%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU634^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n090.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 13:32:40 EDT 2014

% Result   : Timeout 300.01s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU634^2 : TPTP v6.1.0. Released v3.7.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n090.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 10:58:26 CDT 2014
% % CPUTime  : 300.01 
% 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 0x21f4a70>, <kernel.DependentProduct object at 0x21f4c20>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x2013a70>, <kernel.Single object at 0x21f4320>) of role type named emptyset_type
% Using role type
% Declaring emptyset:fofType
% FOF formula (<kernel.Constant object at 0x21f4c20>, <kernel.DependentProduct object at 0x21f4998>) of role type named setadjoin_type
% Using role type
% Declaring setadjoin:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x21f4248>, <kernel.DependentProduct object at 0x21f42d8>) of role type named setunion_type
% Using role type
% Declaring setunion:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x21f4050>, <kernel.Sort object at 0x1edb908>) 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 0x21f4e18>, <kernel.DependentProduct object at 0x21f4c20>) of role type named subset_type
% Using role type
% Declaring subset:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x21f4248>, <kernel.Sort object at 0x1edb908>) of role type named subsetI2_type
% Using role type
% Declaring subsetI2:Prop
% FOF formula (((eq Prop) subsetI2) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((subset A) B)))) of role definition named subsetI2
% A new definition: (((eq Prop) subsetI2) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((subset A) B))))
% Defined: subsetI2:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((subset A) B)))
% FOF formula (<kernel.Constant object at 0x21f4050>, <kernel.Sort object at 0x1edb908>) of role type named setunionE2_type
% Using role type
% Declaring setunionE2:Prop
% FOF formula (((eq Prop) setunionE2) (forall (A:fofType) (Xx:fofType), (((in Xx) (setunion A))->((ex fofType) (fun (X:fofType)=> ((and ((in X) A)) ((in Xx) X))))))) of role definition named setunionE2
% A new definition: (((eq Prop) setunionE2) (forall (A:fofType) (Xx:fofType), (((in Xx) (setunion A))->((ex fofType) (fun (X:fofType)=> ((and ((in X) A)) ((in Xx) X)))))))
% Defined: setunionE2:=(forall (A:fofType) (Xx:fofType), (((in Xx) (setunion A))->((ex fofType) (fun (X:fofType)=> ((and ((in X) A)) ((in Xx) X))))))
% FOF formula (uniqinunit->(subsetI2->(setunionE2->(forall (A:fofType), ((subset (setunion ((setadjoin A) emptyset))) A))))) of role conjecture named setunionsingleton1
% Conjecture to prove = (uniqinunit->(subsetI2->(setunionE2->(forall (A:fofType), ((subset (setunion ((setadjoin A) emptyset))) A))))):Prop
% We need to prove ['(uniqinunit->(subsetI2->(setunionE2->(forall (A:fofType), ((subset (setunion ((setadjoin A) emptyset))) A)))))']
% 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.
% Parameter subset:(fofType->(fofType->Prop)).
% Definition subsetI2:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((subset A) B))):Prop.
% Definition setunionE2:=(forall (A:fofType) (Xx:fofType), (((in Xx) (setunion A))->((ex fofType) (fun (X:fofType)=> ((and ((in X) A)) ((in Xx) X)))))):Prop.
