TSTP Solution File: SEU651^2 by cocATP---0.2.0
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%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU651^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n116.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 300.03s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU651^2 : TPTP v6.1.0. Released v3.7.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n116.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 11:02:56 CDT 2014
% % CPUTime : 300.03
% 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 0x1472830>, <kernel.DependentProduct object at 0x1472d40>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1650368>, <kernel.Single object at 0x14725a8>) of role type named emptyset_type
% Using role type
% Declaring emptyset:fofType
% FOF formula (<kernel.Constant object at 0x1472d40>, <kernel.DependentProduct object at 0x1472488>) of role type named setadjoin_type
% Using role type
% Declaring setadjoin:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x1472ab8>, <kernel.Sort object at 0x1720878>) 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 0x14725f0>, <kernel.Sort object at 0x1720878>) 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 (<kernel.Constant object at 0x1472d40>, <kernel.Sort object at 0x1720878>) of role type named setukpairinjR12_type
% Using role type
% Declaring setukpairinjR12:Prop
% FOF formula (((eq Prop) setukpairinjR12) (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->(((eq fofType) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) ((setadjoin ((setadjoin Xx) emptyset)) emptyset))))) of role definition named setukpairinjR12
% A new definition: (((eq Prop) setukpairinjR12) (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->(((eq fofType) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) ((setadjoin ((setadjoin Xx) emptyset)) emptyset)))))
% Defined: setukpairinjR12:=(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->(((eq fofType) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) ((setadjoin ((setadjoin Xx) emptyset)) emptyset))))
% FOF formula (uniqinunit->(secondinupair->(setukpairinjR12->(forall (Xx:fofType) (Xy:fofType) (Xz:fofType) (Xu:fofType), ((((eq fofType) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) ((setadjoin ((setadjoin Xz) emptyset)) ((setadjoin ((setadjoin Xz) ((setadjoin Xu) emptyset))) emptyset)))->((((eq fofType) Xz) Xu)->(((eq fofType) Xy) Xu))))))) of role conjecture named setukpairinjR1
% Conjecture to prove = (uniqinunit->(secondinupair->(setukpairinjR12->(forall (Xx:fofType) (Xy:fofType) (Xz:fofType) (Xu:fofType), ((((eq fofType) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) ((setadjoin ((setadjoin Xz) emptyset)) ((setadjoin ((setadjoin Xz) ((setadjoin Xu) emptyset))) emptyset)))->((((eq fofType) Xz) Xu)->(((eq fofType) Xy) Xu))))))):Prop
% We need to prove ['(uniqinunit->(secondinupair->(setukpairinjR12->(forall (Xx:fofType) (Xy:fofType) (Xz:fofType) (Xu:fofType), ((((eq fofType) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) ((setadjoin ((setadjoin Xz) emptyset)) ((setadjoin ((setadjoin Xz) ((setadjoin Xu) emptyset))) emptyset)))->((((eq fofType) Xz) Xu)->(((eq fofType) Xy) Xu)))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter emptyset:fofType.
% Parameter setadjoin:(fofType->(fofType->fofType)).
% 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.
% Definition setukpairinjR12:=(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->(((eq fofType) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) ((setadjoin ((setadjoin Xx) emptyset)) emptyset)))):Prop.
% Trying to prove (uniqinunit->(secondinupair->(setukpairinjR12->(forall (Xx:fofType) (Xy:fofType) (Xz:fofType) (Xu:fofType), ((((eq fofType) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) ((setadjoin ((setadjoin Xz) emptyset)) ((setadjoin ((setadjoin Xz) ((setadjoin Xu) emptyset))) emptyset)))->((((eq fofType) Xz) Xu)->(((eq fofType) Xy) Xu)))))))
% Found x30:=(x3 (fun (x5:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x3 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x3 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x5:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x5:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x4:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x4:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x4:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x5:fofType)=> (P Xu))):((P Xu)->(P Xu))
% Found (x2 (fun (x5:fofType)=> (P Xu))) as proof of (P0 Xu)
% Found (x2 (fun (x5:fofType)=> (P Xu))) as proof of (P0 Xu)
% Found x20:=(x2 (fun (x4:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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 (x5:fofType)=> (P Xz))):((P Xz)->(P Xz))
% Found (x2 (fun (x5:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found (x2 (fun (x5:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found x20:=(x2 (fun (x5:fofType)=> (P Xz))):((P Xz)->(P Xz))
% Found (x2 (fun (x5:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found (x2 (fun (x5:fofType)=> (P Xz))) as proof of (P0 Xz)
% 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) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found x20:=(x2 (fun (x4:fofType)=> (P Xz))):((P Xz)->(P Xz))
% Found (x2 (fun (x4:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found (x2 (fun (x4:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) 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 (x4:fofType)=> (P Xz))):((P Xz)->(P Xz))
% Found (x2 (fun (x4:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found (x2 (fun (x4:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found x20:=(x2 (fun (x5:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x30:=(x3 (fun (x5:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x3 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x3 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x30:=(x3 (fun (x5:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x3 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x3 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found eq_ref00:=(eq_ref0 Xz):(((eq fofType) Xz) Xz)
% Found (eq_ref0 Xz) as proof of (((eq fofType) Xz) b)
% Found ((eq_ref fofType) Xz) as proof of (((eq fofType) Xz) b)
% Found ((eq_ref fofType) Xz) as proof of (((eq fofType) Xz) b)
% Found ((eq_ref fofType) Xz) as proof of (((eq fofType) Xz) 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 x30:=(x3 (fun (x4:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x3 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x3 (fun (x4: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) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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 (fun (x4:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x3 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x3 (fun (x4: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) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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 x4:(P Xy)
