Found x4:(P0 B)
% Instantiate: b0:=B:fofType
% Found x4 as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x4:(P0 b)
% Instantiate: b0:=b:fofType
% Found x4 as proof of (P1 b0)
% 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 x4:(P0 B)
% Instantiate: b0:=B:fofType
% Found x4 as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x4:(P0 B)
% Instantiate: b0:=B:fofType
% Found x4 as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b00)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b00)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b00)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found x3:(((eq fofType) ((setminus A) B)) emptyset)
% Instantiate: b0:=emptyset:fofType
% Found x3 as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 A):(((eq fofType) A) A)
% Found (eq_ref0 A) as proof of (P0 A)
% Found ((eq_ref fofType) A) as proof of (P0 A)
% Found ((eq_ref fofType) A) as proof of (P0 A)
% Found eq_ref00:=(eq_ref0 A):(((eq fofType) A) A)
% Found (eq_ref0 A) as proof of (P0 A)
% Found ((eq_ref fofType) A) as proof of (P0 A)
% Found ((eq_ref fofType) A) as proof of (P0 A)
% Found x30:=(x3 (fun (x5:fofType)=> (P0 B))):((P0 B)->(P0 B))
% Found (x3 (fun (x5:fofType)=> (P0 B))) as proof of (P1 B)
% Found (x3 (fun (x5:fofType)=> (P0 B))) as proof of (P1 B)
% Found x4:((in Xx) A)
% Instantiate: Xx0:=Xx:fofType
% Found x4 as proof of ((in Xx0) A)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 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) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 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 x4:((in Xx) A)
% Instantiate: Xx0:=Xx:fofType
% Found x4 as proof of ((in Xx0) A)
% Found x3:(((eq fofType) ((setminus A) B)) emptyset)
% Instantiate: a:=((setminus A) B):fofType;b:=emptyset:fofType
% Found x3 as proof of (((eq fofType) a) b)
% Found x4:(P0 A)
% Instantiate: a:=A:fofType
% Found x4 as proof of (P1 a)
% Found x3:(((eq fofType) ((setminus A) B)) emptyset)
% Instantiate: a:=((setminus A) B):fofType;b:=emptyset:fofType
% Found x3 as proof of (((eq fofType) a) b)
% Found x4:(P0 A)
% Instantiate: a:=A:fofType
% Found x4 as proof of (P1 a)
% Found x4:((in Xx) A)
% Instantiate: Xx0:=Xx:fofType
% Found x4 as proof of ((in Xx0) A)
% Found x4:((in Xx) A)
% Instantiate: Xx0:=Xx:fofType
% Found x4 as proof of ((in Xx0) A)
% Found x3:(((eq fofType) ((setminus A) B)) emptyset)
% Found x3 as proof of (((eq fofType) ((setminus A) B)) b)
% Found x4:((in Xx) A)
% Instantiate: Xx0:=Xx:fofType
% Found x4 as proof of ((in Xx0) A)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) 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) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) 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) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) 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 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) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found x30:=(x3 (fun (x5:fofType)=> (P0 b))):((P0 b)->(P0 b))
% Found (x3 (fun (x5:fofType)=> (P0 b))) as proof of (P1 b)
% Found (x3 (fun (x5:fofType)=> (P0 b))) as proof of (P1 b)
% Found x3:(((eq fofType) ((setminus A) B)) emptyset)
% Found x3 as proof of (((eq fofType) ((setminus A) B)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 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 x4:(P0 b)
% Found x4 as proof of (P1 B)
% Found x4:(P0 B)
% Found x4 as proof of (P1 B)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 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) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 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 x30:=(x3 (fun (x4:fofType)=> (P2 B))):((P2 B)->(P2 B))
% Found (x3 (fun (x4:fofType)=> (P2 B))) as proof of (P3 B)
% Found (x3 (fun (x4:fofType)=> (P2 B))) as proof of (P3 B)
% Found x30:=(x3 (fun (x4:fofType)=> (P2 b))):((P2 b)->(P2 b))
% Found (x3 (fun (x4:fofType)=> (P2 b))) as proof of (P3 b)
% Found (x3 (fun (x4:fofType)=> (P2 b))) as proof of (P3 b)
% Found x30:=(x3 (fun (x4:fofType)=> (P2 B))):((P2 B)->(P2 B))
% Found (x3 (fun (x4:fofType)=> (P2 B))) as proof of (P3 B)
% Found (x3 (fun (x4:fofType)=> (P2 B))) as proof of (P3 B)
% Found x30:=(x3 (fun (x4:fofType)=> (P2 B))):((P2 B)->(P2 B))
% Found (x3 (fun (x4:fofType)=> (P2 B))) as proof of (P3 B)
% Found (x3 (fun (x4:fofType)=> (P2 B))) as proof of (P3 B)
% Found x4:(P0 B)
% Instantiate: b0:=B:fofType
% Found x4 as proof of (P1 b0)
% 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 x4:(P0 B)
% Instantiate: b0:=B:fofType
% Found x4 as proof of (P1 b0)
% 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 x30:=(x3 (fun (x5:fofType)=> (P0 b))):((P0 b)->(P0 b))
% Found (x3 (fun (x5:fofType)=> (P0 b))) as proof of (P1 b)
% Found (x3 (fun (x5:fofType)=> (P0 b))) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (P0 b0)
% Found ((eq_ref fofType) B) as proof of (P0 b0)
% Found ((eq_ref fofType) B) as proof of (P0 b0)
% Found ((eq_ref fofType) B) as proof of (P0 b0)
% 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 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (P0 b0)
% Found ((eq_ref fofType) B) as proof of (P0 b0)
% Found ((eq_ref fofType) B) as proof of (P0 b0)
% Found ((eq_ref fofType) B) as proof of (P0 b0)
% 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 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) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) 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 x4:((in Xx) A)
% Instantiate: Xx0:=Xx:fofType
% Found x4 as proof of ((in Xx0) A)
% Found x30:=(x3 (fun (x4:fofType)=> (P2 A))):((P2 A)->(P2 A))
% Found (x3 (fun (x4:fofType)=> (P2 A))) as proof of (P3 A)
% Found (x3 (fun (x4:fofType)=> (P2 A))) as proof of (P3 A)
% Found x30:=(x3 (fun (x4:fofType)=> (P2 A))):((P2 A)->(P2 A))
% Found (x3 (fun (x4:fofType)=> (P2 A))) as proof of (P3 A)
% Found (x3 (fun (x4:fofType)=> (P2 A))) as proof of (P3 A)
% Found eq_ref000:=(eq_ref00 P2):((P2 A)->(P2 A))
