Propositional Circumscriptions

(1)

HAL Id: inria-00073147

https://hal.inria.fr/inria-00073147

Submitted on 24 May 2006

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub-

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non,

Propositional Circumscriptions

Yves Moinard, Raymond Rolland

To cite this version:

Yves Moinard, Raymond Rolland. Propositional Circumscriptions. [Research Report] RR-3538, IN- RIA. 1998. �inria-00073147�

(2)

a p p o r t

d e r e c h e r c h e

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

Propositional circumscriptions

Yves Moinard and Raymond Rolland

N ˚ 3538

October 1998

TH `EME 3

(3)

(4)

"!#%$ &('*),+.-0/),'1-%2)43657$ '1-02$,898:);'1-=<

>@?BADCFE GHJILK"MNEPORQTSMRUWV"K?BV"CFCFEYXZC[Q\S]?^U_KBET`

UaC[QcbTEDdD`4e^VTK^KBfDEDdD`^SV"K^K^QcUadgdRQTK^SEPd

hiORVcjLEYM@klEDm SV

klQTm^m,VTORMne^E ONEPS]?BEDOgS]?BEoKpG"qcGTrsHutvSYMNV"w;EPOyxDz\zTr{HJzTz[m^QcbTEDd

|}~DY^\\ UaORSD^C[dRSDONUamBMNU_VTKVTOgC[Qc_UWDEDdU_KMNEPORC[dvVcnSaQ\dgdNUaSYQ\_V\bTU_SQ\ORUWV"^dQTdRm,EDSYMRdvVcnSV"CX

CFV"KFdREDK;dNElOREDQTdNV"KBUaKBb;6EY^SEDm^MNU_VTK^d*QTONEC[QTeBEQ\dORQTONE@Q\dim;V"dRdRU_w^WE@ORVTCMR?BElb\U_\EDK[4KBV@_EDeBbTE\E

bTUWTEMg?BEsC[QcUaKm^ONV"m;EPONMRUWEPdvVcnMR?BEsOREDQTdNV"KBU_K^bMg?^Q\K^4dyMRVSYU_OgSY;CFdgSYORUamBMNU_VTK^dD[Esm;ONV4UaeBEQTONU_VT^d

SYVT^K"MREDONX9EYBQTC[mBWEPdnMNVsmÔRV\E dRVTCFE SYVT^K"MNEPOLX:mÔRVTm,EDORMNU_EDdDiEOREDdRMRORU_SYM@VTÔdNMgêBMNVmÔRVTm,VTdRU_MNU_VTK^Q\

SYU_OgSY;CFdgSYORUamBMNU_VTK^dD`6Q\K;eEdR?BVMR?^Q\M{EYTEDKUaKMR?BUad SDQ\dRE\`6Mg?BU_K^bTd{Q\ORE[KBV\M{Mg?^QcMyEDQTdNT[EED\VT\E

Mg?BElmÔREDeÛ_SDQcMNESDQcaSYBa^d*SDQ\dRE\`"dR?BV@UaKBbyMR?;QcM*Mg?BElmÔRVTm,VTdRUWMRUWV"K^Qc^SDQ\dREdRBSYEDd1MRV b\EDM*Qyb\V4VBe[^KêBEPOLX

dRMRQTK^eBUaKBbFVcpMg?BEyWVTb\UaSYQc m^ORVTm,EDORMNU_EDdVc¡SUaORSD^C[dRSDONUamBMNU_VTK;diUaKQTK"[SDQ\dRE\1¢ldnEydNMRU_S][MRVMgORQTeBUWMRUWV"K^Qc

SYU_OgSY;CFdgSYORUamBMNU_VTK^dD`;E?^Q.TEQ\e;Q\mBMREDe£dRUWb"KBU¥¤ SYQ\K"MRWMR?BEWU_MNEPORQ\MR^ORE V"K¦Nm;ONEYEDOREDK"MNUaQcpCFVBeBED_dL§E

dRMR;eBSDQ\OREB_WMR?BECFV"ONE@bTEDKBEPORQ\¦LVTOgC^_QySUaOgSY^C[dgSYORU_mBMRUWV"K"§]`cE^Q\CFUaKBUaKBb{?BEDK[dREYMgd1Vc VTOgCBaQ\d

bTUWTEORU_dRElMRVMg?BEydRQTCEvSUaORSD^C[dRSDONUamBMRUWV"K¨`BQ\K^esm;ONV4UaeBU_K^bMR?^El¤,OgdRM4KBVKsS]?;Q\OgQ\SMREDORUWPQcMRUWV"KFOREDdgB_MY

©¡UaK^Qc__\`6Q\KU_K"MRÛWMRUWTE[m;ONEPdNEPKTMgQcMRUWV"KVcdRVTCFEFVciMg?BEDdREª9SV"^K"MNEDONXN«:mÔRVTm,EDORMNU_EDdlU_dvb\U_\EPKÿ¬1^Q\C[mB_EDd

V\nOREDQ\*SUaORSD^C[dRSDONUamBMRUWV"K^dvUW__;dNMgORQ\MNEMR?^EsBMNU_WU_M:V\Mg?BUad dNMg^eBVTOyMgORQTK^dNaQcMRU_K^bQSYVTC[CFVTKdNEPK^dNE

dRU_MR^Q\MNU_VTK£UaK£MNEPORC[dVciSYU_OgSY^C[dgSYORU_m^MNU_VTK¨v>@?BU_dvm^QTONMvSVTK"MgQcUaK^dlQTONb"^CFEDK"MRdQcbTQ\U_K;dNMldRVTCFESY_QTdRdRUaSYQc

CFEDMR?BVBe^dQTK^em^ONV"m;V"dNEPd@KBEYCFEYMg?BVBe^d@UaK^dNMREDQTe¨`^?BUaS]??;Q.\E{Q[w;EDMNMNEPOlw,ED?^Q.4U_VTOnQ\K;e;dNE{dRU_C[mB_EDO

SYU_OgSY;CFdgSYORUamBMNU_VTK^dMR?;Q\K7MR?BESY_QTdRdRU_SDQcnCFEYMR?^V4e;dY®tvÔ[dNMgêB¯SDQ\K7w;ESYVTK^dRU_eÊDOREDe°QTd[b\U_"UaKBbMR?BE

¤ ORdRMdRMNEPm^diMRVQTORe;d*Q\KsQTBMNV"C[QcMNUaSnQ.FVc6MROgQ\K;dNaQcMRU_KBbdNEDMRdVcpOgBWEPd*UaKsMREDOgCFdVcpSYU_OgSY;CFdgSYORUamBMNU_VTK¨`

?^U_S]?dR?^VTBaeQ\W_VoMNV£^dREdNEPONU_VT;dN_£SUaORSD^C[dRSDONUamBMNU_VTKVTOv?^Q\MvU_M ?^QTdvw,EYEPKm;ONV"m;V"dNEPeMNU__*MR?BE

w,EYbTU_K;KBU_K^b;1¢adNV,`"QTd*EleBEPdRSDONUaw;EvdNBK"MRQTSMRU_SDQc_WFQc_,Mg?BEdREYMgdiV\ V"ORCBaQ\d*?^U_S]?bTUWTElORU_dREMNVFdNV"CFE

bTUWTEDKm^ONV"m;V"dNU_MNU_VTK;Qc6SUaOgSY^C[dgSYORU_mBMRUWV"K¨`4MR?BUaddRMR^e^dg?BVTBae?BEYamMR?BE QTBMNV"CFQ\MNU_DQ\MNU_VTK¨

