%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU652^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n092.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:32:43 EDT 2014

% Result   : Timeout 300.00s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU652^2 : TPTP v6.1.0. Released v3.7.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n092.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 11:03:06 CDT 2014
% % CPUTime  : 300.00 
% 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 0x2617ef0>, <kernel.DependentProduct object at 0x20a5ef0>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x20abd40>, <kernel.Single object at 0x2617e60>) of role type named emptyset_type
% Using role type
% Declaring emptyset:fofType
% FOF formula (<kernel.Constant object at 0x2617c68>, <kernel.DependentProduct object at 0x20a5560>) of role type named setadjoin_type
% Using role type
% Declaring setadjoin:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x2617cf8>, <kernel.Sort object at 0x2470fc8>) of role type named setadjoinIL_type
% Using role type
% Declaring setadjoinIL:Prop
% FOF formula (((eq Prop) setadjoinIL) (forall (Xx:fofType) (Xy:fofType), ((in Xx) ((setadjoin Xx) Xy)))) of role definition named setadjoinIL
% A new definition: (((eq Prop) setadjoinIL) (forall (Xx:fofType) (Xy:fofType), ((in Xx) ((setadjoin Xx) Xy))))
% Defined: setadjoinIL:=(forall (Xx:fofType) (Xy:fofType), ((in Xx) ((setadjoin Xx) Xy)))
% FOF formula (<kernel.Constant object at 0x2617cf8>, <kernel.Sort object at 0x2470fc8>) of role type named uniqinunit_type
% Using role type
% Declaring uniqinunit:Prop
% FOF formula (((eq Prop) uniqinunit) (forall (Xx:fofType) (Xy:fofType), (((in Xx) ((setadjoin Xy) emptyset))->(((eq fofType) Xx) Xy)))) of role definition named uniqinunit
% A new definition: (((eq Prop) uniqinunit) (forall (Xx:fofType) (Xy:fofType), (((in Xx) ((setadjoin Xy) emptyset))->(((eq fofType) Xx) Xy))))
% Defined: uniqinunit:=(forall (Xx:fofType) (Xy:fofType), (((in Xx) ((setadjoin Xy) emptyset))->(((eq fofType) Xx) Xy)))
% FOF formula (<kernel.Constant object at 0x2617cf8>, <kernel.Sort object at 0x2470fc8>) of role type named secondinupair_type
% Using role type
% Declaring secondinupair:Prop
% FOF formula (((eq Prop) secondinupair) (forall (Xx:fofType) (Xy:fofType), ((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset))))) of role definition named secondinupair
% A new definition: (((eq Prop) secondinupair) (forall (Xx:fofType) (Xy:fofType), ((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset)))))
% Defined: secondinupair:=(forall (Xx:fofType) (Xy:fofType), ((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset))))
% FOF formula (setadjoinIL->(uniqinunit->(secondinupair->(forall (Xx:fofType) (Xy:fofType) (Xz:fofType), ((((eq fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) ((setadjoin Xz) emptyset))->(((eq fofType) Xx) Xy)))))) of role conjecture named upairequniteq
% Conjecture to prove = (setadjoinIL->(uniqinunit->(secondinupair->(forall (Xx:fofType) (Xy:fofType) (Xz:fofType), ((((eq fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) ((setadjoin Xz) emptyset))->(((eq fofType) Xx) Xy)))))):Prop
% We need to prove ['(setadjoinIL->(uniqinunit->(secondinupair->(forall (Xx:fofType) (Xy:fofType) (Xz:fofType), ((((eq fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) ((setadjoin Xz) emptyset))->(((eq fofType) Xx) Xy))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter emptyset:fofType.
% Parameter setadjoin:(fofType->(fofType->fofType)).
% Definition setadjoinIL:=(forall (Xx:fofType) (Xy:fofType), ((in Xx) ((setadjoin Xx) Xy))):Prop.
% Definition uniqinunit:=(forall (Xx:fofType) (Xy:fofType), (((in Xx) ((setadjoin Xy) emptyset))->(((eq fofType) Xx) Xy))):Prop.
% Definition secondinupair:=(forall (Xx:fofType) (Xy:fofType), ((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset)))):Prop.
% Trying to prove (setadjoinIL->(uniqinunit->(secondinupair->(forall (Xx:fofType) (Xy:fofType) (Xz:fofType), ((((eq fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) ((setadjoin Xz) emptyset))->(((eq fofType) Xx) Xy))))))
% Found x20:=(x2 (fun (x3:fofType)=> (P Xx))):((P Xx)->(P Xx))
% Found (x2 (fun (x3:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found (x2 (fun (x3:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found x20:=(x2 (fun (x3:fofType)=> (P Xx))):((P Xx)->(P Xx))
% Found (x2 (fun (x3:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found (x2 (fun (x3:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found x3:(P Xx)
% Instantiate: Xx0:=Xx:fofType
% Found x3 as proof of (P0 Xx0)
% Found x40:=(x4 emptyset):((in Xx0) ((setadjoin Xx0) emptyset))
% Found (x4 emptyset) as proof of ((in Xx0) ((setadjoin Xy) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xy) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xy) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xy) emptyset))
% Found x3:(P Xx)
% Instantiate: b:=Xx:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 ((setadjoin Xy) emptyset)):(((eq fofType) ((setadjoin Xy) emptyset)) ((setadjoin Xy) emptyset))
% Found (eq_ref0 ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P Xx))):((P Xx)->(P Xx))
% Found (x2 (fun (x3:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found (x2 (fun (x3:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x3:(P Xy)
% Instantiate: b:=Xy:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x3:(P Xy)
% Instantiate: Xx0:=Xy:fofType
% Found x3 as proof of (P0 Xx0)
% Found x40:=(x4 emptyset):((in Xx0) ((setadjoin Xx0) emptyset))
% Found (x4 emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found x20:=(x2 (fun (x3:fofType)=> (P b))):((P b)->(P b))
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P b))):((P b)->(P b))
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found x20:=(x2 (fun (x3:fofType)=> (P Xx))):((P Xx)->(P Xx))
% Found (x2 (fun (x3:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found (x2 (fun (x3:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xx):((in Xx) ((setadjoin Xy) ((setadjoin Xx) emptyset)))
% Found (x10 Xx) as proof of (P a)
% Found ((x1 Xy) Xx) as proof of (P a)
% Found ((x1 Xy) Xx) as proof of (P a)
% Found ((x1 Xy) Xx) 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) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xx):((in Xx) ((setadjoin Xy) ((setadjoin Xx) emptyset)))
% Found (x10 Xx) as proof of (P ((setadjoin Xy) a))
% Found ((x1 Xy) Xx) as proof of (P ((setadjoin Xy) a))
% Found ((x1 Xy) Xx) as proof of (P ((setadjoin Xy) a))
% Found ((x1 Xy) Xx) as proof of (P ((setadjoin Xy) a))
% Found x20:=(x2 (fun (x3:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found x20:=(x2 (fun (x3:fofType)=> (P Xx))):((P Xx)->(P Xx))
% Found (x2 (fun (x3:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found (x2 (fun (x3:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found x20:=(x2 (fun (x3:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 ((setadjoin Xx) emptyset)):(((eq fofType) ((setadjoin Xx) emptyset)) ((setadjoin Xx) emptyset))
% Found (eq_ref0 ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xy):((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (x10 Xy) as proof of (P a)