% Trying to prove (uniqinunit->(subsetI2->(setunionE2->(forall (A:fofType), ((subset (setunion ((setadjoin A) emptyset))) A)))))
% Found x2:((in Xx) (setunion ((setadjoin A) emptyset)))
% Instantiate: Xx0:=(setunion ((setadjoin A) emptyset)):fofType
% Found x2 as proof of (P Xx0)
% Found x30:((in Xx0) (setunion ((setadjoin Xx) emptyset)))
% Found (fun (x30:((in Xx0) (setunion ((setadjoin Xx) emptyset))))=> x30) as proof of ((in Xx0) (setunion ((setadjoin Xx) emptyset)))
% Found (fun (x30:((in Xx0) (setunion ((setadjoin Xx) emptyset))))=> x30) as proof of (P0 (setunion ((setadjoin Xx) emptyset)))
% Found x2:((in Xx) (setunion ((setadjoin A) emptyset)))
% Instantiate: Xx1:=(setunion ((setadjoin A) emptyset)):fofType;Xx0:=Xx:fofType
% Found x2 as proof of (P0 Xx1)
% Found x30:((in Xx0) (setunion ((setadjoin Xx) emptyset)))
% Found (fun (x30:((in Xx0) (setunion ((setadjoin Xx) emptyset))))=> x30) as proof of ((in Xx0) (setunion ((setadjoin Xx) emptyset)))
% Found (fun (x30:((in Xx0) (setunion ((setadjoin Xx) emptyset))))=> x30) as proof of (P0 (setunion ((setadjoin Xx) emptyset)))
% Found x3:((in Xx0) (setunion ((setadjoin Xx) emptyset)))
% Instantiate: Xx1:=(setunion ((setadjoin Xx) emptyset)):fofType
% Found x3 as proof of (P0 Xx1)
% Found x3:((in Xx0) (setunion ((setadjoin Xx) emptyset)))
% Instantiate: Xx1:=(setunion ((setadjoin Xx) emptyset)):fofType
% Found x3 as proof of (P0 Xx1)
% Found x40:((in Xx1) (setunion ((setadjoin Xx0) emptyset)))
% Found (fun (x40:((in Xx1) (setunion ((setadjoin Xx0) emptyset))))=> x40) as proof of ((in Xx1) (setunion ((setadjoin Xx0) emptyset)))
% Found (fun (x40:((in Xx1) (setunion ((setadjoin Xx0) emptyset))))=> x40) as proof of (P1 (setunion ((setadjoin Xx0) emptyset)))
% Found x40:((in Xx1) (setunion ((setadjoin Xx0) emptyset)))
% Found (fun (x40:((in Xx1) (setunion ((setadjoin Xx0) emptyset))))=> x40) as proof of ((in Xx1) (setunion ((setadjoin Xx0) emptyset)))
% Found (fun (x40:((in Xx1) (setunion ((setadjoin Xx0) emptyset))))=> x40) as proof of (P1 (setunion ((setadjoin Xx0) emptyset)))
% Found x40:((in Xx1) (setunion ((setadjoin Xx0) emptyset)))
% Found (fun (x40:((in Xx1) (setunion ((setadjoin Xx0) emptyset))))=> x40) as proof of ((in Xx1) (setunion ((setadjoin Xx0) emptyset)))
% Found (fun (x40:((in Xx1) (setunion ((setadjoin Xx0) emptyset))))=> x40) as proof of (P1 (setunion ((setadjoin Xx0) emptyset)))
% Found x40:((in Xx1) (setunion ((setadjoin Xx0) emptyset)))
% Found (fun (x40:((in Xx1) (setunion ((setadjoin Xx0) emptyset))))=> x40) as proof of ((in Xx1) (setunion ((setadjoin Xx0) emptyset)))
% Found (fun (x40:((in Xx1) (setunion ((setadjoin Xx0) emptyset))))=> x40) as proof of (P1 (setunion ((setadjoin Xx0) emptyset)))
% Found x40:((in Xx1) (setunion ((setadjoin Xx0) emptyset)))
% Found (fun (x40:((in Xx1) (setunion ((setadjoin Xx0) emptyset))))=> x40) as proof of ((in Xx1) (setunion ((setadjoin Xx0) emptyset)))
% Found (fun (x40:((in Xx1) (setunion ((setadjoin Xx0) emptyset))))=> x40) as proof of (P1 (setunion ((setadjoin Xx0) emptyset)))
% Found x40:((in Xx1) (setunion ((setadjoin Xx0) emptyset)))
% Found (fun (x40:((in Xx1) (setunion ((setadjoin Xx0) emptyset))))=> x40) as proof of ((in Xx1) (setunion ((setadjoin Xx0) emptyset)))
% Found (fun (x40:((in Xx1) (setunion ((setadjoin Xx0) emptyset))))=> x40) as proof of (P1 (setunion ((setadjoin Xx0) emptyset)))
% Found x2:((in Xx) (setunion ((setadjoin A) emptyset)))
% Instantiate: Xx2:=(setunion ((setadjoin A) emptyset)):fofType;Xx1:=Xx:fofType