±²"³ ´gµ¶ ·~\ U_OgSY^C[dgSYORU_m^MNU_VTK¨`BSV"C[CV"KdREDK^dREyONEPQ\dRVTKBUaKBb;`44KBV@_EDeBbTEOREDm^OREDdREDK"MRQ\MNU_VTK¨`4CFU_K^U¥X

C[Q\pCFV4eÊYad@WVTb\UaSc`;K^VTK£CFVTKBVTMNV"KBU_SyOREDQTdNV"KBU_K^b;`^mÔREEPONEPKTMRU_Q\6EDK"MgQcU__CFEDK"MD`;dRSYEDmBMRU_SDQcpeÊQ\^WMUaK4EPOLX

EPK^SET

¸º¹¨»R¼Z½D¾n»@¿À_¼ZÁZÂÃ

ÄÅÆ6ÅÇDÈÉ"Ê¨ËÌ@Í.Î.ÏÐ.ÑÒ ÑRËÎPÓÕÔÕÑNÎTÉ"Ö×ØÙYÚÆpÛ ÜÜÛ ÇYÝÊ¨ÑLÐ.Ñ:Þyß;Æ6È¡ÜÊ¨ÛpÉà(ÑNÓaáÕâpãÖ]Öä¡Ú@å]åæÙçÖyèNÖPÉ"Ñ:ÝºÌËÔÕÓaâ Ì@é]ÔÝ

ê

Ëë(ÐìÔÕë(ÔÕÏ9ËPáí_ë

î

ÅÆpïyÈ¡Æ1É°Ê¨ËÌ@Í.ÎPÏÐPÑðÒ ÑRËÎPÓÕÔÕÑNÎTÉoÖ×ØÙYÚñÆÛ,ÜÜÛ ÇYÝÊ ÑLÐ.Ñ:Þòß^ÆpÈÜ¡Ê¨ÛpÉ°ãÖ]ÖäÚóå]åôÚæñõ]ØöèNåPÉ

ÆËL÷PÌ@é

ê

ÐTáÆpé]ÓÕÓøË

ê

ÐìÎ

ê ÔùYÝºë(Ñ ê.ê

ÑNÏNè]áí_ë

Unit´e de recherche INRIA Rennes

(5)

~ QSUaORSYVTK^dgSYORU_m^MNU_VTKEDdRM;K£VTOgC[Qc_U_dgCFE_V\bTU4BEw^UWEPKQ\e;Q\mBMRfQ\ORQ\U_dRVTK^K^EDCFEDK"MleBE

dREDK;dSYVTC[C^K6`TEDMEPKsm^Q\ORMNUaSY^WU_EDOQ\4ORAYb\_EDdQ.\EPS@E^SEPmBMNU_VTK;dYWEPdE^SEPmBMNU_VTK^ddNV"K"MOREDK^e^^EDdQ\^dgdNU

OgQ\OREDd4BEFm,VTdgdRU_wB_EFEDKMREDK^QTK"MvSYVTC[mBMNEeBEPdyeBVTK^K^fYEDdDlV"^dyeBVTK;KBVTK^d_EDdymÔRU_K^SYU_m;Qc_EDdvmÔNV"mÔRUWfDMNfDd

e;£ORQ\U_dRVTK^KÊDCFEDK"Mm^QTOSUaORSYVTK^dgSYORUamBMNU_VTKSV"K^K4BEDdeÊKBVT;dsSEjLVTÔDVT^dVTÔgKBUadRdRVTK;d@Q\^dgdNUeBEDd

SYVTK"MROREXZEBEPCFm^WEPdQ¤ K¯eBEmÔRfDSUadREDO _EDdF_U_CFU_MNEPdFm;ONfPSUadNEPdeBEPd[mÔNV"mÔRUWfDMNfDdFdgQcMNUadNQcU_MNEDdDlV"^dK^VT^d

OREDdRMROREYU_bTK^VTK^dyQ\SDQ\d{eBE_Q_V\bTU4BEsm^ORVTm,VTdRU_MNU_VTK^KBEDW_E\ EDm,EDK^e;Q\K"MY`¡SEDMNMNEfYMR;eBECFVTK"MRORE4BEsSE

dRED^ SDQ\dEDdRM@eBfLj[dg4sdRQTC[CEPK"MSYVTC[mB_EBEvm,VT;Om,EDOgCFEYMRMROREyeÊywÛWEPKSEPORKÊDOWEPdnmÔNV"mÔRUWfDMNfDdEPdRdREDK4X

MRUWEDW_EDdeBEsaQSUaOgSVTK;dRSDONUamBMNU_VTKEDKbTfDKBfPORQ\(QcU__WEP^ORdD`1Q¤,KeBE jN^dNMRU¥¤,EDOFSEYMRMNEQcsORC[QcMRUWV"K¨`K^VT^d

e^VTK^KBV"K^dS]?;Q4BEsVTU_d4BESEDdRMm;V"dRdRUawBWEf "^UWQc_EDK"MFEDK7MNEPORCFEeBE£SUaORSYVTK^dgSYORU_m^MNU_VTK°eBE£m^ORfX

eÛ_SDQcMRdeBEDdmÔRVTmÔRUWfDMNfPd EYMSVTK"MgONEYXZmÔRVTm;ONU_fYMRfDd{SU_MNfDEDdD VTC[CFEKBVTMROREw^BMEDdRM aQSUaOgSVTK;dRSDONUamBMNU_VTK6`

K^VT^dKBVT^dEDKsMNEDK^VTK^dU_SYU! "U_KBfDOREDK^SYEm^ORffPONEPKTMRUWEDW_ElaQ mBa^dK^QcMg^OREY_WET`#4BU dRB[Mne^QTK^diSYESYQTdY`4SE

4BU¡dfPSYQ\ORMNEFm^Q\ONV\UadleÊaQs_UWMRMNfPORQ\MRÔREFdgÔv^KBEy¦LUaK4fDOREDK;SE[mÔNfYfDOREDK"MNU_EY__E]§mBa^dySVTC[mB_EBETVT^d

fDMRêÛWV"K^diQT^dRdRU;EPKeBfYMgQcU_,aQ KBVTMNU_VTKmBa^dib\fDK^fDOgQc_EeBESYU_OgSV"K^dRSDONUamBMRUWV"KFeÊ@VTOgCB_EDdD`\EPKsm^QTONMRU_SDBWU_EDO

K^VT^dmÔRfDSUadRVTK^d";Q\KêseÊD4EDK;dNEPCwB_EDdeBEV"ORCB_EDdie^VTK^KBEPK"MK^Q\U_dgdgQ\K^SYE${aQC&%DCFEySUaORSYVTK^dgSYORU_mBX