% Found ((x1 Xx) Xy) as proof of (P a)
% Found ((x1 Xx) Xy) as proof of (P a)
% Found ((x1 Xx) Xy) 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) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xy):((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (x10 Xy) as proof of (P ((setadjoin Xx) a))
% Found ((x1 Xx) Xy) as proof of (P ((setadjoin Xx) a))
% Found ((x1 Xx) Xy) as proof of (P ((setadjoin Xx) a))
% Found ((x1 Xx) Xy) as proof of (P ((setadjoin Xx) a))
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 x20:=(x2 (fun (x3:fofType)=> (P b))):((P b)->(P b))
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found (x2 (fun (x3:fofType)=> (P 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) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 emptyset):((in b) ((setadjoin b) emptyset))
% Found (x3 emptyset) as proof of (P b)
% Found ((x b) emptyset) as proof of (P b)
% Found ((x b) emptyset) as proof of (P b)
% Found ((x b) emptyset) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found x3:(P Xx)
% Instantiate: Xx0:=Xx:fofType
% Found x3 as proof of (P0 Xx0)
% Found x40:=(x4 emptyset):((in Xx0) ((setadjoin Xx0) emptyset))
% Found (x4 emptyset) as proof of ((in Xx0) ((setadjoin Xy) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xy) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xy) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xy) emptyset))
% Found x3:(P Xx)
% Instantiate: b:=Xx:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 ((setadjoin Xy) emptyset)):(((eq fofType) ((setadjoin Xy) emptyset)) ((setadjoin Xy) emptyset))
% Found (eq_ref0 ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P Xx))):((P Xx)->(P Xx))
% Found (x2 (fun (x3:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found (x2 (fun (x3:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found x3:(P Xy)
% Instantiate: b:=Xy:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x3:(P Xy)
% Instantiate: Xx0:=Xy:fofType
% Found x3 as proof of (P0 Xx0)
% Found x40:=(x4 emptyset):((in Xx0) ((setadjoin Xx0) emptyset))
% Found (x4 emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found x3:(P Xy)
% Instantiate: Xx0:=Xy:fofType
% Found x3 as proof of (P0 Xx0)
% Found x40:=(x4 emptyset):((in Xx0) ((setadjoin Xx0) emptyset))
% Found (x4 emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found x20:=(x2 (fun (x3:fofType)=> (P b))):((P b)->(P b))
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found x20:=(x2 (fun (x3:fofType)=> (P b))):((P b)->(P b))
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found x3:(P Xx)
% Instantiate: a:=Xx:fofType
% Found x3 as proof of (P0 a)
% Found x2:(((eq fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) ((setadjoin Xz) emptyset))
% Instantiate: a:=((setadjoin Xx) ((setadjoin Xy) emptyset)):fofType;b:=((setadjoin Xz) emptyset):fofType
% Found x2 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) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% 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 ((setadjoin Xy) emptyset)):(((eq fofType) ((setadjoin Xy) emptyset)) ((setadjoin Xy) emptyset))
% Found (eq_ref0 ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found eq_ref00:=(eq_ref0 ((setadjoin Xy) emptyset)):(((eq fofType) ((setadjoin Xy) emptyset)) ((setadjoin Xy) emptyset))
% Found (eq_ref0 ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found x20:=(x2 (fun (x4:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x4:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x4:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found x2:(((eq fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) ((setadjoin Xz) emptyset))
% Instantiate: a:=((setadjoin Xx) ((setadjoin Xy) emptyset)):fofType;b:=((setadjoin Xz) emptyset):fofType
% Found x2 as proof of (((eq fofType) a) b)
% Found x30:=(x3 ((setadjoin Xy) emptyset)):((in Xx) ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (x3 ((setadjoin Xy) emptyset)) as proof of (P a)
% Found ((x Xx) ((setadjoin Xy) emptyset)) as proof of (P a)
% Found ((x Xx) ((setadjoin Xy) emptyset)) 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) ((setadjoin Xy) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xy) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xy) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xy) emptyset))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found x20:=(x2 (fun (x3:fofType)=> (P b))):((P b)->(P b))
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found x20:=(x2 (fun (x3:fofType)=> (P b))):((P b)->(P b))
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found x3:(P1 Xy)
% Instantiate: b:=Xy:fofType
% Found x3 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x3:(P1 Xy)
% Instantiate: b:=Xy:fofType
% Found x3 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x3:(P1 Xy)
% Instantiate: Xx0:=Xy:fofType
% Found x3 as proof of (P2 Xx0)
% Found x40:=(x4 emptyset):((in Xx0) ((setadjoin Xx0) emptyset))
% Found (x4 emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found x3:(P1 Xy)
% Instantiate: Xx0:=Xy:fofType
% Found x3 as proof of (P2 Xx0)
% Found x40:=(x4 emptyset):((in Xx0) ((setadjoin Xx0) emptyset))
% Found (x4 emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found x20:=(x2 (fun (x4:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x4:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x4:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xx):((in Xx) ((setadjoin Xy) ((setadjoin Xx) emptyset)))
% Found (x10 Xx) as proof of (P a)
% Found ((x1 Xy) Xx) as proof of (P a)
% Found ((x1 Xy) Xx) as proof of (P a)
% Found ((x1 Xy) Xx) 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) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xx):((in Xx) ((setadjoin Xy) ((setadjoin Xx) emptyset)))
% Found (x10 Xx) as proof of (P ((setadjoin Xy) a))
% Found ((x1 Xy) Xx) as proof of (P ((setadjoin Xy) a))
% Found ((x1 Xy) Xx) as proof of (P ((setadjoin Xy) a))
% Found ((x1 Xy) Xx) as proof of (P ((setadjoin Xy) a))
% Found x20:=(x2 (fun (x3:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 b))):((P1 b)->(P1 b))
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 b))):((P1 b)->(P1 b))
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found x20:=(x2 (fun (x3:fofType)=> (P0 Xy))):((P0 Xy)->(P0 Xy))
% Found (x2 (fun (x3:fofType)=> (P0 Xy))) as proof of (P1 Xy)
% Found (x2 (fun (x3:fofType)=> (P0 Xy))) as proof of (P1 Xy)
% Found x3:(P b)
% Instantiate: Xx0:=b:fofType
% Found x3 as proof of (P0 Xx0)
% Found x40:=(x4 emptyset):((in Xx0) ((setadjoin Xx0) emptyset))
% Found (x4 emptyset) as proof of ((in Xx0) ((setadjoin Xy) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xy) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xy) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xy) emptyset))
% Found x3:(P b)
% Instantiate: b0:=b:fofType
% Found x3 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found x3:(P Xy)
% Instantiate: b:=Xy:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found x2:(((eq fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) ((setadjoin Xz) emptyset))
