%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU706^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n107.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 13:32:52 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  : SEU706^2 : TPTP v6.1.0. Released v3.7.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n107.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 11:15:41 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 0x834c20>, <kernel.DependentProduct object at 0x8344d0>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x9f7488>, <kernel.Single object at 0x834950>) of role type named emptyset_type
% Using role type
% Declaring emptyset:fofType
% FOF formula (<kernel.Constant object at 0x8344d0>, <kernel.DependentProduct object at 0x834830>) of role type named setadjoin_type
% Using role type
% Declaring setadjoin:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x834fc8>, <kernel.DependentProduct object at 0x834ab8>) of role type named setunion_type
% Using role type
% Declaring setunion:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x834710>, <kernel.Sort object at 0x6ffc68>) 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 0x834680>, <kernel.Sort object at 0x6ffc68>) of role type named in__Cong_type
% Using role type
% Declaring in__Cong:Prop
% FOF formula (((eq Prop) in__Cong) (forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((iff ((in Xx) A)) ((in Xy) B))))))) of role definition named in__Cong
% A new definition: (((eq Prop) in__Cong) (forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((iff ((in Xx) A)) ((in Xy) B)))))))
% Defined: in__Cong:=(forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((iff ((in Xx) A)) ((in Xy) B))))))
% FOF formula (<kernel.Constant object at 0x834fc8>, <kernel.Sort object at 0x6ffc68>) of role type named setadjoin__Cong_type
% Using role type
% Declaring setadjoin__Cong:Prop
% FOF formula (((eq Prop) setadjoin__Cong) (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->(forall (Xz:fofType) (Xu:fofType), ((((eq fofType) Xz) Xu)->(((eq fofType) ((setadjoin Xx) Xz)) ((setadjoin Xy) Xu))))))) of role definition named setadjoin__Cong
% A new definition: (((eq Prop) setadjoin__Cong) (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->(forall (Xz:fofType) (Xu:fofType), ((((eq fofType) Xz) Xu)->(((eq fofType) ((setadjoin Xx) Xz)) ((setadjoin Xy) Xu)))))))
% Defined: setadjoin__Cong:=(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->(forall (Xz:fofType) (Xu:fofType), ((((eq fofType) Xz) Xu)->(((eq fofType) ((setadjoin Xx) Xz)) ((setadjoin Xy) Xu))))))
% FOF formula (<kernel.Constant object at 0x834a70>, <kernel.Sort object at 0x6ffc68>) of role type named setunion__Cong_type
% Using role type
% Declaring setunion__Cong:Prop
% FOF formula (((eq Prop) setunion__Cong) (forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(((eq fofType) (setunion A)) (setunion B))))) of role definition named setunion__Cong
% A new definition: (((eq Prop) setunion__Cong) (forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(((eq fofType) (setunion A)) (setunion B)))))
% Defined: setunion__Cong:=(forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(((eq fofType) (setunion A)) (setunion B))))
% FOF formula (<kernel.Constant object at 0x834cb0>, <kernel.Sort object at 0x6ffc68>) of role type named setunionsingleton_type
% Using role type
% Declaring setunionsingleton:Prop
% FOF formula (((eq Prop) setunionsingleton) (forall (Xx:fofType), (((eq fofType) (setunion ((setadjoin Xx) emptyset))) Xx))) of role definition named setunionsingleton
% A new definition: (((eq Prop) setunionsingleton) (forall (Xx:fofType), (((eq fofType) (setunion ((setadjoin Xx) emptyset))) Xx)))
% Defined: setunionsingleton:=(forall (Xx:fofType), (((eq fofType) (setunion ((setadjoin Xx) emptyset))) Xx))
% FOF formula (<kernel.Constant object at 0x834998>, <kernel.DependentProduct object at 0x834dd0>) of role type named singleton_type
% Using role type
% Declaring singleton:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) singleton) (fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset))))))) of role definition named singleton
% A new definition: (((eq (fofType->Prop)) singleton) (fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset)))))))
% Defined: singleton:=(fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset))))))
% FOF formula (uniqinunit->(in__Cong->(setadjoin__Cong->(setunion__Cong->(setunionsingleton->(forall (X:fofType), ((singleton X)->(forall (Xx:fofType), (((in Xx) X)->(((eq fofType) (setunion X)) Xx)))))))))) of role conjecture named theeq
% Conjecture to prove = (uniqinunit->(in__Cong->(setadjoin__Cong->(setunion__Cong->(setunionsingleton->(forall (X:fofType), ((singleton X)->(forall (Xx:fofType), (((in Xx) X)->(((eq fofType) (setunion X)) Xx)))))))))):Prop
% We need to prove ['(uniqinunit->(in__Cong->(setadjoin__Cong->(setunion__Cong->(setunionsingleton->(forall (X:fofType), ((singleton X)->(forall (Xx:fofType), (((in Xx) X)->(((eq fofType) (setunion X)) Xx))))))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter emptyset:fofType.