MRUWV"K¨`BEYMnKBV"^dneBVTK^K^VTK^dn^KONfPdR^WMgQcMe^EySDQ\OgQ\SYMNfDORUadRQ\MNU_VTKeBEPdSYU_OgSV"K^dgSYORU_mBMRUWV"K^die^EV"ORCB_EDdD`4C&%PCE

e;Q\K^dv_E[SDQ\dvUaK4¤,KBU9¬iKB¤,K¨`;KBEm^Q\ORMNU_EUaC[m;V"ONMgQ\K"MNEFEDdRM{ONfPdNEPONTfYE&aQdRU_bTKBUW¤,SYQ\MNU_VTKU_K"MR^UWMRUWTE\`6EPK

MREDOgCFEDdeBE£OgQcUadNV"K^KBEDCFEPKTMDìeBE'4BEY(4BEDd;KBEDdeBEPdmÔRVTmÔRUWfDMNfPdEDMsSV"KTMgONEYXZm;ONV"mÔNU_fYMRfDdmÔNfPdNEPK"MNfYEPdY

hi_^dRU_EDÔgd@EBEPCFm^WEPd@UW_a^dNMgONEPK"M@"BMNU__UWMRfeBE SYEYMNMRE fYMgêBE)4^QTKêUWd*QcbTUWMeBE{MgORQTe^BUaONE m;ONfPSUadNfPCEPK"M

;KBEdRUWMg^QcMRUWV"KeBVTK^K^fYEm^QTOeBEPdORAYbTWEPd eBEdREDK^dSV"CFC^KEDKMREDOgCFEeBESYU_OgSV"K^dgSYORU_mBMRUWV"K^dD EDMNMNE

m;Q\ORMNU_ESV"KTMRUWEPK"Ml^KBESDONU_MNU(4BEeBEFCFfYMR?^V4eÊDdlSY_QTdRdRU("ÊDdEDMlmÔRfDdREDK"MNEeBEDdCfDMR?BVBeBEPdlUaKBfPeBUWMREDdD EDd

K^VTBTEY_WEPdvCFfDMR?BVBeBEPd{dNESV"K"MNEDK"MREDK"M{eBEDd{SYU_OgSV"K^dRSDONUamBMRUWV"K^dl_EDd{m^_^ddNUaC[mBWEPdY`pV,+_EDd{CFfYMg?BVBeBEDd

SY_QTdRdRU("^EDdnKBfDSYEDdgdNU_MRQ\UWEPK"Mnm;Q\ONV\Uade^EDd@TEDOgdNU_VTK^dmBa^d@EY4VTMNU(4BEDdD

¬iK0SVTK;Sa^dNU_VTK6`nK^VT^dCV"K"MRORVTK^dsSYVTC[CFEDK"MSYEYMNMREfYMg^eBEVT^OgKBU_MsWEPdw^QTdNEPdse-^KBECfDMR?BVBeBE

dRBdNMRfDC[QcMRU4BE@eBEnMgORQTe^^SMRUWV"K[e-;KEPK^dREDCw^WE@eBEORAYbTWEPdUaK4V"ORCFEY__EDd¡EDKFMREDOgCEPd1eBESUaOgSVTK;SYORU_mBMRUWV"K^dD

ED_Qm,EDOgCEDMNMgORQ\UWMyEDKB¤,Ke-^MNU_WUadNEPOy_QdRfDORUWEP^dREDCFEDK"Mv_QSUaOgSVTK;dRSDONUamBMNU_VTKm;V"^O{SEm,VT^O.4BV\U¡EY__E[Q

fDMNf{SV"K0/Y^E eBADdnV"ONU_b\UaKBET

1o¶ P~ ´ 2 UaORSYVTK^dgSYORU_m^MNU_VTK¨Ù_KBfDOREDK^SYEmÔRffPONEPKTMRUWEDW_E\ÙaK4fDOREDK^SYEmÔgêBEPK"MNEm^QTOeBfYQ\BMgdY`1_VcX

bTU4BE e^EDdCFVBeBAY_EDdCFU_KBUaC[Q\4¨` ORQ\U_dRVTK^K^EDCFEDK"M@eBEdREDK^dlSVTC[C^K¨`,OgQcUadRVTK^KBEPCFEDK"M@KBVTK£CFVTK^V\MNV"KBE\`

OREDm;ONfPdNEPKTMgQcMRUWV"KeBEPd@SVTK;K^QcUadRdgQ\K;SEDdD

(6)

D ¶ · c¶

¶ DB¶ ~

¶i¶ ~¶ 2 ²Z² ²

02 ²

D2 ²

G;Wx hONEYXZSYU_OgSY^C[dgSYORU_m^MNU_VTK^dnQ\K;eQCFEDK;Qcb\EPONU_EvVc_V\bTU_SDQc6m^ORVTm,EDORMNU_EDd {y{y{y{{v{ r

G; hONEYEDOREDK"MNUaQc¨EPKTMgQcU__CFEPKTMgd@Q\K^eMg?BEYUaOnWVTb\UaSYQ\ m;ONV"m;EPONMRUWEPdyv{y{{y{y{y{{v{ xTx

¶i¶ ~¶ 2i 7~Pc ¶

Wx vE¤ KBUWMRUWV"K^dQTK^e¤,ORdRM@m^ORVTm,EDORMNU_EDdJv{y{y{{y{y{v{y{{y{y{y{{v{ x

®?^EDK U_dn¤ KBUWMRE\1Mg?BE SUaORSD^C[dRSDONUamBMRUWV"KQc4U_VTCòy{y{v{y{{y{y{y{{v{ xPz

G klE¤,KBUaKBbV"Ô@ONEPdR^WMgd@Q\w,VTBMnMR?Ê{WVTb\UaSYQc¨mÔRVTm,EDORMNU_EDdy{v{y{{y{y{y{{v{^x

>nVSV"^K"MNEDONX:m^ONV"m;EPONMRUWEPdY`4KBVTMdNV ¦RORQ\MNU_VTK^Q\ø§{{y{y{v{y{{y{y{y{{v{\z

¶ 2£ 7~Pc

¶ !

q^Wx vE¤ KBUWMRUWV"K¨`B¤,OgdRMONEPdRB_MRd@QTK^eCVTMNU_QcMNU_VTK;d {{y{y{v{y{{y{y{y{{v{ôG;x

q^ ¬iWUaCFU_K^Q\MNUaKBb[¤^BEDem^ORVTm,VTdRU_MNU_VTK^db\U_\EPd\EYMQTKBV\Mg?BEDOnm,VTdgdNUawB_E{eBE¤,K^UWMRUWV"K y{{v{ôG#"

q^G klE¤,KBUaKBbV"Ô@dNMgêBsV\Mg?BE mÔRVTm,EDORMNU_EDdVcVTOgC^_QFSUaORSD^C[dRSDONUamBMRUWV"Ky{y{{v{

q^

¢S]?;Q\OgQ\SMREDORUWPQcMRUWV"KVcVTOgCBaQ[SUaORSD^C[dRSDONUamBMNU_VTKUaKMg?BEy¤,KBU_MNE SDQ\dRE y{y{{v{

q

q^q >nV"U_K^e;dnVc¡E4BU_.Q\WEPK^SE{w,EYM:EYEPKdREYMgdnVc¡SUaORSD^C[dRSDONUaw;EPesV"ORCBaQ\dó{y{{v{ z