% Instantiate: a:=((setadjoin Xx) ((setadjoin Xy) emptyset)):fofType;b:=((setadjoin Xz) emptyset):fofType
% Found x2 as proof of (((eq fofType) a) b)
% Found x3:(P Xy)
% Instantiate: a:=Xy:fofType
% Found x3 as proof of (P0 a)
% Found x20:=(x2 (fun (x3:fofType)=> (P0 Xy))):((P0 Xy)->(P0 Xy))
% Found (x2 (fun (x3:fofType)=> (P0 Xy))) as proof of (P1 Xy)
% Found (x2 (fun (x3:fofType)=> (P0 Xy))) as proof of (P1 Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found x20:=(x2 (fun (x3:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x3:(P b)
% Found x3 as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 b))):((P1 b)->(P1 b))
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 b))):((P1 b)->(P1 b))
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 x20:=(x2 (fun (x4:fofType)=> (P1 Xx))):((P1 Xx)->(P1 Xx))
% Found (x2 (fun (x4:fofType)=> (P1 Xx))) as proof of (P2 Xx)
% Found (x2 (fun (x4:fofType)=> (P1 Xx))) as proof of (P2 Xx)
% Found x20:=(x2 (fun (x4:fofType)=> (P1 b))):((P1 b)->(P1 b))
% Found (x2 (fun (x4:fofType)=> (P1 b))) as proof of (P2 b)
% Found (x2 (fun (x4:fofType)=> (P1 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) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xx):((in Xx) ((setadjoin Xy) ((setadjoin Xx) emptyset)))
% Found (x10 Xx) as proof of (P1 a)
% Found ((x1 Xy) Xx) as proof of (P1 a)
% Found ((x1 Xy) Xx) as proof of (P1 a)
% Found ((x1 Xy) Xx) as proof of (P1 a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xx):((in Xx) ((setadjoin Xy) ((setadjoin Xx) emptyset)))
% Found (x10 Xx) as proof of (P1 a)
% Found ((x1 Xy) Xx) as proof of (P1 a)
% Found ((x1 Xy) Xx) as proof of (P1 a)
% Found ((x1 Xy) Xx) as proof of (P1 a)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xx):((in Xx) ((setadjoin Xy) ((setadjoin Xx) emptyset)))
% Found (x10 Xx) as proof of (P1 ((setadjoin Xy) a))
% Found ((x1 Xy) Xx) as proof of (P1 ((setadjoin Xy) a))
% Found ((x1 Xy) Xx) as proof of (P1 ((setadjoin Xy) a))
% Found ((x1 Xy) Xx) as proof of (P1 ((setadjoin Xy) a))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xx):((in Xx) ((setadjoin Xy) ((setadjoin Xx) emptyset)))
% Found (x10 Xx) as proof of (P1 ((setadjoin Xy) a))
% Found ((x1 Xy) Xx) as proof of (P1 ((setadjoin Xy) a))
% Found ((x1 Xy) Xx) as proof of (P1 ((setadjoin Xy) a))
% Found ((x1 Xy) Xx) as proof of (P1 ((setadjoin Xy) a))
% Found x20:=(x2 (fun (x3:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found x20:=(x2 (fun (x3:fofType)=> (P b0))):((P b0)->(P b0))
% Found (x2 (fun (x3:fofType)=> (P b0))) as proof of (P0 b0)
% Found (x2 (fun (x3:fofType)=> (P b0))) as proof of (P0 b0)
% Found x2:(((eq fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) ((setadjoin Xz) emptyset))
% Instantiate: a:=((setadjoin Xx) ((setadjoin Xy) emptyset)):fofType;b:=((setadjoin Xz) emptyset):fofType
% Found x2 as proof of (((eq fofType) a) b)
% Found x100:=(x10 Xy):((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (x10 Xy) as proof of (P a)
% Found ((x1 Xx) Xy) as proof of (P a)
% Found ((x1 Xx) Xy) 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) ((setadjoin Xx) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xx) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xx) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xx) emptyset))
% Found x20:=(x2 (fun (x3:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 ((setadjoin Xy) emptyset)):(((eq fofType) ((setadjoin Xy) emptyset)) ((setadjoin Xy) emptyset))
% Found (eq_ref0 ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b0)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b0)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b0)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b0)
% Found eq_ref00:=(eq_ref0 ((setadjoin Xx) emptyset)):(((eq fofType) ((setadjoin Xx) emptyset)) ((setadjoin Xx) emptyset))
% Found (eq_ref0 ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found eq_ref00:=(eq_ref0 ((setadjoin Xx) emptyset)):(((eq fofType) ((setadjoin Xx) emptyset)) ((setadjoin Xx) emptyset))
% Found (eq_ref0 ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b1)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b1)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b1)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) Xy)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xy)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xy)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xy)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xy):((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (x10 Xy) as proof of (P a)
% Found ((x1 Xx) Xy) as proof of (P a)
% Found ((x1 Xx) Xy) as proof of (P a)
% Found ((x1 Xx) Xy) 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) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xy):((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (x10 Xy) as proof of (P a)
% Found ((x1 Xx) Xy) as proof of (P a)
% Found ((x1 Xx) Xy) as proof of (P a)
% Found ((x1 Xx) Xy) 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) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xy):((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (x10 Xy) as proof of (P ((setadjoin Xx) a))
% Found ((x1 Xx) Xy) as proof of (P ((setadjoin Xx) a))
% Found ((x1 Xx) Xy) as proof of (P ((setadjoin Xx) a))
% Found ((x1 Xx) Xy) as proof of (P ((setadjoin Xx) a))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xy):((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (x10 Xy) as proof of (P ((setadjoin Xx) a))
% Found ((x1 Xx) Xy) as proof of (P ((setadjoin Xx) a))
% Found ((x1 Xx) Xy) as proof of (P ((setadjoin Xx) a))
% Found ((x1 Xx) Xy) as proof of (P ((setadjoin Xx) a))
% Found x20:=(x2 (fun (x3:fofType)=> (P0 b))):((P0 b)->(P0 b))
% Found (x2 (fun (x3:fofType)=> (P0 b))) as proof of (P1 b)
% Found (x2 (fun (x3:fofType)=> (P0 b))) as proof of (P1 b)
% Found x3:(P Xy)
% Instantiate: b0:=Xy:fofType
% Found x3 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:(P Xy)
% Instantiate: b0:=Xy:fofType
% Found x3 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 x20:=(x2 (fun (x3:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 b))):((P1 b)->(P1 b))
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found x20:=(x2 (fun (x3:fofType)=> (P b0))):((P b0)->(P b0))
% Found (x2 (fun (x3:fofType)=> (P b0))) as proof of (P0 b0)
% Found (x2 (fun (x3:fofType)=> (P b0))) as proof of (P0 b0)
% Found x3:(P Xy)
% Instantiate: Xx0:=Xy:fofType
% Found x3 as proof of (P0 Xx0)
% Found x40:=(x4 emptyset):((in Xx0) ((setadjoin Xx0) emptyset))
% Found (x4 emptyset) as proof of ((in Xx0) ((setadjoin b) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin b) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin b) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin b) emptyset))
% Found x3:(P Xy)
% Instantiate: Xx0:=Xy:fofType
% Found x3 as proof of (P0 Xx0)
% Found x40:=(x4 emptyset):((in Xx0) ((setadjoin Xx0) emptyset))
% Found (x4 emptyset) as proof of ((in Xx0) ((setadjoin b) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin b) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin b) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin b) emptyset))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (P Xx)