% Found x2 as proof of (P1 Xx2)
% Found x2:((in Xx) (setunion ((setadjoin A) emptyset)))
% Instantiate: Xx2:=(setunion ((setadjoin A) emptyset)):fofType;Xx1:=Xx:fofType
% Found x2 as proof of (P1 Xx2)
% Found x2:((in Xx) (setunion ((setadjoin A) emptyset)))
% Instantiate: Xx1:=(setunion ((setadjoin A) emptyset)):fofType;Xx00:=Xx:fofType
% Found x2 as proof of (P1 Xx1)
% Found x2:((in Xx) (setunion ((setadjoin A) emptyset)))
% Instantiate: Xx1:=(setunion ((setadjoin A) emptyset)):fofType;Xx00:=Xx:fofType
% Found x2 as proof of (P1 Xx1)
% Found x3:((in Xx0) (setunion ((setadjoin Xx) emptyset)))
% Instantiate: Xx2:=(setunion ((setadjoin Xx) emptyset)):fofType;Xx1:=Xx0:fofType
% Found x3 as proof of (P1 Xx2)
% Found x40:((in Xx1) (setunion ((setadjoin Xx0) emptyset)))
% Found (fun (x40:((in Xx1) (setunion ((setadjoin Xx0) emptyset))))=> x40) as proof of ((in Xx1) (setunion ((setadjoin Xx0) emptyset)))
% Found (fun (x40:((in Xx1) (setunion ((setadjoin Xx0) emptyset))))=> x40) as proof of (P1 (setunion ((setadjoin Xx0) emptyset)))
% Found x40:((in Xx1) (setunion ((setadjoin Xx0) emptyset)))
% Found (fun (x40:((in Xx1) (setunion ((setadjoin Xx0) emptyset))))=> x40) as proof of ((in Xx1) (setunion ((setadjoin Xx0) emptyset)))
% Found (fun (x40:((in Xx1) (setunion ((setadjoin Xx0) emptyset))))=> x40) as proof of (P1 (setunion ((setadjoin Xx0) emptyset)))
% Found x4:((in Xx1) (setunion ((setadjoin Xx0) emptyset)))
% Instantiate: Xx2:=(setunion ((setadjoin Xx0) emptyset)):fofType
% Found x4 as proof of (P1 Xx2)
% Found x2:((in Xx) (setunion ((setadjoin A) emptyset)))
% Instantiate: Xx1:=(setunion ((setadjoin A) emptyset)):fofType;Xx0:=Xx:fofType
% Found x2 as proof of (P1 Xx1)
% Found x3:((in Xx0) (setunion ((setadjoin Xx) emptyset)))
% Instantiate: Xx2:=(setunion ((setadjoin Xx) emptyset)):fofType;Xx1:=Xx0:fofType
% Found x3 as proof of (P1 Xx2)
% Found x4:((in Xx1) (setunion ((setadjoin Xx0) emptyset)))
% Instantiate: Xx2:=(setunion ((setadjoin Xx0) emptyset)):fofType
% Found x4 as proof of (P1 Xx2)
% Found x4:((in Xx1) (setunion ((setadjoin Xx0) emptyset)))
% Instantiate: Xx2:=(setunion ((setadjoin Xx0) emptyset)):fofType
% Found x4 as proof of (P1 Xx2)
% Found x4:((in Xx1) (setunion ((setadjoin Xx0) emptyset)))
% Instantiate: Xx2:=(setunion ((setadjoin Xx0) emptyset)):fofType
% Found x4 as proof of (P1 Xx2)
% Found x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of ((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of (P2 (setunion ((setadjoin Xx1) emptyset)))
% Found x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of ((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of (P2 (setunion ((setadjoin Xx1) emptyset)))
% Found x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of ((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of (P2 (setunion ((setadjoin Xx1) emptyset)))
% Found x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of ((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of (P2 (setunion ((setadjoin Xx1) emptyset)))
% Found x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of ((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of (P2 (setunion ((setadjoin Xx1) emptyset)))
% Found x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of ((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of (P2 (setunion ((setadjoin Xx1) emptyset)))
% Found x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of ((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of (P2 (setunion ((setadjoin Xx1) emptyset)))