% Parameter setadjoin:(fofType->(fofType->fofType)).
% Parameter setunion:(fofType->fofType).
% Definition uniqinunit:=(forall (Xx:fofType) (Xy:fofType), (((in Xx) ((setadjoin Xy) emptyset))->(((eq fofType) Xx) Xy))):Prop.
% Definition in__Cong:=(forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((iff ((in Xx) A)) ((in Xy) B)))))):Prop.
% Definition setadjoin__Cong:=(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->(forall (Xz:fofType) (Xu:fofType), ((((eq fofType) Xz) Xu)->(((eq fofType) ((setadjoin Xx) Xz)) ((setadjoin Xy) Xu)))))):Prop.
% Definition setunion__Cong:=(forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(((eq fofType) (setunion A)) (setunion B)))):Prop.
% Definition setunionsingleton:=(forall (Xx:fofType), (((eq fofType) (setunion ((setadjoin Xx) emptyset))) Xx)):Prop.
% Definition singleton:=(fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset)))))):(fofType->Prop).
% Trying to prove (uniqinunit->(in__Cong->(setadjoin__Cong->(setunion__Cong->(setunionsingleton->(forall (X:fofType), ((singleton X)->(forall (Xx:fofType), (((in Xx) X)->(((eq fofType) (setunion X)) Xx))))))))))
% Found x70:(P (setunion X))
% Found (fun (x70:(P (setunion X)))=> x70) as proof of (P (setunion X))
% Found (fun (x70:(P (setunion X)))=> x70) as proof of (P0 (setunion X))
% Found x60:(P (setunion X))
% Found (fun (x60:(P (setunion X)))=> x60) as proof of (P (setunion X))
% Found (fun (x60:(P (setunion X)))=> x60) as proof of (P0 (setunion X))
% Found eq_ref000:=(eq_ref00 P):((P (setunion X))->(P (setunion X)))
% Found (eq_ref00 P) as proof of (P0 (setunion X))
% Found ((eq_ref0 (setunion X)) P) as proof of (P0 (setunion X))
% Found (((eq_ref fofType) (setunion X)) P) as proof of (P0 (setunion X))
% Found (((eq_ref fofType) (setunion X)) P) as proof of (P0 (setunion X))
% Found eq_ref00:=(eq_ref0 (setunion X)):(((eq fofType) (setunion X)) (setunion X))
% Found (eq_ref0 (setunion X)) as proof of (((eq fofType) (setunion X)) b)
% Found ((eq_ref fofType) (setunion X)) as proof of (((eq fofType) (setunion X)) b)
% Found ((eq_ref fofType) (setunion X)) as proof of (((eq fofType) (setunion X)) b)
% Found ((eq_ref fofType) (setunion X)) as proof of (((eq fofType) (setunion X)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found x70:(P Xx)
% Found (fun (x70:(P Xx))=> x70) as proof of (P Xx)
% Found (fun (x70:(P Xx))=> x70) as proof of (P0 Xx)
% Found eq_ref000:=(eq_ref00 P):((P (setunion X))->(P (setunion X)))
% Found (eq_ref00 P) as proof of (P0 (setunion X))
% Found ((eq_ref0 (setunion X)) P) as proof of (P0 (setunion X))
% Found (((eq_ref fofType) (setunion X)) P) as proof of (P0 (setunion X))
% Found (((eq_ref fofType) (setunion X)) P) as proof of (P0 (setunion X))
% Found eq_ref00:=(eq_ref0 (setunion X)):(((eq fofType) (setunion X)) (setunion X))
% Found (eq_ref0 (setunion X)) as proof of (((eq fofType) (setunion X)) b)
% Found ((eq_ref fofType) (setunion X)) as proof of (((eq fofType) (setunion X)) b)
% Found ((eq_ref fofType) (setunion X)) as proof of (((eq fofType) (setunion X)) b)
% Found ((eq_ref fofType) (setunion X)) as proof of (((eq fofType) (setunion X)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref000:=(eq_ref00 P):((P (setunion X))->(P (setunion X)))
% Found (eq_ref00 P) as proof of (P0 (setunion X))
% Found ((eq_ref0 (setunion X)) P) as proof of (P0 (setunion X))
% Found (((eq_ref fofType) (setunion X)) P) as proof of (P0 (setunion X))
% Found (((eq_ref fofType) (setunion X)) P) as proof of (P0 (setunion X))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (setunion X))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (setunion X))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (setunion X))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (setunion X))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% Found (eq_ref00 P) as proof of (P0 Xx)