1¶ ² ² %$

T02n ² ~2P~F^} ¶ [, ~D\ ¶ ~

";Wx ?;Q\OgQ\SMREDORUWPQcMRUWV"KVcVTOgCBaQFSUaORSD^C[dRSDONUamBMNU_VTKªUaK4¤,K^UWMRESYQTdNE«{y{y{y{{v{ qTq

"; vEDdgSYORUamBMNU_VTKVc¡MR?BE dREYMgdnVc6¦Nm,VTdRU_MNU_\EVTOgCBaQ\dL§vQ\dgdRV4SYU_Q\MNEPeMRV'&)(+*,&.-

./102/4365

{7Bx

";G hONV"m;V"dNU_MNU_VTK^Q\6SUaORSD^C[dRSDONUamBMRUWV"KORVTC ?^Q\M@MR?BEDSDQ\K^KBVTM@eBV{{y{y{y{{v{7\q

"; >@?^E ONEPdRm,EDSYMNU_\E{ONVTWEPdVcMg?BE{Q\ORUWV"^d@"U_K;e^dnVc6¦Nm,VTdRU_MNU_\EVTOgCBaQ\dL§{y{y{{v{ôr+

8:9

$ ² ²

<; ¶

~ ¶ ²s¶=

$

² 2¶ ;

T02

¶²

.

² ~

¶

# ~D\%

¶ ~

BWx ©,VTOgCBaQF\EPORdRUWV"K^d\EDOgdg^dB_6\EPORdRUWV"K^d {y{{y{y{v{y{{y{y{y{{v{ôr

B ¢dg?BV"ONM@OREDCFU_K;eBEDO@QTw;V"BM@SY^CB_Q\MNU_4UWM:={y{{y{y{v{y{{y{y{y{{v{ôr

BG klEY\EPORdREyCV"KBV\MRVTK"\`^SDQ\dRE{ONEPQ\dRVTKBUaKBbQTK^eSV"K.jN^K^SYMNU_\E{SV"?BEDOREDK^SYE {y{y{{v{ôr"q

B

vUadjN^K;SMNU_\E SYVT?BEPONEPK^SEyTEDOgdR^dneBUadjN^K^SMRUWTE ORQ\MNU_VTK^Q\WU_M: v{y{{y{y{y{{v{ôr#"

Bq V"?BEDOREDK"M@KBV"KCFVTK^V\MNV"K"s\EPORdg^dnORQ\MNU_VTK^Q\¨CV"KBV\MRVTK" v{y{{y{y{y{{v{ôrTr

B" ¢K^EYm^ONV"m;V"dRQ\ MNVeBEDQ\¨@UWMg?MR?BE m,EDKBb"BUaK^d@E^QTCFm^WEv{y{{y{y{y{{v{ôz#>

? ¶

,2~¶ @

(7)

i

UaOgSY^C[dgSYORU_mBMRUWV"K£?^Q\dvw,EYEDKU_K"MRORVBe^^SYEDew"S QTONMg?"Q\MlMR?^EEPK^e£Vc*Mg?BE[dNED\EDK"MRUWEPdlQ\dQsnQ.V\

V"ORC[Q\WU_YUaKBbsUaC[m;V"ONMgQ\K"MlQ\dgm,EDSMgdlV\iSV"CFCFV"K£dNEPK^dNEFONEPQ\dRVTKBUaKBb,@I:M^dREDdvSaQ\dgdNUaSYQ\p_V\bTU_SyV"OlOREDm^OREX

dREDK"MRU_KBb{4KBV@_EDeBbTE@U_MR?[UaC[mB_U_SYUWM1UaK4VTOgC[QcMRUWV"KV"O1ORB_EDd¡@U_MR?FEYBSYEDmBMRUWV"K^dD`\Qc_WV@UaKBbvMNV OREDQTdNV"KKBV"K

CFV"KBV\MRVTKBUaSYQ\W_\lV"KCFVTKBVTMNV"KTFUadQy¦RKBEYb"QcMNU_\EEDQcMgÔRE]§]`4QTKêsMg?BEydNMgêBVc ¦Nm,VTdRUWMRUWTEmÔRVTm,EDORMNU_EDdL§

?;Q\dw,EYEDK7UaKBUWMRU_Q\MNEPe w"vQ\w;rTqUaK MR?BECFUaeêB_EV\vMg?BEEYU_bT?"MNU_EDdQTKê dNMgêBU_EDe MR?BV"ONV"BbT?^WUaK7Q

SYVTK"MNEYBMV\bTEDKBEPORQ\6m^ONEYEDOREDK"MNUaQc EPKTMgQcU__CFEPKTM@dRU_K;SE w" z#>B`!Q\4z Q\K;eVTMR?BEPO@Q\BMg?BVTOgdY

" MgORQTKBb\EDWEDKBV"BbT?6`DMg?BU_dpU_C[m,VTORMRQTKTM6dRMR;eBv?;Q\d6KBED\EPO6w;EDEDK{QTm^mB_UWEPe{dNEPONU_VT^dR_MNVMg?BE*MgORQTeBUWMRUWV"K^Qc

SYU_OgSY;CFdgSYORUamBMNU_VTK^dD*¢ldQ¤,ORdRMdRMNEDmMRVQTORe;dMg?BUaddNMg^eBT`;E{E^Q\CFUaKBE m^ORVTm,VTdRUWMRUWV"K^Qc¨SUaOgSY^C[dgSYORU_m4X

MRUWV"K^dD`iUaK¯Mg?BEU_K4¤ KBUWMRESYQTdNET°©;V"O[MR?BE£dgQ\cEVcySVTC[m^QTONUadRVTK¨`*EEY\V"cEQcadNV\EPON°SYVTK^SYU_dREY_MR?BE

aQ\ORb\EDW;KBE^mB_VTOREDeSYQTdNE[V\Mg?BEmÔREDeBUaSYQ\MNEsSYU_OgSY^C[dgSYORU_m^MNU_VTK¨{UaKêBEDEDeMR?BEmÔNV"m;EPONMRUWEPd{SV"K^SEPORKBEPe

QTONEMR?BE@dgQ\CFEVTKBEPdY`V"KBW{Mg?BE@SV"KêBU_MNU_VTK^dVc Q\m^mB_UaSYQ\wÛW_UWM: QTONEnCFVTORESYVTC[mB_U_SDQcMNEPeQTKêK^V\M¡eBEYMgQcU_WEPe

?^EDORE\

ElEYBQTCFU_KBEMR?BEvC[QcUaKmÔNV"m;EPONMRUWEPd*V\pmÔNV"m;V"dNU_MNU_VTK;Qc;SYU_OgSY^C[dgSYORU_m^MNU_VTK^dD`TQTKêElmÔREDSUadRE?BUaS]?