% Instantiate: Xx0:=Xy:fofType
% Found x4 as proof of (P0 Xx0)
% Found x4:(P Xy)
% Instantiate: b:=Xy:fofType
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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 (x5:fofType)=> (P Xz))):((P Xz)->(P Xz))
% Found (x2 (fun (x5:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found (x2 (fun (x5:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found x40:(P Xy)
% Instantiate: Xx0:=Xy:fofType
% Found x40 as proof of (P0 Xx0)
% Found x4:(P Xy)
% Instantiate: Xx0:=Xy:fofType
% Found x4 as proof of (P0 Xx0)
% Found x4:(P Xy)
% Instantiate: Xx0:=Xy:fofType
% Found x4 as proof of (P0 Xx0)
% Found x3:(((eq fofType) Xz) Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (((eq fofType) Xz) b)
% Found x40:(P Xy)
% Instantiate: b:=Xy:fofType
% Found x40 as proof of (P0 b)
% Found x4:(P Xy)
% Instantiate: b:=Xy:fofType
% Found x4 as proof of (P0 b)
% Found x3:(((eq fofType) Xz) Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (((eq fofType) Xz) b)
% Found x3:(((eq fofType) Xz) Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (((eq fofType) Xz) b)
% Found x4:(P Xy)
% Instantiate: b:=Xy:fofType
% Found x4 as proof of (P0 b)
% Found x3:(((eq fofType) Xz) Xu)
% Instantiate: b:=Xz:fofType
% Found x3 as proof of (((eq fofType) b) Xu)
% 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 (x5:fofType)=> (P Xz))):((P Xz)->(P Xz))
% Found (x2 (fun (x5:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found (x2 (fun (x5:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found eq_ref00:=(eq_ref0 ((setadjoin Xu) emptyset)):(((eq fofType) ((setadjoin Xu) emptyset)) ((setadjoin Xu) emptyset))
% Found (eq_ref0 ((setadjoin Xu) emptyset)) as proof of (((eq fofType) ((setadjoin Xu) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xu) emptyset)) as proof of (((eq fofType) ((setadjoin Xu) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xu) emptyset)) as proof of (((eq fofType) ((setadjoin Xu) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xu) emptyset)) as proof of (((eq fofType) ((setadjoin Xu) emptyset)) b)
% Found x20:=(x2 (fun (x4:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x3:(((eq fofType) Xz) Xu)
% Instantiate: b:=Xz:fofType
% Found x3 as proof of (((eq fofType) b) Xu)
% 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 (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 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found x4:(P Xu)
% Instantiate: b:=Xu:fofType
% Found x4 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 x20:=(x2 (fun (x5:fofType)=> (P1 Xu))):((P1 Xu)->(P1 Xu))
% Found (x2 (fun (x5:fofType)=> (P1 Xu))) as proof of (P2 Xu)
% Found (x2 (fun (x5:fofType)=> (P1 Xu))) as proof of (P2 Xu)
% Found x20:=(x2 (fun (x5:fofType)=> (P1 Xu))):((P1 Xu)->(P1 Xu))
% Found (x2 (fun (x5:fofType)=> (P1 Xu))) as proof of (P2 Xu)
% Found (x2 (fun (x5:fofType)=> (P1 Xu))) as proof of (P2 Xu)
% Found x3:(((eq fofType) Xz) Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (((eq fofType) Xz) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found x4:(P Xu)
% Instantiate: Xx0:=Xu:fofType
% Found x4 as proof of (P0 Xx0)
% Found x3:(P Xy)
% Instantiate: Xx0:=Xy:fofType
% Found x3 as proof of (P0 Xx0)
% Found x20:=(x2 (fun (x5:fofType)=> (P Xu))):((P Xu)->(P Xu))
% Found (x2 (fun (x5:fofType)=> (P Xu))) as proof of (P0 Xu)
% Found (x2 (fun (x5:fofType)=> (P Xu))) as proof of (P0 Xu)
% Found eq_ref00:=(eq_ref0 ((setadjoin Xz) emptyset)):(((eq fofType) ((setadjoin Xz) emptyset)) ((setadjoin Xz) emptyset))
% Found (eq_ref0 ((setadjoin Xz) emptyset)) as proof of (((eq fofType) ((setadjoin Xz) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xz) emptyset)) as proof of (((eq fofType) ((setadjoin Xz) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xz) emptyset)) as proof of (((eq fofType) ((setadjoin Xz) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xz) emptyset)) as proof of (((eq fofType) ((setadjoin Xz) emptyset)) b)
% Found eq_ref00:=(eq_ref0 ((setadjoin Xz) emptyset)):(((eq fofType) ((setadjoin Xz) emptyset)) ((setadjoin Xz) emptyset))
% Found (eq_ref0 ((setadjoin Xz) emptyset)) as proof of (((eq fofType) ((setadjoin Xz) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xz) emptyset)) as proof of (((eq fofType) ((setadjoin Xz) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xz) emptyset)) as proof of (((eq fofType) ((setadjoin Xz) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xz) emptyset)) as proof of (((eq fofType) ((setadjoin Xz) emptyset)) b)
% Found x3:(P Xy)
% Instantiate: b:=Xy:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xz):(((eq fofType) Xz) Xz)
% Found (eq_ref0 Xz) as proof of (((eq fofType) Xz) b)
% Found ((eq_ref fofType) Xz) as proof of (((eq fofType) Xz) b)
% Found ((eq_ref fofType) Xz) as proof of (((eq fofType) Xz) b)
% Found ((eq_ref fofType) Xz) as proof of (((eq fofType) Xz) b)
% Found x20:=(x2 (fun (x4:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x4: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) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found x20:=(x2 (fun (x4:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x4: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) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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 (x5:fofType)=> (P Xu))):((P Xu)->(P Xu))
% Found (x2 (fun (x5:fofType)=> (P Xu))) as proof of (P0 Xu)
% Found (x2 (fun (x5:fofType)=> (P Xu))) as proof of (P0 Xu)
% Found x4:(P Xz)
% Instantiate: b:=Xz:fofType
% Found x4 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 x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found x4:(P Xz)
% Instantiate: b:=Xz:fofType
% Found x4 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 x20:=(x2 (fun (x5:fofType)=> (P1 Xz))):((P1 Xz)->(P1 Xz))
% Found (x2 (fun (x5:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% Found (x2 (fun (x5:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% Found x20:=(x2 (fun (x5:fofType)=> (P1 Xz))):((P1 Xz)->(P1 Xz))
% Found (x2 (fun (x5:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% Found (x2 (fun (x5:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% Found x20:=(x2 (fun (x5:fofType)=> (P1 Xz))):((P1 Xz)->(P1 Xz))
% Found (x2 (fun (x5:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% Found (x2 (fun (x5:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% Found x20:=(x2 (fun (x5:fofType)=> (P1 Xz))):((P1 Xz)->(P1 Xz))
% Found (x2 (fun (x5:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% Found (x2 (fun (x5:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% Found x20:=(x2 (fun (x5:fofType)=> (P1 Xz))):((P1 Xz)->(P1 Xz))
