%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU630^1 : 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 13:32:39 EDT 2014

% Result   : Timeout 300.07s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU630^1 : 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 10:57:31 CDT 2014
% % CPUTime  : 300.07 
% 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 0xd70ab8>, <kernel.DependentProduct object at 0xd708c0>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xd70ef0>, <kernel.DependentProduct object at 0xd70dd0>) of role type named exu_type
% Using role type
% Declaring exu:((fofType->Prop)->Prop)
% FOF formula (((eq ((fofType->Prop)->Prop)) exu) (fun (Xphi:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy)))))))) of role definition named exu
% A new definition: (((eq ((fofType->Prop)->Prop)) exu) (fun (Xphi:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy))))))))
% Defined: exu:=(fun (Xphi:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy)))))))
% FOF formula (<kernel.Constant object at 0xd70dd0>, <kernel.Sort object at 0x101e098>) of role type named setextAx_type
% Using role type
% Declaring setextAx:Prop
% FOF formula (((eq Prop) setextAx) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), ((iff ((in Xx) A)) ((in Xx) B)))->(((eq fofType) A) B)))) of role definition named setextAx
% A new definition: (((eq Prop) setextAx) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), ((iff ((in Xx) A)) ((in Xx) B)))->(((eq fofType) A) B))))
% Defined: setextAx:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), ((iff ((in Xx) A)) ((in Xx) B)))->(((eq fofType) A) B)))
% FOF formula (<kernel.Constant object at 0xc4f7a0>, <kernel.Single object at 0xd70830>) of role type named emptyset_type
% Using role type
% Declaring emptyset:fofType
% FOF formula (<kernel.Constant object at 0xc4fef0>, <kernel.Sort object at 0x101e098>) of role type named emptysetAx_type
% Using role type
% Declaring emptysetAx:Prop
% FOF formula (((eq Prop) emptysetAx) (forall (Xx:fofType), (((in Xx) emptyset)->False))) of role definition named emptysetAx
% A new definition: (((eq Prop) emptysetAx) (forall (Xx:fofType), (((in Xx) emptyset)->False)))
% Defined: emptysetAx:=(forall (Xx:fofType), (((in Xx) emptyset)->False))
% FOF formula (<kernel.Constant object at 0xd70ab8>, <kernel.DependentProduct object at 0xd70488>) of role type named setadjoin_type
% Using role type
% Declaring setadjoin:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0xd704d0>, <kernel.Sort object at 0x101e098>) of role type named setadjoinAx_type
% Using role type
% Declaring setadjoinAx:Prop
% FOF formula (((eq Prop) setadjoinAx) (forall (Xx:fofType) (A:fofType) (Xy:fofType), ((iff ((in Xy) ((setadjoin Xx) A))) ((or (((eq fofType) Xy) Xx)) ((in Xy) A))))) of role definition named setadjoinAx
% A new definition: (((eq Prop) setadjoinAx) (forall (Xx:fofType) (A:fofType) (Xy:fofType), ((iff ((in Xy) ((setadjoin Xx) A))) ((or (((eq fofType) Xy) Xx)) ((in Xy) A)))))
% Defined: setadjoinAx:=(forall (Xx:fofType) (A:fofType) (Xy:fofType), ((iff ((in Xy) ((setadjoin Xx) A))) ((or (((eq fofType) Xy) Xx)) ((in Xy) A))))
% FOF formula (<kernel.Constant object at 0xd70dd0>, <kernel.DependentProduct object at 0xd70c20>) of role type named powerset_type
% Using role type
% Declaring powerset:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0xd70b48>, <kernel.Sort object at 0x101e098>) of role type named powersetAx_type
% Using role type
% Declaring powersetAx:Prop
% FOF formula (((eq Prop) powersetAx) (forall (A:fofType) (B:fofType), ((iff ((in B) (powerset A))) (forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))))) of role definition named powersetAx
% A new definition: (((eq Prop) powersetAx) (forall (A:fofType) (B:fofType), ((iff ((in B) (powerset A))) (forall (Xx:fofType), (((in Xx) B)->((in Xx) A))))))
% Defined: powersetAx:=(forall (A:fofType) (B:fofType), ((iff ((in B) (powerset A))) (forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))))
% FOF formula (<kernel.Constant object at 0xc537a0>, <kernel.DependentProduct object at 0xd70cb0>) of role type named setunion_type
% Using role type
% Declaring setunion:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0xd70758>, <kernel.Sort object at 0x101e098>) of role type named setunionAx_type
% Using role type
% Declaring setunionAx:Prop
% FOF formula (((eq Prop) setunionAx) (forall (A:fofType) (Xx:fofType), ((iff ((in Xx) (setunion A))) ((ex fofType) (fun (B:fofType)=> ((and ((in Xx) B)) ((in B) A))))))) of role definition named setunionAx
% A new definition: (((eq Prop) setunionAx) (forall (A:fofType) (Xx:fofType), ((iff ((in Xx) (setunion A))) ((ex fofType) (fun (B:fofType)=> ((and ((in Xx) B)) ((in B) A)))))))
% Defined: setunionAx:=(forall (A:fofType) (Xx:fofType), ((iff ((in Xx) (setunion A))) ((ex fofType) (fun (B:fofType)=> ((and ((in Xx) B)) ((in B) A))))))
% FOF formula (<kernel.Constant object at 0xd70c20>, <kernel.Single object at 0xd70758>) of role type named omega_type
% Using role type
% Declaring omega:fofType
% FOF formula (<kernel.Constant object at 0xd70368>, <kernel.Sort object at 0x101e098>) of role type named omega0Ax_type
% Using role type
% Declaring omega0Ax:Prop
% FOF formula (((eq Prop) omega0Ax) ((in emptyset) omega)) of role definition named omega0Ax
% A new definition: (((eq Prop) omega0Ax) ((in emptyset) omega))
% Defined: omega0Ax:=((in emptyset) omega)
% FOF formula (<kernel.Constant object at 0xd70dd0>, <kernel.Sort object at 0x101e098>) of role type named omegaSAx_type
% Using role type
% Declaring omegaSAx:Prop
% FOF formula (((eq Prop) omegaSAx) (forall (Xx:fofType), (((in Xx) omega)->((in ((setadjoin Xx) Xx)) omega)))) of role definition named omegaSAx
% A new definition: (((eq Prop) omegaSAx) (forall (Xx:fofType), (((in Xx) omega)->((in ((setadjoin Xx) Xx)) omega))))
% Defined: omegaSAx:=(forall (Xx:fofType), (((in Xx) omega)->((in ((setadjoin Xx) Xx)) omega)))
% FOF formula (<kernel.Constant object at 0xd70dd0>, <kernel.Sort object at 0x101e098>) of role type named omegaIndAx_type
% Using role type
% Declaring omegaIndAx:Prop
% FOF formula (((eq Prop) omegaIndAx) (forall (A:fofType), (((and ((in emptyset) A)) (forall (Xx:fofType), (((and ((in Xx) omega)) ((in Xx) A))->((in ((setadjoin Xx) Xx)) A))))->(forall (Xx:fofType), (((in Xx) omega)->((in Xx) A)))))) of role definition named omegaIndAx
% A new definition: (((eq Prop) omegaIndAx) (forall (A:fofType), (((and ((in emptyset) A)) (forall (Xx:fofType), (((and ((in Xx) omega)) ((in Xx) A))->((in ((setadjoin Xx) Xx)) A))))->(forall (Xx:fofType), (((in Xx) omega)->((in Xx) A))))))
% Defined: omegaIndAx:=(forall (A:fofType), (((and ((in emptyset) A)) (forall (Xx:fofType), (((and ((in Xx) omega)) ((in Xx) A))->((in ((setadjoin Xx) Xx)) A))))->(forall (Xx:fofType), (((in Xx) omega)->((in Xx) A)))))
% FOF formula (<kernel.Constant object at 0xd70dd0>, <kernel.Sort object at 0x101e098>) of role type named replAx_type
% Using role type
% Declaring replAx:Prop
% FOF formula (((eq Prop) replAx) (forall (Xphi:(fofType->(fofType->Prop))) (A:fofType), ((forall (Xx:fofType), (((in Xx) A)->(exu (fun (Xy:fofType)=> ((Xphi Xx) Xy)))))->((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) ((Xphi Xy) Xx))))))))))) of role definition named replAx
% A new definition: (((eq Prop) replAx) (forall (Xphi:(fofType->(fofType->Prop))) (A:fofType), ((forall (Xx:fofType), (((in Xx) A)->(exu (fun (Xy:fofType)=> ((Xphi Xx) Xy)))))->((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) ((Xphi Xy) Xx)))))))))))
% Defined: replAx:=(forall (Xphi:(fofType->(fofType->Prop))) (A:fofType), ((forall (Xx:fofType), (((in Xx) A)->(exu (fun (Xy:fofType)=> ((Xphi Xx) Xy)))))->((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) ((Xphi Xy) Xx))))))))))
% FOF formula (<kernel.Constant object at 0xf6d0e0>, <kernel.Sort object at 0x101e098>) of role type named foundationAx_type
% Using role type
% Declaring foundationAx:Prop
% FOF formula (((eq Prop) foundationAx) (forall (A:fofType), (((ex fofType) (fun (Xx:fofType)=> ((in Xx) A)))->((ex fofType) (fun (B:fofType)=> ((and ((in B) A)) (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) B)) ((in Xx) A))))->False))))))) of role definition named foundationAx
% A new definition: (((eq Prop) foundationAx) (forall (A:fofType), (((ex fofType) (fun (Xx:fofType)=> ((in Xx) A)))->((ex fofType) (fun (B:fofType)=> ((and ((in B) A)) (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) B)) ((in Xx) A))))->False)))))))
% Defined: foundationAx:=(forall (A:fofType), (((ex fofType) (fun (Xx:fofType)=> ((in Xx) A)))->((ex fofType) (fun (B:fofType)=> ((and ((in B) A)) (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) B)) ((in Xx) A))))->False))))))
% FOF formula (<kernel.Constant object at 0xf6d4d0>, <kernel.Sort object at 0x101e098>) of role type named wellorderingAx_type
% Using role type
% Declaring wellorderingAx:Prop
% FOF formula (((eq Prop) wellorderingAx) (forall (A:fofType), ((ex fofType) (fun (B:fofType)=> ((and ((and ((and (forall (C:fofType), (((in C) B)->(forall (Xx:fofType), (((in Xx) C)->((in Xx) A)))))) (forall (Xx:fofType) (Xy:fofType), (((and ((in Xx) A)) ((in Xy) A))->((forall (C:fofType), (((in C) B)->((iff ((in Xx) C)) ((in Xy) C))))->(((eq fofType) Xx) Xy)))))) (forall (C:fofType) (D:fofType), (((and ((in C) B)) ((in D) B))->((or (forall (Xx:fofType), (((in Xx) C)->((in Xx) D)))) (forall (Xx:fofType), (((in Xx) D)->((in Xx) C)))))))) (forall (C:fofType), (((and (forall (Xx:fofType), (((in Xx) C)->((in Xx) A)))) ((ex fofType) (fun (Xx:fofType)=> ((in Xx) C))))->((ex fofType) (fun (D:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((and ((and ((in D) B)) ((in Xx) C))) (((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) D)) ((in Xy) C))))->False))) (forall (E:fofType), (((in E) B)->((or (forall (Xy:fofType), (((in Xy) E)->((in Xy) D)))) ((in Xx) E)))))))))))))))) of role definition named wellorderingAx
% A new definition: (((eq Prop) wellorderingAx) (forall (A:fofType), ((ex fofType) (fun (B:fofType)=> ((and ((and ((and (forall (C:fofType), (((in C) B)->(forall (Xx:fofType), (((in Xx) C)->((in Xx) A)))))) (forall (Xx:fofType) (Xy:fofType), (((and ((in Xx) A)) ((in Xy) A))->((forall (C:fofType), (((in C) B)->((iff ((in Xx) C)) ((in Xy) C))))->(((eq fofType) Xx) Xy)))))) (forall (C:fofType) (D:fofType), (((and ((in C) B)) ((in D) B))->((or (forall (Xx:fofType), (((in Xx) C)->((in Xx) D)))) (forall (Xx:fofType), (((in Xx) D)->((in Xx) C)))))))) (forall (C:fofType), (((and (forall (Xx:fofType), (((in Xx) C)->((in Xx) A)))) ((ex fofType) (fun (Xx:fofType)=> ((in Xx) C))))->((ex fofType) (fun (D:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((and ((and ((in D) B)) ((in Xx) C))) (((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) D)) ((in Xy) C))))->False))) (forall (E:fofType), (((in E) B)->((or (forall (Xy:fofType), (((in Xy) E)->((in Xy) D)))) ((in Xx) E))))))))))))))))
% Defined: wellorderingAx:=(forall (A:fofType), ((ex fofType) (fun (B:fofType)=> ((and ((and ((and (forall (C:fofType), (((in C) B)->(forall (Xx:fofType), (((in Xx) C)->((in Xx) A)))))) (forall (Xx:fofType) (Xy:fofType), (((and ((in Xx) A)) ((in Xy) A))->((forall (C:fofType), (((in C) B)->((iff ((in Xx) C)) ((in Xy) C))))->(((eq fofType) Xx) Xy)))))) (forall (C:fofType) (D:fofType), (((and ((in C) B)) ((in D) B))->((or (forall (Xx:fofType), (((in Xx) C)->((in Xx) D)))) (forall (Xx:fofType), (((in Xx) D)->((in Xx) C)))))))) (forall (C:fofType), (((and (forall (Xx:fofType), (((in Xx) C)->((in Xx) A)))) ((ex fofType) (fun (Xx:fofType)=> ((in Xx) C))))->((ex fofType) (fun (D:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((and ((and ((in D) B)) ((in Xx) C))) (((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) D)) ((in Xy) C))))->False))) (forall (E:fofType), (((in E) B)->((or (forall (Xy:fofType), (((in Xy) E)->((in Xy) D)))) ((in Xx) E)))))))))))))))
% FOF formula (<kernel.Constant object at 0xf6d3b0>, <kernel.DependentProduct object at 0xf6d200>) of role type named descr_type
% Using role type
% Declaring descr:((fofType->Prop)->fofType)
% FOF formula (<kernel.Constant object at 0xf6def0>, <kernel.Sort object at 0x101e098>) of role type named descrp_type
% Using role type
% Declaring descrp:Prop
% FOF formula (((eq Prop) descrp) (forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->(Xphi (descr (fun (Xx:fofType)=> (Xphi Xx))))))) of role definition named descrp
% A new definition: (((eq Prop) descrp) (forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->(Xphi (descr (fun (Xx:fofType)=> (Xphi Xx)))))))
% Defined: descrp:=(forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->(Xphi (descr (fun (Xx:fofType)=> (Xphi Xx))))))
% FOF formula (<kernel.Constant object at 0xf6df38>, <kernel.DependentProduct object at 0xf6dfc8>) of role type named dsetconstr_type
% Using role type
% Declaring dsetconstr:(fofType->((fofType->Prop)->fofType))
% FOF formula (<kernel.Constant object at 0xf6d440>, <kernel.Sort object at 0x101e098>) of role type named dsetconstrI_type
% Using role type
% Declaring dsetconstrI:Prop
% FOF formula (((eq Prop) dsetconstrI) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))) of role definition named dsetconstrI
% A new definition: (((eq Prop) dsetconstrI) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))
% Defined: dsetconstrI:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))
% FOF formula (<kernel.Constant object at 0xf6def0>, <kernel.Sort object at 0x101e098>) of role type named dsetconstrEL_type
% Using role type
% Declaring dsetconstrEL:Prop
% FOF formula (((eq Prop) dsetconstrEL) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->((in Xx) A)))) of role definition named dsetconstrEL
% A new definition: (((eq Prop) dsetconstrEL) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->((in Xx) A))))
% Defined: dsetconstrEL:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->((in Xx) A)))
% FOF formula (<kernel.Constant object at 0xf6d3b0>, <kernel.Sort object at 0x101e098>) of role type named dsetconstrER_type
% Using role type
% Declaring dsetconstrER:Prop
% FOF formula (((eq Prop) dsetconstrER) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->(Xphi Xx)))) of role definition named dsetconstrER
% A new definition: (((eq Prop) dsetconstrER) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->(Xphi Xx))))
% Defined: dsetconstrER:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->(Xphi Xx)))
% FOF formula (<kernel.Constant object at 0xf6de60>, <kernel.Sort object at 0x101e098>) of role type named exuE1_type
% Using role type
% Declaring exuE1:Prop
% FOF formula (((eq Prop) exuE1) (forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->((ex fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy))))))))) of role definition named exuE1
% A new definition: (((eq Prop) exuE1) (forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->((ex fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy)))))))))
% Defined: exuE1:=(forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->((ex fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy))))))))
% FOF formula (<kernel.Constant object at 0xf6de60>, <kernel.DependentProduct object at 0xd8b3b0>) of role type named prop2set_type
% Using role type
% Declaring prop2set:(Prop->fofType)
% FOF formula (<kernel.Constant object at 0xf6def0>, <kernel.Sort object at 0x101e098>) of role type named prop2setE_type
% Using role type
% Declaring prop2setE:Prop
% FOF formula (((eq Prop) prop2setE) (forall (Xphi:Prop) (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi))) of role definition named prop2setE
% A new definition: (((eq Prop) prop2setE) (forall (Xphi:Prop) (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi)))
% Defined: prop2setE:=(forall (Xphi:Prop) (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi))
% FOF formula (<kernel.Constant object at 0xd8bef0>, <kernel.Sort object at 0x101e098>) of role type named emptysetE_type
% Using role type
% Declaring emptysetE:Prop
% FOF formula (((eq Prop) emptysetE) (forall (Xx:fofType), (((in Xx) emptyset)->(forall (Xphi:Prop), Xphi)))) of role definition named emptysetE