QTONUaQ\K"MyVcEDQ\S]?m^ORVTm,EDORM:?BVT_e^dDs>VV"^O{4KBV@_EDeBbTE\`6Mg?BEbTOREDQ\MyC[QcjLVTORUWM:£V\Mg?BEDdREsONEPdR^WMgd{Q\ORE

KÊY{`1Q\Kê¯ONEYEDOREDK^SYEDd QTONEsbTUWTEDKVTOMR?ÊE^SYEDmBMRUWV"K^dY>@?ÊmÔRVTm,EDORMNU_EDd dRMR;eBUWEPe°?BEPONEQTONEdNUaC[mBWE

ª(E^SEPmBMQsEY0¦RQ\4BU_WUaQ\ORT§yV"KBEDd]«@QTKêMR?ÊY?^Q.TE EDQTdNQ\KêU_C[m,VTORMRQ\K"MUaK"MNEPORmÔREYMgQcMRUWV"K^dUaK£MNEPORC[d

V\p4KBV@WEPeBb\EONEPm^ONEPdNEPK"MRQcMRUWV"K¨©;VTOiE^Q\C[mB_E\`4Mg?BEEY_ "K^VK¦NSDQ\dRElOREDQ\dRVTK^U_KBbc§`TVTOlª kv«]`4CFEPQ\K^d

Mg?^QcMD`,UW*E4KBV%Mg?^QcM$# %'&)(+* ` Q\K^e£Q\_dRVsMR?;QcM,# -.&)(+* ` MR?BEPK¨`,UWiQc_pE4KBVQ\w,VT^M0/2143%3 -5* U_d

Mg?^QcMnU_M@U_d 6 # 7 # -8 `^Evb\EDMnMR?BE{EYBm,EDSYMNEPeSYVTK^SY_^dRU_VTKsMg?^QcM7/214393 -.*:(+3 & i>@?^U_dnbTUWTEDdMR?BE

C[Q\U_KCFV\MNU_QcMRUWV"KV"OyMR?BUad{dRMR^eB {U_M{U_dKBEDSYEDdgdRQTON£MRV4KBV?BUaS]?m^ORVTm,EDORMNU_EDd{?^V\aeUaKVTOgeBEDOvMNV

4KBV0?BEYMg?BEDOSYU_OgSY;CFdgSYORUamBMNU_VTKU_dQTe^Q\m^MNEDeMNV?;QcMnEynQ\K"MnVTO@KBVTMY

Eb\U_\E@Q\_dRV{M:VyEYBQTC[mBWEPd*dg?BV@U_K^by?^V¯MR?ÊldNMgêBVc¨MR?BEPdNE@UaK"MRBU_MNU_\EDWFdNUaC[mB_ElQ\Kê[K^Q\MRÔgQc

m;ONV"m;EPONMRUWEPdC[Q.?^Q.TE dNV"CE{UaC[m;V"ONMgQ\K"MMREDS]?^KBUaSYQ\pSV"K^dRE4BEDK;SEDdDtvKBE E^QTCFm^WE ^dREDdQ\KUaK4¤,KBU_MNE

QTONUaQ\K"MpV\ª kv«cEEDdRMRQ\w^WUadR?MR?^Q\M1dNV"CEnQ.{Vc;EYBm;ONEPdRdRU_K^b¤,KBU_MNESYU_OgSY;CFdgSYORUamBMNU_VTK^dVTK^W{Mg?^Q\K^4d

MRV£MR?BEDU_O¦LUaK^Q\SDSEPdRdRU_w^WEFVTOgC^_QTd:§]`peBV4EDd{K^V\M{EBMREDKêMRV£MR?BEUaK4¤,KBU_MNESYQ\dRE\hONEPSUadNEDWTÙ_M{EBMNEPKê^d

V"KB_UaK°Mg?BESYQ\dREDd?BEDK¯MR?BUadFEBMNEPK^dRUWV"KU_dFEPQ\dR\`1Q\K^e¯U_K7m^Q\ORMNUaSY^_QTO U_MFeBV4EPdKBVTMEYBMNEDK;e°?BEPK

QTON4UaKBbFm;ONV"m;V"dNU_MNU_VTK^dnQTONE{mÔREDdREDK"MY1>@?BUad@OREDdgBWM@nQ\dn^KÊ^m;EPSMREDeVTO@^dD*¢lK^V\MR?ÊDOnE^QTCFm^WE{^dREDd

Qm;ONV"m;EPONM:°SDQc_WEPe%ª9ORQ\MR?BEPOdNMgORQTKBb\EDW;«OgQcMNU_VTK;QcCFVTKBVTMNV"KTT®EdR?BVó?BV{`ONV"C MR?^E4KBVK

QTSM@Mg?^QcMlQTK"KBVTKMgONU_4U_Q\6SUaORSD^C[dRSDONUamBMRUWV"KQ\_dRUW¤;EDd@OgQcMRUWV"K^Qc6CFVTK^V\MNV"K"\`^E C[Q.eBEDe;^SE Mg?^QcMQ

MREDS]?^K^U_SDQc6OREDdgBWMn?BUaS]?QTdnw;EDWU_EYTEDeMNVw,E{MROgBE SYQTK^KBV\M@w,E{MROgBEyU_KOREDQ\WU_M:\

>@?BEPdNEE^Q\C[mB_EDdlWEDMl^dMg?BUaK^MR?^Q\MÔRMR?BEPOldRMRêÛWEPdVTKMg?BEdg^w4jLEPSMD`,KBVTMlVTK^WQ\ORE KBEDSYEDdgdRQTON

UaKVTOgeBEDOMNV[UaCFm;ONVTElVT;OSYVTC[m^ORED?BEPK^dRUWV"KsVcMR?BEynQ.sSUaORSD^C[dRSDONUamBMNU_VTKF¦NOREDQTdNV"K^dL§`"w^BMSV"BaeQcadRV

bTUWTEQTONU_VT^d@CFV"ONEvMNEPS]?^KBUaSYQcONEPdRB_MRd@QTdnQw;V"K";dY

;VTm,EB_W£Q\_dRV;`;dRVTCFE{V\¡Mg?BEOREDdgB_MRdbTUWTEDKUaKMR?BUadMREBMlSV"Bae£w;E;dNEPeU_KV"OReBEPO@MNVs?^EYam£MR?BE

QTBMNV"C[QcMNU_DQ\MNU_VTKVc1SUaORSD^C[dRSDONUamBMNU_VTK6

¢d@MR?BEE^Q\C[mB_EDdnV\¡m^OgQ\SYMNUaSYQ\6^dNE{V\¡SYU_OgSY;CFdgSYORUamBMNU_VTKdR?^V{`BUWM@Uad@b\EPKBEDOgQc__C^S]?CFVTORE K^QX