% Found ((eq_ref fofType) Xx) as proof of (P Xx)
% Found ((eq_ref fofType) Xx) as proof of (P Xx)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found x20:=(x2 (fun (x3:fofType)=> (P b))):((P b)->(P b))
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found (x2 (fun (x3:fofType)=> (P 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) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found x20:=(x2 (fun (x3:fofType)=> (P b))):((P b)->(P b))
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found x20:=(x2 (fun (x3:fofType)=> (P b))):((P b)->(P b))
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 b))):((P1 b)->(P1 b))
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 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 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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:(P Xy)
% Found x3 as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 ((setadjoin Xx) emptyset)):(((eq fofType) ((setadjoin Xx) emptyset)) ((setadjoin Xx) emptyset))
% Found (eq_ref0 ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found eq_ref00:=(eq_ref0 ((setadjoin Xx) emptyset)):(((eq fofType) ((setadjoin Xx) emptyset)) ((setadjoin Xx) emptyset))
% Found (eq_ref0 ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found eq_ref00:=(eq_ref0 ((setadjoin Xx) emptyset)):(((eq fofType) ((setadjoin Xx) emptyset)) ((setadjoin Xx) emptyset))
% Found (eq_ref0 ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found eq_ref00:=(eq_ref0 ((setadjoin Xx) emptyset)):(((eq fofType) ((setadjoin Xx) emptyset)) ((setadjoin Xx) emptyset))
% Found (eq_ref0 ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xy):((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (x10 Xy) as proof of (P1 a)
% Found ((x1 Xx) Xy) as proof of (P1 a)
% Found ((x1 Xx) Xy) as proof of (P1 a)
% Found ((x1 Xx) Xy) as proof of (P1 a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xy):((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (x10 Xy) as proof of (P1 a)
% Found ((x1 Xx) Xy) as proof of (P1 a)
% Found ((x1 Xx) Xy) as proof of (P1 a)
% Found ((x1 Xx) Xy) as proof of (P1 a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xy):((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (x10 Xy) as proof of (P1 a)
% Found ((x1 Xx) Xy) as proof of (P1 a)
% Found ((x1 Xx) Xy) as proof of (P1 a)
% Found ((x1 Xx) Xy) as proof of (P1 a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xy):((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (x10 Xy) as proof of (P1 a)
% Found ((x1 Xx) Xy) as proof of (P1 a)
% Found ((x1 Xx) Xy) as proof of (P1 a)
% Found ((x1 Xx) Xy) as proof of (P1 a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xy):((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (x10 Xy) as proof of (P1 ((setadjoin Xx) a))
% Found ((x1 Xx) Xy) as proof of (P1 ((setadjoin Xx) a))
% Found ((x1 Xx) Xy) as proof of (P1 ((setadjoin Xx) a))
% Found ((x1 Xx) Xy) as proof of (P1 ((setadjoin Xx) a))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xy):((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (x10 Xy) as proof of (P1 ((setadjoin Xx) a))
% Found ((x1 Xx) Xy) as proof of (P1 ((setadjoin Xx) a))
% Found ((x1 Xx) Xy) as proof of (P1 ((setadjoin Xx) a))
% Found ((x1 Xx) Xy) as proof of (P1 ((setadjoin Xx) a))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xy):((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (x10 Xy) as proof of (P1 ((setadjoin Xx) a))
% Found ((x1 Xx) Xy) as proof of (P1 ((setadjoin Xx) a))
% Found ((x1 Xx) Xy) as proof of (P1 ((setadjoin Xx) a))
% Found ((x1 Xx) Xy) as proof of (P1 ((setadjoin Xx) a))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xy):((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (x10 Xy) as proof of (P1 ((setadjoin Xx) a))
% Found ((x1 Xx) Xy) as proof of (P1 ((setadjoin Xx) a))
% Found ((x1 Xx) Xy) as proof of (P1 ((setadjoin Xx) a))
% Found ((x1 Xx) Xy) as proof of (P1 ((setadjoin Xx) a))
% Found eq_ref000:=(eq_ref00 P):((P Xy)->(P Xy))
% Found (eq_ref00 P) as proof of (P0 Xy)
% Found ((eq_ref0 Xy) P) as proof of (P0 Xy)
% Found (((eq_ref fofType) Xy) P) as proof of (P0 Xy)
% Found (((eq_ref fofType) Xy) P) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 ((setadjoin b) emptyset)):(((eq fofType) ((setadjoin b) emptyset)) ((setadjoin b) emptyset))
% Found (eq_ref0 ((setadjoin b) emptyset)) as proof of (((eq fofType) ((setadjoin b) emptyset)) b0)
% Found ((eq_ref fofType) ((setadjoin b) emptyset)) as proof of (((eq fofType) ((setadjoin b) emptyset)) b0)
% Found ((eq_ref fofType) ((setadjoin b) emptyset)) as proof of (((eq fofType) ((setadjoin b) emptyset)) b0)
% Found ((eq_ref fofType) ((setadjoin b) emptyset)) as proof of (((eq fofType) ((setadjoin b) emptyset)) b0)
% Found eq_ref00:=(eq_ref0 ((setadjoin b) emptyset)):(((eq fofType) ((setadjoin b) emptyset)) ((setadjoin b) emptyset))
% Found (eq_ref0 ((setadjoin b) emptyset)) as proof of (((eq fofType) ((setadjoin b) emptyset)) b0)
% Found ((eq_ref fofType) ((setadjoin b) emptyset)) as proof of (((eq fofType) ((setadjoin b) emptyset)) b0)
% Found ((eq_ref fofType) ((setadjoin b) emptyset)) as proof of (((eq fofType) ((setadjoin b) emptyset)) b0)
% Found ((eq_ref fofType) ((setadjoin b) emptyset)) as proof of (((eq fofType) ((setadjoin b) emptyset)) b0)
% Found x20:=(x2 (fun (x3:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P b0))):((P b0)->(P b0))
% Found (x2 (fun (x3:fofType)=> (P b0))) as proof of (P0 b0)
% Found (x2 (fun (x3:fofType)=> (P b0))) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 x3:(P b)
% Instantiate: b0:=b:fofType
% Found x3 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 b):((in b) ((setadjoin Xy) ((setadjoin b) emptyset)))
% Found (x10 b) as proof of (P a)
% Found ((x1 Xy) b) as proof of (P a)
% Found ((x1 Xy) b) as proof of (P a)
% Found ((x1 Xy) b) as proof of (P a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P 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 (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 b):((in b) ((setadjoin Xy) ((setadjoin b) emptyset)))
% Found (x10 b) as proof of (P ((setadjoin Xy) a))
% Found ((x1 Xy) b) as proof of (P ((setadjoin Xy) a))
% Found ((x1 Xy) b) as proof of (P ((setadjoin Xy) a))
% Found ((x1 Xy) b) as proof of (P ((setadjoin Xy) a))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 (P b0)
% Found ((eq_ref fofType) b) as proof of (P b0)
% Found ((eq_ref fofType) b) as proof of (P b0)
% Found ((eq_ref fofType) b) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 ((setadjoin ((setadjoin Xy) emptyset)) emptyset)):(((eq fofType) ((setadjoin ((setadjoin Xy) emptyset)) emptyset)) ((setadjoin ((setadjoin Xy) emptyset)) emptyset))
% Found (eq_ref0 ((setadjoin ((setadjoin Xy) emptyset)) emptyset)) as proof of (((eq fofType) ((setadjoin ((setadjoin Xy) emptyset)) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin ((setadjoin Xy) emptyset)) emptyset)) as proof of (((eq fofType) ((setadjoin ((setadjoin Xy) emptyset)) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin ((setadjoin Xy) emptyset)) emptyset)) as proof of (((eq fofType) ((setadjoin ((setadjoin Xy) emptyset)) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin ((setadjoin Xy) emptyset)) emptyset)) as proof of (((eq fofType) ((setadjoin ((setadjoin Xy) emptyset)) emptyset)) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) Xx)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xx)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xx)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xx)