% A new definition: (((eq Prop) emptysetE) (forall (Xx:fofType), (((in Xx) emptyset)->(forall (Xphi:Prop), Xphi))))
% Defined: emptysetE:=(forall (Xx:fofType), (((in Xx) emptyset)->(forall (Xphi:Prop), Xphi)))
% FOF formula (<kernel.Constant object at 0xd8b8c0>, <kernel.Sort object at 0x101e098>) of role type named emptysetimpfalse_type
% Using role type
% Declaring emptysetimpfalse:Prop
% FOF formula (((eq Prop) emptysetimpfalse) (forall (Xx:fofType), (((in Xx) emptyset)->False))) of role definition named emptysetimpfalse
% A new definition: (((eq Prop) emptysetimpfalse) (forall (Xx:fofType), (((in Xx) emptyset)->False)))
% Defined: emptysetimpfalse:=(forall (Xx:fofType), (((in Xx) emptyset)->False))
% FOF formula (<kernel.Constant object at 0xd8b830>, <kernel.Sort object at 0x101e098>) of role type named notinemptyset_type
% Using role type
% Declaring notinemptyset:Prop
% FOF formula (((eq Prop) notinemptyset) (forall (Xx:fofType), (((in Xx) emptyset)->False))) of role definition named notinemptyset
% A new definition: (((eq Prop) notinemptyset) (forall (Xx:fofType), (((in Xx) emptyset)->False)))
% Defined: notinemptyset:=(forall (Xx:fofType), (((in Xx) emptyset)->False))
% FOF formula (<kernel.Constant object at 0xd8bb90>, <kernel.Sort object at 0x101e098>) of role type named exuE3e_type
% Using role type
% Declaring exuE3e:Prop
% FOF formula (((eq Prop) exuE3e) (forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->((ex fofType) (fun (Xx:fofType)=> (Xphi Xx)))))) of role definition named exuE3e
% A new definition: (((eq Prop) exuE3e) (forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->((ex fofType) (fun (Xx:fofType)=> (Xphi Xx))))))
% Defined: exuE3e:=(forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->((ex fofType) (fun (Xx:fofType)=> (Xphi Xx)))))
% FOF formula (<kernel.Constant object at 0xd8b518>, <kernel.Sort object at 0x101e098>) of role type named setext_type
% Using role type
% Declaring setext:Prop
% FOF formula (((eq Prop) setext) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))->(((eq fofType) A) B))))) of role definition named setext
% A new definition: (((eq Prop) setext) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))->(((eq fofType) A) B)))))
% Defined: setext:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))->(((eq fofType) A) B))))
% FOF formula (<kernel.Constant object at 0xd8b5f0>, <kernel.Sort object at 0x101e098>) of role type named emptyI_type
% Using role type
% Declaring emptyI:Prop
% FOF formula (((eq Prop) emptyI) (forall (A:fofType), ((forall (Xx:fofType), (((in Xx) A)->False))->(((eq fofType) A) emptyset)))) of role definition named emptyI
% A new definition: (((eq Prop) emptyI) (forall (A:fofType), ((forall (Xx:fofType), (((in Xx) A)->False))->(((eq fofType) A) emptyset))))
% Defined: emptyI:=(forall (A:fofType), ((forall (Xx:fofType), (((in Xx) A)->False))->(((eq fofType) A) emptyset)))
% FOF formula (<kernel.Constant object at 0xf6e368>, <kernel.Sort object at 0x101e098>) of role type named noeltsimpempty_type
% Using role type
% Declaring noeltsimpempty:Prop
% FOF formula (((eq Prop) noeltsimpempty) (forall (A:fofType), ((forall (Xx:fofType), (((in Xx) A)->False))->(((eq fofType) A) emptyset)))) of role definition named noeltsimpempty
% A new definition: (((eq Prop) noeltsimpempty) (forall (A:fofType), ((forall (Xx:fofType), (((in Xx) A)->False))->(((eq fofType) A) emptyset))))
% Defined: noeltsimpempty:=(forall (A:fofType), ((forall (Xx:fofType), (((in Xx) A)->False))->(((eq fofType) A) emptyset)))
% FOF formula (<kernel.Constant object at 0xf6e200>, <kernel.Sort object at 0x101e098>) of role type named setbeta_type
% Using role type
% Declaring setbeta:Prop
% FOF formula (((eq Prop) setbeta) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((iff ((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))) (Xphi Xx))))) of role definition named setbeta
% A new definition: (((eq Prop) setbeta) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((iff ((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))) (Xphi Xx)))))
% Defined: setbeta:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((iff ((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))) (Xphi Xx))))
% FOF formula (<kernel.Constant object at 0xf6e050>, <kernel.DependentProduct object at 0xd8bb00>) of role type named nonempty_type
% Using role type
% Declaring nonempty:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) nonempty) (fun (Xx:fofType)=> (not (((eq fofType) Xx) emptyset)))) of role definition named nonempty
% A new definition: (((eq (fofType->Prop)) nonempty) (fun (Xx:fofType)=> (not (((eq fofType) Xx) emptyset))))
% Defined: nonempty:=(fun (Xx:fofType)=> (not (((eq fofType) Xx) emptyset)))
% FOF formula (<kernel.Constant object at 0xf6e050>, <kernel.Sort object at 0x101e098>) of role type named nonemptyE1_type
% Using role type
% Declaring nonemptyE1:Prop
% FOF formula (((eq Prop) nonemptyE1) (forall (A:fofType), ((nonempty A)->((ex fofType) (fun (Xx:fofType)=> ((in Xx) A)))))) of role definition named nonemptyE1
% A new definition: (((eq Prop) nonemptyE1) (forall (A:fofType), ((nonempty A)->((ex fofType) (fun (Xx:fofType)=> ((in Xx) A))))))
% Defined: nonemptyE1:=(forall (A:fofType), ((nonempty A)->((ex fofType) (fun (Xx:fofType)=> ((in Xx) A)))))
% FOF formula (<kernel.Constant object at 0xf6e368>, <kernel.Sort object at 0x101e098>) of role type named nonemptyI_type
% Using role type
% Declaring nonemptyI:Prop
% FOF formula (((eq Prop) nonemptyI) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))) of role definition named nonemptyI
% A new definition: (((eq Prop) nonemptyI) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))
% Defined: nonemptyI:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))
% FOF formula (<kernel.Constant object at 0xd8bdd0>, <kernel.Sort object at 0x101e098>) of role type named nonemptyI1_type
% Using role type
% Declaring nonemptyI1:Prop
% FOF formula (((eq Prop) nonemptyI1) (forall (A:fofType), (((ex fofType) (fun (Xx:fofType)=> ((in Xx) A)))->(nonempty A)))) of role definition named nonemptyI1
% A new definition: (((eq Prop) nonemptyI1) (forall (A:fofType), (((ex fofType) (fun (Xx:fofType)=> ((in Xx) A)))->(nonempty A))))
% Defined: nonemptyI1:=(forall (A:fofType), (((ex fofType) (fun (Xx:fofType)=> ((in Xx) A)))->(nonempty A)))
% FOF formula (<kernel.Constant object at 0xd8b4d0>, <kernel.Sort object at 0x101e098>) of role type named setadjoinIL_type
% Using role type
% Declaring setadjoinIL:Prop
% FOF formula (((eq Prop) setadjoinIL) (forall (Xx:fofType) (Xy:fofType), ((in Xx) ((setadjoin Xx) Xy)))) of role definition named setadjoinIL
% A new definition: (((eq Prop) setadjoinIL) (forall (Xx:fofType) (Xy:fofType), ((in Xx) ((setadjoin Xx) Xy))))
% Defined: setadjoinIL:=(forall (Xx:fofType) (Xy:fofType), ((in Xx) ((setadjoin Xx) Xy)))
% FOF formula (<kernel.Constant object at 0xd8bd40>, <kernel.Sort object at 0x101e098>) of role type named emptyinunitempty_type
% Using role type
% Declaring emptyinunitempty:Prop
% FOF formula (((eq Prop) emptyinunitempty) ((in emptyset) ((setadjoin emptyset) emptyset))) of role definition named emptyinunitempty
% A new definition: (((eq Prop) emptyinunitempty) ((in emptyset) ((setadjoin emptyset) emptyset)))
% Defined: emptyinunitempty:=((in emptyset) ((setadjoin emptyset) emptyset))
% FOF formula (<kernel.Constant object at 0xd8b4d0>, <kernel.Sort object at 0x101e098>) of role type named setadjoinIR_type
% Using role type
% Declaring setadjoinIR:Prop
% FOF formula (((eq Prop) setadjoinIR) (forall (Xx:fofType) (A:fofType) (Xy:fofType), (((in Xy) A)->((in Xy) ((setadjoin Xx) A))))) of role definition named setadjoinIR
% A new definition: (((eq Prop) setadjoinIR) (forall (Xx:fofType) (A:fofType) (Xy:fofType), (((in Xy) A)->((in Xy) ((setadjoin Xx) A)))))
% Defined: setadjoinIR:=(forall (Xx:fofType) (A:fofType) (Xy:fofType), (((in Xy) A)->((in Xy) ((setadjoin Xx) A))))
% FOF formula (<kernel.Constant object at 0xd8b4d0>, <kernel.Sort object at 0x101e098>) of role type named setadjoinE_type
% Using role type
% Declaring setadjoinE:Prop
% FOF formula (((eq Prop) setadjoinE) (forall (Xx:fofType) (A:fofType) (Xy:fofType), (((in Xy) ((setadjoin Xx) A))->(forall (Xphi:Prop), (((((eq fofType) Xy) Xx)->Xphi)->((((in Xy) A)->Xphi)->Xphi)))))) of role definition named setadjoinE
% A new definition: (((eq Prop) setadjoinE) (forall (Xx:fofType) (A:fofType) (Xy:fofType), (((in Xy) ((setadjoin Xx) A))->(forall (Xphi:Prop), (((((eq fofType) Xy) Xx)->Xphi)->((((in Xy) A)->Xphi)->Xphi))))))
% Defined: setadjoinE:=(forall (Xx:fofType) (A:fofType) (Xy:fofType), (((in Xy) ((setadjoin Xx) A))->(forall (Xphi:Prop), (((((eq fofType) Xy) Xx)->Xphi)->((((in Xy) A)->Xphi)->Xphi)))))
% FOF formula (<kernel.Constant object at 0xd8b560>, <kernel.Sort object at 0x101e098>) of role type named setadjoinOr_type
% Using role type
% Declaring setadjoinOr:Prop
% FOF formula (((eq Prop) setadjoinOr) (forall (Xx:fofType) (A:fofType) (Xy:fofType), (((in Xy) ((setadjoin Xx) A))->((or (((eq fofType) Xy) Xx)) ((in Xy) A))))) of role definition named setadjoinOr
% A new definition: (((eq Prop) setadjoinOr) (forall (Xx:fofType) (A:fofType) (Xy:fofType), (((in Xy) ((setadjoin Xx) A))->((or (((eq fofType) Xy) Xx)) ((in Xy) A)))))
% Defined: setadjoinOr:=(forall (Xx:fofType) (A:fofType) (Xy:fofType), (((in Xy) ((setadjoin Xx) A))->((or (((eq fofType) Xy) Xx)) ((in Xy) A))))
% FOF formula (<kernel.Constant object at 0xd817e8>, <kernel.Sort object at 0x101e098>) of role type named setoftrueEq_type
% Using role type
% Declaring setoftrueEq:Prop
% FOF formula (((eq Prop) setoftrueEq) (forall (A:fofType), (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> True))) A))) of role definition named setoftrueEq
% A new definition: (((eq Prop) setoftrueEq) (forall (A:fofType), (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> True))) A)))
% Defined: setoftrueEq:=(forall (A:fofType), (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> True))) A))
% FOF formula (<kernel.Constant object at 0xd818c0>, <kernel.Sort object at 0x101e098>) of role type named powersetI_type
% Using role type
% Declaring powersetI:Prop
% FOF formula (((eq Prop) powersetI) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))->((in B) (powerset A))))) of role definition named powersetI
% A new definition: (((eq Prop) powersetI) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))->((in B) (powerset A)))))
% Defined: powersetI:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))->((in B) (powerset A))))
% FOF formula (<kernel.Constant object at 0xd81128>, <kernel.Sort object at 0x101e098>) of role type named emptyinPowerset_type
% Using role type
% Declaring emptyinPowerset:Prop
% FOF formula (((eq Prop) emptyinPowerset) (forall (A:fofType), ((in emptyset) (powerset A)))) of role definition named emptyinPowerset
% A new definition: (((eq Prop) emptyinPowerset) (forall (A:fofType), ((in emptyset) (powerset A))))
% Defined: emptyinPowerset:=(forall (A:fofType), ((in emptyset) (powerset A)))
% FOF formula (<kernel.Constant object at 0xd81518>, <kernel.Sort object at 0x101e098>) of role type named emptyInPowerset_type
% Using role type
% Declaring emptyInPowerset:Prop
% FOF formula (((eq Prop) emptyInPowerset) (forall (A:fofType), ((in emptyset) (powerset A)))) of role definition named emptyInPowerset
% A new definition: (((eq Prop) emptyInPowerset) (forall (A:fofType), ((in emptyset) (powerset A))))
% Defined: emptyInPowerset:=(forall (A:fofType), ((in emptyset) (powerset A)))
% FOF formula (<kernel.Constant object at 0xd81a28>, <kernel.Sort object at 0x101e098>) of role type named powersetE_type
% Using role type
% Declaring powersetE:Prop
% FOF formula (((eq Prop) powersetE) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in B) (powerset A))->(((in Xx) B)->((in Xx) A))))) of role definition named powersetE
% A new definition: (((eq Prop) powersetE) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in B) (powerset A))->(((in Xx) B)->((in Xx) A)))))
% Defined: powersetE:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in B) (powerset A))->(((in Xx) B)->((in Xx) A))))
% FOF formula (<kernel.Constant object at 0xd819e0>, <kernel.Sort object at 0x101e098>) of role type named setunionI_type
% Using role type
% Declaring setunionI:Prop
% FOF formula (((eq Prop) setunionI) (forall (A:fofType) (Xx:fofType) (B:fofType), (((in Xx) B)->(((in B) A)->((in Xx) (setunion A)))))) of role definition named setunionI
% A new definition: (((eq Prop) setunionI) (forall (A:fofType) (Xx:fofType) (B:fofType), (((in Xx) B)->(((in B) A)->((in Xx) (setunion A))))))
% Defined: setunionI:=(forall (A:fofType) (Xx:fofType) (B:fofType), (((in Xx) B)->(((in B) A)->((in Xx) (setunion A)))))
% FOF formula (<kernel.Constant object at 0xd81320>, <kernel.Sort object at 0x101e098>) of role type named setunionE_type
% Using role type
% Declaring setunionE:Prop
% FOF formula (((eq Prop) setunionE) (forall (A:fofType) (Xx:fofType), (((in Xx) (setunion A))->(forall (Xphi:Prop), ((forall (B:fofType), (((in Xx) B)->(((in B) A)->Xphi)))->Xphi))))) of role definition named setunionE
% A new definition: (((eq Prop) setunionE) (forall (A:fofType) (Xx:fofType), (((in Xx) (setunion A))->(forall (Xphi:Prop), ((forall (B:fofType), (((in Xx) B)->(((in B) A)->Xphi)))->Xphi)))))
% Defined: setunionE:=(forall (A:fofType) (Xx:fofType), (((in Xx) (setunion A))->(forall (Xphi:Prop), ((forall (B:fofType), (((in Xx) B)->(((in B) A)->Xphi)))->Xphi))))
% FOF formula (<kernel.Constant object at 0xd81170>, <kernel.Sort object at 0x101e098>) of role type named subPowSU_type
% Using role type
% Declaring subPowSU:Prop
% FOF formula (((eq Prop) subPowSU) (forall (A:fofType) (Xx:fofType), (((in Xx) A)->((in Xx) (powerset (setunion A)))))) of role definition named subPowSU
% A new definition: (((eq Prop) subPowSU) (forall (A:fofType) (Xx:fofType), (((in Xx) A)->((in Xx) (powerset (setunion A))))))
% Defined: subPowSU:=(forall (A:fofType) (Xx:fofType), (((in Xx) A)->((in Xx) (powerset (setunion A)))))
% FOF formula (<kernel.Constant object at 0xd81758>, <kernel.Sort object at 0x101e098>) of role type named exuE2_type
% Using role type
% Declaring exuE2:Prop
% FOF formula (((eq Prop) exuE2) (forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (Xphi Xy)) (((eq fofType) Xy) Xx)))))))) of role definition named exuE2
% A new definition: (((eq Prop) exuE2) (forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (Xphi Xy)) (((eq fofType) Xy) Xx))))))))
% Defined: exuE2:=(forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (Xphi Xy)) (((eq fofType) Xy) Xx)))))))
% FOF formula (<kernel.Constant object at 0xd81488>, <kernel.Sort object at 0x101e098>) of role type named nonemptyImpWitness_type
% Using role type
% Declaring nonemptyImpWitness:Prop
% FOF formula (((eq Prop) nonemptyImpWitness) (forall (A:fofType), ((nonempty A)->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) True)))))) of role definition named nonemptyImpWitness
% A new definition: (((eq Prop) nonemptyImpWitness) (forall (A:fofType), ((nonempty A)->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) True))))))
% Defined: nonemptyImpWitness:=(forall (A:fofType), ((nonempty A)->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) True)))))
% FOF formula (<kernel.Constant object at 0xd815a8>, <kernel.Sort object at 0x101e098>) 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 0xd81f38>, <kernel.Sort object at 0x101e098>) of role type named notinsingleton_type
% Using role type
% Declaring notinsingleton:Prop
% FOF formula (((eq Prop) notinsingleton) (forall (Xx:fofType) (Xy:fofType), ((not (((eq fofType) Xx) Xy))->(((in Xy) ((setadjoin Xx) emptyset))->False)))) of role definition named notinsingleton
% A new definition: (((eq Prop) notinsingleton) (forall (Xx:fofType) (Xy:fofType), ((not (((eq fofType) Xx) Xy))->(((in Xy) ((setadjoin Xx) emptyset))->False))))
% Defined: notinsingleton:=(forall (Xx:fofType) (Xy:fofType), ((not (((eq fofType) Xx) Xy))->(((in Xy) ((setadjoin Xx) emptyset))->False)))
% FOF formula (<kernel.Constant object at 0xd81050>, <kernel.Sort object at 0x101e098>) of role type named eqinunit_type
% Using role type
% Declaring eqinunit:Prop