Mg^OgQc*Q\K;edRUaCFm^WEMRV^dNEMg?BEsCFVTORE[b\EDK^EDOgQc*KBVTMNU_VTKSYQc__EDeVTOgCBaQSUaORSD^C[dRSDONUamBMRUWV"K¨s>@?4^dyE

dRMR;eBQcadNV{Mg?BU_d\EPORdRU_VTK[UaKbTOREDQ\M*eBEYMgQcU__dDitvKBEVc6V"^OiOREDdgB_MRdQ\K^dREPORdiQm^ORVTwB_EDC dRMRQcMREDesQTd*V"m;EPK

w"<Q\"U_K;dNV"KUaKxPz\z MR?BE S]?^QTORQTSMREDORUWPQcMNU_VTKsVcVTOgCBaQSYU_OgSY;CFdgSYORUamBMNU_VTK¨

(8)

E{w;EDb\UaKª9dNEPSMNU_VTKG"«w"sQFONEPCUaKêBEPOnQ\w,VTBM@mÔRVTm,VTdRUWMRUWV"K^Qc mÔREEPONEPKTMRU_Q\ EDK"MRQ\UWaCFEDK"MRdD`^Q\dMR?Û_d

UadlK^VOREYaQcMRUWTEY_sEY_¥X:4KBVK¨`;EeBVKBV\MbTUWTE Qcb"QcUaKMg?BEm;ONV4VcdVc*MR?^EONEPdR^WMgdb\U_\EPK?BEDOREsª(dREYE

klzTz'^V"O1mÔNEPSUadNE@OREEPONEPK^SEPdQTKê[mÔRV"V\dY« lVTMNUaSE?BVEYTEDOMR?^Q\M1E@eBEPm^Q\ORM*dNU_bTKÛ¥¤,SDQ\K"MN_yORVTC

Mg?BEyU_K"MgONUaSYQ\MNEFª(Q\K;eMg?BEDdREvSYVTC[mB_U_SDQcMRUWV"K^dnQ\ORE^dREY_EDdgdVTOndNMg^eB4UaKBbSUaORSD^C[dRSDONUamBMNU_VTK;dY`4EYTEDKU_KMR?BE

m;ONEPeBU_SDQcMRESYQ\_SDBa^d«7¦ !"L§iVTOONED_Q\MNEPeyVTOgC[Qc_U_dgC[d^dREDeU_K0 z#>;Q\K^e{U_MRdVTW_VcX

EDOgdD>@?BEPKª9dNEPSMNU_VTK «]`\Ee^EDQcBUaKFbTOREDQ\MeBEDMRQ\UWad¡@UWMg?[m^ONV"m;V"dNU_MNU_VTK;Qc4SUaORSD^C[dRSDONUamBMNU_VTK;dYE@bTUWTE

Mg?BEm;ONEPSUadNE.QTONUaQ\K"MgdVc*Mg?BE[mÔNV"m;EPONMRUWEPd?BUaS]?QTONEdRQ\MNUadL¤;EPe¨vEb\U_\EQ\WMR?ÊFmÔRV4VcdD`,UaK^SY_êÛ_KBb

Q\WiMR?BEsSYVT^K"MNEPOLXZE^QTCFm^WEPdY`6UaKVTOgeBEDOyMRVC[Q\cEm^OREDSYU_dRE[MR?BEw;V"OReBEPOyWUaKBEsw,EYM:EYEPKMg?BEm^ORVTm,EDORMNU_EDd

dgQcMRU_dN¤;EPew"SUaORSD^C[dRSDONUamBMRUWV"K^dQTK^eONED_Q\MNEDem^ONV"m;EPONMRUWEPdv?BU_S]?Q\OREFK^V\MydRQ\MNUadL¤;EPe¨>@?BEPK¯ª9dNEPSMRUWV"K

q"«`4EEYBQTCFU_KBEVTOgC^_QSUaORSD^C[dRSDONUamBMNU_VTK6`T?BUaS]?sUad\EPON^dREB¨UaKQTm^mB_U_SDQcMRUWV"K^diV\SUaOgSY^C[dgSYORU_m4X

MRUWV"K^dDìmÔRV"UaeBUaKBbMg?ÔREYEE4BU_.Q\WEPK"MFeBEY¤,KBU_MNU_VTK^dD°EE^Q\CFUaKBE?ÊDK°M:VdNEDMRdFVcV"ORCBaQ\dFQ\ORE

¦NE4BU_Qc_EDK"M:§l@U_MR?ONEPdRm,EDSYMMRVV"ORCBaQSUaOgSY^C[dgSYORU_mBMRUWV"K¨`4Q\K^eEydR?^V=?T[UaKsQTSMM:VFeBU$# EPONEPKTM

"UaK^e^dVcE4BU_Qc_EDK^SYEvC^dNMnw,EySYVTK^dRUaeBEDOREDe¨1¢l_dRV;`4Evdg?BV®Mg?^QcMnUaKsMR?^E¤ KBUWMRE{SYQ\dREvMR?BE{KBVTMNU_VTKsV\

V"ORCBaQSUaOgSY^C[dgSYORU_mBMRUWV"K£UadE 4BUWQ\WEPKTMMNVMR?BEQTm^m^Q\OREDK"MRWCFVTOREb\EPKBEDOgQc¡KBVTMNU_VTKV\SY;CBaQcMRUWTE

QTKêSYVTK^dRU_dRMNEPK^S£mÔREDdREDOR4U_K^bmÔREEDOREDK"MRU_Q\pEDK"MgQcU__CFEDK"MDy>@?Û_dvaQ\dRMOREDdgBWMQTdm;ONV"w^Q\wB_£ONEPQ\eBMNV

bTEYM1V"BMY`"w;EPSYQ\;dNE@E?^Q.\E@eBUadgSV\EPONEPeU_M*UaKFM:V OREDSYEDK"M*Q\m^m;Q\OREDK"MN_^K^OREYaQcMREDe[m^QTm;EPORd1Q\M*MR?BE@MRU_CFE

V\m^ONUaK"MNUaKBb&%¬*aQ\w,VTOgQcMRU_KBbORVTCòQ£4KBVKONEPdR^WMD`Es?^Q.\Esdg?BVK?BV MR?BEEY_U_CFUaK^QcMRUWV"KVc@MR?BE

¤;4EPem^ORVTm,VTdRUWMRUWV"K^dUaKQsVTOgCBaQSYU_OgSY^C[dgSYORU_m^MNU_VTK£C[Q\\EDdlm;ONEPSUadNE Mg?BEFE4BU_.Q\WEPK^SEFw;EDM:EDEDKV"OLX

CBaQSYU_OgSY^C[dgSYORU_m^MNU_VTKQTK^edgSEPmBMNUaSYQ\¨h¡V"VTWE,dneBEYQ\B_MRd@U_MR?BV"BM@SV"K^dNMgORQ\U_K"MD¡>@?^EyCFV"ONEMNEDS]?;KBU_SDQc

OREDdgB_MRdQ\w,VTBMV"ORCB_QSUaORSD^C[dRSDONUamBMRUWV"K£ª(QTK^eQ\_dRVQEY%ONED_Q\MNEDeONEPdR^WMgdQTw;V"BMnVTOgeBU_K;Q\ORFm^ORVTm,VcX

dRU_MNU_VTK^Q\6SUaORSD^C[dRSDONUamBMNU_VTK «iQTONEyEYBQTCFU_KBEPeUaKdNEPSMRUWV"K ";*>@?BEDORE\`^Mg?BE m^ORVTwB_EDCðVc¡MR?BE{E "^UWQc_EDK;SEDd