% Found x20:=(x2 (fun (x3:fofType)=> (P b0))):((P b0)->(P b0))
% Found (x2 (fun (x3:fofType)=> (P b0))) as proof of (P0 b0)
% Found (x2 (fun (x3:fofType)=> (P b0))) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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:(P b)
% Instantiate: Xx0:=b:fofType
% Found x3 as proof of (P0 Xx0)
% Found x40:=(x4 emptyset):((in Xx0) ((setadjoin Xx0) emptyset))
% Found (x4 emptyset) as proof of ((in Xx0) ((setadjoin Xy) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xy) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xy) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xy) emptyset))
% Found x20:=(x2 (fun (x3:fofType)=> (P1 b))):((P1 b)->(P1 b))
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 b))):((P1 b)->(P1 b))
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 b))):((P1 b)->(P1 b))
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 b))):((P1 b)->(P1 b))
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 Xx))):((P1 Xx)->(P1 Xx))
% Found (x2 (fun (x3:fofType)=> (P1 Xx))) as proof of (P2 Xx)
% Found (x2 (fun (x3:fofType)=> (P1 Xx))) as proof of (P2 Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (P Xy)
% Found ((eq_ref fofType) Xy) as proof of (P Xy)
% Found ((eq_ref fofType) Xy) as proof of (P Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 b))):((P1 b)->(P1 b))
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 x20:=(x2 (fun (x3:fofType)=> (P b0))):((P b0)->(P b0))
% Found (x2 (fun (x3:fofType)=> (P b0))) as proof of (P0 b0)
% Found (x2 (fun (x3:fofType)=> (P b0))) as proof of (P0 b0)
% Found x30:=(x3 emptyset):((in Xy) ((setadjoin Xy) emptyset))
% Found (x3 emptyset) as proof of ((in Xy) ((setadjoin b) emptyset))
% Found ((x Xy) emptyset) as proof of ((in Xy) ((setadjoin b) emptyset))
% Found ((x Xy) emptyset) as proof of ((in Xy) ((setadjoin b) emptyset))
% Found ((x Xy) emptyset) as proof of ((in Xy) ((setadjoin b) emptyset))
% Found x20:=(x2 (fun (x3:fofType)=> (P b))):((P b)->(P b))
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b00)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b00)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b00)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 x30:=(x3 emptyset):((in b) ((setadjoin b) emptyset))
% Found (x3 emptyset) as proof of (P b)
% Found ((x b) emptyset) as proof of (P b)
% Found ((x b) emptyset) as proof of (P b)
% Found ((x b) emptyset) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found x30:=(x3 emptyset):((in b) ((setadjoin b) emptyset))
% Found (x3 emptyset) as proof of (P b)
% Found ((x b) emptyset) as proof of (P b)
% Found ((x b) emptyset) as proof of (P b)
% Found ((x b) emptyset) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found x20:=(x2 (fun (x3:fofType)=> (P b0))):((P b0)->(P b0))
% Found (x2 (fun (x3:fofType)=> (P b0))) as proof of (P0 b0)
% Found (x2 (fun (x3:fofType)=> (P b0))) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setadjoin b) emptyset))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setadjoin b) emptyset))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setadjoin b) emptyset))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setadjoin b) emptyset))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found x20:=(x2 (fun (x3:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P b))):((P b)->(P b))
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) Xx)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xx)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xx)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found x20:=(x2 (fun (x3:fofType)=> (P Xx))):((P Xx)->(P Xx))
% Found (x2 (fun (x3:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found (x2 (fun (x3:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found x2:(((eq fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) ((setadjoin Xz) emptyset))
% Found x2 as proof of (((eq fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xy):((in Xy) ((setadjoin b) ((setadjoin Xy) emptyset)))
% Found (x10 Xy) as proof of (P a)
% Found ((x1 b) Xy) as proof of (P a)
% Found ((x1 b) Xy) as proof of (P a)
% Found ((x1 b) Xy) 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) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xy):((in Xy) ((setadjoin b) ((setadjoin Xy) emptyset)))
% Found (x10 Xy) as proof of (P a)
% Found ((x1 b) Xy) as proof of (P a)
% Found ((x1 b) Xy) as proof of (P a)
% Found ((x1 b) Xy) 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) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xy):((in Xy) ((setadjoin b) ((setadjoin Xy) emptyset)))
% Found (x10 Xy) as proof of (P ((setadjoin b) a))
% Found ((x1 b) Xy) as proof of (P ((setadjoin b) a))
% Found ((x1 b) Xy) as proof of (P ((setadjoin b) a))
% Found ((x1 b) Xy) as proof of (P ((setadjoin b) a))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xy):((in Xy) ((setadjoin b) ((setadjoin Xy) emptyset)))
% Found (x10 Xy) as proof of (P ((setadjoin b) a))
% Found ((x1 b) Xy) as proof of (P ((setadjoin b) a))
% Found ((x1 b) Xy) as proof of (P ((setadjoin b) a))
% Found ((x1 b) Xy) as proof of (P ((setadjoin b) a))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 emptyset):((in b) ((setadjoin b) emptyset))
% Found (x3 emptyset) as proof of (P1 b)
% Found ((x b) emptyset) as proof of (P1 b)
% Found ((x b) emptyset) as proof of (P1 b)
% Found ((x b) emptyset) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found x30:=(x3 emptyset):((in b) ((setadjoin b) emptyset))
% Found (x3 emptyset) as proof of (P1 b)
% Found ((x b) emptyset) as proof of (P1 b)
% Found ((x b) emptyset) as proof of (P1 b)
% Found ((x b) emptyset) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found x30:=(x3 emptyset):((in b) ((setadjoin b) emptyset))
% Found (x3 emptyset) as proof of (P1 b)
% Found ((x b) emptyset) as proof of (P1 b)
% Found ((x b) emptyset) as proof of (P1 b)
% Found ((x b) emptyset) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found x30:=(x3 emptyset):((in b) ((setadjoin b) emptyset))
% Found (x3 emptyset) as proof of (P1 b)
% Found ((x b) emptyset) as proof of (P1 b)
% Found ((x b) emptyset) as proof of (P1 b)
% Found ((x b) emptyset) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xx):((in Xx) ((setadjoin ((setadjoin Xy) a)) ((setadjoin Xx) emptyset)))
% Found (x10 Xx) as proof of (P0 a)
% Found ((x1 ((setadjoin Xy) a)) Xx) as proof of (P0 a)
% Found ((x1 ((setadjoin Xy) a)) Xx) as proof of (P0 a)
% Found ((x1 ((setadjoin Xy) a)) Xx) as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xx):((in Xx) ((setadjoin ((setadjoin Xy) a)) ((setadjoin Xx) emptyset)))
% Found (x10 Xx) as proof of (P0 a)
% Found ((x1 ((setadjoin Xy) a)) Xx) as proof of (P0 a)
% Found ((x1 ((setadjoin Xy) a)) Xx) as proof of (P0 a)