% FOF formula (((eq Prop) eqinunit) (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((in Xx) ((setadjoin Xy) emptyset))))) of role definition named eqinunit
% A new definition: (((eq Prop) eqinunit) (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((in Xx) ((setadjoin Xy) emptyset)))))
% Defined: eqinunit:=(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((in Xx) ((setadjoin Xy) emptyset))))
% FOF formula (<kernel.Constant object at 0xd81ef0>, <kernel.Sort object at 0x101e098>) of role type named singletonsswitch_type
% Using role type
% Declaring singletonsswitch:Prop
% FOF formula (((eq Prop) singletonsswitch) (forall (Xx:fofType) (Xy:fofType), (((in Xx) ((setadjoin Xy) emptyset))->((in Xy) ((setadjoin Xx) emptyset))))) of role definition named singletonsswitch
% A new definition: (((eq Prop) singletonsswitch) (forall (Xx:fofType) (Xy:fofType), (((in Xx) ((setadjoin Xy) emptyset))->((in Xy) ((setadjoin Xx) emptyset)))))
% Defined: singletonsswitch:=(forall (Xx:fofType) (Xy:fofType), (((in Xx) ((setadjoin Xy) emptyset))->((in Xy) ((setadjoin Xx) emptyset))))
% FOF formula (<kernel.Constant object at 0xd810e0>, <kernel.Sort object at 0x101e098>) of role type named upairsetE_type
% Using role type
% Declaring upairsetE:Prop
% FOF formula (((eq Prop) upairsetE) (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((in Xz) ((setadjoin Xx) ((setadjoin Xy) emptyset)))->((or (((eq fofType) Xz) Xx)) (((eq fofType) Xz) Xy))))) of role definition named upairsetE
% A new definition: (((eq Prop) upairsetE) (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((in Xz) ((setadjoin Xx) ((setadjoin Xy) emptyset)))->((or (((eq fofType) Xz) Xx)) (((eq fofType) Xz) Xy)))))
% Defined: upairsetE:=(forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((in Xz) ((setadjoin Xx) ((setadjoin Xy) emptyset)))->((or (((eq fofType) Xz) Xx)) (((eq fofType) Xz) Xy))))
% FOF formula (<kernel.Constant object at 0xd81fc8>, <kernel.Sort object at 0x101e098>) of role type named upairsetIL_type
% Using role type
% Declaring upairsetIL:Prop
% FOF formula (((eq Prop) upairsetIL) (forall (Xx:fofType) (Xy:fofType), ((in Xx) ((setadjoin Xx) ((setadjoin Xy) emptyset))))) of role definition named upairsetIL
% A new definition: (((eq Prop) upairsetIL) (forall (Xx:fofType) (Xy:fofType), ((in Xx) ((setadjoin Xx) ((setadjoin Xy) emptyset)))))
% Defined: upairsetIL:=(forall (Xx:fofType) (Xy:fofType), ((in Xx) ((setadjoin Xx) ((setadjoin Xy) emptyset))))
% FOF formula (<kernel.Constant object at 0xd81bd8>, <kernel.Sort object at 0x101e098>) of role type named upairsetIR_type
% Using role type
% Declaring upairsetIR:Prop
% FOF formula (((eq Prop) upairsetIR) (forall (Xx:fofType) (Xy:fofType), ((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset))))) of role definition named upairsetIR
% A new definition: (((eq Prop) upairsetIR) (forall (Xx:fofType) (Xy:fofType), ((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset)))))
% Defined: upairsetIR:=(forall (Xx:fofType) (Xy:fofType), ((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset))))
% FOF formula (<kernel.Constant object at 0xd81098>, <kernel.Sort object at 0x101e098>) of role type named emptyE1_type
% Using role type
% Declaring emptyE1:Prop
% FOF formula (((eq Prop) emptyE1) (forall (A:fofType) (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->((((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset)->False)))) of role definition named emptyE1
% A new definition: (((eq Prop) emptyE1) (forall (A:fofType) (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->((((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset)->False))))
% Defined: emptyE1:=(forall (A:fofType) (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->((((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset)->False)))
% FOF formula (<kernel.Constant object at 0xd81b48>, <kernel.Sort object at 0x101e098>) of role type named vacuousDall_type
% Using role type
% Declaring vacuousDall:Prop
% FOF formula (((eq Prop) vacuousDall) (forall (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) emptyset)->(Xphi Xx)))) of role definition named vacuousDall
% A new definition: (((eq Prop) vacuousDall) (forall (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) emptyset)->(Xphi Xx))))
% Defined: vacuousDall:=(forall (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) emptyset)->(Xphi Xx)))
% FOF formula (<kernel.Constant object at 0xd81b90>, <kernel.Sort object at 0x101e098>) of role type named quantDeMorgan1_type
% Using role type
% Declaring quantDeMorgan1:Prop
% FOF formula (((eq Prop) quantDeMorgan1) (forall (A:fofType) (Xphi:(fofType->Prop)), (((forall (Xx:fofType), (((in Xx) A)->(Xphi Xx)))->False)->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((Xphi Xx)->False))))))) of role definition named quantDeMorgan1
% A new definition: (((eq Prop) quantDeMorgan1) (forall (A:fofType) (Xphi:(fofType->Prop)), (((forall (Xx:fofType), (((in Xx) A)->(Xphi Xx)))->False)->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((Xphi Xx)->False)))))))
% Defined: quantDeMorgan1:=(forall (A:fofType) (Xphi:(fofType->Prop)), (((forall (Xx:fofType), (((in Xx) A)->(Xphi Xx)))->False)->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((Xphi Xx)->False))))))
% FOF formula (<kernel.Constant object at 0xd81b00>, <kernel.Sort object at 0x101e098>) of role type named quantDeMorgan2_type
% Using role type
% Declaring quantDeMorgan2:Prop
% FOF formula (((eq Prop) quantDeMorgan2) (forall (A:fofType) (Xphi:(fofType->Prop)), ((forall (Xx:fofType), (((in Xx) A)->((Xphi Xx)->False)))->(((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->False)))) of role definition named quantDeMorgan2
% A new definition: (((eq Prop) quantDeMorgan2) (forall (A:fofType) (Xphi:(fofType->Prop)), ((forall (Xx:fofType), (((in Xx) A)->((Xphi Xx)->False)))->(((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->False))))
% Defined: quantDeMorgan2:=(forall (A:fofType) (Xphi:(fofType->Prop)), ((forall (Xx:fofType), (((in Xx) A)->((Xphi Xx)->False)))->(((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->False)))
% FOF formula (<kernel.Constant object at 0xd81560>, <kernel.Sort object at 0x101e098>) of role type named quantDeMorgan3_type
% Using role type
% Declaring quantDeMorgan3:Prop
% FOF formula (((eq Prop) quantDeMorgan3) (forall (A:fofType) (Xphi:(fofType->Prop)), ((((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->False)->(forall (Xx:fofType), (((in Xx) A)->((Xphi Xx)->False)))))) of role definition named quantDeMorgan3
% A new definition: (((eq Prop) quantDeMorgan3) (forall (A:fofType) (Xphi:(fofType->Prop)), ((((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->False)->(forall (Xx:fofType), (((in Xx) A)->((Xphi Xx)->False))))))
% Defined: quantDeMorgan3:=(forall (A:fofType) (Xphi:(fofType->Prop)), ((((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->False)->(forall (Xx:fofType), (((in Xx) A)->((Xphi Xx)->False)))))
% FOF formula (<kernel.Constant object at 0xd81f80>, <kernel.Sort object at 0x101e098>) of role type named quantDeMorgan4_type
% Using role type
% Declaring quantDeMorgan4:Prop
% FOF formula (((eq Prop) quantDeMorgan4) (forall (A:fofType) (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((Xphi Xx)->False))))->((forall (Xx:fofType), (((in Xx) A)->(Xphi Xx)))->False)))) of role definition named quantDeMorgan4
% A new definition: (((eq Prop) quantDeMorgan4) (forall (A:fofType) (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((Xphi Xx)->False))))->((forall (Xx:fofType), (((in Xx) A)->(Xphi Xx)))->False))))
% Defined: quantDeMorgan4:=(forall (A:fofType) (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((Xphi Xx)->False))))->((forall (Xx:fofType), (((in Xx) A)->(Xphi Xx)))->False)))
% FOF formula (<kernel.Constant object at 0xd81dd0>, <kernel.Sort object at 0x101e098>) of role type named prop2setI_type
% Using role type
% Declaring prop2setI:Prop
% FOF formula (((eq Prop) prop2setI) (forall (Xphi:Prop), (Xphi->((in emptyset) (prop2set Xphi))))) of role definition named prop2setI
% A new definition: (((eq Prop) prop2setI) (forall (Xphi:Prop), (Xphi->((in emptyset) (prop2set Xphi)))))
% Defined: prop2setI:=(forall (Xphi:Prop), (Xphi->((in emptyset) (prop2set Xphi))))
% FOF formula (<kernel.Constant object at 0xd81dd0>, <kernel.DependentProduct object at 0xf5c4d0>) of role type named set2prop_type
% Using role type
% Declaring set2prop:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0xd81f80>, <kernel.Sort object at 0x101e098>) of role type named prop2set2propI_type
% Using role type
% Declaring prop2set2propI:Prop
% FOF formula (((eq Prop) prop2set2propI) (forall (Xphi:Prop), (Xphi->(set2prop (prop2set Xphi))))) of role definition named prop2set2propI
% A new definition: (((eq Prop) prop2set2propI) (forall (Xphi:Prop), (Xphi->(set2prop (prop2set Xphi)))))
% Defined: prop2set2propI:=(forall (Xphi:Prop), (Xphi->(set2prop (prop2set Xphi))))
% FOF formula (<kernel.Constant object at 0xd81dd0>, <kernel.Sort object at 0x101e098>) of role type named notdexE_type
% Using role type
% Declaring notdexE:Prop
% FOF formula (((eq Prop) notdexE) (forall (A:fofType) (Xphi:(fofType->Prop)), ((((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->False)->(forall (Xx:fofType), (((in Xx) A)->((Xphi Xx)->False)))))) of role definition named notdexE
% A new definition: (((eq Prop) notdexE) (forall (A:fofType) (Xphi:(fofType->Prop)), ((((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->False)->(forall (Xx:fofType), (((in Xx) A)->((Xphi Xx)->False))))))
% Defined: notdexE:=(forall (A:fofType) (Xphi:(fofType->Prop)), ((((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->False)->(forall (Xx:fofType), (((in Xx) A)->((Xphi Xx)->False)))))
% FOF formula (<kernel.Constant object at 0xf5c050>, <kernel.Sort object at 0x101e098>) of role type named notdallE_type
% Using role type
% Declaring notdallE:Prop
% FOF formula (((eq Prop) notdallE) (forall (A:fofType) (Xphi:(fofType->Prop)), (((forall (Xx:fofType), (((in Xx) A)->(Xphi Xx)))->False)->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((Xphi Xx)->False))))))) of role definition named notdallE
% A new definition: (((eq Prop) notdallE) (forall (A:fofType) (Xphi:(fofType->Prop)), (((forall (Xx:fofType), (((in Xx) A)->(Xphi Xx)))->False)->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((Xphi Xx)->False)))))))
% Defined: notdallE:=(forall (A:fofType) (Xphi:(fofType->Prop)), (((forall (Xx:fofType), (((in Xx) A)->(Xphi Xx)))->False)->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((Xphi Xx)->False))))))
% FOF formula (<kernel.Constant object at 0xf5c488>, <kernel.Sort object at 0x101e098>) of role type named exuI1_type
% Using role type
% Declaring exuI1:Prop
% FOF formula (((eq Prop) exuI1) (forall (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy))))))->(exu (fun (Xx:fofType)=> (Xphi Xx)))))) of role definition named exuI1
% A new definition: (((eq Prop) exuI1) (forall (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy))))))->(exu (fun (Xx:fofType)=> (Xphi Xx))))))
% Defined: exuI1:=(forall (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy))))))->(exu (fun (Xx:fofType)=> (Xphi Xx)))))
% FOF formula (<kernel.Constant object at 0xf5c8c0>, <kernel.Sort object at 0x101e098>) of role type named exuI3_type
% Using role type
% Declaring exuI3:Prop
% FOF formula (((eq Prop) exuI3) (forall (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> (Xphi Xx)))->((forall (Xx:fofType) (Xy:fofType), ((Xphi Xx)->((Xphi Xy)->(((eq fofType) Xx) Xy))))->(exu (fun (Xx:fofType)=> (Xphi Xx))))))) of role definition named exuI3
% A new definition: (((eq Prop) exuI3) (forall (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> (Xphi Xx)))->((forall (Xx:fofType) (Xy:fofType), ((Xphi Xx)->((Xphi Xy)->(((eq fofType) Xx) Xy))))->(exu (fun (Xx:fofType)=> (Xphi Xx)))))))
% Defined: exuI3:=(forall (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> (Xphi Xx)))->((forall (Xx:fofType) (Xy:fofType), ((Xphi Xx)->((Xphi Xy)->(((eq fofType) Xx) Xy))))->(exu (fun (Xx:fofType)=> (Xphi Xx))))))
% FOF formula (<kernel.Constant object at 0xf5c320>, <kernel.Sort object at 0x101e098>) of role type named exuI2_type
% Using role type
% Declaring exuI2:Prop
% FOF formula (((eq Prop) exuI2) (forall (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (Xphi Xy)) (((eq fofType) Xy) Xx)))))->(exu (fun (Xx:fofType)=> (Xphi Xx)))))) of role definition named exuI2
% A new definition: (((eq Prop) exuI2) (forall (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (Xphi Xy)) (((eq fofType) Xy) Xx)))))->(exu (fun (Xx:fofType)=> (Xphi Xx))))))
% Defined: exuI2:=(forall (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (Xphi Xy)) (((eq fofType) Xy) Xx)))))->(exu (fun (Xx:fofType)=> (Xphi Xx)))))
% FOF formula (<kernel.Constant object at 0xf5c7a0>, <kernel.Sort object at 0x101e098>) of role type named inCongP_type
% Using role type
% Declaring inCongP:Prop
% FOF formula (((eq Prop) inCongP) (forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->(((in Xx) A)->((in Xy) B))))))) of role definition named inCongP
% A new definition: (((eq Prop) inCongP) (forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->(((in Xx) A)->((in Xy) B)))))))
% Defined: inCongP:=(forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->(((in Xx) A)->((in Xy) B))))))
% FOF formula (<kernel.Constant object at 0xf5c830>, <kernel.Sort object at 0x101e098>) 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 0xf5c7e8>, <kernel.Sort object at 0x101e098>) of role type named exuE3u_type
% Using role type
% Declaring exuE3u:Prop
% FOF formula (((eq Prop) exuE3u) (forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->(forall (Xx:fofType) (Xy:fofType), ((Xphi Xx)->((Xphi Xy)->(((eq fofType) Xx) Xy))))))) of role definition named exuE3u
% A new definition: (((eq Prop) exuE3u) (forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->(forall (Xx:fofType) (Xy:fofType), ((Xphi Xx)->((Xphi Xy)->(((eq fofType) Xx) Xy)))))))
% Defined: exuE3u:=(forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->(forall (Xx:fofType) (Xy:fofType), ((Xphi Xx)->((Xphi Xy)->(((eq fofType) Xx) Xy))))))
% FOF formula (<kernel.Constant object at 0xf5c560>, <kernel.Sort object at 0x101e098>) of role type named exu__Cong_type
% Using role type
% Declaring exu__Cong:Prop
% FOF formula (((eq Prop) exu__Cong) (forall (Xphi:(fofType->Prop)) (Xpsi:(fofType->Prop)), ((forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((iff (Xphi Xx)) (Xpsi Xy))))->((iff (exu (fun (Xx:fofType)=> (Xphi Xx)))) (exu (fun (Xx:fofType)=> (Xpsi Xx))))))) of role definition named exu__Cong
% A new definition: (((eq Prop) exu__Cong) (forall (Xphi:(fofType->Prop)) (Xpsi:(fofType->Prop)), ((forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((iff (Xphi Xx)) (Xpsi Xy))))->((iff (exu (fun (Xx:fofType)=> (Xphi Xx)))) (exu (fun (Xx:fofType)=> (Xpsi Xx)))))))
% Defined: exu__Cong:=(forall (Xphi:(fofType->Prop)) (Xpsi:(fofType->Prop)), ((forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((iff (Xphi Xx)) (Xpsi Xy))))->((iff (exu (fun (Xx:fofType)=> (Xphi Xx)))) (exu (fun (Xx:fofType)=> (Xpsi Xx))))))
% FOF formula (<kernel.Constant object at 0xf5c638>, <kernel.Sort object at 0x101e098>) of role type named emptyset__Cong_type
% Using role type
% Declaring emptyset__Cong:Prop
% FOF formula (((eq Prop) emptyset__Cong) (((eq fofType) emptyset) emptyset)) of role definition named emptyset__Cong
% A new definition: (((eq Prop) emptyset__Cong) (((eq fofType) emptyset) emptyset))
% Defined: emptyset__Cong:=(((eq fofType) emptyset) emptyset)
% FOF formula (<kernel.Constant object at 0xf5ccf8>, <kernel.Sort object at 0x101e098>) 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 0xf5ce18>, <kernel.Sort object at 0x101e098>) of role type named powerset__Cong_type
% Using role type
% Declaring powerset__Cong:Prop
% FOF formula (((eq Prop) powerset__Cong) (forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(((eq fofType) (powerset A)) (powerset B))))) of role definition named powerset__Cong
% A new definition: (((eq Prop) powerset__Cong) (forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(((eq fofType) (powerset A)) (powerset B)))))
