TSTP Solution File: SEU510^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU510^1 : TPTP v6.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n186.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 13:32:20 EDT 2014
% Result : Theorem 260.23s
% Output : Proof 260.23s
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----ERROR: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU510^1 : TPTP v6.1.0. Released v3.7.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n186.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 10:27:06 CDT 2014
% % CPUTime : 260.23
% 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 0xe6d170>, <kernel.DependentProduct object at 0xe6d050>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0xb74cb0>, <kernel.DependentProduct object at 0xe6d320>) 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 0xe6d320>, <kernel.Sort object at 0xb6ffc8>) 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 0xe6d440>, <kernel.Single object at 0xe6d320>) of role type named emptyset_type
% Using role type
% Declaring emptyset:fofType
% FOF formula (<kernel.Constant object at 0xe6d488>, <kernel.Sort object at 0xb6ffc8>) 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 0xe6d440>, <kernel.DependentProduct object at 0xe8b320>) of role type named setadjoin_type
% Using role type
% Declaring setadjoin:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0xe6d488>, <kernel.Sort object at 0xb6ffc8>) 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 0xe6d488>, <kernel.DependentProduct object at 0xe8b0e0>) of role type named powerset_type
% Using role type
% Declaring powerset:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0xe6d488>, <kernel.Sort object at 0xb6ffc8>) 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 0xe8ba70>, <kernel.DependentProduct object at 0x10e2908>) of role type named setunion_type
% Using role type
% Declaring setunion:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0xe8b170>, <kernel.Sort object at 0xb6ffc8>) 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 0xe8b830>, <kernel.Single object at 0xe8b170>) of role type named omega_type
% Using role type
% Declaring omega:fofType
% FOF formula (<kernel.Constant object at 0xe8ba70>, <kernel.Sort object at 0xb6ffc8>) 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 0xe8ba70>, <kernel.Sort object at 0xb6ffc8>) 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 0xe8b710>, <kernel.Sort object at 0xb6ffc8>) 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 0xe6ad40>, <kernel.Sort object at 0xb6ffc8>) 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 0x10e2320>, <kernel.Sort object at 0xb6ffc8>) 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 0xcaab90>, <kernel.Sort object at 0xb6ffc8>) 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 0xcaab90>, <kernel.DependentProduct object at 0x10e28c0>) of role type named descr_type
% Using role type
% Declaring descr:((fofType->Prop)->fofType)
% FOF formula (<kernel.Constant object at 0xcaaef0>, <kernel.Sort object at 0xb6ffc8>) 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 0x10e2950>, <kernel.DependentProduct object at 0x10e2830>) of role type named dsetconstr_type
% Using role type
% Declaring dsetconstr:(fofType->((fofType->Prop)->fofType))
% FOF formula (<kernel.Constant object at 0x10e2a70>, <kernel.Sort object at 0xb6ffc8>) 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 0x10e2bd8>, <kernel.Sort object at 0xb6ffc8>) 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 0x10e2710>, <kernel.Sort object at 0xb6ffc8>) 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 0x10e2dd0>, <kernel.Sort object at 0xb6ffc8>) 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 0x10e2c68>, <kernel.DependentProduct object at 0x10e22d8>) of role type named prop2set_type
% Using role type
% Declaring prop2set:(Prop->fofType)
% FOF formula (((eq (Prop->fofType)) prop2set) (fun (Xphi:Prop)=> ((dsetconstr (powerset emptyset)) (fun (Xx:fofType)=> Xphi)))) of role definition named prop2set
% A new definition: (((eq (Prop->fofType)) prop2set) (fun (Xphi:Prop)=> ((dsetconstr (powerset emptyset)) (fun (Xx:fofType)=> Xphi))))
% Defined: prop2set:=(fun (Xphi:Prop)=> ((dsetconstr (powerset emptyset)) (fun (Xx:fofType)=> Xphi)))
% FOF formula (<kernel.Constant object at 0x10e2488>, <kernel.Sort object at 0xb6ffc8>) 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 0x10e25f0>, <kernel.Sort object at 0xb6ffc8>) 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 0x10e22d8>, <kernel.Sort object at 0xb6ffc8>) 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 0x10e22d8>, <kernel.Sort object at 0xb6ffc8>) 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 0x10e22d8>, <kernel.Sort object at 0xb6ffc8>) 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 0xe8c488>, <kernel.Sort object at 0xb6ffc8>) 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 0xe8c638>, <kernel.Sort object at 0xb6ffc8>) 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 0xe8c2d8>, <kernel.Sort object at 0xb6ffc8>) 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 0xe8c950>, <kernel.Sort object at 0xb6ffc8>) 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 0xe8c128>, <kernel.DependentProduct object at 0xe8cc20>) 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 0xe8cc20>, <kernel.Sort object at 0xb6ffc8>) 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 (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->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))))))))))))))))))))))))))) of role conjecture named nonemptyI
% 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->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))))))))))))))))))))))))))):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->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))))))))))))))))))))))))))))']
% 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.