% Found ((eq_ref0 Xx) P) as proof of (P0 Xx)
% Found (((eq_ref fofType) Xx) P) as proof of (P0 Xx)
% Found (((eq_ref fofType) Xx) P) as proof of (P0 Xx)
% Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% Found (eq_ref00 P) as proof of (P0 Xx)
% Found ((eq_ref0 Xx) P) as proof of (P0 Xx)
% Found (((eq_ref fofType) Xx) P) as proof of (P0 Xx)
% Found (((eq_ref fofType) Xx) P) as proof of (P0 Xx)
% Found eq_ref000:=(eq_ref00 P):((P (setunion X))->(P (setunion X)))
% Found (eq_ref00 P) as proof of (P0 (setunion X))
% Found ((eq_ref0 (setunion X)) P) as proof of (P0 (setunion X))
% Found (((eq_ref fofType) (setunion X)) P) as proof of (P0 (setunion X))
% Found (((eq_ref fofType) (setunion X)) P) as proof of (P0 (setunion X))
% Found eq_ref00:=(eq_ref0 (setunion X)):(((eq fofType) (setunion X)) (setunion X))
% Found (eq_ref0 (setunion X)) as proof of (((eq fofType) (setunion X)) b)
% Found ((eq_ref fofType) (setunion X)) as proof of (((eq fofType) (setunion X)) b)
% Found ((eq_ref fofType) (setunion X)) as proof of (((eq fofType) (setunion X)) b)
% Found ((eq_ref fofType) (setunion X)) as proof of (((eq fofType) (setunion X)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (setunion X))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (setunion X))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (setunion X))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (setunion X))
% Found x90:=(x9 (fun (x11:fofType)=> (P Xx))):((P Xx)->(P Xx))
% Found (x9 (fun (x11:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found (x9 (fun (x11:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 A):(((eq fofType) A) A)
% Found (eq_ref0 A) as proof of (((eq fofType) A) X)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) X)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) X)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) X)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (setunion X))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (setunion X))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (setunion X))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (setunion X))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 A):(((eq fofType) A) A)
% Found (eq_ref0 A) as proof of (((eq fofType) A) X)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) X)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) X)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) X)
% Found eq_ref00:=(eq_ref0 A):(((eq fofType) A) A)
% Found (eq_ref0 A) as proof of (((eq fofType) A) X)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) X)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) X)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) X)
% Found x6:(P (setunion X))
% Instantiate: Xx0:=(setunion X):fofType
% Found x6 as proof of (P0 Xx0)
% Found x90:=(x9 (fun (x11:fofType)=> (P Xx))):((P Xx)->(P Xx))
% Found (x9 (fun (x11:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found (x9 (fun (x11:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found x90:=(x9 (fun (x11:fofType)=> (P Xx))):((P Xx)->(P Xx))
% Found (x9 (fun (x11:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found (x9 (fun (x11:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found x6:(P (setunion X))
% Instantiate: b:=(setunion X):fofType
% Found x6 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 A):(((eq fofType) A) A)
% Found (eq_ref0 A) as proof of (((eq fofType) A) X)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) X)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) X)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) X)