% Defined: powerset__Cong:=(forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(((eq fofType) (powerset A)) (powerset B))))
% FOF formula (<kernel.Constant object at 0xf5ccb0>, <kernel.Sort object at 0x101e098>) 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 0xf5cf38>, <kernel.Sort object at 0x101e098>) of role type named omega__Cong_type
% Using role type
% Declaring omega__Cong:Prop
% FOF formula (((eq Prop) omega__Cong) (((eq fofType) omega) omega)) of role definition named omega__Cong
% A new definition: (((eq Prop) omega__Cong) (((eq fofType) omega) omega))
% Defined: omega__Cong:=(((eq fofType) omega) omega)
% FOF formula (<kernel.Constant object at 0xf5cc20>, <kernel.Sort object at 0x101e098>) of role type named exuEu_type
% Using role type
% Declaring exuEu:Prop
% FOF formula (((eq Prop) exuEu) (forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->(forall (Xx:fofType) (Xy:fofType), ((Xphi Xx)->((Xphi Xy)->(((eq fofType) Xx) Xy))))))) of role definition named exuEu
% A new definition: (((eq Prop) exuEu) (forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->(forall (Xx:fofType) (Xy:fofType), ((Xphi Xx)->((Xphi Xy)->(((eq fofType) Xx) Xy)))))))
% Defined: exuEu:=(forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->(forall (Xx:fofType) (Xy:fofType), ((Xphi Xx)->((Xphi Xy)->(((eq fofType) Xx) Xy))))))
% FOF formula (<kernel.Constant object at 0xf5ca70>, <kernel.Sort object at 0x101e098>) of role type named descr__Cong_type
% Using role type
% Declaring descr__Cong:Prop
% FOF formula (((eq Prop) descr__Cong) (forall (Xphi:(fofType->Prop)) (Xpsi:(fofType->Prop)), ((forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((iff (Xphi Xx)) (Xpsi Xy))))->((exu (fun (Xx:fofType)=> (Xphi Xx)))->((exu (fun (Xx:fofType)=> (Xpsi Xx)))->(((eq fofType) (descr (fun (Xx:fofType)=> (Xphi Xx)))) (descr (fun (Xx:fofType)=> (Xpsi Xx))))))))) of role definition named descr__Cong
% A new definition: (((eq Prop) descr__Cong) (forall (Xphi:(fofType->Prop)) (Xpsi:(fofType->Prop)), ((forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((iff (Xphi Xx)) (Xpsi Xy))))->((exu (fun (Xx:fofType)=> (Xphi Xx)))->((exu (fun (Xx:fofType)=> (Xpsi Xx)))->(((eq fofType) (descr (fun (Xx:fofType)=> (Xphi Xx)))) (descr (fun (Xx:fofType)=> (Xpsi Xx)))))))))
% Defined: descr__Cong:=(forall (Xphi:(fofType->Prop)) (Xpsi:(fofType->Prop)), ((forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((iff (Xphi Xx)) (Xpsi Xy))))->((exu (fun (Xx:fofType)=> (Xphi Xx)))->((exu (fun (Xx:fofType)=> (Xpsi Xx)))->(((eq fofType) (descr (fun (Xx:fofType)=> (Xphi Xx)))) (descr (fun (Xx:fofType)=> (Xpsi Xx))))))))
% FOF formula (<kernel.Constant object at 0xf5c908>, <kernel.Sort object at 0x101e098>) of role type named dsetconstr__Cong_type
% Using role type
% Declaring dsetconstr__Cong:Prop
% FOF formula (((eq Prop) dsetconstr__Cong) (forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(forall (Xphi:(fofType->Prop)) (Xpsi:(fofType->Prop)), ((forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((((eq fofType) Xx) Xy)->((iff (Xphi Xx)) (Xpsi Xy)))))))->(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))))))) of role definition named dsetconstr__Cong
% A new definition: (((eq Prop) dsetconstr__Cong) (forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(forall (Xphi:(fofType->Prop)) (Xpsi:(fofType->Prop)), ((forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((((eq fofType) Xx) Xy)->((iff (Xphi Xx)) (Xpsi Xy)))))))->(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))))))))
% Defined: dsetconstr__Cong:=(forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(forall (Xphi:(fofType->Prop)) (Xpsi:(fofType->Prop)), ((forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((((eq fofType) Xx) Xy)->((iff (Xphi Xx)) (Xpsi Xy)))))))->(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))))))
% FOF formula (<kernel.Constant object at 0xf5cab8>, <kernel.DependentProduct object at 0xf5cfc8>) of role type named subset_type
% Using role type
% Declaring subset:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xf5c9e0>, <kernel.DependentProduct object at 0xf5cea8>) of role type named disjoint_type
% Using role type
% Declaring disjoint:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xf5c908>, <kernel.DependentProduct object at 0xf5cab8>) of role type named setsmeet_type
% Using role type
% Declaring setsmeet:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xf5cdd0>, <kernel.Sort object at 0x101e098>) of role type named subsetI1_type
% Using role type
% Declaring subsetI1:Prop
% FOF formula (((eq Prop) subsetI1) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((subset A) B)))) of role definition named subsetI1
% A new definition: (((eq Prop) subsetI1) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((subset A) B))))
% Defined: subsetI1:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((subset A) B)))
% FOF formula (<kernel.Constant object at 0xf5cd40>, <kernel.Sort object at 0x101e098>) of role type named eqimpsubset2_type
% Using role type
% Declaring eqimpsubset2:Prop
% FOF formula (((eq Prop) eqimpsubset2) (forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->((subset B) A)))) of role definition named eqimpsubset2
% A new definition: (((eq Prop) eqimpsubset2) (forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->((subset B) A))))
% Defined: eqimpsubset2:=(forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->((subset B) A)))
% FOF formula (<kernel.Constant object at 0xf5c908>, <kernel.Sort object at 0x101e098>) of role type named eqimpsubset1_type
% Using role type
% Declaring eqimpsubset1:Prop
% FOF formula (((eq Prop) eqimpsubset1) (forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->((subset A) B)))) of role definition named eqimpsubset1
% A new definition: (((eq Prop) eqimpsubset1) (forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->((subset A) B))))
% Defined: eqimpsubset1:=(forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->((subset A) B)))
% FOF formula (<kernel.Constant object at 0xf5cea8>, <kernel.Sort object at 0x101e098>) 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 0xf5c6c8>, <kernel.Sort object at 0x101e098>) of role type named emptysetsubset_type
% Using role type
% Declaring emptysetsubset:Prop
% FOF formula (((eq Prop) emptysetsubset) (forall (A:fofType), ((subset emptyset) A))) of role definition named emptysetsubset
% A new definition: (((eq Prop) emptysetsubset) (forall (A:fofType), ((subset emptyset) A)))
% Defined: emptysetsubset:=(forall (A:fofType), ((subset emptyset) A))
% FOF formula (<kernel.Constant object at 0xf5c1b8>, <kernel.Sort object at 0x101e098>) of role type named subsetE_type
% Using role type
% Declaring subsetE:Prop
% FOF formula (((eq Prop) subsetE) (forall (A:fofType) (B:fofType) (Xx:fofType), (((subset A) B)->(((in Xx) A)->((in Xx) B))))) of role definition named subsetE
% A new definition: (((eq Prop) subsetE) (forall (A:fofType) (B:fofType) (Xx:fofType), (((subset A) B)->(((in Xx) A)->((in Xx) B)))))
% Defined: subsetE:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((subset A) B)->(((in Xx) A)->((in Xx) B))))
% FOF formula (<kernel.Constant object at 0xf5c0e0>, <kernel.Sort object at 0x101e098>) of role type named subsetE2_type
% Using role type
% Declaring subsetE2:Prop
% FOF formula (((eq Prop) subsetE2) (forall (A:fofType) (B:fofType) (Xx:fofType), (((subset A) B)->((((in Xx) B)->False)->(((in Xx) A)->False))))) of role definition named subsetE2
% A new definition: (((eq Prop) subsetE2) (forall (A:fofType) (B:fofType) (Xx:fofType), (((subset A) B)->((((in Xx) B)->False)->(((in Xx) A)->False)))))
% Defined: subsetE2:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((subset A) B)->((((in Xx) B)->False)->(((in Xx) A)->False))))
% FOF formula (<kernel.Constant object at 0xf5c518>, <kernel.Sort object at 0x101e098>) of role type named notsubsetI_type
% Using role type
% Declaring notsubsetI:Prop
% FOF formula (((eq Prop) notsubsetI) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((((in Xx) B)->False)->(((subset A) B)->False))))) of role definition named notsubsetI
% A new definition: (((eq Prop) notsubsetI) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((((in Xx) B)->False)->(((subset A) B)->False)))))
% Defined: notsubsetI:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((((in Xx) B)->False)->(((subset A) B)->False))))
% FOF formula (<kernel.Constant object at 0xf5c518>, <kernel.Sort object at 0x101e098>) of role type named notequalI1_type
% Using role type
% Declaring notequalI1:Prop
% FOF formula (((eq Prop) notequalI1) (forall (A:fofType) (B:fofType), ((((subset A) B)->False)->(not (((eq fofType) A) B))))) of role definition named notequalI1
% A new definition: (((eq Prop) notequalI1) (forall (A:fofType) (B:fofType), ((((subset A) B)->False)->(not (((eq fofType) A) B)))))
% Defined: notequalI1:=(forall (A:fofType) (B:fofType), ((((subset A) B)->False)->(not (((eq fofType) A) B))))
% FOF formula (<kernel.Constant object at 0xf5c518>, <kernel.Sort object at 0x101e098>) of role type named notequalI2_type
% Using role type
% Declaring notequalI2:Prop
% FOF formula (((eq Prop) notequalI2) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((((in Xx) B)->False)->(not (((eq fofType) A) B)))))) of role definition named notequalI2
% A new definition: (((eq Prop) notequalI2) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((((in Xx) B)->False)->(not (((eq fofType) A) B))))))
% Defined: notequalI2:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((((in Xx) B)->False)->(not (((eq fofType) A) B)))))
% FOF formula (<kernel.Constant object at 0xf5f368>, <kernel.Sort object at 0x101e098>) of role type named subsetRefl_type
% Using role type
% Declaring subsetRefl:Prop
% FOF formula (((eq Prop) subsetRefl) (forall (A:fofType), ((subset A) A))) of role definition named subsetRefl
% A new definition: (((eq Prop) subsetRefl) (forall (A:fofType), ((subset A) A)))
% Defined: subsetRefl:=(forall (A:fofType), ((subset A) A))
% FOF formula (<kernel.Constant object at 0xf5f710>, <kernel.Sort object at 0x101e098>) of role type named subsetTrans_type
% Using role type
% Declaring subsetTrans:Prop
% FOF formula (((eq Prop) subsetTrans) (forall (A:fofType) (B:fofType) (C:fofType), (((subset A) B)->(((subset B) C)->((subset A) C))))) of role definition named subsetTrans
% A new definition: (((eq Prop) subsetTrans) (forall (A:fofType) (B:fofType) (C:fofType), (((subset A) B)->(((subset B) C)->((subset A) C)))))
% Defined: subsetTrans:=(forall (A:fofType) (B:fofType) (C:fofType), (((subset A) B)->(((subset B) C)->((subset A) C))))
% FOF formula (<kernel.Constant object at 0xf5f3b0>, <kernel.Sort object at 0x101e098>) of role type named setadjoinSub_type
% Using role type
% Declaring setadjoinSub:Prop
% FOF formula (((eq Prop) setadjoinSub) (forall (Xx:fofType) (A:fofType), ((subset A) ((setadjoin Xx) A)))) of role definition named setadjoinSub
% A new definition: (((eq Prop) setadjoinSub) (forall (Xx:fofType) (A:fofType), ((subset A) ((setadjoin Xx) A))))
% Defined: setadjoinSub:=(forall (Xx:fofType) (A:fofType), ((subset A) ((setadjoin Xx) A)))
% FOF formula (<kernel.Constant object at 0xf5f5a8>, <kernel.Sort object at 0x101e098>) of role type named setadjoinSub2_type
% Using role type
% Declaring setadjoinSub2:Prop
% FOF formula (((eq Prop) setadjoinSub2) (forall (A:fofType) (Xx:fofType) (B:fofType), (((subset A) B)->((subset A) ((setadjoin Xx) B))))) of role definition named setadjoinSub2
% A new definition: (((eq Prop) setadjoinSub2) (forall (A:fofType) (Xx:fofType) (B:fofType), (((subset A) B)->((subset A) ((setadjoin Xx) B)))))
% Defined: setadjoinSub2:=(forall (A:fofType) (Xx:fofType) (B:fofType), (((subset A) B)->((subset A) ((setadjoin Xx) B))))
% FOF formula (<kernel.Constant object at 0xf5f128>, <kernel.Sort object at 0x101e098>) of role type named subset2powerset_type
% Using role type
% Declaring subset2powerset:Prop
% FOF formula (((eq Prop) subset2powerset) (forall (A:fofType) (B:fofType), (((subset A) B)->((in A) (powerset B))))) of role definition named subset2powerset
% A new definition: (((eq Prop) subset2powerset) (forall (A:fofType) (B:fofType), (((subset A) B)->((in A) (powerset B)))))
% Defined: subset2powerset:=(forall (A:fofType) (B:fofType), (((subset A) B)->((in A) (powerset B))))
% FOF formula (<kernel.Constant object at 0xf5f8c0>, <kernel.Sort object at 0x101e098>) of role type named setextsub_type
% Using role type
% Declaring setextsub:Prop
% FOF formula (((eq Prop) setextsub) (forall (A:fofType) (B:fofType), (((subset A) B)->(((subset B) A)->(((eq fofType) A) B))))) of role definition named setextsub
% A new definition: (((eq Prop) setextsub) (forall (A:fofType) (B:fofType), (((subset A) B)->(((subset B) A)->(((eq fofType) A) B)))))
% Defined: setextsub:=(forall (A:fofType) (B:fofType), (((subset A) B)->(((subset B) A)->(((eq fofType) A) B))))
% FOF formula (<kernel.Constant object at 0xf5f680>, <kernel.Sort object at 0x101e098>) of role type named subsetemptysetimpeq_type
% Using role type
% Declaring subsetemptysetimpeq:Prop
% FOF formula (((eq Prop) subsetemptysetimpeq) (forall (A:fofType), (((subset A) emptyset)->(((eq fofType) A) emptyset)))) of role definition named subsetemptysetimpeq
% A new definition: (((eq Prop) subsetemptysetimpeq) (forall (A:fofType), (((subset A) emptyset)->(((eq fofType) A) emptyset))))
% Defined: subsetemptysetimpeq:=(forall (A:fofType), (((subset A) emptyset)->(((eq fofType) A) emptyset)))
% FOF formula (<kernel.Constant object at 0xf5f200>, <kernel.Sort object at 0x101e098>) of role type named powersetI1_type
% Using role type
% Declaring powersetI1:Prop
% FOF formula (((eq Prop) powersetI1) (forall (A:fofType) (B:fofType), (((subset B) A)->((in B) (powerset A))))) of role definition named powersetI1
% A new definition: (((eq Prop) powersetI1) (forall (A:fofType) (B:fofType), (((subset B) A)->((in B) (powerset A)))))
% Defined: powersetI1:=(forall (A:fofType) (B:fofType), (((subset B) A)->((in B) (powerset A))))
% FOF formula (<kernel.Constant object at 0xf5f950>, <kernel.Sort object at 0x101e098>) of role type named powersetE1_type
% Using role type
% Declaring powersetE1:Prop
% FOF formula (((eq Prop) powersetE1) (forall (A:fofType) (B:fofType), (((in B) (powerset A))->((subset B) A)))) of role definition named powersetE1
% A new definition: (((eq Prop) powersetE1) (forall (A:fofType) (B:fofType), (((in B) (powerset A))->((subset B) A))))
% Defined: powersetE1:=(forall (A:fofType) (B:fofType), (((in B) (powerset A))->((subset B) A)))
% FOF formula (<kernel.Constant object at 0xf5f638>, <kernel.Sort object at 0x101e098>) of role type named inPowerset_type
% Using role type
% Declaring inPowerset:Prop
% FOF formula (((eq Prop) inPowerset) (forall (A:fofType), ((in A) (powerset A)))) of role definition named inPowerset
% A new definition: (((eq Prop) inPowerset) (forall (A:fofType), ((in A) (powerset A))))
% Defined: inPowerset:=(forall (A:fofType), ((in A) (powerset A)))
% FOF formula (<kernel.Constant object at 0xf5f0e0>, <kernel.Sort object at 0x101e098>) of role type named powersetsubset_type
% Using role type
% Declaring powersetsubset:Prop
% FOF formula (((eq Prop) powersetsubset) (forall (A:fofType) (B:fofType), (((subset A) B)->((subset (powerset A)) (powerset B))))) of role definition named powersetsubset
% A new definition: (((eq Prop) powersetsubset) (forall (A:fofType) (B:fofType), (((subset A) B)->((subset (powerset A)) (powerset B)))))
% Defined: powersetsubset:=(forall (A:fofType) (B:fofType), (((subset A) B)->((subset (powerset A)) (powerset B))))
% FOF formula (<kernel.Constant object at 0xf5f4d0>, <kernel.Sort object at 0x101e098>) of role type named sepInPowerset_type
% Using role type
% Declaring sepInPowerset:Prop
% FOF formula (((eq Prop) sepInPowerset) (forall (A:fofType) (Xphi:(fofType->Prop)), ((in ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) (powerset A)))) of role definition named sepInPowerset
% A new definition: (((eq Prop) sepInPowerset) (forall (A:fofType) (Xphi:(fofType->Prop)), ((in ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) (powerset A))))
% Defined: sepInPowerset:=(forall (A:fofType) (Xphi:(fofType->Prop)), ((in ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) (powerset A)))