% Found (eq_ref00 P2) as proof of (P3 A)
% Found ((eq_ref0 A) P2) as proof of (P3 A)
% Found (((eq_ref fofType) A) P2) as proof of (P3 A)
% Found (((eq_ref fofType) A) P2) as proof of (P3 A)
% Found x30:=(x3 (fun (x4:fofType)=> (P2 A))):((P2 A)->(P2 A))
% Found (x3 (fun (x4:fofType)=> (P2 A))) as proof of (P3 A)
% Found (x3 (fun (x4:fofType)=> (P2 A))) as proof of (P3 A)
% Found x4:((in Xx) A)
% Instantiate: b0:=A:fofType
% Found (fun (x4:((in Xx) A))=> x4) as proof of ((in Xx) b0)
% Found (fun (Xx:fofType) (x4:((in Xx) A))=> x4) as proof of (((in Xx) A)->((in Xx) b0))
% Found (fun (Xx:fofType) (x4:((in Xx) A))=> x4) as proof of (forall (Xx:fofType), (((in Xx) A)->((in Xx) b0)))
% Found (x100 (fun (Xx:fofType) (x4:((in Xx) A))=> x4)) as proof of (P0 b0)
% Found ((x10 b0) (fun (Xx:fofType) (x4:((in Xx) A))=> x4)) as proof of (P0 b0)
% Found (((x1 A) b0) (fun (Xx:fofType) (x4:((in Xx) A))=> x4)) as proof of (P0 b0)
% Found (((x1 A) b0) (fun (Xx:fofType) (x4:((in Xx) A))=> x4)) as proof of (P0 b0)
% Found x30:=(x3 (fun (x4:fofType)=> ((in Xx) A))):(((in Xx) A)->((in Xx) A))
% Found (x3 (fun (x4:fofType)=> ((in Xx) A))) as proof of (P0 A)
% Found (x3 (fun (x4:fofType)=> ((in Xx) A))) 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) 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) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) B)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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 x30:=(x3 (fun (x4:fofType)=> (P0 B))):((P0 B)->(P0 B))
% Found (x3 (fun (x4:fofType)=> (P0 B))) as proof of (P1 B)
% Found (x3 (fun (x4:fofType)=> (P0 B))) as proof of (P1 B)
% Found eq_ref000:=(eq_ref00 P0):((P0 B)->(P0 B))
% Found (eq_ref00 P0) as proof of (P1 B)
% Found ((eq_ref0 B) P0) as proof of (P1 B)
% Found (((eq_ref fofType) B) P0) as proof of (P1 B)
% Found (((eq_ref fofType) B) P0) as proof of (P1 B)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x4:((in Xx) A)
% Instantiate: b0:=A:fofType
% Found x4 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b1)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b1)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b1)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b1)
% Found x4:(P0 b)
% Instantiate: b0:=b:fofType
% Found x4 as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% 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 (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% 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 (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% 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) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 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) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 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) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P0 b0)
% Found ((eq_ref fofType) b) as proof of (P0 b0)
% Found ((eq_ref fofType) b) as proof of (P0 b0)
% Found ((eq_ref fofType) b) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 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) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 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 x3:(((eq fofType) ((setminus A) B)) emptyset)
% Found x3 as proof of (((eq fofType) ((setminus A) B)) emptyset)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) A)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) A)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) A)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) A)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b1)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b1)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b1)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) A)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) A)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) A)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) A)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b1)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b1)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b1)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b1)
% Found x30:=(x3 (fun (x4:fofType)=> (P0 B))):((P0 B)->(P0 B))
% Found (x3 (fun (x4:fofType)=> (P0 B))) as proof of (P1 B)
% Found (x3 (fun (x4:fofType)=> (P0 B))) as proof of (P1 B)
% Found x30:=(x3 (fun (x4:fofType)=> (P0 b0))):((P0 b0)->(P0 b0))
% Found (x3 (fun (x4:fofType)=> (P0 b0))) as proof of (P1 b0)
% Found (x3 (fun (x4:fofType)=> (P0 b0))) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) B)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) B)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) B)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) B)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found x30:=(x3 (fun (x4:fofType)=> (P0 B))):((P0 B)->(P0 B))
% Found (x3 (fun (x4:fofType)=> (P0 B))) as proof of (P1 B)
% Found (x3 (fun (x4:fofType)=> (P0 B))) as proof of (P1 B)
% Found eq_ref000:=(eq_ref00 P0):((P0 B)->(P0 B))
% Found (eq_ref00 P0) as proof of (P1 B)
% Found ((eq_ref0 B) P0) as proof of (P1 B)
% Found (((eq_ref fofType) B) P0) as proof of (P1 B)
% Found (((eq_ref fofType) B) P0) as proof of (P1 B)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (P0 B)
% Found ((eq_ref fofType) B) as proof of (P0 B)
% Found ((eq_ref fofType) B) as proof of (P0 B)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (P0 B)
% Found ((eq_ref fofType) B) as proof of (P0 B)
% Found ((eq_ref fofType) B) as proof of (P0 B)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 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) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) 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) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) A)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) 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) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 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 x3:(((eq fofType) ((setminus A) B)) emptyset)