% Found x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of ((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of (P2 (setunion ((setadjoin Xx1) emptyset)))
% Found x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of ((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of (P2 (setunion ((setadjoin Xx1) emptyset)))
% Found x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of ((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of (P2 (setunion ((setadjoin Xx1) emptyset)))
% Found x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of ((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of (P2 (setunion ((setadjoin Xx1) emptyset)))
% Found x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of ((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of (P2 (setunion ((setadjoin Xx1) emptyset)))
% Found x2:((in Xx) (setunion ((setadjoin A) emptyset)))
% Instantiate: Xx3:=(setunion ((setadjoin A) emptyset)):fofType;Xx2:=Xx:fofType
% Found x2 as proof of (P2 Xx3)
% Found x2:((in Xx) (setunion ((setadjoin A) emptyset)))
% Instantiate: Xx3:=(setunion ((setadjoin A) emptyset)):fofType;Xx2:=Xx:fofType
% Found x2 as proof of (P2 Xx3)
% Found x2:((in Xx) (setunion ((setadjoin A) emptyset)))
% Instantiate: Xx2:=(setunion ((setadjoin A) emptyset)):fofType;Xx10:=Xx:fofType
% Found x2 as proof of (P2 Xx2)
% Found x2:((in Xx) (setunion ((setadjoin A) emptyset)))
% Instantiate: Xx00:=Xx:fofType;Xx10:=(setunion ((setadjoin A) emptyset)):fofType
% Found x2 as proof of (P2 Xx10)
% Found x2:((in Xx) (setunion ((setadjoin A) emptyset)))
% Instantiate: Xx2:=(setunion ((setadjoin A) emptyset)):fofType;Xx10:=Xx:fofType
% Found x2 as proof of (P2 Xx2)
% Found x2:((in Xx) (setunion ((setadjoin A) emptyset)))
% Instantiate: Xx00:=Xx:fofType;Xx10:=(setunion ((setadjoin A) emptyset)):fofType
% Found x2 as proof of (P2 Xx10)
% Found x2:((in Xx) (setunion ((setadjoin A) emptyset)))
% Instantiate: Xx3:=(setunion ((setadjoin A) emptyset)):fofType;Xx2:=Xx:fofType
% Found x2 as proof of (P2 Xx3)
% Found x2:((in Xx) (setunion ((setadjoin A) emptyset)))
% Instantiate: Xx2:=(setunion ((setadjoin A) emptyset)):fofType;Xx1:=Xx:fofType
% Found x2 as proof of (P2 Xx2)
% Found x2:((in Xx) (setunion ((setadjoin A) emptyset)))
% Instantiate: Xx2:=(setunion ((setadjoin A) emptyset)):fofType;Xx1:=Xx:fofType
% Found x2 as proof of (P2 Xx2)
% Found x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of ((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of (P2 (setunion ((setadjoin Xx1) emptyset)))
% Found x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of ((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of (P2 (setunion ((setadjoin Xx1) emptyset)))
% Found x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of ((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of (P2 (setunion ((setadjoin Xx1) emptyset)))
% Found x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of ((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of (P2 (setunion ((setadjoin Xx1) emptyset)))
% Found x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of ((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of (P2 (setunion ((setadjoin Xx1) emptyset)))
% Found x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of ((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of (P2 (setunion ((setadjoin Xx1) emptyset)))
% Found x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of ((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of (P2 (setunion ((setadjoin Xx1) emptyset)))