% Found x6:(P0 (setunion A))
% Instantiate: A:=((setadjoin Xx) emptyset):fofType
% Found x6 as proof of (P0 (setunion ((setadjoin Xx) emptyset)))
% Found (x300 x6) as proof of (P0 Xx)
% Found ((x30 P0) x6) as proof of (P0 Xx)
% Found (((x3 Xx) P0) x6) as proof of (P0 Xx)
% Found (fun (x6:(P0 (setunion A)))=> (((x3 Xx) P0) x6)) as proof of (P0 Xx)
% Found (fun (P0:(fofType->Prop)) (x6:(P0 (setunion A)))=> (((x3 Xx) P0) x6)) as proof of ((P0 (setunion A))->(P0 Xx))
% Found (fun (P0:(fofType->Prop)) (x6:(P0 (setunion A)))=> (((x3 Xx) P0) x6)) as proof of (P (setunion A))
% Found x5:(P0 (setunion A))
% Instantiate: A:=((setadjoin Xx) emptyset):fofType
% Found x5 as proof of (P0 (setunion ((setadjoin Xx) emptyset)))
% Found (x300 x5) as proof of (P0 Xx)
% Found ((x30 P0) x5) as proof of (P0 Xx)
% Found (((x3 Xx) P0) x5) as proof of (P0 Xx)
% Found (fun (x5:(P0 (setunion A)))=> (((x3 Xx) P0) x5)) as proof of (P0 Xx)
% Found (fun (P0:(fofType->Prop)) (x5:(P0 (setunion A)))=> (((x3 Xx) P0) x5)) as proof of ((P0 (setunion A))->(P0 Xx))
% Found (fun (x50:((in Xx) X)) (P0:(fofType->Prop)) (x5:(P0 (setunion A)))=> (((x3 Xx) P0) x5)) as proof of (((eq fofType) (setunion A)) Xx)
% Found x5:(P0 (setunion A))
% Instantiate: A:=((setadjoin Xx) emptyset):fofType
% Found x5 as proof of (P0 (setunion ((setadjoin Xx) emptyset)))
% Found (x300 x5) as proof of (P0 Xx)
% Found ((x30 P0) x5) as proof of (P0 Xx)
% Found (((x3 Xx) P0) x5) as proof of (P0 Xx)
% Found (fun (x5:(P0 (setunion A)))=> (((x3 Xx) P0) x5)) as proof of (P0 Xx)
% Found (fun (P0:(fofType->Prop)) (x5:(P0 (setunion A)))=> (((x3 Xx) P0) x5)) as proof of ((P0 (setunion A))->(P0 Xx))
% Found (fun (x50:((in Xx) X)) (P0:(fofType->Prop)) (x5:(P0 (setunion A)))=> (((x3 Xx) P0) x5)) as proof of (((eq fofType) (setunion A)) Xx)
% Found (fun (x50:((in Xx) X)) (P0:(fofType->Prop)) (x5:(P0 (setunion A)))=> (((x3 Xx) P0) x5)) as proof of (P (setunion A))
% Found x4:(P0 (setunion A))
% Instantiate: A:=((setadjoin Xx) emptyset):fofType
% Found x4 as proof of (P0 (setunion ((setadjoin Xx) emptyset)))
% Found (x300 x4) as proof of (P0 Xx)
% Found ((x30 P0) x4) as proof of (P0 Xx)
% Found (((x3 Xx) P0) x4) as proof of (P0 Xx)
% Found (fun (x4:(P0 (setunion A)))=> (((x3 Xx) P0) x4)) as proof of (P0 Xx)
% Found (fun (P0:(fofType->Prop)) (x4:(P0 (setunion A)))=> (((x3 Xx) P0) x4)) as proof of ((P0 (setunion A))->(P0 Xx))
% Found (fun (x50:((in Xx) X)) (P0:(fofType->Prop)) (x4:(P0 (setunion A)))=> (((x3 Xx) P0) x4)) as proof of (((eq fofType) (setunion A)) Xx)
% Found x6:(P (setunion X))
% Instantiate: A:=X:fofType
% Found x6 as proof of (P0 (setunion A))
% Found eq_ref00:=(eq_ref0 A):(((eq fofType) A) A)
% Found (eq_ref0 A) as proof of (((eq fofType) A) ((setadjoin Xx) emptyset))
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) ((setadjoin Xx) emptyset))
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) ((setadjoin Xx) emptyset))
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) ((setadjoin Xx) emptyset))
% Found x6:(P (setunion X))
% Instantiate: Xx0:=(setunion X):fofType
% Found x6 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) X)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) X)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) X)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) X)
% Found eq_ref00:=(eq_ref0 A):(((eq fofType) A) A)
% Found (eq_ref0 A) as proof of (((eq fofType) A) X)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) X)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) X)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) X)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (setunion X))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (setunion X))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (setunion X))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (setunion X))