% Found (x2 (fun (x5:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% Found (x2 (fun (x5:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% Found x20:=(x2 (fun (x5:fofType)=> (P1 Xz))):((P1 Xz)->(P1 Xz))
% Found (x2 (fun (x5:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% Found (x2 (fun (x5:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% Found x4:(P Xz)
% Instantiate: Xx0:=Xz:fofType
% Found x4 as proof of (P0 Xx0)
% Found x4:(P Xz)
% Instantiate: Xx0:=Xz:fofType
% Found x4 as proof of (P0 Xx0)
% 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:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) b) Xu)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found x20:=(x2 (fun (x5:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x30:=(x3 (fun (x5:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x3 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x3 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x3:(P Xy)
% Found x3 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) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found x20:=(x2 (fun (x4:fofType)=> (P1 Xz))):((P1 Xz)->(P1 Xz))
% Found (x2 (fun (x4:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% Found (x2 (fun (x4:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% Found x20:=(x2 (fun (x4:fofType)=> (P1 Xz))):((P1 Xz)->(P1 Xz))
% Found (x2 (fun (x4:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% Found (x2 (fun (x4:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% Found x20:=(x2 (fun (x4:fofType)=> (P1 Xz))):((P1 Xz)->(P1 Xz))
% Found (x2 (fun (x4:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% Found (x2 (fun (x4:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% Found x20:=(x2 (fun (x4:fofType)=> (P1 Xz))):((P1 Xz)->(P1 Xz))
% Found (x2 (fun (x4:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% Found (x2 (fun (x4:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% 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 x000:=(x00 Xy):((in Xy) ((setadjoin Xu) ((setadjoin Xy) emptyset)))
% Found (x00 Xy) as proof of (P a)
% Found ((x0 Xu) Xy) as proof of (P a)
% Found ((x0 Xu) Xy) as proof of (P a)
% Found ((x0 Xu) 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 x000:=(x00 Xy):((in Xy) ((setadjoin Xu) ((setadjoin Xy) emptyset)))
% Found (x00 Xy) as proof of (P ((setadjoin Xu) a))
% Found ((x0 Xu) Xy) as proof of (P ((setadjoin Xu) a))
% Found ((x0 Xu) Xy) as proof of (P ((setadjoin Xu) a))
% Found ((x0 Xu) Xy) as proof of (P ((setadjoin Xu) a))
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) 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 x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) b)
% Found x30:=(x3 (fun (x4:fofType)=> (P Xu))):((P Xu)->(P Xu))
% Found (x3 (fun (x4:fofType)=> (P Xu))) as proof of (P0 Xu)
% Found (x3 (fun (x4:fofType)=> (P Xu))) as proof of (P0 Xu)
% Found eq_ref00:=(eq_ref0 ((setadjoin Xz) emptyset)):(((eq fofType) ((setadjoin Xz) emptyset)) ((setadjoin Xz) emptyset))
% Found (eq_ref0 ((setadjoin Xz) emptyset)) as proof of (((eq fofType) ((setadjoin Xz) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xz) emptyset)) as proof of (((eq fofType) ((setadjoin Xz) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xz) emptyset)) as proof of (((eq fofType) ((setadjoin Xz) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xz) emptyset)) as proof of (((eq fofType) ((setadjoin Xz) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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) 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 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) 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 (((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 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) 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 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xz)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xz)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xz)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xz)
% 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)=> (P b))):((P b)->(P b))
% Found (x2 (fun (x4:fofType)=> (P b))) as proof of (P0 b)
% Found (x2 (fun (x4: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 (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 Xz):(((eq fofType) Xz) Xz)
% Found (eq_ref0 Xz) as proof of (((eq fofType) Xz) b)
% Found ((eq_ref fofType) Xz) as proof of (((eq fofType) Xz) b)
% Found ((eq_ref fofType) Xz) as proof of (((eq fofType) Xz) b)
% Found ((eq_ref fofType) Xz) as proof of (((eq fofType) Xz) b)
% Found x20:=(x2 (fun (x5:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x5:fofType)=> (P0 Xy))):((P0 Xy)->(P0 Xy))
% Found (x2 (fun (x5:fofType)=> (P0 Xy))) as proof of (P Xy)
% Found (x2 (fun (x5:fofType)=> (P0 Xy))) as proof of (P Xy)
% Found x3:(((eq fofType) Xz) Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (((eq fofType) Xz) 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 (x5:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x3:(((eq fofType) Xz) Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (((eq fofType) Xz) 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 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) 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 (x4:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x3:(P Xz)
% Instantiate: b:=Xz: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 x20:=(x2 (fun (x4:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x4:fofType)=> (P1 Xz))):((P1 Xz)->(P1 Xz))
% Found (x2 (fun (x4:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% Found (x2 (fun (x4:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% Found x20:=(x2 (fun (x4:fofType)=> (P1 Xz))):((P1 Xz)->(P1 Xz))
% Found (x2 (fun (x4:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% Found (x2 (fun (x4:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% Found x3:(P Xz)
% Instantiate: Xx0:=Xz:fofType
% Found x3 as proof of (P0 Xx0)
% 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 x000:=(x00 Xy):((in Xy) ((setadjoin Xz) ((setadjoin Xy) emptyset)))
% Found (x00 Xy) as proof of (P a)
% Found ((x0 Xz) Xy) as proof of (P a)
% Found ((x0 Xz) Xy) as proof of (P a)
% Found ((x0 Xz) 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 x000:=(x00 Xy):((in Xy) ((setadjoin Xz) ((setadjoin Xy) emptyset)))
% Found (x00 Xy) as proof of (P ((setadjoin Xz) a))
% Found ((x0 Xz) Xy) as proof of (P ((setadjoin Xz) a))
% Found ((x0 Xz) Xy) as proof of (P ((setadjoin Xz) a))
% Found ((x0 Xz) Xy) as proof of (P ((setadjoin Xz) 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 x000:=(x00 Xy):((in Xy) ((setadjoin Xz) ((setadjoin Xy) emptyset)))
% Found (x00 Xy) as proof of (P a)