% FOF formula (<kernel.Constant object at 0xf5f830>, <kernel.Sort object at 0x101e098>) of role type named sepSubset_type
% Using role type
% Declaring sepSubset:Prop
% FOF formula (((eq Prop) sepSubset) (forall (A:fofType) (Xphi:(fofType->Prop)), ((subset ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) A))) of role definition named sepSubset
% A new definition: (((eq Prop) sepSubset) (forall (A:fofType) (Xphi:(fofType->Prop)), ((subset ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) A)))
% Defined: sepSubset:=(forall (A:fofType) (Xphi:(fofType->Prop)), ((subset ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) A))
% FOF formula (<kernel.Constant object at 0xf5fb00>, <kernel.DependentProduct object at 0xf5f7a0>) of role type named binunion_type
% Using role type
% Declaring binunion:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0xf5f518>, <kernel.Sort object at 0x101e098>) of role type named binunionIL_type
% Using role type
% Declaring binunionIL:Prop
% FOF formula (((eq Prop) binunionIL) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((in Xx) ((binunion A) B))))) of role definition named binunionIL
% A new definition: (((eq Prop) binunionIL) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((in Xx) ((binunion A) B)))))
% Defined: binunionIL:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((in Xx) ((binunion A) B))))
% FOF formula (<kernel.Constant object at 0xf5f830>, <kernel.Sort object at 0x101e098>) of role type named upairset2IR_type
% Using role type
% Declaring upairset2IR:Prop
% FOF formula (((eq Prop) upairset2IR) (forall (Xx:fofType) (Xy:fofType), ((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset))))) of role definition named upairset2IR
% A new definition: (((eq Prop) upairset2IR) (forall (Xx:fofType) (Xy:fofType), ((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset)))))
% Defined: upairset2IR:=(forall (Xx:fofType) (Xy:fofType), ((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset))))
% FOF formula (<kernel.Constant object at 0xf5fef0>, <kernel.Sort object at 0x101e098>) of role type named binunionIR_type
% Using role type
% Declaring binunionIR:Prop
% FOF formula (((eq Prop) binunionIR) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) B)->((in Xx) ((binunion A) B))))) of role definition named binunionIR
% A new definition: (((eq Prop) binunionIR) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) B)->((in Xx) ((binunion A) B)))))
% Defined: binunionIR:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) B)->((in Xx) ((binunion A) B))))
% FOF formula (<kernel.Constant object at 0xf5fea8>, <kernel.Sort object at 0x101e098>) of role type named binunionEcases_type
% Using role type
% Declaring binunionEcases:Prop
% FOF formula (((eq Prop) binunionEcases) (forall (A:fofType) (B:fofType) (Xx:fofType) (Xphi:Prop), (((in Xx) ((binunion A) B))->((((in Xx) A)->Xphi)->((((in Xx) B)->Xphi)->Xphi))))) of role definition named binunionEcases
% A new definition: (((eq Prop) binunionEcases) (forall (A:fofType) (B:fofType) (Xx:fofType) (Xphi:Prop), (((in Xx) ((binunion A) B))->((((in Xx) A)->Xphi)->((((in Xx) B)->Xphi)->Xphi)))))
% Defined: binunionEcases:=(forall (A:fofType) (B:fofType) (Xx:fofType) (Xphi:Prop), (((in Xx) ((binunion A) B))->((((in Xx) A)->Xphi)->((((in Xx) B)->Xphi)->Xphi))))
% FOF formula (<kernel.Constant object at 0xf5f5f0>, <kernel.Sort object at 0x101e098>) of role type named binunionE_type
% Using role type
% Declaring binunionE:Prop
% FOF formula (((eq Prop) binunionE) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((binunion A) B))->((or ((in Xx) A)) ((in Xx) B))))) of role definition named binunionE
% A new definition: (((eq Prop) binunionE) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((binunion A) B))->((or ((in Xx) A)) ((in Xx) B)))))
% Defined: binunionE:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((binunion A) B))->((or ((in Xx) A)) ((in Xx) B))))
% FOF formula (<kernel.Constant object at 0xf5fe60>, <kernel.Sort object at 0x101e098>) of role type named binunionLsub_type
% Using role type
% Declaring binunionLsub:Prop
% FOF formula (((eq Prop) binunionLsub) (forall (A:fofType) (B:fofType), ((subset A) ((binunion A) B)))) of role definition named binunionLsub
% A new definition: (((eq Prop) binunionLsub) (forall (A:fofType) (B:fofType), ((subset A) ((binunion A) B))))
% Defined: binunionLsub:=(forall (A:fofType) (B:fofType), ((subset A) ((binunion A) B)))
% FOF formula (<kernel.Constant object at 0xf5fb90>, <kernel.Sort object at 0x101e098>) of role type named binunionRsub_type
% Using role type
% Declaring binunionRsub:Prop
% FOF formula (((eq Prop) binunionRsub) (forall (A:fofType) (B:fofType), ((subset B) ((binunion A) B)))) of role definition named binunionRsub
% A new definition: (((eq Prop) binunionRsub) (forall (A:fofType) (B:fofType), ((subset B) ((binunion A) B))))
% Defined: binunionRsub:=(forall (A:fofType) (B:fofType), ((subset B) ((binunion A) B)))
% FOF formula (<kernel.Constant object at 0xf5fcf8>, <kernel.DependentProduct object at 0xf5ff38>) of role type named binintersect_type
% Using role type
% Declaring binintersect:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0xf5fcb0>, <kernel.Sort object at 0x101e098>) of role type named binintersectI_type
% Using role type
% Declaring binintersectI:Prop
% FOF formula (((eq Prop) binintersectI) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(((in Xx) B)->((in Xx) ((binintersect A) B)))))) of role definition named binintersectI
% A new definition: (((eq Prop) binintersectI) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(((in Xx) B)->((in Xx) ((binintersect A) B))))))
% Defined: binintersectI:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(((in Xx) B)->((in Xx) ((binintersect A) B)))))
% FOF formula (<kernel.Constant object at 0xf5fb90>, <kernel.Sort object at 0x101e098>) of role type named binintersectSubset5_type
% Using role type
% Declaring binintersectSubset5:Prop
% FOF formula (((eq Prop) binintersectSubset5) (forall (A:fofType) (B:fofType) (C:fofType), (((subset C) A)->(((subset C) B)->((subset C) ((binintersect A) B)))))) of role definition named binintersectSubset5
% A new definition: (((eq Prop) binintersectSubset5) (forall (A:fofType) (B:fofType) (C:fofType), (((subset C) A)->(((subset C) B)->((subset C) ((binintersect A) B))))))
% Defined: binintersectSubset5:=(forall (A:fofType) (B:fofType) (C:fofType), (((subset C) A)->(((subset C) B)->((subset C) ((binintersect A) B)))))
% FOF formula (<kernel.Constant object at 0xf5fcf8>, <kernel.Sort object at 0x101e098>) of role type named binintersectEL_type
% Using role type
% Declaring binintersectEL:Prop
% FOF formula (((eq Prop) binintersectEL) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((binintersect A) B))->((in Xx) A)))) of role definition named binintersectEL
% A new definition: (((eq Prop) binintersectEL) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((binintersect A) B))->((in Xx) A))))
% Defined: binintersectEL:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((binintersect A) B))->((in Xx) A)))
% FOF formula (<kernel.Constant object at 0xf5fb48>, <kernel.Sort object at 0x101e098>) of role type named binintersectLsub_type
% Using role type
% Declaring binintersectLsub:Prop
% FOF formula (((eq Prop) binintersectLsub) (forall (A:fofType) (B:fofType), ((subset ((binintersect A) B)) A))) of role definition named binintersectLsub
% A new definition: (((eq Prop) binintersectLsub) (forall (A:fofType) (B:fofType), ((subset ((binintersect A) B)) A)))
% Defined: binintersectLsub:=(forall (A:fofType) (B:fofType), ((subset ((binintersect A) B)) A))
% FOF formula (<kernel.Constant object at 0xf5fd40>, <kernel.Sort object at 0x101e098>) of role type named binintersectSubset2_type
% Using role type
% Declaring binintersectSubset2:Prop
% FOF formula (((eq Prop) binintersectSubset2) (forall (A:fofType) (B:fofType), (((subset A) B)->(((eq fofType) ((binintersect A) B)) A)))) of role definition named binintersectSubset2
% A new definition: (((eq Prop) binintersectSubset2) (forall (A:fofType) (B:fofType), (((subset A) B)->(((eq fofType) ((binintersect A) B)) A))))
% Defined: binintersectSubset2:=(forall (A:fofType) (B:fofType), (((subset A) B)->(((eq fofType) ((binintersect A) B)) A)))
% FOF formula (<kernel.Constant object at 0xf5fd40>, <kernel.Sort object at 0x101e098>) of role type named binintersectSubset3_type
% Using role type
% Declaring binintersectSubset3:Prop
% FOF formula (((eq Prop) binintersectSubset3) (forall (A:fofType) (B:fofType), ((((eq fofType) ((binintersect A) B)) B)->((subset B) A)))) of role definition named binintersectSubset3
% A new definition: (((eq Prop) binintersectSubset3) (forall (A:fofType) (B:fofType), ((((eq fofType) ((binintersect A) B)) B)->((subset B) A))))
% Defined: binintersectSubset3:=(forall (A:fofType) (B:fofType), ((((eq fofType) ((binintersect A) B)) B)->((subset B) A)))
% FOF formula (<kernel.Constant object at 0xf5fd40>, <kernel.Sort object at 0x101e098>) of role type named binintersectER_type
% Using role type
% Declaring binintersectER:Prop
% FOF formula (((eq Prop) binintersectER) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((binintersect A) B))->((in Xx) B)))) of role definition named binintersectER
% A new definition: (((eq Prop) binintersectER) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((binintersect A) B))->((in Xx) B))))
% Defined: binintersectER:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((binintersect A) B))->((in Xx) B)))
% FOF formula (<kernel.Constant object at 0xf675a8>, <kernel.Sort object at 0x101e098>) of role type named disjointsetsI1_type
% Using role type
% Declaring disjointsetsI1:Prop
% FOF formula (((eq Prop) disjointsetsI1) (forall (A:fofType) (B:fofType), ((((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((in Xx) B))))->False)->(((eq fofType) ((binintersect A) B)) emptyset)))) of role definition named disjointsetsI1
% A new definition: (((eq Prop) disjointsetsI1) (forall (A:fofType) (B:fofType), ((((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((in Xx) B))))->False)->(((eq fofType) ((binintersect A) B)) emptyset))))
% Defined: disjointsetsI1:=(forall (A:fofType) (B:fofType), ((((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((in Xx) B))))->False)->(((eq fofType) ((binintersect A) B)) emptyset)))
% FOF formula (<kernel.Constant object at 0xf67440>, <kernel.Sort object at 0x101e098>) of role type named binintersectRsub_type
% Using role type
% Declaring binintersectRsub:Prop
% FOF formula (((eq Prop) binintersectRsub) (forall (A:fofType) (B:fofType), ((subset ((binintersect A) B)) B))) of role definition named binintersectRsub
% A new definition: (((eq Prop) binintersectRsub) (forall (A:fofType) (B:fofType), ((subset ((binintersect A) B)) B)))
% Defined: binintersectRsub:=(forall (A:fofType) (B:fofType), ((subset ((binintersect A) B)) B))
% FOF formula (<kernel.Constant object at 0xf67050>, <kernel.Sort object at 0x101e098>) of role type named binintersectSubset4_type
% Using role type
% Declaring binintersectSubset4:Prop
% FOF formula (((eq Prop) binintersectSubset4) (forall (A:fofType) (B:fofType), (((subset B) A)->(((eq fofType) ((binintersect A) B)) B)))) of role definition named binintersectSubset4
% A new definition: (((eq Prop) binintersectSubset4) (forall (A:fofType) (B:fofType), (((subset B) A)->(((eq fofType) ((binintersect A) B)) B))))
% Defined: binintersectSubset4:=(forall (A:fofType) (B:fofType), (((subset B) A)->(((eq fofType) ((binintersect A) B)) B)))
% FOF formula (<kernel.Constant object at 0xf67488>, <kernel.Sort object at 0x101e098>) of role type named binintersectSubset1_type
% Using role type
% Declaring binintersectSubset1:Prop
% FOF formula (((eq Prop) binintersectSubset1) (forall (A:fofType) (B:fofType), ((((eq fofType) ((binintersect A) B)) A)->((subset A) B)))) of role definition named binintersectSubset1
% A new definition: (((eq Prop) binintersectSubset1) (forall (A:fofType) (B:fofType), ((((eq fofType) ((binintersect A) B)) A)->((subset A) B))))
% Defined: binintersectSubset1:=(forall (A:fofType) (B:fofType), ((((eq fofType) ((binintersect A) B)) A)->((subset A) B)))
% FOF formula (<kernel.Constant object at 0xf675f0>, <kernel.Sort object at 0x101e098>) of role type named bs114d_type
% Using role type
% Declaring bs114d:Prop
% FOF formula (((eq Prop) bs114d) (forall (A:fofType) (B:fofType) (C:fofType), (((eq fofType) ((binintersect A) ((binunion B) C))) ((binunion ((binintersect A) B)) ((binintersect A) C))))) of role definition named bs114d
% A new definition: (((eq Prop) bs114d) (forall (A:fofType) (B:fofType) (C:fofType), (((eq fofType) ((binintersect A) ((binunion B) C))) ((binunion ((binintersect A) B)) ((binintersect A) C)))))
% Defined: bs114d:=(forall (A:fofType) (B:fofType) (C:fofType), (((eq fofType) ((binintersect A) ((binunion B) C))) ((binunion ((binintersect A) B)) ((binintersect A) C))))
% FOF formula (<kernel.Constant object at 0xf67710>, <kernel.DependentProduct object at 0xf677a0>) of role type named regular_type
% Using role type
% Declaring regular:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0xf67128>, <kernel.DependentProduct object at 0xf672d8>) of role type named setminus_type
% Using role type
% Declaring setminus:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0xf675f0>, <kernel.Sort object at 0x101e098>) of role type named setminusI_type
% Using role type
% Declaring setminusI:Prop
% FOF formula (((eq Prop) setminusI) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((((in Xx) B)->False)->((in Xx) ((setminus A) B)))))) of role definition named setminusI
% A new definition: (((eq Prop) setminusI) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((((in Xx) B)->False)->((in Xx) ((setminus A) B))))))
% Defined: setminusI:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((((in Xx) B)->False)->((in Xx) ((setminus A) B)))))
% FOF formula (<kernel.Constant object at 0xf67680>, <kernel.Sort object at 0x101e098>) of role type named setminusEL_type
% Using role type
% Declaring setminusEL:Prop
% FOF formula (((eq Prop) setminusEL) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((setminus A) B))->((in Xx) A)))) of role definition named setminusEL
% A new definition: (((eq Prop) setminusEL) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((setminus A) B))->((in Xx) A))))
% Defined: setminusEL:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((setminus A) B))->((in Xx) A)))
% FOF formula (<kernel.Constant object at 0xf67878>, <kernel.Sort object at 0x101e098>) of role type named setminusER_type
% Using role type
% Declaring setminusER:Prop
% FOF formula (((eq Prop) setminusER) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((setminus A) B))->(((in Xx) B)->False)))) of role definition named setminusER
% A new definition: (((eq Prop) setminusER) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((setminus A) B))->(((in Xx) B)->False))))
% Defined: setminusER:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((setminus A) B))->(((in Xx) B)->False)))
% FOF formula (<kernel.Constant object at 0xf67a28>, <kernel.Sort object at 0x101e098>) of role type named setminusSubset2_type
% Using role type
% Declaring setminusSubset2:Prop
% FOF formula (((eq Prop) setminusSubset2) (forall (A:fofType) (B:fofType), (((subset A) B)->(((eq fofType) ((setminus A) B)) emptyset)))) of role definition named setminusSubset2
% A new definition: (((eq Prop) setminusSubset2) (forall (A:fofType) (B:fofType), (((subset A) B)->(((eq fofType) ((setminus A) B)) emptyset))))
% Defined: setminusSubset2:=(forall (A:fofType) (B:fofType), (((subset A) B)->(((eq fofType) ((setminus A) B)) emptyset)))
% FOF formula (<kernel.Constant object at 0xf67950>, <kernel.Sort object at 0x101e098>) of role type named setminusERneg_type
% Using role type
% Declaring setminusERneg:Prop
% FOF formula (((eq Prop) setminusERneg) (forall (A:fofType) (B:fofType) (Xx:fofType), ((((in Xx) ((setminus A) B))->False)->(((in Xx) A)->((in Xx) B))))) of role definition named setminusERneg
% A new definition: (((eq Prop) setminusERneg) (forall (A:fofType) (B:fofType) (Xx:fofType), ((((in Xx) ((setminus A) B))->False)->(((in Xx) A)->((in Xx) B)))))