% Found ((x1 ((setadjoin Xy) a)) Xx) as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xx):((in Xx) ((setadjoin ((setadjoin Xy) a)) ((setadjoin Xx) emptyset)))
% Found (x10 Xx) as proof of (P0 ((setadjoin ((setadjoin Xy) a)) a))
% Found ((x1 ((setadjoin Xy) a)) Xx) as proof of (P0 ((setadjoin ((setadjoin Xy) a)) a))
% Found ((x1 ((setadjoin Xy) a)) Xx) as proof of (P0 ((setadjoin ((setadjoin Xy) a)) a))
% Found ((x1 ((setadjoin Xy) a)) Xx) as proof of (P0 ((setadjoin ((setadjoin Xy) a)) a))
% Found x20:=(x2 (fun (x3:fofType)=> (P b))):((P b)->(P b))
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found x20:=(x2 (fun (x3:fofType)=> (P b))):((P b)->(P b))
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% 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 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b1)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b1)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b1)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) Xy)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) Xy)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) Xy)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) Xy)
% 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 x20:=(x2 (fun (x3:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found eq_ref00:=(eq_ref0 ((setadjoin ((setadjoin Xx) emptyset)) emptyset)):(((eq fofType) ((setadjoin ((setadjoin Xx) emptyset)) emptyset)) ((setadjoin ((setadjoin Xx) emptyset)) emptyset))
% Found (eq_ref0 ((setadjoin ((setadjoin Xx) emptyset)) emptyset)) as proof of (((eq fofType) ((setadjoin ((setadjoin Xx) emptyset)) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin ((setadjoin Xx) emptyset)) emptyset)) as proof of (((eq fofType) ((setadjoin ((setadjoin Xx) emptyset)) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin ((setadjoin Xx) emptyset)) emptyset)) as proof of (((eq fofType) ((setadjoin ((setadjoin Xx) emptyset)) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin ((setadjoin Xx) emptyset)) emptyset)) as proof of (((eq fofType) ((setadjoin ((setadjoin Xx) emptyset)) emptyset)) b)
% Found x3:(P Xy)
% Instantiate: Xx0:=Xy:fofType
% Found x3 as proof of (P0 Xx0)
% Found x40:=(x4 emptyset):((in Xx0) ((setadjoin Xx0) emptyset))
% Found (x4 emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found x2:(((eq fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) ((setadjoin Xz) emptyset))
% Found x2 as proof of (((eq fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) b)
% Found x20:=(x2 (fun (x3:fofType)=> (P0 Xy))):((P0 Xy)->(P0 Xy))
% Found (x2 (fun (x3:fofType)=> (P0 Xy))) as proof of (P1 Xy)
% Found (x2 (fun (x3:fofType)=> (P0 Xy))) as proof of (P1 Xy)
% Found eq_ref00:=(eq_ref0 ((setadjoin Xy) emptyset)):(((eq fofType) ((setadjoin Xy) emptyset)) ((setadjoin Xy) emptyset))
% Found (eq_ref0 ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b0)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b0)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b0)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b0)
% Found x20:=(x2 (fun (x3:fofType)=> (P b))):((P b)->(P b))
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found x3:(P Xx)
% Instantiate: a:=Xx:fofType
% Found x3 as proof of (P0 a)
% Found x2:(((eq fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) ((setadjoin Xz) emptyset))
% Instantiate: a:=((setadjoin Xx) ((setadjoin Xy) emptyset)):fofType;b:=((setadjoin Xz) emptyset):fofType
% Found x2 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) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% 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) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 b):((in b) ((setadjoin Xy) ((setadjoin b) emptyset)))
% Found (x10 b) as proof of (P a)
% Found ((x1 Xy) b) as proof of (P a)
% Found ((x1 Xy) b) as proof of (P a)
% Found ((x1 Xy) b) 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) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 b):((in b) ((setadjoin Xy) ((setadjoin b) emptyset)))
% Found (x10 b) as proof of (P ((setadjoin Xy) a))
% Found ((x1 Xy) b) as proof of (P ((setadjoin Xy) a))
% Found ((x1 Xy) b) as proof of (P ((setadjoin Xy) a))
% Found ((x1 Xy) b) as proof of (P ((setadjoin Xy) a))
% Found eq_ref00:=(eq_ref0 ((setadjoin Xy) emptyset)):(((eq fofType) ((setadjoin Xy) emptyset)) ((setadjoin Xy) emptyset))
% Found (eq_ref0 ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found eq_ref00:=(eq_ref0 ((setadjoin Xy) emptyset)):(((eq fofType) ((setadjoin Xy) emptyset)) ((setadjoin Xy) emptyset))
% Found (eq_ref0 ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b)
% Found x20:=(x2 (fun (x4:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x4:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x4:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x20:=(x2 (fun (x4:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x4:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x4:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) Xy)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xy)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xy)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b1)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b1)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b1)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setadjoin Xy) emptyset))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setadjoin Xy) emptyset))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setadjoin Xy) emptyset))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setadjoin Xy) emptyset))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found x2:(((eq fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) ((setadjoin Xz) emptyset))
% Instantiate: a:=((setadjoin Xx) ((setadjoin Xy) emptyset)):fofType;b:=((setadjoin Xz) emptyset):fofType
% Found x2 as proof of (((eq fofType) a) b)
% Found x30:=(x3 ((setadjoin Xy) emptyset)):((in Xx) ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (x3 ((setadjoin Xy) emptyset)) as proof of (P a)
% Found ((x Xx) ((setadjoin Xy) emptyset)) as proof of (P a)
% Found ((x Xx) ((setadjoin Xy) emptyset)) 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) ((setadjoin Xy) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xy) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xy) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xy) emptyset))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found x20:=(x2 (fun (x3:fofType)=> (P b))):((P b)->(P b))
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found (x2 (fun (x3:fofType)=> (P 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) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xy):((in Xy) ((setadjoin ((setadjoin Xx) a)) ((setadjoin Xy) emptyset)))
% Found (x10 Xy) as proof of (P0 a)
% Found ((x1 ((setadjoin Xx) a)) Xy) as proof of (P0 a)
% Found ((x1 ((setadjoin Xx) a)) Xy) as proof of (P0 a)
% Found ((x1 ((setadjoin Xx) a)) Xy) as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xy):((in Xy) ((setadjoin ((setadjoin Xx) a)) ((setadjoin Xy) emptyset)))
% Found (x10 Xy) as proof of (P0 a)
% Found ((x1 ((setadjoin Xx) a)) Xy) as proof of (P0 a)