% Found ((x0 Xz) Xy) as proof of (P a)
% Found ((x0 Xz) Xy) as proof of (P a)
% Found ((x0 Xz) Xy) as proof of (P a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xz)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xz)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xz)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xz)
% 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 x000:=(x00 Xy):((in Xy) ((setadjoin Xz) ((setadjoin Xy) emptyset)))
% Found (x00 Xy) as proof of (P ((setadjoin Xz) a))
% Found ((x0 Xz) Xy) as proof of (P ((setadjoin Xz) a))
% Found ((x0 Xz) Xy) as proof of (P ((setadjoin Xz) a))
% Found ((x0 Xz) Xy) as proof of (P ((setadjoin Xz) a))
% 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 (x4:fofType)=> (P Xz))):((P Xz)->(P Xz))
% Found (x2 (fun (x4:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found (x2 (fun (x4:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found x3:(((eq fofType) Xz) Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (((eq fofType) Xz) 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 x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found x3:(((eq fofType) Xz) Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (((eq fofType) Xz) b)
% Found x20:=(x2 (fun (x4:fofType)=> (P Xz))):((P Xz)->(P Xz))
% Found (x2 (fun (x4:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found (x2 (fun (x4:fofType)=> (P Xz))) as proof of (P0 Xz)
% 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 x30:=(x3 (fun (x5:fofType)=> (P b))):((P b)->(P b))
% Found (x3 (fun (x5:fofType)=> (P b))) as proof of (P0 b)
% Found (x3 (fun (x5:fofType)=> (P b))) as proof of (P0 b)
% Found x3:(((eq fofType) Xz) Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (((eq fofType) Xz) b)
% Found x4:(P Xy)
% Instantiate: b:=Xy:fofType
% Found x4 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 (x4:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x4:fofType)=> (P0 Xy))):((P0 Xy)->(P0 Xy))
% Found (x2 (fun (x4:fofType)=> (P0 Xy))) as proof of (P Xy)
% Found (x2 (fun (x4:fofType)=> (P0 Xy))) as proof of (P Xy)
% Found x20:=(x2 (fun (x4:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x5:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x5:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x5:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x20:=(x2 (fun (x5:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x5:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x5:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x4:(P Xy)
% Instantiate: Xx0:=Xy:fofType
% Found x4 as proof of (P0 Xx0)
% Found x20:=(x2 (fun (x5:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x5:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x5:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x20:=(x2 (fun (x5:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x5:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x5:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x4:(P Xy)
% Instantiate: Xx0:=Xy:fofType
% Found x4 as proof of (P0 Xx0)
% Found x20:=(x2 (fun (x5:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x5:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x5:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x20:=(x2 (fun (x5:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x2 (fun (x5:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x2 (fun (x5:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found x3:(((eq fofType) Xz) Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (((eq fofType) Xz) b)
% Found x4:(P Xy)
% Instantiate: b:=Xy:fofType
% Found x4 as proof of (P0 b)
% Found x30:=(x3 (fun (x4:fofType)=> (P b))):((P b)->(P b))
% Found (x3 (fun (x4:fofType)=> (P b))) as proof of (P0 b)
% Found (x3 (fun (x4: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) 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 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b0)
% Found x20:=(x2 (fun (x5:fofType)=> (P Xu))):((P Xu)->(P Xu))
% Found (x2 (fun (x5:fofType)=> (P Xu))) as proof of (P0 Xu)
% Found (x2 (fun (x5:fofType)=> (P Xu))) as proof of (P0 Xu)
% Found x20:=(x2 (fun (x5:fofType)=> (P Xu))):((P Xu)->(P Xu))
% Found (x2 (fun (x5:fofType)=> (P Xu))) as proof of (P0 Xu)
% Found (x2 (fun (x5:fofType)=> (P Xu))) as proof of (P0 Xu)
% Found x20:=(x2 (fun (x4:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x4:(P Xy)
% Instantiate: Xx0:=Xy:fofType
% Found x4 as proof of (P0 Xx0)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found x4:(P Xy)
% Instantiate: b:=Xy:fofType
% Found x4 as proof of (P0 b)
% Found x3:(((eq fofType) Xz) Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (((eq fofType) Xz) 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 (x3:fofType)=> (P Xz))):((P Xz)->(P Xz))
% Found (x2 (fun (x3:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found (x2 (fun (x3:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found x20:=(x2 (fun (x5:fofType)=> (P b))):((P b)->(P b))
% Found (x2 (fun (x5:fofType)=> (P b))) as proof of (P0 b)
% Found (x2 (fun (x5:fofType)=> (P b))) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xz):(((eq fofType) Xz) Xz)
% Found (eq_ref0 Xz) as proof of (((eq fofType) Xz) b)
% Found ((eq_ref fofType) Xz) as proof of (((eq fofType) Xz) b)
% Found ((eq_ref fofType) Xz) as proof of (((eq fofType) Xz) b)
% Found ((eq_ref fofType) Xz) as proof of (((eq fofType) Xz) 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 Xz):(((eq fofType) Xz) Xz)
% Found (eq_ref0 Xz) as proof of (((eq fofType) Xz) b)
% Found ((eq_ref fofType) Xz) as proof of (((eq fofType) Xz) b)
% Found ((eq_ref fofType) Xz) as proof of (((eq fofType) Xz) b)
% Found ((eq_ref fofType) Xz) as proof of (((eq fofType) Xz) 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 ((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 Xz):(((eq fofType) Xz) Xz)
% Found (eq_ref0 Xz) as proof of (((eq fofType) Xz) b)
% Found ((eq_ref fofType) Xz) as proof of (((eq fofType) Xz) b)
% Found ((eq_ref fofType) Xz) as proof of (((eq fofType) Xz) b)
% Found ((eq_ref fofType) Xz) as proof of (((eq fofType) Xz) 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 Xz):(((eq fofType) Xz) Xz)
% Found (eq_ref0 Xz) as proof of (((eq fofType) Xz) b)
% Found ((eq_ref fofType) Xz) as proof of (((eq fofType) Xz) b)
% Found ((eq_ref fofType) Xz) as proof of (((eq fofType) Xz) b)
% Found ((eq_ref fofType) Xz) as proof of (((eq fofType) Xz) 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 (x5:fofType)=> (P Xz))):((P Xz)->(P Xz))
% Found (x2 (fun (x5:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found (x2 (fun (x5:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found x30:=(x3 (fun (x4:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x3 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x3 (fun (x4:fofType)=> (P Xy))) as proof of (P0 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 x000:=(x00 Xu):((in Xu) ((setadjoin Xy) ((setadjoin Xu) emptyset)))