% Defined: setminusERneg:=(forall (A:fofType) (B:fofType) (Xx:fofType), ((((in Xx) ((setminus A) B))->False)->(((in Xx) A)->((in Xx) B))))
% FOF formula (<kernel.Constant object at 0xf67c20>, <kernel.Sort object at 0x101e098>) of role type named setminusELneg_type
% Using role type
% Declaring setminusELneg:Prop
% FOF formula (((eq Prop) setminusELneg) (forall (A:fofType) (B:fofType) (Xx:fofType), ((((in Xx) ((setminus A) B))->False)->((((in Xx) B)->False)->(((in Xx) A)->False))))) of role definition named setminusELneg
% A new definition: (((eq Prop) setminusELneg) (forall (A:fofType) (B:fofType) (Xx:fofType), ((((in Xx) ((setminus A) B))->False)->((((in Xx) B)->False)->(((in Xx) A)->False)))))
% Defined: setminusELneg:=(forall (A:fofType) (B:fofType) (Xx:fofType), ((((in Xx) ((setminus A) B))->False)->((((in Xx) B)->False)->(((in Xx) A)->False))))
% FOF formula (<kernel.Constant object at 0xf67248>, <kernel.Sort object at 0x101e098>) of role type named setminusILneg_type
% Using role type
% Declaring setminusILneg:Prop
% FOF formula (((eq Prop) setminusILneg) (forall (A:fofType) (B:fofType) (Xx:fofType), ((((in Xx) A)->False)->(((in Xx) ((setminus A) B))->False)))) of role definition named setminusILneg
% A new definition: (((eq Prop) setminusILneg) (forall (A:fofType) (B:fofType) (Xx:fofType), ((((in Xx) A)->False)->(((in Xx) ((setminus A) B))->False))))
% Defined: setminusILneg:=(forall (A:fofType) (B:fofType) (Xx:fofType), ((((in Xx) A)->False)->(((in Xx) ((setminus A) B))->False)))
% FOF formula (<kernel.Constant object at 0xf67098>, <kernel.Sort object at 0x101e098>) of role type named setminusIRneg_type
% Using role type
% Declaring setminusIRneg:Prop
% FOF formula (((eq Prop) setminusIRneg) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) B)->(((in Xx) ((setminus A) B))->False)))) of role definition named setminusIRneg
% A new definition: (((eq Prop) setminusIRneg) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) B)->(((in Xx) ((setminus A) B))->False))))
% Defined: setminusIRneg:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) B)->(((in Xx) ((setminus A) B))->False)))
% FOF formula (<kernel.Constant object at 0xf67b48>, <kernel.Sort object at 0x101e098>) of role type named setminusLsub_type
% Using role type
% Declaring setminusLsub:Prop
% FOF formula (((eq Prop) setminusLsub) (forall (A:fofType) (B:fofType), ((subset ((setminus A) B)) A))) of role definition named setminusLsub
% A new definition: (((eq Prop) setminusLsub) (forall (A:fofType) (B:fofType), ((subset ((setminus A) B)) A)))
% Defined: setminusLsub:=(forall (A:fofType) (B:fofType), ((subset ((setminus A) B)) A))
% FOF formula (<kernel.Constant object at 0xf67638>, <kernel.Sort object at 0x101e098>) of role type named setminusSubset1_type
% Using role type
% Declaring setminusSubset1:Prop
% FOF formula (((eq Prop) setminusSubset1) (forall (A:fofType) (B:fofType), ((((eq fofType) ((setminus A) B)) emptyset)->((subset A) B)))) of role definition named setminusSubset1
% A new definition: (((eq Prop) setminusSubset1) (forall (A:fofType) (B:fofType), ((((eq fofType) ((setminus A) B)) emptyset)->((subset A) B))))
% Defined: setminusSubset1:=(forall (A:fofType) (B:fofType), ((((eq fofType) ((setminus A) B)) emptyset)->((subset A) B)))
% FOF formula (<kernel.Constant object at 0xf67d88>, <kernel.DependentProduct object at 0xf67ea8>) of role type named symdiff_type
% Using role type
% Declaring symdiff:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0xf67fc8>, <kernel.Sort object at 0x101e098>) of role type named symdiffE_type
% Using role type
% Declaring symdiffE:Prop
% FOF formula (((eq Prop) symdiffE) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((symdiff A) B))->(forall (Xphi:Prop), ((((in Xx) A)->((((in Xx) B)->False)->Xphi))->(((((in Xx) A)->False)->(((in Xx) B)->Xphi))->Xphi)))))) of role definition named symdiffE
% A new definition: (((eq Prop) symdiffE) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((symdiff A) B))->(forall (Xphi:Prop), ((((in Xx) A)->((((in Xx) B)->False)->Xphi))->(((((in Xx) A)->False)->(((in Xx) B)->Xphi))->Xphi))))))
% Defined: symdiffE:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((symdiff A) B))->(forall (Xphi:Prop), ((((in Xx) A)->((((in Xx) B)->False)->Xphi))->(((((in Xx) A)->False)->(((in Xx) B)->Xphi))->Xphi)))))
% FOF formula (<kernel.Constant object at 0xf67638>, <kernel.Sort object at 0x101e098>) of role type named symdiffI1_type
% Using role type
% Declaring symdiffI1:Prop
% FOF formula (((eq Prop) symdiffI1) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((((in Xx) B)->False)->((in Xx) ((symdiff A) B)))))) of role definition named symdiffI1
% A new definition: (((eq Prop) symdiffI1) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((((in Xx) B)->False)->((in Xx) ((symdiff A) B))))))
% Defined: symdiffI1:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((((in Xx) B)->False)->((in Xx) ((symdiff A) B)))))
% FOF formula (<kernel.Constant object at 0xf677a0>, <kernel.Sort object at 0x101e098>) of role type named symdiffI2_type
% Using role type
% Declaring symdiffI2:Prop
% FOF formula (((eq Prop) symdiffI2) (forall (A:fofType) (B:fofType) (Xx:fofType), ((((in Xx) A)->False)->(((in Xx) B)->((in Xx) ((symdiff A) B)))))) of role definition named symdiffI2
% A new definition: (((eq Prop) symdiffI2) (forall (A:fofType) (B:fofType) (Xx:fofType), ((((in Xx) A)->False)->(((in Xx) B)->((in Xx) ((symdiff A) B))))))
% Defined: symdiffI2:=(forall (A:fofType) (B:fofType) (Xx:fofType), ((((in Xx) A)->False)->(((in Xx) B)->((in Xx) ((symdiff A) B)))))
% FOF formula (<kernel.Constant object at 0xf67908>, <kernel.Sort object at 0x101e098>) of role type named symdiffIneg1_type
% Using role type
% Declaring symdiffIneg1:Prop
% FOF formula (((eq Prop) symdiffIneg1) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(((in Xx) B)->(((in Xx) ((symdiff A) B))->False))))) of role definition named symdiffIneg1
% A new definition: (((eq Prop) symdiffIneg1) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(((in Xx) B)->(((in Xx) ((symdiff A) B))->False)))))
% Defined: symdiffIneg1:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(((in Xx) B)->(((in Xx) ((symdiff A) B))->False))))
% FOF formula (<kernel.Constant object at 0xf67710>, <kernel.Sort object at 0x101e098>) of role type named symdiffIneg2_type
% Using role type
% Declaring symdiffIneg2:Prop
% FOF formula (((eq Prop) symdiffIneg2) (forall (A:fofType) (B:fofType) (Xx:fofType), ((((in Xx) A)->False)->((((in Xx) B)->False)->(((in Xx) ((symdiff A) B))->False))))) of role definition named symdiffIneg2
% A new definition: (((eq Prop) symdiffIneg2) (forall (A:fofType) (B:fofType) (Xx:fofType), ((((in Xx) A)->False)->((((in Xx) B)->False)->(((in Xx) ((symdiff A) B))->False)))))
% Defined: symdiffIneg2:=(forall (A:fofType) (B:fofType) (Xx:fofType), ((((in Xx) A)->False)->((((in Xx) B)->False)->(((in Xx) ((symdiff A) B))->False))))
% FOF formula (<kernel.Constant object at 0xf67f80>, <kernel.DependentProduct object at 0xf67c68>) of role type named iskpair_type
% Using role type
% Declaring iskpair:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) iskpair) (fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) (setunion A))) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) (setunion A))) (((eq fofType) A) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))))))))))) of role definition named iskpair
% A new definition: (((eq (fofType->Prop)) iskpair) (fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) (setunion A))) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) (setunion A))) (((eq fofType) A) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset)))))))))))
% Defined: iskpair:=(fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) (setunion A))) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) (setunion A))) (((eq fofType) A) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))))))))))
% FOF formula (<kernel.Constant object at 0xf67710>, <kernel.Sort object at 0x101e098>) 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 0xf67d88>, <kernel.Sort object at 0x101e098>) of role type named setukpairIL_type
% Using role type
% Declaring setukpairIL:Prop
% FOF formula (((eq Prop) setukpairIL) (forall (Xx:fofType) (Xy:fofType), ((in Xx) (setunion ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset)))))) of role definition named setukpairIL
% A new definition: (((eq Prop) setukpairIL) (forall (Xx:fofType) (Xy:fofType), ((in Xx) (setunion ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))))))
% Defined: setukpairIL:=(forall (Xx:fofType) (Xy:fofType), ((in Xx) (setunion ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset)))))
% FOF formula (<kernel.Constant object at 0xf670e0>, <kernel.Sort object at 0x101e098>) of role type named setukpairIR_type
% Using role type
% Declaring setukpairIR:Prop
% FOF formula (((eq Prop) setukpairIR) (forall (Xx:fofType) (Xy:fofType), ((in Xy) (setunion ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset)))))) of role definition named setukpairIR
% A new definition: (((eq Prop) setukpairIR) (forall (Xx:fofType) (Xy:fofType), ((in Xy) (setunion ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))))))
% Defined: setukpairIR:=(forall (Xx:fofType) (Xy:fofType), ((in Xy) (setunion ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset)))))
% FOF formula (<kernel.Constant object at 0xf676c8>, <kernel.Sort object at 0x101e098>) of role type named kpairiskpair_type
% Using role type
% Declaring kpairiskpair:Prop
% FOF formula (((eq Prop) kpairiskpair) (forall (Xx:fofType) (Xy:fofType), (iskpair ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))))) of role definition named kpairiskpair
% A new definition: (((eq Prop) kpairiskpair) (forall (Xx:fofType) (Xy:fofType), (iskpair ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset)))))
% Defined: kpairiskpair:=(forall (Xx:fofType) (Xy:fofType), (iskpair ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))))
% FOF formula (<kernel.Constant object at 0xf676c8>, <kernel.DependentProduct object at 0xd944d0>) of role type named kpair_type
% Using role type
% Declaring kpair:(fofType->(fofType->fofType))
% FOF formula (((eq (fofType->(fofType->fofType))) kpair) (fun (Xx:fofType) (Xy:fofType)=> ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset)))) of role definition named kpair
% A new definition: (((eq (fofType->(fofType->fofType))) kpair) (fun (Xx:fofType) (Xy:fofType)=> ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))))
% Defined: kpair:=(fun (Xx:fofType) (Xy:fofType)=> ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset)))
% FOF formula (<kernel.Constant object at 0xf67d88>, <kernel.Sort object at 0x101e098>) of role type named kpairp_type
% Using role type
% Declaring kpairp:Prop
% FOF formula (((eq Prop) kpairp) (forall (Xx:fofType) (Xy:fofType), (iskpair ((kpair Xx) Xy)))) of role definition named kpairp
% A new definition: (((eq Prop) kpairp) (forall (Xx:fofType) (Xy:fofType), (iskpair ((kpair Xx) Xy))))
% Defined: kpairp:=(forall (Xx:fofType) (Xy:fofType), (iskpair ((kpair Xx) Xy)))
% FOF formula (<kernel.Constant object at 0xd943f8>, <kernel.DependentProduct object at 0xd944d0>) of role type named cartprod_type
% Using role type
% Declaring cartprod:(fofType->(fofType->fofType))
% FOF formula (((eq (fofType->(fofType->fofType))) cartprod) (fun (A:fofType) (B:fofType)=> ((dsetconstr (powerset (powerset ((binunion A) B)))) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) ((ex fofType) (fun (Xz:fofType)=> ((and ((in Xz) B)) (((eq fofType) Xx) ((kpair Xy) Xz)))))))))))) of role definition named cartprod
% A new definition: (((eq (fofType->(fofType->fofType))) cartprod) (fun (A:fofType) (B:fofType)=> ((dsetconstr (powerset (powerset ((binunion A) B)))) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) ((ex fofType) (fun (Xz:fofType)=> ((and ((in Xz) B)) (((eq fofType) Xx) ((kpair Xy) Xz))))))))))))
% Defined: cartprod:=(fun (A:fofType) (B:fofType)=> ((dsetconstr (powerset (powerset ((binunion A) B)))) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) ((ex fofType) (fun (Xz:fofType)=> ((and ((in Xz) B)) (((eq fofType) Xx) ((kpair Xy) Xz)))))))))))
% FOF formula (<kernel.Constant object at 0xd944d0>, <kernel.Sort object at 0x101e098>) of role type named singletonsubset_type
% Using role type
% Declaring singletonsubset:Prop
% FOF formula (((eq Prop) singletonsubset) (forall (A:fofType) (Xx:fofType), (((in Xx) A)->((subset ((setadjoin Xx) emptyset)) A)))) of role definition named singletonsubset
% A new definition: (((eq Prop) singletonsubset) (forall (A:fofType) (Xx:fofType), (((in Xx) A)->((subset ((setadjoin Xx) emptyset)) A))))
% Defined: singletonsubset:=(forall (A:fofType) (Xx:fofType), (((in Xx) A)->((subset ((setadjoin Xx) emptyset)) A)))
% FOF formula (<kernel.Constant object at 0xd940e0>, <kernel.Sort object at 0x101e098>) of role type named singletoninpowerset_type
% Using role type
% Declaring singletoninpowerset:Prop
% FOF formula (((eq Prop) singletoninpowerset) (forall (A:fofType) (Xx:fofType), (((in Xx) A)->((in ((setadjoin Xx) emptyset)) (powerset A))))) of role definition named singletoninpowerset
% A new definition: (((eq Prop) singletoninpowerset) (forall (A:fofType) (Xx:fofType), (((in Xx) A)->((in ((setadjoin Xx) emptyset)) (powerset A)))))
% Defined: singletoninpowerset:=(forall (A:fofType) (Xx:fofType), (((in Xx) A)->((in ((setadjoin Xx) emptyset)) (powerset A))))
% FOF formula (<kernel.Constant object at 0xd94710>, <kernel.Sort object at 0x101e098>) of role type named singletoninpowunion_type
% Using role type
% Declaring singletoninpowunion:Prop
% FOF formula (((eq Prop) singletoninpowunion) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((in ((setadjoin Xx) emptyset)) (powerset ((binunion A) B)))))) of role definition named singletoninpowunion
% A new definition: (((eq Prop) singletoninpowunion) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((in ((setadjoin Xx) emptyset)) (powerset ((binunion A) B))))))
% Defined: singletoninpowunion:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((in ((setadjoin Xx) emptyset)) (powerset ((binunion A) B)))))
% FOF formula (<kernel.Constant object at 0xd947a0>, <kernel.Sort object at 0x101e098>) of role type named upairset2E_type
% Using role type
% Declaring upairset2E:Prop
% FOF formula (((eq Prop) upairset2E) (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((in Xz) ((setadjoin Xx) ((setadjoin Xy) emptyset)))->((or (((eq fofType) Xz) Xx)) (((eq fofType) Xz) Xy))))) of role definition named upairset2E
% A new definition: (((eq Prop) upairset2E) (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((in Xz) ((setadjoin Xx) ((setadjoin Xy) emptyset)))->((or (((eq fofType) Xz) Xx)) (((eq fofType) Xz) Xy)))))
% Defined: upairset2E:=(forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((in Xz) ((setadjoin Xx) ((setadjoin Xy) emptyset)))->((or (((eq fofType) Xz) Xx)) (((eq fofType) Xz) Xy))))
% FOF formula (<kernel.Constant object at 0xd94680>, <kernel.Sort object at 0x101e098>) of role type named upairsubunion_type
% Using role type
% Declaring upairsubunion:Prop
% FOF formula (((eq Prop) upairsubunion) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((subset ((setadjoin Xx) ((setadjoin Xy) emptyset))) ((binunion A) B))))))) of role definition named upairsubunion
% A new definition: (((eq Prop) upairsubunion) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((subset ((setadjoin Xx) ((setadjoin Xy) emptyset))) ((binunion A) B)))))))
% Defined: upairsubunion:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((subset ((setadjoin Xx) ((setadjoin Xy) emptyset))) ((binunion A) B))))))
% FOF formula (<kernel.Constant object at 0xd94b48>, <kernel.Sort object at 0x101e098>) of role type named upairinpowunion_type
% Using role type
% Declaring upairinpowunion:Prop
% FOF formula (((eq Prop) upairinpowunion) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((in ((setadjoin Xx) ((setadjoin Xy) emptyset))) (powerset ((binunion A) B)))))))) of role definition named upairinpowunion