% Definition prop2set:=(fun (Xphi:Prop)=> ((dsetconstr (powerset emptyset)) (fun (Xx:fofType)=> Xphi))):(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.
% 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->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))))))))))))))))))))))))))))
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx0:=emptyset:fofType
% Found x4 as proof of ((in Xx0) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx0:=emptyset:fofType
% Found x4 as proof of ((in Xx0) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx0:=emptyset:fofType
% Found x4 as proof of ((in Xx0) omega)
% Found x4:omega0Ax
% Instantiate: Xx0:=emptyset:fofType
% Found x4 as proof of ((in Xx0) omega)
% Found x4:omega0Ax
% Instantiate: Xx0:=emptyset:fofType
% Found x4 as proof of ((in Xx0) omega)
% Found x4:omega0Ax
% Instantiate: Xx0:=emptyset:fofType
% Found x4 as proof of ((in Xx0) omega)
% Found x4:omega0Ax
% Instantiate: Xx0:=emptyset:fofType
% Found x4 as proof of ((in Xx0) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx0:=emptyset:fofType
% Found x4 as proof of ((in Xx0) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx0:=emptyset:fofType
% Found x4 as proof of ((in Xx0) omega)
% Found x4:omega0Ax
% Instantiate: Xx0:=emptyset:fofType
% Found x4 as proof of ((in Xx0) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx0:=emptyset:fofType
% Found x4 as proof of ((in Xx0) omega)
% Found x4:omega0Ax
% Instantiate: Xx0:=emptyset:fofType
% Found x4 as proof of ((in Xx0) omega)
% Found x4:omega0Ax
% Instantiate: Xx0:=emptyset:fofType
% Found x4 as proof of ((in Xx0) omega)
% Found x4:omega0Ax
% Instantiate: Xx0:=emptyset:fofType
% Found x4 as proof of ((in Xx0) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx0:=emptyset:fofType
% Found x4 as proof of ((in Xx0) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx:=emptyset:fofType
% Found x4 as proof of ((in Xx) omega)
% Found x4:omega0Ax
% Instantiate: Xx0:=emptyset:fofType
% Found x4 as proof of ((in Xx0) omega)
% Found x4:omega0Ax
% Instantiate: Xx0:=emptyset:fofType
% Found x4 as proof of ((in Xx0) omega)
% Found x25:((in Xx) A)
% Instantiate: Xx0:=Xx:fofType
% Found x25 as proof of ((in Xx0) A)
% Found x26:(Xphi Xx)
% Instantiate: Xx0:=Xx:fofType
% Found x26 as proof of (Xphi Xx0)
% Found ((x11000 x25) x26) as proof of ((in Xx0) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))
% Found (((x1100 Xx0) x25) x26) as proof of ((in Xx0) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))
% Found ((((x110 Xphi) Xx0) x25) x26) as proof of ((in Xx0) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))
% Found (((((x11 A) Xphi) Xx0) x25) x26) as proof of ((in Xx0) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))
% Found (((((x11 A) Xphi) Xx0) x25) x26) as proof of ((in Xx0) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))
% Found (x270 (((((x11 A) Xphi) Xx0) x25) x26)) as proof of ((in Xx0) emptyset)
% Found ((x27 (in Xx0)) (((((x11 A) Xphi) Xx0) x25) x26)) as proof of ((in Xx0) emptyset)
% Found ((x27 (in Xx0)) (((((x11 A) Xphi) Xx0) x25) x26)) as proof of ((in Xx0) emptyset)
% Found (x00 ((x27 (in Xx0)) (((((x11 A) Xphi) Xx0) x25) x26))) as proof of False
% Found ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26))) as proof of False
% Found (fun (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of False
% Found (fun (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))
% Found (fun (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of ((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))
% Found (fun (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))
% Found (fun (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (forall (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))
% Found (fun (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (forall (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))
% Found (fun (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))
% Found (fun (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))
% Found (fun (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))))
% Found (fun (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))))
% Found (fun (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))))))
% Found (fun (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))))))
% Found (fun (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))))))))
% Found (fun (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))))))))
% Found (fun (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))))))))))
% Found (fun (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))))))))))