% Found (x00 Xu) as proof of (P a)
% Found ((x0 Xy) Xu) as proof of (P a)
% Found ((x0 Xy) Xu) as proof of (P a)
% Found ((x0 Xy) Xu) 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 x000:=(x00 Xu):((in Xu) ((setadjoin Xy) ((setadjoin Xu) emptyset)))
% Found (x00 Xu) as proof of (P ((setadjoin Xy) a))
% Found ((x0 Xy) Xu) as proof of (P ((setadjoin Xy) a))
% Found ((x0 Xy) Xu) as proof of (P ((setadjoin Xy) a))
% Found ((x0 Xy) Xu) as proof of (P ((setadjoin Xy) a))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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 x000:=(x00 Xy):((in Xy) ((setadjoin Xz) ((setadjoin Xy) emptyset)))
% Found (x00 Xy) as proof of (P a)
% Found ((x0 Xz) Xy) as proof of (P a)
% Found ((x0 Xz) Xy) as proof of (P a)
% Found ((x0 Xz) 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) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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 x000:=(x00 Xy):((in Xy) ((setadjoin Xz) ((setadjoin Xy) emptyset)))
% Found (x00 Xy) as proof of (P ((setadjoin Xz) a))
% Found ((x0 Xz) Xy) as proof of (P ((setadjoin Xz) a))
% Found ((x0 Xz) Xy) as proof of (P ((setadjoin Xz) a))
% Found ((x0 Xz) Xy) as proof of (P ((setadjoin Xz) a))
% Found x4:(P Xy)
% Found x4 as proof of (P0 Xy)
% Found x3:(((eq fofType) Xz) Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (((eq fofType) Xz) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found x20:=(x2 (fun (x5:fofType)=> (P Xz))):((P Xz)->(P Xz))
% Found (x2 (fun (x5:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found (x2 (fun (x5:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found x20:=(x2 (fun (x5:fofType)=> (P Xz))):((P Xz)->(P Xz))
% Found (x2 (fun (x5:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found (x2 (fun (x5:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found x30:=(x3 (fun (x5:fofType)=> (P Xu))):((P Xu)->(P Xu))
% Found (x3 (fun (x5:fofType)=> (P Xu))) as proof of (P0 Xu)
% Found (x3 (fun (x5:fofType)=> (P Xu))) as proof of (P0 Xu)
% Found x20:=(x2 (fun (x5:fofType)=> (P Xz))):((P Xz)->(P Xz))
% Found (x2 (fun (x5:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found (x2 (fun (x5:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found x20:=(x2 (fun (x5:fofType)=> (P Xz))):((P Xz)->(P Xz))
% Found (x2 (fun (x5:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found (x2 (fun (x5:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found x20:=(x2 (fun (x5:fofType)=> (P Xz))):((P Xz)->(P Xz))
% Found (x2 (fun (x5:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found (x2 (fun (x5:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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 (x4:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x4: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 (x4:fofType)=> (P Xz))):((P Xz)->(P Xz))
% Found (x2 (fun (x4:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found (x2 (fun (x4:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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 (x4:fofType)=> (P Xz))):((P Xz)->(P Xz))
% Found (x2 (fun (x4:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found (x2 (fun (x4:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found eq_ref00:=(eq_ref0 ((setadjoin Xz) emptyset)):(((eq fofType) ((setadjoin Xz) emptyset)) ((setadjoin Xz) emptyset))
% Found (eq_ref0 ((setadjoin Xz) emptyset)) as proof of (((eq fofType) ((setadjoin Xz) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xz) emptyset)) as proof of (((eq fofType) ((setadjoin Xz) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xz) emptyset)) as proof of (((eq fofType) ((setadjoin Xz) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xz) emptyset)) as proof of (((eq fofType) ((setadjoin Xz) emptyset)) b)
% Found x4:(P Xy)
% Found x4 as proof of (P0 Xy)
% Found x3:(((eq fofType) Xz) Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (((eq fofType) Xz) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((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 eq_ref00:=(eq_ref0 ((setadjoin Xz) emptyset)):(((eq fofType) ((setadjoin Xz) emptyset)) ((setadjoin Xz) emptyset))
% Found (eq_ref0 ((setadjoin Xz) emptyset)) as proof of (((eq fofType) ((setadjoin Xz) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xz) emptyset)) as proof of (((eq fofType) ((setadjoin Xz) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xz) emptyset)) as proof of (((eq fofType) ((setadjoin Xz) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xz) emptyset)) as proof of (((eq fofType) ((setadjoin Xz) emptyset)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) b) Xu)
% Found x20:=(x2 (fun (x5:fofType)=> (P Xu))):((P Xu)->(P Xu))
% Found (x2 (fun (x5:fofType)=> (P Xu))) as proof of (P0 Xu)
% Found (x2 (fun (x5:fofType)=> (P Xu))) as proof of (P0 Xu)
% Found x20:=(x2 (fun (x5:fofType)=> (P Xu))):((P Xu)->(P Xu))
% Found (x2 (fun (x5:fofType)=> (P Xu))) as proof of (P0 Xu)
% Found (x2 (fun (x5:fofType)=> (P Xu))) as proof of (P0 Xu)
% Found x20:=(x2 (fun (x4:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x4:fofType)=> (P b))):((P b)->(P b))
% Found (x2 (fun (x4:fofType)=> (P b))) as proof of (P0 b)
% Found (x2 (fun (x4:fofType)=> (P b))) as proof of (P0 b)
% Found x30:=(x3 (fun (x5:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x3 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x3 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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 (x4:fofType)=> (P Xz))):((P Xz)->(P Xz))
% Found (x2 (fun (x4:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found (x2 (fun (x4:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found x30:=(x3 (fun (x5:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x3 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x3 (fun (x5: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) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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 x000:=(x00 Xz):((in Xz) ((setadjoin Xy) ((setadjoin Xz) emptyset)))
% Found (x00 Xz) as proof of (P a)
% Found ((x0 Xy) Xz) as proof of (P a)
% Found ((x0 Xy) Xz) as proof of (P a)
% Found ((x0 Xy) Xz) 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 x000:=(x00 Xz):((in Xz) ((setadjoin Xy) ((setadjoin Xz) emptyset)))
% Found (x00 Xz) as proof of (P a)
% Found ((x0 Xy) Xz) as proof of (P a)
% Found ((x0 Xy) Xz) as proof of (P a)
% Found ((x0 Xy) Xz) 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 x000:=(x00 Xz):((in Xz) ((setadjoin Xy) ((setadjoin Xz) emptyset)))
% Found (x00 Xz) as proof of (P ((setadjoin Xy) a))
% Found ((x0 Xy) Xz) as proof of (P ((setadjoin Xy) a))
% Found ((x0 Xy) Xz) as proof of (P ((setadjoin Xy) a))