% Found eq_ref00:=(eq_ref0 (setunion X)):(((eq fofType) (setunion X)) (setunion X))
% Found (eq_ref0 (setunion X)) as proof of (((eq fofType) (setunion X)) b)
% Found ((eq_ref fofType) (setunion X)) as proof of (((eq fofType) (setunion X)) b)
% Found ((eq_ref fofType) (setunion X)) as proof of (((eq fofType) (setunion X)) b)
% Found ((eq_ref fofType) (setunion X)) as proof of (((eq fofType) (setunion X)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 A):(((eq fofType) A) A)
% Found (eq_ref0 A) as proof of (((eq fofType) A) X)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) X)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) X)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) X)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x6:(P0 b)
% Instantiate: b:=(setunion X):fofType
% Found (fun (x6:(P0 b))=> x6) as proof of (P0 (setunion X))
% Found (fun (P0:(fofType->Prop)) (x6:(P0 b))=> x6) as proof of ((P0 b)->(P0 (setunion X)))
% Found (fun (P0:(fofType->Prop)) (x6:(P0 b))=> x6) as proof of (P b)
% Found x8:(P (setunion X))
% Instantiate: Xx0:=(setunion X):fofType
% Found x8 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) X)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) X)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) X)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) X)
% Found x6:(P Xx)
% Instantiate: b:=Xx:fofType
% Found x6 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (setunion X)):(((eq fofType) (setunion X)) (setunion X))
% Found (eq_ref0 (setunion X)) as proof of (((eq fofType) (setunion X)) b)
% Found ((eq_ref fofType) (setunion X)) as proof of (((eq fofType) (setunion X)) b)
% Found ((eq_ref fofType) (setunion X)) as proof of (((eq fofType) (setunion X)) b)
% Found ((eq_ref fofType) (setunion X)) as proof of (((eq fofType) (setunion X)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (setunion X))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (setunion X))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (setunion X))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (setunion X))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x6:(P (setunion X))
% Instantiate: Xx0:=(setunion X):fofType
% Found x6 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) (setunion X))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (setunion X))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (setunion X))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (setunion X))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x8:(P (setunion X))
% Instantiate: b:=(setunion X):fofType
% Found x8 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x6:(P Xx)
% Instantiate: Xx0:=Xx:fofType
% Found x6 as proof of (P0 Xx0)
% Found x6:(P (setunion X))
% Instantiate: b:=(setunion X):fofType
% Found x6 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 A):(((eq fofType) A) A)
% Found (eq_ref0 A) as proof of (((eq fofType) A) X)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) X)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) X)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) X)
% Found eq_ref00:=(eq_ref0 A):(((eq fofType) A) A)
% Found (eq_ref0 A) as proof of (((eq fofType) A) X)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) X)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) X)
% Found ((eq_ref fofType) A) as proof of (((eq fofType) A) X)
% Found eq_ref00:=(eq_ref0 A):(((eq fofType) A) A)
% Found (eq_ref0 A) as
% EOF
%------------------------------------------------------------------------------