% Found ((x1 ((setadjoin Xx) a)) Xy) as proof of (P0 a)
% Found ((x1 ((setadjoin Xx) a)) Xy) as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xy):((in Xy) ((setadjoin ((setadjoin Xx) a)) ((setadjoin Xy) emptyset)))
% Found (x10 Xy) as proof of (P0 ((setadjoin ((setadjoin Xx) a)) a))
% Found ((x1 ((setadjoin Xx) a)) Xy) as proof of (P0 ((setadjoin ((setadjoin Xx) a)) a))
% Found ((x1 ((setadjoin Xx) a)) Xy) as proof of (P0 ((setadjoin ((setadjoin Xx) a)) a))
% Found ((x1 ((setadjoin Xx) a)) Xy) as proof of (P0 ((setadjoin ((setadjoin Xx) a)) a))
% Found x3:(P1 Xy)
% Instantiate: b:=Xy:fofType
% Found x3 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x3:(P1 Xy)
% Instantiate: b:=Xy:fofType
% Found x3 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 emptyset):((in b0) ((setadjoin b0) emptyset))
% Found (x3 emptyset) as proof of (P b0)
% Found ((x b0) emptyset) as proof of (P b0)
% Found ((x b0) emptyset) as proof of (P b0)
% Found ((x b0) emptyset) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found x30:=(x3 emptyset):((in b0) ((setadjoin b0) emptyset))
% Found (x3 emptyset) as proof of (P b0)
% Found ((x b0) emptyset) as proof of (P b0)
% Found ((x b0) emptyset) as proof of (P b0)
% Found ((x b0) emptyset) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found x3:(P1 Xy)
% Instantiate: Xx0:=Xy:fofType
% Found x3 as proof of (P2 Xx0)
% Found x40:=(x4 emptyset):((in Xx0) ((setadjoin Xx0) emptyset))
% Found (x4 emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found x3:(P1 Xy)
% Instantiate: Xx0:=Xy:fofType
% Found x3 as proof of (P2 Xx0)
% Found x40:=(x4 emptyset):((in Xx0) ((setadjoin Xx0) emptyset))
% Found (x4 emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found x3:(P1 Xy)
% Instantiate: Xx0:=Xy:fofType
% Found x3 as proof of (P2 Xx0)
% Found x40:=(x4 emptyset):((in Xx0) ((setadjoin Xx0) emptyset))
% Found (x4 emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found x3:(P1 Xy)
% Instantiate: Xx0:=Xy:fofType
% Found x3 as proof of (P2 Xx0)
% Found x40:=(x4 emptyset):((in Xx0) ((setadjoin Xx0) emptyset))
% Found (x4 emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xx) emptyset))
% Found x20:=(x2 (fun (x4:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x4:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x4:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 b))):((P1 b)->(P1 b))
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 b))):((P1 b)->(P1 b))
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 b))):((P1 b)->(P1 b))
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 b))):((P1 b)->(P1 b))
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found x3:(P b)
% Instantiate: Xx0:=b:fofType
% Found x3 as proof of (P0 Xx0)
% Found x40:=(x4 emptyset):((in Xx0) ((setadjoin Xx0) emptyset))
% Found (x4 emptyset) as proof of ((in Xx0) ((setadjoin Xy) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xy) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xy) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xy) emptyset))
% Found x3:(P b)
% Instantiate: Xx0:=b:fofType
% Found x3 as proof of (P0 Xx0)
% Found x40:=(x4 emptyset):((in Xx0) ((setadjoin Xx0) emptyset))
% Found (x4 emptyset) as proof of ((in Xx0) ((setadjoin Xy) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xy) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xy) emptyset))
% Found ((x Xx0) emptyset) as proof of ((in Xx0) ((setadjoin Xy) emptyset))
% Found x20:=(x2 (fun (x3:fofType)=> (P0 Xy))):((P0 Xy)->(P0 Xy))
% Found (x2 (fun (x3:fofType)=> (P0 Xy))) as proof of (P1 Xy)
% Found (x2 (fun (x3:fofType)=> (P0 Xy))) as proof of (P1 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P0 Xy))):((P0 Xy)->(P0 Xy))
% Found (x2 (fun (x3:fofType)=> (P0 Xy))) as proof of (P1 Xy)
% Found (x2 (fun (x3:fofType)=> (P0 Xy))) as proof of (P1 Xy)
% Found x3:(P b)
% Instantiate: b0:=b:fofType
% Found x3 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found x3:(P b)
% Instantiate: b0:=b:fofType
% Found x3 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found x3:(P Xy)
% Instantiate: b:=Xy:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x2:(((eq fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) ((setadjoin Xz) emptyset))
% Found x2 as proof of (((eq fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found x3:(P Xy)
% Instantiate: a:=Xy:fofType
% Found x3 as proof of (P0 a)
% Found x2:(((eq fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) ((setadjoin Xz) emptyset))
% Instantiate: a:=((setadjoin Xx) ((setadjoin Xy) emptyset)):fofType;b:=((setadjoin Xz) emptyset):fofType
% Found x2 as proof of (((eq fofType) a) b)
% Found x2:(((eq fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) ((setadjoin Xz) emptyset))
% Instantiate: a:=((setadjoin Xx) ((setadjoin Xy) emptyset)):fofType;b:=((setadjoin Xz) emptyset):fofType
% Found x2 as proof of (((eq fofType) a) b)
% Found x3:(P Xy)
% Instantiate: a:=Xy:fofType
% Found x3 as proof of (P0 a)
% Found x20:=(x2 (fun (x3:fofType)=> (P0 Xy))):((P0 Xy)->(P0 Xy))
% Found (x2 (fun (x3:fofType)=> (P0 Xy))) as proof of (P1 Xy)
% Found (x2 (fun (x3:fofType)=> (P0 Xy))) as proof of (P1 Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% 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) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found x3:(P b)
% Found x3 as proof of (P0 Xx)
% Found x20:=(x2 (fun (x3:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P b))):((P b)->(P b))
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found x20:=(x2 (fun (x3:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x3:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 b))):((P1 b)->(P1 b))
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 b))):((P1 b)->(P1 b))
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 b))):((P1 b)->(P1 b))
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 b))):((P1 b)->(P1 b))
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found (x2 (fun (x3:fofType)=> (P1 b))) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found x20:=(x2 (fun (x4:fofType)=> (P1 Xx))):((P1 Xx)->(P1 Xx))
% Found (x2 (fun (x4:fofType)=> (P1 Xx))) as proof of (P2 Xx)
% Found (x2 (fun (x4:fofType)=> (P1 Xx))) as proof of (P2 Xx)
% Found x20:=(x2 (fun (x4:fofType)=> (P1 b))):((P1 b)->(P1 b))
% Found (x2 (fun (x4:fofType)=> (P1 b))) as proof of (P2 b)
% Found (x2 (fun (x4:fofType)=> (P1 b))) as proof of (P2 b)
% Found x20:=(x2 (fun (x4:fofType)=> (P1 Xx))):((P1 Xx)->(P1 Xx))
% Found (x2 (fun (x4:fofType)=> (P1 Xx))) as proof of (P2 Xx)
% Found (x2 (fun (x4:fofType)=> (P1 Xx))) as proof of (P2 Xx)
% Found x20:=(x2 (fun (x4:fofType)=> (P1 b))):((P1 b)->(P1 b))
% Found (x2 (fun (x4:fofType)=> (P1 b))) as proof of (P2 b)
% Found (x2 (fun (x4:fofType)=> (P1 b))) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xx):((in Xx) ((setadjoin Xy) ((setadjoin Xx) emptyset)))
% Found (x10 Xx) as proof of (P1 a)
% Found ((x1 Xy) Xx) as proof of (P1 a)
% Found ((x1 Xy) Xx) as proof of (P1 a)
% Found ((x1 Xy) Xx) as proof of (P1 a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xx):((in Xx) ((setadjoin Xy) ((setadjoin Xx) emptyset)))