% Found ((x0 Xy) Xz) as proof of (P ((setadjoin Xy) a))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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 Xz) emptyset)):(((eq fofType) ((setadjoin Xz) emptyset)) ((setadjoin Xz) emptyset))
% Found (eq_ref0 ((setadjoin Xz) emptyset)) as proof of (((eq fofType) ((setadjoin Xz) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xz) emptyset)) as proof of (((eq fofType) ((setadjoin Xz) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xz) emptyset)) as proof of (((eq fofType) ((setadjoin Xz) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin Xz) emptyset)) as proof of (((eq fofType) ((setadjoin Xz) 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 x000:=(x00 Xz):((in Xz) ((setadjoin Xy) ((setadjoin Xz) emptyset)))
% Found (x00 Xz) as proof of (P ((setadjoin Xy) a))
% Found ((x0 Xy) Xz) as proof of (P ((setadjoin Xy) a))
% Found ((x0 Xy) Xz) as proof of (P ((setadjoin Xy) a))
% Found ((x0 Xy) Xz) as proof of (P ((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 x000:=(x00 Xz):((in Xz) ((setadjoin Xy) ((setadjoin Xz) emptyset)))
% Found (x00 Xz) as proof of (P a)
% Found ((x0 Xy) Xz) as proof of (P a)
% Found ((x0 Xy) Xz) as proof of (P a)
% Found ((x0 Xy) Xz) 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 x000:=(x00 Xz):((in Xz) ((setadjoin Xy) ((setadjoin Xz) emptyset)))
% Found (x00 Xz) as proof of (P ((setadjoin Xy) a))
% Found ((x0 Xy) Xz) as proof of (P ((setadjoin Xy) a))
% Found ((x0 Xy) Xz) as proof of (P ((setadjoin Xy) a))
% Found ((x0 Xy) Xz) as proof of (P ((setadjoin Xy) a))
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) b) Xu)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) 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 (((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 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found x4:(P Xz)
% Instantiate: b:=Xz:fofType
% Found x4 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 x20:=(x2 (fun (x5:fofType)=> (P Xu))):((P Xu)->(P Xu))
% Found (x2 (fun (x5:fofType)=> (P Xu))) as proof of (P0 Xu)
% Found (x2 (fun (x5:fofType)=> (P Xu))) as proof of (P0 Xu)
% Found eq_ref00:=(eq_ref0 Xz):(((eq fofType) Xz) Xz)
% Found (eq_ref0 Xz) as proof of (((eq fofType) Xz) b0)
% Found ((eq_ref fofType) Xz) as proof of (((eq fofType) Xz) b0)
% Found ((eq_ref fofType) Xz) as proof of (((eq fofType) Xz) b0)
% Found ((eq_ref fofType) Xz) as proof of (((eq fofType) Xz) 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 x30:=(x3 (fun (x5:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x3 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x3 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x5:fofType)=> (P1 Xz))):((P1 Xz)->(P1 Xz))
% Found (x2 (fun (x5:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% Found (x2 (fun (x5:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% Found x20:=(x2 (fun (x5:fofType)=> (P1 Xz))):((P1 Xz)->(P1 Xz))
% Found (x2 (fun (x5:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% Found (x2 (fun (x5:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% Found x4:(P Xz)
% Instantiate: Xx0:=Xz:fofType
% Found x4 as proof of (P0 Xx0)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) 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:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xz)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xz)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xz)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xz)
% 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) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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 x4:(P Xz)
% Instantiate: b:=Xz:fofType
% Found x4 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 x20:=(x2 (fun (x4:fofType)=> (P Xz))):((P Xz)->(P Xz))
% Found (x2 (fun (x4:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found (x2 (fun (x4:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found x20:=(x2 (fun (x4:fofType)=> (P Xz))):((P Xz)->(P Xz))
% Found (x2 (fun (x4:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found (x2 (fun (x4:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) 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 (x5:fofType)=> (P1 Xz))):((P1 Xz)->(P1 Xz))
% Found (x2 (fun (x5:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% Found (x2 (fun (x5:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% Found x20:=(x2 (fun (x5:fofType)=> (P1 Xz))):((P1 Xz)->(P1 Xz))
% Found (x2 (fun (x5:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% Found (x2 (fun (x5:fofType)=> (P1 Xz))) as proof of (P2 Xz)
% Found x4:(P Xz)
% Instantiate: Xx0:=Xz:fofType
% Found x4 as proof of (P0 Xx0)
% Found x30:=(x3 (fun (x4:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x3 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x3 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 Xz):(((eq fofType) Xz) Xz)
% Found (eq_ref0 Xz) as proof of (((eq fofType) Xz) b0)
% Found ((eq_ref fofType) Xz) as proof of (((eq fofType) Xz) b0)
% Found ((eq_ref fofType) Xz) as proof of (((eq fofType) Xz) b0)
% Found ((eq_ref fofType) Xz) as proof of (((eq fofType) Xz) 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) Xz)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xz)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xz)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xz)
% 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 (x5:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x5:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x3:(((eq fofType) Xz) Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (((eq fofType) Xz) 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 (x5:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x5:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) 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 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) 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 (x4:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x30:=(x3 (fun (x5:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x3 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x3 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x30:=(x3 (fun (x5:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x3 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x3 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x5:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x5:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x5:fofType)=> (P Xy))) 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) Xz)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xz)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xz)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xz)