% Found x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of ((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of (P2 (setunion ((setadjoin Xx1) emptyset)))
% Found x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of ((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of (P2 (setunion ((setadjoin Xx1) emptyset)))
% Found x2:((in Xx) (setunion ((setadjoin A) emptyset)))
% Instantiate: Xx00:=Xx:fofType;Xx10:=(setunion ((setadjoin A) emptyset)):fofType
% Found x2 as proof of (P2 Xx10)
% Found x2:((in Xx) (setunion ((setadjoin A) emptyset)))
% Instantiate: Xx3:=(setunion ((setadjoin A) emptyset)):fofType;Xx2:=Xx:fofType
% Found x2 as proof of (P2 Xx3)
% Found x2:((in Xx) (setunion ((setadjoin A) emptyset)))
% Instantiate: Xx2:=(setunion ((setadjoin A) emptyset)):fofType;Xx10:=Xx:fofType
% Found x2 as proof of (P2 Xx2)
% Found x2:((in Xx) (setunion ((setadjoin A) emptyset)))
% Instantiate: Xx1:=(setunion ((setadjoin A) emptyset)):fofType;Xx01:=Xx:fofType
% Found x2 as proof of (P2 Xx1)
% Found x2:((in Xx) (setunion ((setadjoin A) emptyset)))
% Instantiate: Xx1:=(setunion ((setadjoin A) emptyset)):fofType;Xx01:=Xx:fofType
% Found x2 as proof of (P2 Xx1)
% Found x3:((in Xx0) (setunion ((setadjoin Xx) emptyset)))
% Instantiate: Xx3:=(setunion ((setadjoin Xx) emptyset)):fofType;Xx2:=Xx0:fofType
% Found x3 as proof of (P2 Xx3)
% Found x3:((in Xx0) (setunion ((setadjoin Xx) emptyset)))
% Instantiate: Xx2:=(setunion ((setadjoin Xx) emptyset)):fofType;Xx10:=Xx0:fofType
% Found x3 as proof of (P2 Xx2)
% Found x3:((in Xx0) (setunion ((setadjoin Xx) emptyset)))
% Instantiate: Xx3:=(setunion ((setadjoin Xx) emptyset)):fofType;Xx2:=Xx0:fofType
% Found x3 as proof of (P2 Xx3)
% Found x3:((in Xx0) (setunion ((setadjoin Xx) emptyset)))
% Instantiate: Xx2:=(setunion ((setadjoin Xx) emptyset)):fofType;Xx10:=Xx0:fofType
% Found x3 as proof of (P2 Xx2)
% Found x2:((in Xx) (setunion ((setadjoin A) emptyset)))
% Instantiate: Xx2:=(setunion ((setadjoin A) emptyset)):fofType;Xx1:=Xx:fofType
% Found x2 as proof of (P2 Xx2)
% Found x2:((in Xx) (setunion ((setadjoin A) emptyset)))
% Instantiate: Xx2:=(setunion ((setadjoin A) emptyset)):fofType;Xx1:=Xx:fofType
% Found x2 as proof of (P2 Xx2)
% Found x4:((in Xx1) (setunion ((setadjoin Xx0) emptyset)))
% Instantiate: Xx3:=(setunion ((setadjoin Xx0) emptyset)):fofType;Xx2:=Xx1:fofType
% Found x4 as proof of (P2 Xx3)
% Found x2:((in Xx) (setunion ((setadjoin A) emptyset)))
% Instantiate: Xx2:=(setunion ((setadjoin A) emptyset)):fofType;Xx1:=Xx:fofType
% Found x2 as proof of (P2 Xx2)
% Found x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of ((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of (P2 (setunion ((setadjoin Xx1) emptyset)))
% Found x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of ((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of (P2 (setunion ((setadjoin Xx1) emptyset)))
% Found x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of ((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Found (fun (x50:((in Xx2) (setunion ((setadjoin Xx1) emptyset))))=> x50) as proof of (P2 (setunion ((setadjoin Xx1) emptyset)))
% Found x2:((in Xx) (setunion ((setadjoin A) emptyset)))
% Instantiate: Xx3:=(setunion ((setadjoin A) emptyset)):fofType;Xx2:=Xx:fofType
% Found x2 as proof of (P2 Xx3)
% Found x2:((in Xx) (setunion ((setadjoin A) emptyset)))
% Instantiate: Xx2:=(setunion ((setadjoin A) emptyset)):fofType;Xx1:=Xx:fofType