% Found (x10 Xx) as proof of (P1 a)
% Found ((x1 Xy) Xx) as proof of (P1 a)
% Found ((x1 Xy) Xx) as proof of (P1 a)
% Found ((x1 Xy) Xx) as proof of (P1 a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xx):((in Xx) ((setadjoin Xy) ((setadjoin Xx) emptyset)))
% Found (x10 Xx) as proof of (P1 ((setadjoin Xy) a))
% Found ((x1 Xy) Xx) as proof of (P1 ((setadjoin Xy) a))
% Found ((x1 Xy) Xx) as proof of (P1 ((setadjoin Xy) a))
% Found ((x1 Xy) Xx) as proof of (P1 ((setadjoin Xy) a))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xx):((in Xx) ((setadjoin Xy) ((setadjoin Xx) emptyset)))
% Found (x10 Xx) as proof of (P1 ((setadjoin Xy) a))
% Found ((x1 Xy) Xx) as proof of (P1 ((setadjoin Xy) a))
% Found ((x1 Xy) Xx) as proof of (P1 ((setadjoin Xy) a))
% Found ((x1 Xy) Xx) as proof of (P1 ((setadjoin Xy) a))
% Found x20:=(x2 (fun (x3:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x20:=(x2 (fun (x3:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x3:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x30:=(x3 emptyset):((in b) ((setadjoin b) emptyset))
% Found (x3 emptyset) as proof of (P0 b)
% Found ((x b) emptyset) as proof of (P0 b)
% Found ((x b) emptyset) as proof of (P0 b)
% Found ((x b) emptyset) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found x20:=(x2 (fun (x3:fofType)=> (P b0))):((P b0)->(P b0))
% Found (x2 (fun (x3:fofType)=> (P b0))) as proof of (P0 b0)
% Found (x2 (fun (x3:fofType)=> (P b0))) as proof of (P0 b0)
% Found x20:=(x2 (fun (x3:fofType)=> (P b0))):((P b0)->(P b0))
% Found (x2 (fun (x3:fofType)=> (P b0))) as proof of (P0 b0)
% Found (x2 (fun (x3:fofType)=> (P b0))) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found x20:=(x2 (fun (x3:fofType)=> (P b))):((P b)->(P b))
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found (x2 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found x2:(((eq fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) ((setadjoin Xz) emptyset))
% Instantiate: a:=((setadjoin Xx) ((setadjoin Xy) emptyset)):fofType;b:=((setadjoin Xz) emptyset):fofType
% Found x2 as proof of (((eq fofType) a) b)
% Found x100:=(x10 Xy):((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (x10 Xy) as proof of (P a)
% Found ((x1 Xx) Xy) as proof of (P a)
% Found ((x1 Xx) Xy) 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) ((setadjoin Xx) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xx) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xx) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xx) emptyset))
% Found x2:(((eq fofType) ((setadjoin Xx) ((setadjoin Xy) emptyset))) ((setadjoin Xz) emptyset))
% Instantiate: a:=((setadjoin Xx) ((setadjoin Xy) emptyset)):fofType;b:=((setadjoin Xz) emptyset):fofType
% Found x2 as proof of (((eq fofType) a) b)
% Found x100:=(x10 Xy):((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (x10 Xy) as proof of (P a)
% Found ((x1 Xx) Xy) as proof of (P a)
% Found ((x1 Xx) Xy) 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) ((setadjoin Xx) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xx) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xx) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin Xx) emptyset))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((setadjoin b) emptyset))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setadjoin b) emptyset))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setadjoin b) emptyset))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((setadjoin b) emptyset))
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 ((setadjoin Xy) emptyset)):(((eq fofType) ((setadjoin Xy) emptyset)) ((setadjoin Xy) emptyset))
% Found (eq_ref0 ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b0)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b0)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b0)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b0)
% Found eq_ref00:=(eq_ref0 ((setadjoin Xy) emptyset)):(((eq fofType) ((setadjoin Xy) emptyset)) ((setadjoin Xy) emptyset))
% Found (eq_ref0 ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b0)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b0)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b0)
% Found ((eq_ref fofType) ((setadjoin Xy) emptyset)) as proof of (((eq fofType) ((setadjoin Xy) emptyset)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 emptyset):((in b0) ((setadjoin b0) emptyset))
% Found (x3 emptyset) as proof of (P b0)
% Found ((x b0) emptyset) as proof of (P b0)
% Found ((x b0) emptyset) as proof of (P b0)
% Found ((x b0) emptyset) as proof of (P 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 emptyset):((in b) ((setadjoin b) emptyset))
% Found (x3 emptyset) as proof of (P b0)
% Found ((x b) emptyset) as proof of (P b0)
% Found ((x b) emptyset) as proof of (P b0)
% Found ((x b) emptyset) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 ((setadjoin Xx) emptyset)):(((eq fofType) ((setadjoin Xx) emptyset)) ((setadjoin Xx) emptyset))
% Found (eq_ref0 ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xx) emptyset)) as proof of (((eq fofType) ((setadjoin Xx) emptyset)) b)
% Found x3:(P1 Xy)
% Instantiate: b:=Xy:fofType
% Found x3 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x3:(P1 Xy)
% Instantiate: b:=Xy:fofType
% Found x3 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found x20:=(x2 (fun (x4:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x4:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x4:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b1)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b1)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b1)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) Xy)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xy)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xy)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xy)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xy):((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (x10 Xy) as proof of (P a)
% Found ((x1 Xx) Xy) as proof of (P a)
% Found ((x1 Xx) Xy) as proof of (P a)
% Found ((x1 Xx) Xy) 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) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) emptyset)
% Found x100:=(x10 Xy):((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset)))
% Found (x10 Xy) as proof of (P ((setadjoin Xx) a))
% Found ((x1 Xx) Xy) as proof of (P ((setadjoin Xx) a))
% Found ((x1 Xx) Xy) as proof of (P ((setadjoin Xx) a))
% Found ((x1 Xx) Xy) as proof of (P ((setadjoin Xx) a))
% Found x20:=(x2 (fun (x3:fofType)=> (P0 b))):((P0 b)->(P0 b))
% Found (x2 (fun (x3:fofType)=> (P0 b))) as proof of (P1 b)
% Found (x2 (fun (x3:fofType)=> (P0 b))) as proof of (P1 b)
% Found x20:=(x2 (fun (x3:fofType)=> (P0 b))):((P0 b)->(P0 b))
% Found (x2 (fun (x3:fofType)=> (P0 b))) as proof of (P1 b)
% Found (x2 (fun (x3:fofType)=> (P0 b))) as proof of (P1 b)
% Found x3:(P Xy)
% Instantiate: b0:=Xy:fofType
% Found x3 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:(P Xy)
% Instantiate: b0:=Xy:fofType
% Found x3 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 fof
% EOF
%------------------------------------------------------------------------------