% 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:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found x3:(((eq fofType) Xz) Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (((eq fofType) Xz) 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 (x4:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 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 x000:=(x00 Xz):((in Xz) ((setadjoin Xy) ((setadjoin Xz) emptyset)))
% Found (x00 Xz) as proof of (P a)
% Found ((x0 Xy) Xz) as proof of (P a)
% Found ((x0 Xy) Xz) as proof of (P a)
% Found ((x0 Xy) Xz) as proof of (P a)
% Found x3:(((eq fofType) Xz) Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (((eq fofType) Xz) b)
% Found x20:=(x2 (fun (x4:fofType)=> (P Xz))):((P Xz)->(P Xz))
% Found (x2 (fun (x4:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found (x2 (fun (x4:fofType)=> (P Xz))) as proof of (P0 Xz)
% 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) 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 x000:=(x00 Xz):((in Xz) ((setadjoin Xy) ((setadjoin Xz) emptyset)))
% Found (x00 Xz) as proof of (P ((setadjoin Xy) a))
% Found ((x0 Xy) Xz) as proof of (P ((setadjoin Xy) a))
% Found ((x0 Xy) Xz) as proof of (P ((setadjoin Xy) a))
% Found ((x0 Xy) Xz) as proof of (P ((setadjoin Xy) a))
% Found x30:=(x3 (fun (x5:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x3 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x3 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x30:=(x3 (fun (x5:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x3 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x3 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) 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 (x4:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) b) Xu)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) b) Xu)
% Found x4:(P Xu)
% Instantiate: b:=Xu:fofType
% Found x4 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 x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found x3:(((eq fofType) Xz) Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (((eq fofType) Xz) b)
% Found x20:=(x2 (fun (x5:fofType)=> (P1 Xu))):((P1 Xu)->(P1 Xu))
% Found (x2 (fun (x5:fofType)=> (P1 Xu))) as proof of (P2 Xu)
% Found (x2 (fun (x5:fofType)=> (P1 Xu))) as proof of (P2 Xu)
% Found x20:=(x2 (fun (x5:fofType)=> (P1 Xu))):((P1 Xu)->(P1 Xu))
% Found (x2 (fun (x5:fofType)=> (P1 Xu))) as proof of (P2 Xu)
% Found (x2 (fun (x5:fofType)=> (P1 Xu))) as proof of (P2 Xu)
% Found x4:(P Xu)
% Instantiate: Xx0:=Xu:fofType
% Found x4 as proof of (P0 Xx0)
% 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 x000:=(x00 Xy):((in Xy) ((setadjoin Xz) ((setadjoin Xy) emptyset)))
% Found (x00 Xy) as proof of (P a)
% Found ((x0 Xz) Xy) as proof of (P a)
% Found ((x0 Xz) Xy) as proof of (P a)
% Found ((x0 Xz) Xy) as proof of (P a)
% Found x20:=(x2 (fun (x5:fofType)=> (P1 Xu))):((P1 Xu)->(P1 Xu))
% Found (x2 (fun (x5:fofType)=> (P1 Xu))) as proof of (P2 Xu)
% Found (x2 (fun (x5:fofType)=> (P1 Xu))) as proof of (P2 Xu)
% Found x20:=(x2 (fun (x5:fofType)=> (P1 Xu))):((P1 Xu)->(P1 Xu))
% Found (x2 (fun (x5:fofType)=> (P1 Xu))) as proof of (P2 Xu)
% Found (x2 (fun (x5:fofType)=> (P1 Xu))) as proof of (P2 Xu)
% 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 x000:=(x00 Xy):((in Xy) ((setadjoin Xz) ((setadjoin Xy) emptyset)))
% Found (x00 Xy) as proof of (P ((setadjoin Xz) a))
% Found ((x0 Xz) Xy) as proof of (P ((setadjoin Xz) a))
% Found ((x0 Xz) Xy) as proof of (P ((setadjoin Xz) a))
% Found ((x0 Xz) Xy) as proof of (P ((setadjoin Xz) a))
% Found x3:(((eq fofType) Xz) Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (((eq fofType) Xz) b)
% Found x20:=(x2 (fun (x4:fofType)=> (P Xz))):((P Xz)->(P Xz))
% Found (x2 (fun (x4:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found (x2 (fun (x4:fofType)=> (P Xz))) as proof of (P0 Xz)
% 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 (((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 (x4:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 Xz):(((eq fofType) Xz) Xz)
% Found (eq_ref0 Xz) as proof of (((eq fofType) Xz) b)
% Found ((eq_ref fofType) Xz) as proof of (((eq fofType) Xz) b)
% Found ((eq_ref fofType) Xz) as proof of (((eq fofType) Xz) b)
% Found ((eq_ref fofType) Xz) as proof of (((eq fofType) Xz) 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 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found x20:=(x2 (fun (x4:fofType)=> (P Xz))):((P Xz)->(P Xz))
% Found (x2 (fun (x4:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found (x2 (fun (x4:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found x30:=(x3 (fun (x4:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x3 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x3 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x30:=(x3 (fun (x4:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x3 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x3 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x4:(P Xu)
% Instantiate: b:=Xu:fofType
% Found x4 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 x3:(((eq fofType) Xz) Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (((eq fofType) Xz) 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 x000:=(x00 Xy):((in Xy) ((setadjoin Xz) ((setadjoin Xy) emptyset)))
% Found (x00 Xy) as proof of (P a)
% Found ((x0 Xz) Xy) as proof of (P a)
% Found ((x0 Xz) Xy) as proof of (P a)
% Found ((x0 Xz) Xy) as proof of (P a)
% Found x30:=(x3 (fun (x5:fofType)=> (P b))):((P b)->(P b))
% Found (x3 (fun (x5:fofType)=> (P b))) as proof of (P0 b)
% Found (x3 (fun (x5:fofType)=> (P b))) as proof of (P0 b)
% Found x3:(((eq fofType) Xz) Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (((eq fofType) Xz) b)
% Found x20:=(x2 (fun (x5:fofType)=> (P1 Xu))):((P1 Xu)->(P1 Xu))
% Found (x2 (fun (x5:fofType)=> (P1 Xu))) as proof of (P2 Xu)
% Found (x2 (fun (x5:fofType)=> (P1 Xu))) as proof of (P2 Xu)
% Found x20:=(x2 (fun (x5:fofType)=> (P1 Xu))):((P1 Xu)->(P1 Xu))
% Found (x2 (fun (x5:fofType)=> (P1 Xu))) as proof of (P2 Xu)
% Found (x2 (fun (x5:fofType)=> (P1 Xu))) as proof of (P2 Xu)
% 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 x000:=(x00 Xy):((in Xy) ((setadjoin Xz) ((setadjoin Xy) emptyset)))
% Found (x00 Xy) as proof of (P ((setadjoin Xz) a))
% Found ((x0 Xz) Xy) as proof of (P ((setadjoin Xz) a))
% Found ((x0 Xz) Xy) as proof of (P ((setadjoin Xz) a))
% Found ((x0 Xz) Xy) as proof of (P ((setadjoin Xz) a))
% Found x4:(P Xu)
% Instantiate: Xx0:=Xu:fofType
% Found x4 as proof of (P0 Xx0)
% 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 x000:=(x00 Xy):((in Xy) ((setadjoin Xz) ((setadjoin Xy) emptyset)))
% Found (x00 Xy) as proof of (P a)
% Found ((x0 Xz) Xy) as proof of (P a)
% Found ((x0 Xz) Xy) as proof of (P a)