V\ dREYMgd1Vc VTOgC^_QTd¡@UWMg?ONEPdRm,EDSYM1MNVyVTOgC^_QySUaOgSY^C[dgSYORU_mBMRUWV"KUadie^EY\EDWV"m;EPe¨`\QTK^eFUWM*Uad*dg?BVK[?BV

Mg?BUad1b\U_\EPd1K^QcMg^ORQ\W_ORU_dREnMNV{Mg?BEUaKTMgONVBe^;SMNU_VTKFV\ Q\ORU_VT^d¡dREYMRd*Vc^¦Nm,VTdRUWMRUWTEnVTOgCBaQ\dL§]6I:M*Uad*4KBVK

MRUW_MR?BEU_K"MRORVBe^^SYMNU_VTK£V\¡Mg?BEK^V\MNU_VTKVciSUaOgSY^C[dgSYORU_mBMRUWV"KMR?^Q\MlMR?^EFKBVTMNU_VTKV\¦Nm,VTdRUWMRUWTE{VTOgC^_QTd:§

m^_Q.BdQFSYEDK"MROgQc ORV\_E\ ;lVEYTEDOD`"QTK^eOgQcMg?BEDOndRMROgQ\KBbTEY_\`"?^QcMnMR?^U_d@KBVTMNU_VTKeBEDKBVTMNEPdnE^Q\SYMN_U_KMR?BE

SDQ\dRElV\pVTOgC^_QFSUaORSD^C[dRSDONUamBMRUWV"K¨`4VTOEY\EPKsUaKMg?BE{SYQTdNEvVcpV"OReÛ_K^QTONª9mÔNV"m;V"dNU_MNU_VTK;Qc VTOmÔREDeBUaSYQ\MNE.«

SYU_OgSY;CFdgSYORUamBMNU_VTK@UWMg?[Q\OR"UaKBbvVTw4jLEPSMgdY`"?^Q\e[KBED\EDO1w,EYEPKdNMg^eBU_EDe¨¡EdR?^V¯MR?;QcM*Q\ORU_VT^d1KBVTMNU_VTK^d

V\¨¦Rm,VTdRUWMRUWTEV"ORCBaQ\dL§yQ\ORE{KBEDSYEDdgdRQTONT1ILKMR?BUadlCFVTOREyMNEPS]?^KBUaSYQcdNEPSMNU_VTKQ\_dRV;`BMg?BEm^ORVTwB_EDCðVc1MR?BE

S]?;Q\OgQ\SMREDORUWPQcMRUWV"K{Vc MR?BEK^V\MNU_VTKVc VTOgC^_QySUaOgSY^C[dgSYORU_mBMRUWV"K UaKFMR?BEUaK4¤,K^UWMRESYQ\dREnU_didNVTWTEDe¨6MRV{VT^O

4KBV@_EDe^b\E\`4U_M@U_dnMg?BEy¤,OgdNM@MRU_CFE{Mg?^QcMdg^S]?QFS]?;Q\OgQ\SMREDORUWPQcMRUWV"KsONEPdR^WM@Q\m;m;EPQ\OgdUaKMR?BE{_U_MNEDOgQcMg^ORE\

©¡UaK^Qc_Wª(dREDSYMNU_VTK \«SV"CFEDd@Q[ORQ\MR?BEPO@eBEYMgQcU_WEPeU_K"MR^UWMRUWTE{E^mBaQ\K^Q\MNU_VTKsV\Mg?BE C[QcUaKm^ONV"m;EPONMRUWEPdY`

QTKêsSYVT^K"MNEPOimÔRVTm,EDORMNU_EDdD`4Q\ddNV"CEVc6Mg?BEDC QTONElK^V\MiTEDOREY_¨4KBVKËvE^mBaQcUaK?"[EMg?BUaK^

Mg?^QcM@Mg?BE dREYM@VcMR?BE Q\_OREDQTeBs4KBVKm^ONV"m;EPONMRUWEPdnVc1SUaORSD^C[dRSDONUamBMRUWV"KC[Q\\EDdnMR?;QcMSUaOgSY^C[dgSYORU_mBMRUWV"K

Uad{Qb\V4VBeSYQ\K;eBU_e;QcMNEFV"OyMROgQ\K^dR_Q\MNUaKBb£dNEDMRd{V\OgB_EDdy@U_MR?E^SYEDmBMRUWV"K^dYILKVTOgeBEPOyMNVSV"K4¤,OgCôMR?^U_d

V"mBUaKBUWV"K¨`pEY^Q\C[mB_EDdyVc@OREDQc*SYU_OgSY;CFdgSYORUamBMNU_VTK^dy^dREDeV"O{MROgQ\K^dRaQcMNUaKBbdNV"CFEsORB_EDd{QTONE[bTUWTEDK¨tvKBE

'(

ï{Æpå]å) *6ËÏ,+\Ñ.-]Î

ê

ÌÎ0/21ÑRËëÓÕÔÕÑLëà31Ë

ê

à31.Ñ*Í.ë(ÑLÏ(Ñ

ê

à1ëÑLÍ\é]ëàã+cÑLíWé]ëÑlèNå]åÙYäZáÅaàÐ.ÑNËÓÕÏ,*pÔà314-]ëÑRËgà¡Ð.Ñ:àZËÔÕÓÕÏ5*Ôà31

/NÔÕë/LÎ.Ì@Ï6/LëÔÕÍPà(ÔÕé

ê

ÏË

ê

ÐÍ.ëÑ:í_ÑLëÑ

ê

à(ÔøËÓ^Ñ

ê

à9ËÔÕÓÕÌ@Ñ

ê

à(ÏRÉ.Ô

ê

à31.Ñ1Í.ëÑNÐPÔ7/RËgà(Ñ8/NËÓ7/NÎPÓÕÏË

ê

ÐlÔ

ê

à61.Ñ*Í.ëé]Ícé]Ï9Ôà(ÔÕé

ê

ËÓ /NËÓ7/LÎ.ÓÕÎ.ÏNá,ÈÏ

à61.ÑÏ9Î0+:9(Ñ./:àiÔÕÏ¡ë9Ëgà31.ÑLë;/Né]Ì@ÍPÓÕÑLÞ\É4Ô

ê

ÍËëà(Ô7/NÎPÓøËëià31.ÑnÓÕÔÕÌ@Ôà(Ï¡éí à31.ÑnÔ

ê

à9ÑLëÑLÏ(à(Ô

ê

-{Í.ëé]Í\ÑLëà9ÔÕÑLÏËë(Ñ

ê

éàiËÓ*6ËN÷DÏ*ÑRËÏ÷{à9é

+\ÑlÍ.ëÑ./NÔÕÏ(ÑLÐÑ:ÞPË/:à9Ó÷É<*¨Ñ=1ËLùÑvÐ.Ñ./LÔÕÐ.ÑLÐà9éÑ:ÞDà(ë9Ë/:à@à31.ÑvëÑLÏ9Î.Óà(ÏíWé]ënÍ.ëé]Ícé]Ï9Ôà(ÔÕé