% A new definition: (((eq Prop) upairinpowunion) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((in ((setadjoin Xx) ((setadjoin Xy) emptyset))) (powerset ((binunion A) B))))))))
% Defined: upairinpowunion:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((in ((setadjoin Xx) ((setadjoin Xy) emptyset))) (powerset ((binunion A) B)))))))
% FOF formula (<kernel.Constant object at 0xd94560>, <kernel.Sort object at 0x101e098>) of role type named ubforcartprodlem1_type
% Using role type
% Declaring ubforcartprodlem1:Prop
% FOF formula (((eq Prop) ubforcartprodlem1) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((subset ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset ((binunion A) B)))))))) of role definition named ubforcartprodlem1
% A new definition: (((eq Prop) ubforcartprodlem1) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((subset ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset ((binunion A) B))))))))
% Defined: ubforcartprodlem1:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((subset ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset ((binunion A) B)))))))
% FOF formula (<kernel.Constant object at 0xd94320>, <kernel.Sort object at 0x101e098>) of role type named ubforcartprodlem2_type
% Using role type
% Declaring ubforcartprodlem2:Prop
% FOF formula (((eq Prop) ubforcartprodlem2) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((in ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset (powerset ((binunion A) B))))))))) of role definition named ubforcartprodlem2
% A new definition: (((eq Prop) ubforcartprodlem2) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((in ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset (powerset ((binunion A) B)))))))))
% Defined: ubforcartprodlem2:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((in ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset (powerset ((binunion A) B))))))))
% FOF formula (<kernel.Constant object at 0xd94c68>, <kernel.Sort object at 0x101e098>) of role type named ubforcartprodlem3_type
% Using role type
% Declaring ubforcartprodlem3:Prop
% FOF formula (((eq Prop) ubforcartprodlem3) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((in ((kpair Xx) Xy)) (powerset (powerset ((binunion A) B))))))))) of role definition named ubforcartprodlem3
% A new definition: (((eq Prop) ubforcartprodlem3) (forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((in ((kpair Xx) Xy)) (powerset (powerset ((binunion A) B)))))))))
% Defined: ubforcartprodlem3:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((in ((kpair Xx) Xy)) (powerset (powerset ((binunion A) B))))))))
% FOF formula (setextAx->(emptysetAx->(setadjoinAx->(powersetAx->(setunionAx->(omega0Ax->(omegaSAx->(omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(nonemptyI->(nonemptyI1->(setadjoinIL->(emptyinunitempty->(setadjoinIR->(setadjoinE->(setadjoinOr->(setoftrueEq->(powersetI->(emptyinPowerset->(emptyInPowerset->(powersetE->(setunionI->(setunionE->(subPowSU->(exuE2->(nonemptyImpWitness->(uniqinunit->(notinsingleton->(eqinunit->(singletonsswitch->(upairsetE->(upairsetIL->(upairsetIR->(emptyE1->(vacuousDall->(quantDeMorgan1->(quantDeMorgan2->(quantDeMorgan3->(quantDeMorgan4->(prop2setI->(prop2set2propI->(notdexE->(notdallE->(exuI1->(exuI3->(exuI2->(inCongP->(in__Cong->(exuE3u->(exu__Cong->(emptyset__Cong->(setadjoin__Cong->(powerset__Cong->(setunion__Cong->(omega__Cong->(exuEu->(descr__Cong->(dsetconstr__Cong->(subsetI1->(eqimpsubset2->(eqimpsubset1->(subsetI2->(emptysetsubset->(subsetE->(subsetE2->(notsubsetI->(notequalI1->(notequalI2->(subsetRefl->(subsetTrans->(setadjoinSub->(setadjoinSub2->(subset2powerset->(setextsub->(subsetemptysetimpeq->(powersetI1->(powersetE1->(inPowerset->(powersetsubset->(sepInPowerset->(sepSubset->(binunionIL->(upairset2IR->(binunionIR->(binunionEcases->(binunionE->(binunionLsub->(binunionRsub->(binintersectI->(binintersectSubset5->(binintersectEL->(binintersectLsub->(binintersectSubset2->(binintersectSubset3->(binintersectER->(disjointsetsI1->(binintersectRsub->(binintersectSubset4->(binintersectSubset1->(bs114d->(setminusI->(setminusEL->(setminusER->(setminusSubset2->(setminusERneg->(setminusELneg->(setminusILneg->(setminusIRneg->(setminusLsub->(setminusSubset1->(symdiffE->(symdiffI1->(symdiffI2->(symdiffIneg1->(symdiffIneg2->(secondinupair->(setukpairIL->(setukpairIR->(kpairiskpair->(kpairp->(singletonsubset->(singletoninpowerset->(singletoninpowunion->(upairset2E->(upairsubunion->(upairinpowunion->(ubforcartprodlem1->(ubforcartprodlem2->(ubforcartprodlem3->(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((in ((kpair Xx) Xy)) ((cartprod A) B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) of role conjecture named cartprodpairin
% Conjecture to prove = (setextAx->(emptysetAx->(setadjoinAx->(powersetAx->(setunionAx->(omega0Ax->(omegaSAx->(omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(nonemptyI->(nonemptyI1->(setadjoinIL->(emptyinunitempty->(setadjoinIR->(setadjoinE->(setadjoinOr->(setoftrueEq->(powersetI->(emptyinPowerset->(emptyInPowerset->(powersetE->(setunionI->(setunionE->(subPowSU->(exuE2->(nonemptyImpWitness->(uniqinunit->(notinsingleton->(eqinunit->(singletonsswitch->(upairsetE->(upairsetIL->(upairsetIR->(emptyE1->(vacuousDall->(quantDeMorgan1->(quantDeMorgan2->(quantDeMorgan3->(quantDeMorgan4->(prop2setI->(prop2set2propI->(notdexE->(notdallE->(exuI1->(exuI3->(exuI2->(inCongP->(in__Cong->(exuE3u->(exu__Cong->(emptyset__Cong->(setadjoin__Cong->(powerset__Cong->(setunion__Cong->(omega__Cong->(exuEu->(descr__Cong->(dsetconstr__Cong->(subsetI1->(eqimpsubset2->(eqimpsubset1->(subsetI2->(emptysetsubset->(subsetE->(subsetE2->(notsubsetI->(notequalI1->(notequalI2->(subsetRefl->(subsetTrans->(setadjoinSub->(setadjoinSub2->(subset2powerset->(setextsub->(subsetemptysetimpeq->(powersetI1->(powersetE1->(inPowerset->(powersetsubset->(sepInPowerset->(sepSubset->(binunionIL->(upairset2IR->(binunionIR->(binunionEcases->(binunionE->(binunionLsub->(binunionRsub->(binintersectI->(binintersectSubset5->(binintersectEL->(binintersectLsub->(binintersectSubset2->(binintersectSubset3->(binintersectER->(disjointsetsI1->(binintersectRsub->(binintersectSubset4->(binintersectSubset1->(bs114d->(setminusI->(setminusEL->(setminusER->(setminusSubset2->(setminusERneg->(setminusELneg->(setminusILneg->(setminusIRneg->(setminusLsub->(setminusSubset1->(symdiffE->(symdiffI1->(symdiffI2->(symdiffIneg1->(symdiffIneg2->(secondinupair->(setukpairIL->(setukpairIR->(kpairiskpair->(kpairp->(singletonsubset->(singletoninpowerset->(singletoninpowunion->(upairset2E->(upairsubunion->(upairinpowunion->(ubforcartprodlem1->(ubforcartprodlem2->(ubforcartprodlem3->(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((in ((kpair Xx) Xy)) ((cartprod A) B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))):Prop
% We need to prove ['(setextAx->(emptysetAx->(setadjoinAx->(powersetAx->(setunionAx->(omega0Ax->(omegaSAx->(omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(nonemptyI->(nonemptyI1->(setadjoinIL->(emptyinunitempty->(setadjoinIR->(setadjoinE->(setadjoinOr->(setoftrueEq->(powersetI->(emptyinPowerset->(emptyInPowerset->(powersetE->(setunionI->(setunionE->(subPowSU->(exuE2->(nonemptyImpWitness->(uniqinunit->(notinsingleton->(eqinunit->(singletonsswitch->(upairsetE->(upairsetIL->(upairsetIR->(emptyE1->(vacuousDall->(quantDeMorgan1->(quantDeMorgan2->(quantDeMorgan3->(quantDeMorgan4->(prop2setI->(prop2set2propI->(notdexE->(notdallE->(exuI1->(exuI3->(exuI2->(inCongP->(in__Cong->(exuE3u->(exu__Cong->(emptyset__Cong->(setadjoin__Cong->(powerset__Cong->(setunion__Cong->(omega__Cong->(exuEu->(descr__Cong->(dsetconstr__Cong->(subsetI1->(eqimpsubset2->(eqimpsubset1->(subsetI2->(emptysetsubset->(subsetE->(subsetE2->(notsubsetI->(notequalI1->(notequalI2->(subsetRefl->(subsetTrans->(setadjoinSub->(setadjoinSub2->(subset2powerset->(setextsub->(subsetemptysetimpeq->(powersetI1->(powersetE1->(inPowerset->(powersetsubset->(sepInPowerset->(sepSubset->(binunionIL->(upairset2IR->(binunionIR->(binunionEcases->(binunionE->(binunionLsub->(binunionRsub->(binintersectI->(binintersectSubset5->(binintersectEL->(binintersectLsub->(binintersectSubset2->(binintersectSubset3->(binintersectER->(disjointsetsI1->(binintersectRsub->(binintersectSubset4->(binintersectSubset1->(bs114d->(setminusI->(setminusEL->(setminusER->(setminusSubset2->(setminusERneg->(setminusELneg->(setminusILneg->(setminusIRneg->(setminusLsub->(setminusSubset1->(symdiffE->(symdiffI1->(symdiffI2->(symdiffIneg1->(symdiffIneg2->(secondinupair->(setukpairIL->(setukpairIR->(kpairiskpair->(kpairp->(singletonsubset->(singletoninpowerset->(singletoninpowunion->(upairset2E->(upairsubunion->(upairinpowunion->(ubforcartprodlem1->(ubforcartprodlem2->(ubforcartprodlem3->(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((in ((kpair Xx) Xy)) ((cartprod A) B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Definition exu:=(fun (Xphi:(fofType->Prop))=> ((ex fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy))))))):((fofType->Prop)->Prop).
% Definition setextAx:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), ((iff ((in Xx) A)) ((in Xx) B)))->(((eq fofType) A) B))):Prop.
% Parameter emptyset:fofType.
% Definition emptysetAx:=(forall (Xx:fofType), (((in Xx) emptyset)->False)):Prop.
% Parameter setadjoin:(fofType->(fofType->fofType)).
% Definition setadjoinAx:=(forall (Xx:fofType) (A:fofType) (Xy:fofType), ((iff ((in Xy) ((setadjoin Xx) A))) ((or (((eq fofType) Xy) Xx)) ((in Xy) A)))):Prop.
% Parameter powerset:(fofType->fofType).
% Definition powersetAx:=(forall (A:fofType) (B:fofType), ((iff ((in B) (powerset A))) (forall (Xx:fofType), (((in Xx) B)->((in Xx) A))))):Prop.
% Parameter setunion:(fofType->fofType).
% Definition setunionAx:=(forall (A:fofType) (Xx:fofType), ((iff ((in Xx) (setunion A))) ((ex fofType) (fun (B:fofType)=> ((and ((in Xx) B)) ((in B) A)))))):Prop.
% Parameter omega:fofType.
% Definition omega0Ax:=((in emptyset) omega):Prop.
% Definition omegaSAx:=(forall (Xx:fofType), (((in Xx) omega)->((in ((setadjoin Xx) Xx)) omega))):Prop.
% Definition omegaIndAx:=(forall (A:fofType), (((and ((in emptyset) A)) (forall (Xx:fofType), (((and ((in Xx) omega)) ((in Xx) A))->((in ((setadjoin Xx) Xx)) A))))->(forall (Xx:fofType), (((in Xx) omega)->((in Xx) A))))):Prop.
% Definition replAx:=(forall (Xphi:(fofType->(fofType->Prop))) (A:fofType), ((forall (Xx:fofType), (((in Xx) A)->(exu (fun (Xy:fofType)=> ((Xphi Xx) Xy)))))->((ex fofType) (fun (B:fofType)=> (forall (Xx:fofType), ((iff ((in Xx) B)) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) ((Xphi Xy) Xx)))))))))):Prop.
% Definition foundationAx:=(forall (A:fofType), (((ex fofType) (fun (Xx:fofType)=> ((in Xx) A)))->((ex fofType) (fun (B:fofType)=> ((and ((in B) A)) (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) B)) ((in Xx) A))))->False)))))):Prop.
% Definition wellorderingAx:=(forall (A:fofType), ((ex fofType) (fun (B:fofType)=> ((and ((and ((and (forall (C:fofType), (((in C) B)->(forall (Xx:fofType), (((in Xx) C)->((in Xx) A)))))) (forall (Xx:fofType) (Xy:fofType), (((and ((in Xx) A)) ((in Xy) A))->((forall (C:fofType), (((in C) B)->((iff ((in Xx) C)) ((in Xy) C))))->(((eq fofType) Xx) Xy)))))) (forall (C:fofType) (D:fofType), (((and ((in C) B)) ((in D) B))->((or (forall (Xx:fofType), (((in Xx) C)->((in Xx) D)))) (forall (Xx:fofType), (((in Xx) D)->((in Xx) C)))))))) (forall (C:fofType), (((and (forall (Xx:fofType), (((in Xx) C)->((in Xx) A)))) ((ex fofType) (fun (Xx:fofType)=> ((in Xx) C))))->((ex fofType) (fun (D:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((and ((and ((in D) B)) ((in Xx) C))) (((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) D)) ((in Xy) C))))->False))) (forall (E:fofType), (((in E) B)->((or (forall (Xy:fofType), (((in Xy) E)->((in Xy) D)))) ((in Xx) E))))))))))))))):Prop.
% Parameter descr:((fofType->Prop)->fofType).
% Definition descrp:=(forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->(Xphi (descr (fun (Xx:fofType)=> (Xphi Xx)))))):Prop.
% Parameter dsetconstr:(fofType->((fofType->Prop)->fofType)).
% Definition dsetconstrI:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))):Prop.
% Definition dsetconstrEL:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->((in Xx) A))):Prop.
% Definition dsetconstrER:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->(Xphi Xx))):Prop.
% Definition exuE1:=(forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->((ex fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy)))))))):Prop.
% Parameter prop2set:(Prop->fofType).
% Definition prop2setE:=(forall (Xphi:Prop) (Xx:fofType), (((in Xx) (prop2set Xphi))->Xphi)):Prop.
% Definition emptysetE:=(forall (Xx:fofType), (((in Xx) emptyset)->(forall (Xphi:Prop), Xphi))):Prop.
% Definition emptysetimpfalse:=(forall (Xx:fofType), (((in Xx) emptyset)->False)):Prop.
% Definition notinemptyset:=(forall (Xx:fofType), (((in Xx) emptyset)->False)):Prop.
% Definition exuE3e:=(forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->((ex fofType) (fun (Xx:fofType)=> (Xphi Xx))))):Prop.
% Definition setext:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))->(((eq fofType) A) B)))):Prop.
% Definition emptyI:=(forall (A:fofType), ((forall (Xx:fofType), (((in Xx) A)->False))->(((eq fofType) A) emptyset))):Prop.
% Definition noeltsimpempty:=(forall (A:fofType), ((forall (Xx:fofType), (((in Xx) A)->False))->(((eq fofType) A) emptyset))):Prop.
% Definition setbeta:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((iff ((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))) (Xphi Xx)))):Prop.
% Definition nonempty:=(fun (Xx:fofType)=> (not (((eq fofType) Xx) emptyset))):(fofType->Prop).
% Definition nonemptyE1:=(forall (A:fofType), ((nonempty A)->((ex fofType) (fun (Xx:fofType)=> ((in Xx) A))))):Prop.
% Definition nonemptyI:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))):Prop.
% Definition nonemptyI1:=(forall (A:fofType), (((ex fofType) (fun (Xx:fofType)=> ((in Xx) A)))->(nonempty A))):Prop.
% Definition setadjoinIL:=(forall (Xx:fofType) (Xy:fofType), ((in Xx) ((setadjoin Xx) Xy))):Prop.
% Definition emptyinunitempty:=((in emptyset) ((setadjoin emptyset) emptyset)):Prop.
% Definition setadjoinIR:=(forall (Xx:fofType) (A:fofType) (Xy:fofType), (((in Xy) A)->((in Xy) ((setadjoin Xx) A)))):Prop.
% Definition setadjoinE:=(forall (Xx:fofType) (A:fofType) (Xy:fofType), (((in Xy) ((setadjoin Xx) A))->(forall (Xphi:Prop), (((((eq fofType) Xy) Xx)->Xphi)->((((in Xy) A)->Xphi)->Xphi))))):Prop.
% Definition setadjoinOr:=(forall (Xx:fofType) (A:fofType) (Xy:fofType), (((in Xy) ((setadjoin Xx) A))->((or (((eq fofType) Xy) Xx)) ((in Xy) A)))):Prop.
% Definition setoftrueEq:=(forall (A:fofType), (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> True))) A)):Prop.
% Definition powersetI:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))->((in B) (powerset A)))):Prop.
% Definition emptyinPowerset:=(forall (A:fofType), ((in emptyset) (powerset A))):Prop.
% Definition emptyInPowerset:=(forall (A:fofType), ((in emptyset) (powerset A))):Prop.
% Definition powersetE:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in B) (powerset A))->(((in Xx) B)->((in Xx) A)))):Prop.
% Definition setunionI:=(forall (A:fofType) (Xx:fofType) (B:fofType), (((in Xx) B)->(((in B) A)->((in Xx) (setunion A))))):Prop.
% Definition setunionE:=(forall (A:fofType) (Xx:fofType), (((in Xx) (setunion A))->(forall (Xphi:Prop), ((forall (B:fofType), (((in Xx) B)->(((in B) A)->Xphi)))->Xphi)))):Prop.
% Definition subPowSU:=(forall (A:fofType) (Xx:fofType), (((in Xx) A)->((in Xx) (powerset (setunion A))))):Prop.
% Definition exuE2:=(forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (Xphi Xy)) (((eq fofType) Xy) Xx))))))):Prop.
% Definition nonemptyImpWitness:=(forall (A:fofType), ((nonempty A)->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) True))))):Prop.
% Definition uniqinunit:=(forall (Xx:fofType) (Xy:fofType), (((in Xx) ((setadjoin Xy) emptyset))->(((eq fofType) Xx) Xy))):Prop.
% Definition notinsingleton:=(forall (Xx:fofType) (Xy:fofType), ((not (((eq fofType) Xx) Xy))->(((in Xy) ((setadjoin Xx) emptyset))->False))):Prop.
% Definition eqinunit:=(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((in Xx) ((setadjoin Xy) emptyset)))):Prop.