% Found ((x0 Xz) 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) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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 x000:=(x00 Xy):((in Xy) ((setadjoin Xz) ((setadjoin Xy) emptyset)))
% Found (x00 Xy) as proof of (P ((setadjoin Xz) a))
% Found ((x0 Xz) Xy) as proof of (P ((setadjoin Xz) a))
% Found ((x0 Xz) Xy) as proof of (P ((setadjoin Xz) a))
% Found ((x0 Xz) Xy) as proof of (P ((setadjoin Xz) a))
% Found x20:=(x2 (fun (x5:fofType)=> (P1 Xu))):((P1 Xu)->(P1 Xu))
% Found (x2 (fun (x5:fofType)=> (P1 Xu))) as proof of (P2 Xu)
% Found (x2 (fun (x5:fofType)=> (P1 Xu))) as proof of (P2 Xu)
% Found x20:=(x2 (fun (x5:fofType)=> (P1 Xu))):((P1 Xu)->(P1 Xu))
% Found (x2 (fun (x5:fofType)=> (P1 Xu))) as proof of (P2 Xu)
% Found (x2 (fun (x5:fofType)=> (P1 Xu))) as proof of (P2 Xu)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xz)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xz)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xz)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xz)
% 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:(((eq fofType) Xz) Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (((eq fofType) Xz) 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xz)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xz)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xz)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xz)
% 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 (fun (x4:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x3 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x3 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x30:=(x3 (fun (x4:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x3 (fun (x4:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x3 (fun (x4: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) 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 x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) b) Xu)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) b) Xu)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) b) Xu)
% Found x20:=(x2 (fun (x5:fofType)=> (P b))):((P b)->(P b))
% Found (x2 (fun (x5:fofType)=> (P b))) as proof of (P0 b)
% Found (x2 (fun (x5:fofType)=> (P b))) as proof of (P0 b)
% Found x4:(P Xy)
% Instantiate: Xx0:=Xy:fofType
% Found x4 as proof of (P0 Xx0)
% Found x3:(((eq fofType) Xz) Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (((eq fofType) Xz) 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 x4:(P Xy)
% Instantiate: b:=Xy:fofType
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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) 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 (x4:fofType)=> (P Xu))):((P Xu)->(P Xu))
% Found (x2 (fun (x4:fofType)=> (P Xu))) as proof of (P0 Xu)
% Found (x2 (fun (x4:fofType)=> (P Xu))) as proof of (P0 Xu)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) 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 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) 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 x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) 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 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) 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 x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) 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 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) 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 x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) b)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) b)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) b)
% Found x20:=(x2 (fun (x5:fofType)=> (P b))):((P b)->(P b))
% Found (x2 (fun (x5:fofType)=> (P b))) as proof of (P0 b)
% Found (x2 (fun (x5:fofType)=> (P b))) as proof of (P0 b)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found x20:=(x2 (fun (x5:fofType)=> (P Xz))):((P Xz)->(P Xz))
% Found (x2 (fun (x5:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found (x2 (fun (x5:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found x20:=(x2 (fun (x5:fofType)=> (P Xz))):((P Xz)->(P Xz))
% Found (x2 (fun (x5:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found (x2 (fun (x5:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found x20:=(x2 (fun (x5:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x2 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x2 (fun (x5:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x20:=(x2 (fun (x5:fofType)=> (P Xz))):((P Xz)->(P Xz))
% Found (x2 (fun (x5:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found (x2 (fun (x5:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found x20:=(x2 (fun (x5:fofType)=> (P Xz))):((P Xz)->(P Xz))
% Found (x2 (fun (x5:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found (x2 (fun (x5:fofType)=> (P Xz))) as proof of (P0 Xz)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found x3:(((eq fofType) Xz) Xu)
% Found x3 as proof of (((eq fofType) Xz) Xu)
% Found x40:(P Xy)
% Instantiate: Xx0:=Xy:fofType
% Found x40 as proof of (P0 Xx0)
% Found x40:(P0 Xy)
% Instantiate: Xx0:=Xy:fofType
% Found x40 as proof of (P Xx0)
% Found x4:(P Xy)
% Instantiate: Xx0:=Xy:fofType
% Found x4 as proof of (P0 Xx0)
% Found x4:(P Xy)
% Instantiate: Xx0:=Xy:fofType
% Found x4 as proof of (P0 Xx0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xz)
% 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 (x4:fofType)=> (P Xu))):((P Xu)->(P Xu))
% Found (x2 (fun (x4:fofType)=> (P Xu))) as proof of (P0 Xu)
% Found (x2 (fun (x4:fofType)=> (P Xu))) as proof of (P0 Xu)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) 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 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) 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 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) 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 x3:(((eq fofType) Xz) Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (((eq fofType) Xz) b)
% Found x40:(P Xy)
% Instantiate: b:=Xy:fofType
% Found x40 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) 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 x40:(P0 Xy)
% Instantiate: b:=Xy:fofType
% Found x40 as proof of (P b)
% Found x3:(((eq fofType) Xz) Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (((eq fofType) Xz) b)
% Found x3:(((eq fofType) Xz) Xu)
% Instantiate: b:=Xu:fofType
% Found x3 as proof of (((eq fofType) Xz) b)
% Found x4:(P Xy)
% Instantiate: b:=Xy:fofType
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) b)
% Found ((eq_ref fofType) Xu) as proof of (((eq fofType) Xu) 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 Xu):(((eq fofType) Xu) Xu)
% Found (eq_ref0 Xu) as proof of (((eq fofType) Xu) b)
% EOF
%------------------------------------------------------------------------------