% Found x2 as proof of (P2 Xx2)
% Found x2:((in Xx) (setunion ((setadjoin A) emptyset)))
% Instantiate: Xx2:=(setunion ((setadjoin A) emptyset)):fofType;Xx1:=Xx:fofType
% Found x2 as proof of (P2 Xx2)
% Found x5:((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Instantiate: Xx3:=(setunion ((setadjoin Xx1) emptyset)):fofType
% Found x5 as proof of (P2 Xx3)
% Found x2:((in Xx) (setunion ((setadjoin A) emptyset)))
% Instantiate: Xx1:=(setunion ((setadjoin A) emptyset)):fofType;Xx00:=Xx:fofType
% Found x2 as proof of (P2 Xx1)
% Found x2:((in Xx) (setunion ((setadjoin A) emptyset)))
% Instantiate: Xx2:=(setunion ((setadjoin A) emptyset)):fofType;Xx1:=Xx:fofType
% Found x2 as proof of (P2 Xx2)
% Found x2:((in Xx) (setunion ((setadjoin A) emptyset)))
% Instantiate: Xx1:=(setunion ((setadjoin A) emptyset)):fofType;Xx00:=Xx:fofType
% Found x2 as proof of (P2 Xx1)
% Found x3:((in Xx0) (setunion ((setadjoin Xx) emptyset)))
% Instantiate: Xx3:=(setunion ((setadjoin Xx) emptyset)):fofType;Xx2:=Xx0:fofType
% Found x3 as proof of (P2 Xx3)
% Found x3:((in Xx0) (setunion ((setadjoin Xx) emptyset)))
% Instantiate: Xx2:=(setunion ((setadjoin Xx) emptyset)):fofType;Xx10:=Xx0:fofType
% Found x3 as proof of (P2 Xx2)
% Found x3:((in Xx0) (setunion ((setadjoin Xx) emptyset)))
% Instantiate: Xx3:=(setunion ((setadjoin Xx) emptyset)):fofType;Xx2:=Xx0:fofType
% Found x3 as proof of (P2 Xx3)
% Found x3:((in Xx0) (setunion ((setadjoin Xx) emptyset)))
% Instantiate: Xx2:=(setunion ((setadjoin Xx) emptyset)):fofType;Xx1:=Xx0:fofType
% Found x3 as proof of (P2 Xx2)
% Found x3:((in Xx0) (setunion ((setadjoin Xx) emptyset)))
% Instantiate: Xx2:=(setunion ((setadjoin Xx) emptyset)):fofType;Xx10:=Xx0:fofType
% Found x3 as proof of (P2 Xx2)
% Found x4:((in Xx1) (setunion ((setadjoin Xx0) emptyset)))
% Instantiate: Xx3:=(setunion ((setadjoin Xx0) emptyset)):fofType;Xx2:=Xx1:fofType
% Found x4 as proof of (P2 Xx3)
% Found x4:((in Xx1) (setunion ((setadjoin Xx0) emptyset)))
% Instantiate: Xx3:=(setunion ((setadjoin Xx0) emptyset)):fofType;Xx2:=Xx1:fofType
% Found x4 as proof of (P2 Xx3)
% Found x5:((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Instantiate: Xx3:=(setunion ((setadjoin Xx1) emptyset)):fofType
% Found x5 as proof of (P2 Xx3)
% Found x5:((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Instantiate: Xx3:=(setunion ((setadjoin Xx1) emptyset)):fofType
% Found x5 as proof of (P2 Xx3)
% Found x5:((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Instantiate: Xx3:=(setunion ((setadjoin Xx1) emptyset)):fofType
% Found x5 as proof of (P2 Xx3)
% Found x3:((in Xx0) (setunion ((setadjoin Xx) emptyset)))
% Instantiate: Xx2:=(setunion ((setadjoin Xx) emptyset)):fofType;Xx1:=Xx0:fofType
% Found x3 as proof of (P2 Xx2)
% Found x4:((in Xx1) (setunion ((setadjoin Xx0) emptyset)))
% Instantiate: Xx3:=(setunion ((setadjoin Xx0) emptyset)):fofType;Xx2:=Xx1:fofType
% Found x4 as proof of (P2 Xx3)
% Found x5:((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Instantiate: Xx3:=(setunion ((setadjoin Xx1) emptyset)):fofType
% Found x5 as proof of (P2 Xx3)
% Found x5:((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Instantiate: Xx3:=(setunion ((setadjoin Xx1) emptyset)):fofType
% Found x5 as proof of (P2 Xx3)
% Found x5:((in Xx2) (setunion ((setadjoin Xx1) emptyset)))
% Instantiate: Xx3:=(setunion ((setadjoin Xx1) emptyset)):fofType
% Found x5 as proof of (P2 Xx3)
% EOF
%------------------------------------------------------------------------------