% Definition singletonsswitch:=(forall (Xx:fofType) (Xy:fofType), (((in Xx) ((setadjoin Xy) emptyset))->((in Xy) ((setadjoin Xx) emptyset)))):Prop.
% Definition upairsetE:=(forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((in Xz) ((setadjoin Xx) ((setadjoin Xy) emptyset)))->((or (((eq fofType) Xz) Xx)) (((eq fofType) Xz) Xy)))):Prop.
% Definition upairsetIL:=(forall (Xx:fofType) (Xy:fofType), ((in Xx) ((setadjoin Xx) ((setadjoin Xy) emptyset)))):Prop.
% Definition upairsetIR:=(forall (Xx:fofType) (Xy:fofType), ((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset)))):Prop.
% Definition emptyE1:=(forall (A:fofType) (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->((((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) emptyset)->False))):Prop.
% Definition vacuousDall:=(forall (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) emptyset)->(Xphi Xx))):Prop.
% Definition quantDeMorgan1:=(forall (A:fofType) (Xphi:(fofType->Prop)), (((forall (Xx:fofType), (((in Xx) A)->(Xphi Xx)))->False)->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((Xphi Xx)->False)))))):Prop.
% Definition quantDeMorgan2:=(forall (A:fofType) (Xphi:(fofType->Prop)), ((forall (Xx:fofType), (((in Xx) A)->((Xphi Xx)->False)))->(((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->False))):Prop.
% Definition quantDeMorgan3:=(forall (A:fofType) (Xphi:(fofType->Prop)), ((((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->False)->(forall (Xx:fofType), (((in Xx) A)->((Xphi Xx)->False))))):Prop.
% Definition quantDeMorgan4:=(forall (A:fofType) (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((Xphi Xx)->False))))->((forall (Xx:fofType), (((in Xx) A)->(Xphi Xx)))->False))):Prop.
% Definition prop2setI:=(forall (Xphi:Prop), (Xphi->((in emptyset) (prop2set Xphi)))):Prop.
% Parameter set2prop:(fofType->Prop).
% Definition prop2set2propI:=(forall (Xphi:Prop), (Xphi->(set2prop (prop2set Xphi)))):Prop.
% Definition notdexE:=(forall (A:fofType) (Xphi:(fofType->Prop)), ((((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->False)->(forall (Xx:fofType), (((in Xx) A)->((Xphi Xx)->False))))):Prop.
% Definition notdallE:=(forall (A:fofType) (Xphi:(fofType->Prop)), (((forall (Xx:fofType), (((in Xx) A)->(Xphi Xx)))->False)->((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((Xphi Xx)->False)))))):Prop.
% Definition exuI1:=(forall (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> ((and (Xphi Xx)) (forall (Xy:fofType), ((Xphi Xy)->(((eq fofType) Xx) Xy))))))->(exu (fun (Xx:fofType)=> (Xphi Xx))))):Prop.
% Definition exuI3:=(forall (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> (Xphi Xx)))->((forall (Xx:fofType) (Xy:fofType), ((Xphi Xx)->((Xphi Xy)->(((eq fofType) Xx) Xy))))->(exu (fun (Xx:fofType)=> (Xphi Xx)))))):Prop.
% Definition exuI2:=(forall (Xphi:(fofType->Prop)), (((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (Xphi Xy)) (((eq fofType) Xy) Xx)))))->(exu (fun (Xx:fofType)=> (Xphi Xx))))):Prop.
% Definition inCongP:=(forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->(((in Xx) A)->((in Xy) B)))))):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 exuE3u:=(forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->(forall (Xx:fofType) (Xy:fofType), ((Xphi Xx)->((Xphi Xy)->(((eq fofType) Xx) Xy)))))):Prop.
% Definition exu__Cong:=(forall (Xphi:(fofType->Prop)) (Xpsi:(fofType->Prop)), ((forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((iff (Xphi Xx)) (Xpsi Xy))))->((iff (exu (fun (Xx:fofType)=> (Xphi Xx)))) (exu (fun (Xx:fofType)=> (Xpsi Xx)))))):Prop.
% Definition emptyset__Cong:=(((eq fofType) emptyset) emptyset):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 powerset__Cong:=(forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(((eq fofType) (powerset A)) (powerset B)))):Prop.
% Definition setunion__Cong:=(forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(((eq fofType) (setunion A)) (setunion B)))):Prop.
% Definition omega__Cong:=(((eq fofType) omega) omega):Prop.
% Definition exuEu:=(forall (Xphi:(fofType->Prop)), ((exu (fun (Xx:fofType)=> (Xphi Xx)))->(forall (Xx:fofType) (Xy:fofType), ((Xphi Xx)->((Xphi Xy)->(((eq fofType) Xx) Xy)))))):Prop.
% Definition descr__Cong:=(forall (Xphi:(fofType->Prop)) (Xpsi:(fofType->Prop)), ((forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((iff (Xphi Xx)) (Xpsi Xy))))->((exu (fun (Xx:fofType)=> (Xphi Xx)))->((exu (fun (Xx:fofType)=> (Xpsi Xx)))->(((eq fofType) (descr (fun (Xx:fofType)=> (Xphi Xx)))) (descr (fun (Xx:fofType)=> (Xpsi Xx)))))))):Prop.
% Definition dsetconstr__Cong:=(forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(forall (Xphi:(fofType->Prop)) (Xpsi:(fofType->Prop)), ((forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((((eq fofType) Xx) Xy)->((iff (Xphi Xx)) (Xpsi Xy)))))))->(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))))))):Prop.
% Parameter subset:(fofType->(fofType->Prop)).
% Parameter disjoint:(fofType->(fofType->Prop)).
% Parameter setsmeet:(fofType->(fofType->Prop)).
% Definition subsetI1:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((subset A) B))):Prop.
% Definition eqimpsubset2:=(forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->((subset B) A))):Prop.
% Definition eqimpsubset1:=(forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->((subset A) B))):Prop.
% Definition subsetI2:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((subset A) B))):Prop.
% Definition emptysetsubset:=(forall (A:fofType), ((subset emptyset) A)):Prop.
% Definition subsetE:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((subset A) B)->(((in Xx) A)->((in Xx) B)))):Prop.
% Definition subsetE2:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((subset A) B)->((((in Xx) B)->False)->(((in Xx) A)->False)))):Prop.
% Definition notsubsetI:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((((in Xx) B)->False)->(((subset A) B)->False)))):Prop.
% Definition notequalI1:=(forall (A:fofType) (B:fofType), ((((subset A) B)->False)->(not (((eq fofType) A) B)))):Prop.
% Definition notequalI2:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((((in Xx) B)->False)->(not (((eq fofType) A) B))))):Prop.
% Definition subsetRefl:=(forall (A:fofType), ((subset A) A)):Prop.
% Definition subsetTrans:=(forall (A:fofType) (B:fofType) (C:fofType), (((subset A) B)->(((subset B) C)->((subset A) C)))):Prop.
% Definition setadjoinSub:=(forall (Xx:fofType) (A:fofType), ((subset A) ((setadjoin Xx) A))):Prop.
% Definition setadjoinSub2:=(forall (A:fofType) (Xx:fofType) (B:fofType), (((subset A) B)->((subset A) ((setadjoin Xx) B)))):Prop.
% Definition subset2powerset:=(forall (A:fofType) (B:fofType), (((subset A) B)->((in A) (powerset B)))):Prop.
% Definition setextsub:=(forall (A:fofType) (B:fofType), (((subset A) B)->(((subset B) A)->(((eq fofType) A) B)))):Prop.
% Definition subsetemptysetimpeq:=(forall (A:fofType), (((subset A) emptyset)->(((eq fofType) A) emptyset))):Prop.
% Definition powersetI1:=(forall (A:fofType) (B:fofType), (((subset B) A)->((in B) (powerset A)))):Prop.
% Definition powersetE1:=(forall (A:fofType) (B:fofType), (((in B) (powerset A))->((subset B) A))):Prop.
% Definition inPowerset:=(forall (A:fofType), ((in A) (powerset A))):Prop.
% Definition powersetsubset:=(forall (A:fofType) (B:fofType), (((subset A) B)->((subset (powerset A)) (powerset B)))):Prop.
% Definition sepInPowerset:=(forall (A:fofType) (Xphi:(fofType->Prop)), ((in ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) (powerset A))):Prop.
% Definition sepSubset:=(forall (A:fofType) (Xphi:(fofType->Prop)), ((subset ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) A)):Prop.
% Parameter binunion:(fofType->(fofType->fofType)).
% Definition binunionIL:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((in Xx) ((binunion A) B)))):Prop.
% Definition upairset2IR:=(forall (Xx:fofType) (Xy:fofType), ((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset)))):Prop.
% Definition binunionIR:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) B)->((in Xx) ((binunion A) B)))):Prop.
% Definition binunionEcases:=(forall (A:fofType) (B:fofType) (Xx:fofType) (Xphi:Prop), (((in Xx) ((binunion A) B))->((((in Xx) A)->Xphi)->((((in Xx) B)->Xphi)->Xphi)))):Prop.
% Definition binunionE:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((binunion A) B))->((or ((in Xx) A)) ((in Xx) B)))):Prop.
% Definition binunionLsub:=(forall (A:fofType) (B:fofType), ((subset A) ((binunion A) B))):Prop.
% Definition binunionRsub:=(forall (A:fofType) (B:fofType), ((subset B) ((binunion A) B))):Prop.
% Parameter binintersect:(fofType->(fofType->fofType)).
% Definition binintersectI:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(((in Xx) B)->((in Xx) ((binintersect A) B))))):Prop.
% Definition binintersectSubset5:=(forall (A:fofType) (B:fofType) (C:fofType), (((subset C) A)->(((subset C) B)->((subset C) ((binintersect A) B))))):Prop.
% Definition binintersectEL:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((binintersect A) B))->((in Xx) A))):Prop.
% Definition binintersectLsub:=(forall (A:fofType) (B:fofType), ((subset ((binintersect A) B)) A)):Prop.
% Definition binintersectSubset2:=(forall (A:fofType) (B:fofType), (((subset A) B)->(((eq fofType) ((binintersect A) B)) A))):Prop.
% Definition binintersectSubset3:=(forall (A:fofType) (B:fofType), ((((eq fofType) ((binintersect A) B)) B)->((subset B) A))):Prop.
% Definition binintersectER:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((binintersect A) B))->((in Xx) B))):Prop.
% Definition disjointsetsI1:=(forall (A:fofType) (B:fofType), ((((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) ((in Xx) B))))->False)->(((eq fofType) ((binintersect A) B)) emptyset))):Prop.
% Definition binintersectRsub:=(forall (A:fofType) (B:fofType), ((subset ((binintersect A) B)) B)):Prop.
% Definition binintersectSubset4:=(forall (A:fofType) (B:fofType), (((subset B) A)->(((eq fofType) ((binintersect A) B)) B))):Prop.
% Definition binintersectSubset1:=(forall (A:fofType) (B:fofType), ((((eq fofType) ((binintersect A) B)) A)->((subset A) B))):Prop.
% Definition bs114d:=(forall (A:fofType) (B:fofType) (C:fofType), (((eq fofType) ((binintersect A) ((binunion B) C))) ((binunion ((binintersect A) B)) ((binintersect A) C)))):Prop.
% Parameter regular:(fofType->Prop).
% Parameter setminus:(fofType->(fofType->fofType)).
% Definition setminusI:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((((in Xx) B)->False)->((in Xx) ((setminus A) B))))):Prop.
% Definition setminusEL:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((setminus A) B))->((in Xx) A))):Prop.
% Definition setminusER:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((setminus A) B))->(((in Xx) B)->False))):Prop.
% Definition setminusSubset2:=(forall (A:fofType) (B:fofType), (((subset A) B)->(((eq fofType) ((setminus A) B)) emptyset))):Prop.
% Definition setminusERneg:=(forall (A:fofType) (B:fofType) (Xx:fofType), ((((in Xx) ((setminus A) B))->False)->(((in Xx) A)->((in Xx) B)))):Prop.
% Definition setminusELneg:=(forall (A:fofType) (B:fofType) (Xx:fofType), ((((in Xx) ((setminus A) B))->False)->((((in Xx) B)->False)->(((in Xx) A)->False)))):Prop.
% Definition setminusILneg:=(forall (A:fofType) (B:fofType) (Xx:fofType), ((((in Xx) A)->False)->(((in Xx) ((setminus A) B))->False))):Prop.
% Definition setminusIRneg:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) B)->(((in Xx) ((setminus A) B))->False))):Prop.
% Definition setminusLsub:=(forall (A:fofType) (B:fofType), ((subset ((setminus A) B)) A)):Prop.
% Definition setminusSubset1:=(forall (A:fofType) (B:fofType), ((((eq fofType) ((setminus A) B)) emptyset)->((subset A) B))):Prop.
% Parameter symdiff:(fofType->(fofType->fofType)).
% Definition symdiffE:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) ((symdiff A) B))->(forall (Xphi:Prop), ((((in Xx) A)->((((in Xx) B)->False)->Xphi))->(((((in Xx) A)->False)->(((in Xx) B)->Xphi))->Xphi))))):Prop.
% Definition symdiffI1:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((((in Xx) B)->False)->((in Xx) ((symdiff A) B))))):Prop.
% Definition symdiffI2:=(forall (A:fofType) (B:fofType) (Xx:fofType), ((((in Xx) A)->False)->(((in Xx) B)->((in Xx) ((symdiff A) B))))):Prop.
% Definition symdiffIneg1:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(((in Xx) B)->(((in Xx) ((symdiff A) B))->False)))):Prop.
% Definition symdiffIneg2:=(forall (A:fofType) (B:fofType) (Xx:fofType), ((((in Xx) A)->False)->((((in Xx) B)->False)->(((in Xx) ((symdiff A) B))->False)))):Prop.
% Definition iskpair:=(fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) (setunion A))) ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) (setunion A))) (((eq fofType) A) ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset)))))))))):(fofType->Prop).
% Definition secondinupair:=(forall (Xx:fofType) (Xy:fofType), ((in Xy) ((setadjoin Xx) ((setadjoin Xy) emptyset)))):Prop.
% Definition setukpairIL:=(forall (Xx:fofType) (Xy:fofType), ((in Xx) (setunion ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))))):Prop.
% Definition setukpairIR:=(forall (Xx:fofType) (Xy:fofType), ((in Xy) (setunion ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))))):Prop.
% Definition kpairiskpair:=(forall (Xx:fofType) (Xy:fofType), (iskpair ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset)))):Prop.
% Definition kpair:=(fun (Xx:fofType) (Xy:fofType)=> ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))):(fofType->(fofType->fofType)).
% Definition kpairp:=(forall (Xx:fofType) (Xy:fofType), (iskpair ((kpair Xx) Xy))):Prop.
% Definition cartprod:=(fun (A:fofType) (B:fofType)=> ((dsetconstr (powerset (powerset ((binunion A) B)))) (fun (Xx:fofType)=> ((ex fofType) (fun (Xy:fofType)=> ((and ((in Xy) A)) ((ex fofType) (fun (Xz:fofType)=> ((and ((in Xz) B)) (((eq fofType) Xx) ((kpair Xy) Xz))))))))))):(fofType->(fofType->fofType)).
% Definition singletonsubset:=(forall (A:fofType) (Xx:fofType), (((in Xx) A)->((subset ((setadjoin Xx) emptyset)) A))):Prop.
% Definition singletoninpowerset:=(forall (A:fofType) (Xx:fofType), (((in Xx) A)->((in ((setadjoin Xx) emptyset)) (powerset A)))):Prop.
% Definition singletoninpowunion:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->((in ((setadjoin Xx) emptyset)) (powerset ((binunion A) B))))):Prop.
% Definition upairset2E:=(forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((in Xz) ((setadjoin Xx) ((setadjoin Xy) emptyset)))->((or (((eq fofType) Xz) Xx)) (((eq fofType) Xz) Xy)))):Prop.
% Definition upairsubunion:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((subset ((setadjoin Xx) ((setadjoin Xy) emptyset))) ((binunion A) B)))))):Prop.
% Definition upairinpowunion:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((in ((setadjoin Xx) ((setadjoin Xy) emptyset))) (powerset ((binunion A) B))))))):Prop.
% Definition ubforcartprodlem1:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((subset ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset ((binunion A) B))))))):Prop.
% Definition ubforcartprodlem2:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((in ((setadjoin ((setadjoin Xx) emptyset)) ((setadjoin ((setadjoin Xx) ((setadjoin Xy) emptyset))) emptyset))) (powerset (powerset ((binunion A) B)))))))):Prop.
% Definition ubforcartprodlem3:=(forall (A:fofType) (B:fofType) (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((in ((kpair Xx) Xy)) (powerset (powerset ((binunion A) B)))))))):Prop.
% Trying to prove (setextAx->(emptysetAx->(setadjoinAx->(powersetAx->(setunionAx->(omega0Ax->(omegaSAx->(omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(nonemptyI->(nonemptyI1->(setadjoinIL->(emptyinunitempty->(setadjoinIR->(setadjoinE->(setadjoinOr->(setoftrueEq->(powersetI->(emptyinPowerset->(emptyInPowerset->(powersetE->(setunionI->(setunionE->(subPowSU->(exuE2->(nonemptyImpWitness->(uniqinunit->(notinsingleton->(eqinunit->(singletonsswitch->(upairsetE->(upairsetIL->(upairsetIR->(emptyE1->(vacuousDall->(quantDeMorgan1->(quantDeMorgan2->(quantDeMorgan3->(quantDeMorgan4->(prop2setI->(prop2set2propI->(notdexE->(notdallE->(exuI1->(exuI3->(exuI2->(inCongP->(in__Cong->(exuE3u->(exu__Cong->(emptyset__Cong->(
% EOF
%------------------------------------------------------------------------------