% Found (fun (x14:exuE1) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))))))))))))
% Found (fun (x13:dsetconstrER) (x14:exuE1) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))))))))))))
% Found (fun (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))))))))))))))
% Found (fun (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))))))))))))))
% Found (fun (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))))))))))))))))
% Found (fun (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))))))))))))))))
% Found (fun (x8:foundationAx) (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))))))))))))))))))
% Found (fun (x7:replAx) (x8:foundationAx) (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))))))))))))))))))
% Found (fun (x6:omegaIndAx) (x7:replAx) (x8:foundationAx) (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))))))))))))))))))))
% Found (fun (x5:omegaSAx) (x6:omegaIndAx) (x7:replAx) (x8:foundationAx) (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))))))))))))))))))))
% Found (fun (x4:omega0Ax) (x5:omegaSAx) (x6:omegaIndAx) (x7:replAx) (x8:foundationAx) (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (omegaSAx->(omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))))))))))))))))))))))
% Found (fun (x3:setunionAx) (x4:omega0Ax) (x5:omegaSAx) (x6:omegaIndAx) (x7:replAx) (x8:foundationAx) (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (omega0Ax->(omegaSAx->(omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))))))))))))))))))))))
% Found (fun (x2:powersetAx) (x3:setunionAx) (x4:omega0Ax) (x5:omegaSAx) (x6:omegaIndAx) (x7:replAx) (x8:foundationAx) (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (setunionAx->(omega0Ax->(omegaSAx->(omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))))))))))))))))))))))))
% Found (fun (x1:setadjoinAx) (x2:powersetAx) (x3:setunionAx) (x4:omega0Ax) (x5:omegaSAx) (x6:omegaIndAx) (x7:replAx) (x8:foundationAx) (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (powersetAx->(setunionAx->(omega0Ax->(omegaSAx->(omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))))))))))))))))))))))))
% Found (fun (x0:emptysetAx) (x1:setadjoinAx) (x2:powersetAx) (x3:setunionAx) (x4:omega0Ax) (x5:omegaSAx) (x6:omegaIndAx) (x7:replAx) (x8:foundationAx) (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (setadjoinAx->(powersetAx->(setunionAx->(omega0Ax->(omegaSAx->(omegaIndAx->(replAx->(foundationAx->(wellorderingAx->(descrp->(dsetconstrI->(dsetconstrEL->(dsetconstrER->(exuE1->(prop2setE->(emptysetE->(emptysetimpfalse->(notinemptyset->(exuE3e->(setext->(emptyI->(noeltsimpempty->(setbeta->(nonemptyE1->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))))))))))))))))))))))))))
% Found (fun (x:setextAx) (x0:emptysetAx) (x1:setadjoinAx) (x2:powersetAx) (x3:setunionAx) (x4:omega0Ax) (x5:omegaSAx) (x6:omegaIndAx) (x7:replAx) (x8:foundationAx) (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (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->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))))))))))))))))))))))))))
% Found (fun (x:setextAx) (x0:emptysetAx) (x1:setadjoinAx) (x2:powersetAx) (x3:setunionAx) (x4:omega0Ax) (x5:omegaSAx) (x6:omegaIndAx) (x7:replAx) (x8:foundationAx) (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26)))) as proof of (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->(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->(nonempty ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))))))))))))))))))))))))))))
% Got proof (fun (x:setextAx) (x0:emptysetAx) (x1:setadjoinAx) (x2:powersetAx) (x3:setunionAx) (x4:omega0Ax) (x5:omegaSAx) (x6:omegaIndAx) (x7:replAx) (x8:foundationAx) (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26))))
% Time elapsed = 258.731538s
% node=15512 cost=1240.000000 depth=43
% ::::::::::::::::::::::
% % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% (fun (x:setextAx) (x0:emptysetAx) (x1:setadjoinAx) (x2:powersetAx) (x3:setunionAx) (x4:omega0Ax) (x5:omegaSAx) (x6:omegaIndAx) (x7:replAx) (x8:foundationAx) (x9:wellorderingAx) (x10:descrp) (x11:dsetconstrI) (x12:dsetconstrEL) (x13:dsetconstrER) (x14:exuE1) (x15:prop2setE) (x16:emptysetE) (x17:emptysetimpfalse) (x18:notinemptyset) (x19:exuE3e) (x20:setext) (x21:emptyI) (x22:noeltsimpempty) (x23:setbeta) (x24:nonemptyE1) (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType) (x25:((in Xx) A)) (x26:(Xphi Xx)) (x27:(((eq fofType) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))) emptyset))=> ((x0 Xx) ((x27 (in Xx)) (((((x11 A) Xphi) Xx) x25) x26))))
% % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% EOF
%------------------------------------------------------------------------------