% Found x3 as proof of (((eq fofType) ((setminus A) B)) emptyset)
% Found x3:(((eq fofType) ((setminus A) B)) emptyset)
% Found x3 as proof of (((eq fofType) ((setminus A) B)) b)
% Found x4:(P0 A)
% Instantiate: b0:=A:fofType
% Found x4 as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found x4:(P0 A)
% Instantiate: b0:=A:fofType
% Found x4 as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found x4:(P0 A)
% Instantiate: b0:=A:fofType
% Found x4 as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 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) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 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) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 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) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 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) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 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) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 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) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 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) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 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 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 A):(((eq fofType) A) A)
% Found (eq_ref0 A) as proof of (P0 b0)
% Found ((eq_ref fofType) A) as proof of (P0 b0)
% Found ((eq_ref fofType) A) as proof of (P0 b0)
% Found ((eq_ref fofType) A) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found eq_ref00:=(eq_ref0 A):(((eq fofType) A) A)
% Found (eq_ref0 A) as proof of (P0 b0)
% Found ((eq_ref fofType) A) as proof of (P0 b0)
% Found ((eq_ref fofType) A) as proof of (P0 b0)
% Found ((eq_ref fofType) A) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 A):(((eq fofType) A) A)
% Found (eq_ref0 A) as proof of (P0 b0)
% Found ((eq_ref fofType) A) as proof of (P0 b0)
% Found ((eq_ref fofType) A) as proof of (P0 b0)
% Found ((eq_ref fofType) A) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b0)
% Found x4:(P0 A)
% Found x4 as proof of (P1 A)
% Found x4:(P0 A)
% Found x4 as proof of (P1 A)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b1)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b1)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b1)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b1)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b1)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b1)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b00)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b00)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b00)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b00)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b00)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b00)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 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) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 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 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) B)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) B)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) B)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) B)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found x30:=(x3 (fun (x4:fofType)=> (P0 b0))):((P0 b0)->(P0 b0))
% Found (x3 (fun (x4:fofType)=> (P0 b0))) as proof of (P1 b0)
% Found (x3 (fun (x4:fofType)=> (P0 b0))) as proof of (P1 b0)
% Found x30:=(x3 (fun (x4:fofType)=> (P0 b0))):((P0 b0)->(P0 b0))
% Found (x3 (fun (x4:fofType)=> (P0 b0))) as proof of (P1 b0)
% Found (x3 (fun (x4:fofType)=> (P0 b0))) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 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) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 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 x30:=(x3 (fun (x4:fofType)=> (P0 b))):((P0 b)->(P0 b))
% Found (x3 (fun (x4:fofType)=> (P0 b))) as proof of (P1 b)
% Found (x3 (fun (x4:fofType)=> (P0 b))) as proof of (P1 b)
% Found x30:=(x3 (fun (x4:fofType)=> (P0 A))):((P0 A)->(P0 A))
% Found (x3 (fun (x4:fofType)=> (P0 A))) as proof of (P1 A)
% Found (x3 (fun (x4:fofType)=> (P0 A))) as proof of (P1 A)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b00)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b00)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b00)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b00)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b00)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b00)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) A)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) A)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) A)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) A)
% Found eq_ref00:=(eq_ref0 B):(((eq fofType) B) B)
% Found (eq_ref0 B) as proof of (((eq fofType) B) b1)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b1)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b1)
% Found ((eq_ref fofType) B) as proof of (((eq fofType) B) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 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) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 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) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 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) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 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) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) B)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 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)
% EOF
%------------------------------------------------------------------------------