ê

ËÓ,/LÔÕë/LÎ.Ì@Ï6/LëÔÕÍPà9ÔÕé

ê

ÏRÉ&*,1PÔ7/21>1ËÏ

-]ÔùÑ

ê

à61PÑlÍPë(ÑLÏ9Ñ

ê

àëÑLÍcé]ëàNá@?A1.Ñ;B3+.Ô7-DCëÑNÍcé]ëànÔÕÏiËÓÕÌ@é]Ï(àiË/61.ÔÕÑ:ùÑNÐTÉ,é

ê Ó÷Ôà ê

ÑLÑLÐ.ÏiÍcé]ÓÕÔÕÏ61.Ô

ê

-.ÉBË

ê

Ðà31.ÔÕÏiÍ\é]ÓÕÔÕÏ31.Ô

ê -

ÌËN÷àZËE]ÑÏ9é]Ì@Ñ1à(ÔÕÌ@ÑÉ0+.ÎPà1Ôà5*pÔÕÓÕÓ +cÑÍ.Î+.ÓÕÔÕÏ61.ÑLÐ{Ô

ê Ë ê

ÑRËëí_ÎPà(Î.ëÑ]áF?A1DÎPÏRÉcí_é]ëpëÑNÏ(Î.Óà(Ï1Ë+cé]ÎPàF-]Ñ

ê

ÑLë9ËÓ;Í.ëÑ:í_ÑLëÑ

ê

à(ÔøËÓ

Ñ ê à9ËÔÕÓÕÌ@Ñ

ê

à(ÏRÉÑ:ùÑ

ê

*,1PÑ

ê

à61.ÑLÏ(ÑëÑLÏ9Î.Óà(Ï ËëÑé]ÎPë(ÏNÉ* ÑpÐPé

ê

éà Í.ëéRùDÔÕÐ.Ñ6à61PÑpÍPë(éYéí_ÏG1.ÑLë(Ñ]ÉYÔ

ê

é]ëÐ.ÑLë,à(éFE]ÑNÑLÍnà31.ÑpÍ.ë(ÑLÏ(Ñ

ê à

ë(ÑLÍcé]ëàpÏ31.é]ëà6Ñ

ê

é]Î-1"ÉcË

ê

ÐH*¨ÑëÑ:í_ÑLë¨à(éé]Î.ëIB3+PÔ7-DCíWÎPà(Î.ëÑ¡ë(ÑLÍcé]ëàRá<Jé* ÑLùÑLëLÉËÓÕÓcà61PÑ¡ë(ÑLÏ(Î.Óà9ÏK/Lé

ê

/LÑLë

ê Ôê

-nÏ9ÍcÑ./LÔL!/NËÓÕÓ÷

/NÔÕë/LÎ.Ì@Ï6/LëÔÕÍPà(ÔÕé

ê

Ï¨ËëÑÍ.ëéRùÑLÐÔ

ê

à31.ÔÕÏ Í.ëÑLÏ9Ñ

ê

à ë(ÑLÍcé]ëàNÉ.Ñ:Þ:/LÑNÍDàpË1ùÑLë÷@Ï9ÌËÓÕÓ

ê

ÎPÌM+cÑLë éíTÑRËÏ÷@é]ëI* ÑNÓÕÓ!E

ê

éN*

ê

ëÑLÏ9Î.Óà(ÏRá

(9)

V\@MR?BEPdNEE^Q\C[mB_EDddR?BVd?BV MR?BUaddRMR;eBSYQ\Kw,EQTm^mB_UWEPeUaKVTOgeBEDO MNVeBEPSUaeBE?^U_S]?°SYU_OgSY;CX

dgSYORUamBMNU_VTK¯U_d[w,EYMNMREDO[MRVMgORQTK^dNaQcMREdRVTCFEb\U_\EPK¯dREYMFVcvOgB_EDdD¯¢lK^V\MR?^EDOFE^Q\C[mB_EdR?BVdFMg?^QcMFE

SDQ\K^K^V\M@E^m,EDSYMMNV4VC^S]?ONV"C Mg?BU_ddNMg^eBQc_VTKBETiMg?BEOREDQcdNU_MR^Q\MNU_VTKMRVsw;EMROgQ\K^dR_Q\MNEPeC^dRMlw;E

dRMR;eBUWEPeSYQ\ORE^W_UaKVTOgeBEDOyMRV£VTwBMgQcUaKQ\KQ\m^m;ONV"m^ONUaQcMREMgORQTK^dR_Q\MNU_VTK¨¢l_dRV;`MR?^U_d{EY^Q\C[mB_EsdR?BVd

Mg?^QcMU_K7dNV"CFESYQTdNEPd ?BEPKMR?^EMgORQTeBUWMRUWV"K°^dREDdF^KBU_VTK^dVclSY_QTdRdRUaSYQcSUaORSD^C[dRSDONUamBMRUWV"K^dY`¡UaKQTSMQ

;KBU4BEvV"ORCB_QFSUaOgSY^C[dgSYORU_mBMRUWV"KsbTUWTEDdnQ[w;EDMNMNEPOdRV\aBMNU_VTK¨¡ILKQc_¨MR?BEPdNEyEYBQTC[mBWEPdY`BEydR?BV ?BV

Qm;EPONMRU_KBEPK"MSV"CwBUaK^Q\MNU_VTKVcMg?BEdREYMRdVcnV"ORCB_QTd Q\dgdRV4SYU_Q\MNEPeMRVUaK^eBU_4U_e^;QcOgB_EDdCFQ.b\U_\EsQ

bTV4V4eQ\K;dNEDOVTOnMgORQTK^dR_Q\MNUaKBbMg?BEl¦RORB_E]§{SV"OROREDdgm;V"K^eBUaKBbMRV[MR?BE dREYM@V\Mg?BEDdRE¦LUaK^eBU_4U_e^;Qc6OgBWEPd:§]

El?^Q.TEMgQ\\EDKFbTOREDQ\M¡SDQ\OREnU_KQ\MNMRORUaw^BMNUaKBb QTKTONEPdRB_M*Q\w,VT^M*SUaORSD^C[dRSDONUamBMNU_VTKFMRV{MR?BE@¤ ORdRM1MNEY4M

ª(VTO*Q\M1WEPQ\dRM*MNV Q{CFV"ONE@ED_QTw;V"ORQ\MNEDeFMREBMiw"Mg?BEldgQ\CFEQ\BMg?BVTOd «?BEDORE@U_MiQ\m^m,EDQTORdD`cMRV MR?BEw;EPdNM*V\

V"^Op4KBV@_EDe^b\E\`.ED\EDKyUaKSDQ\dREDdp?BEDK{Mg?BEnONED_Q\MNU_VTKy@U_MR? V"^O6VKONEPdRB_MpnQ\dKBV\MVTw"4U_VT^dD6E?^Q.TE

MgONU_EDeMNVsC[QTcEyQ\d@C[Q\K"SYVTK^KBEPSMRUWV"K^d@Q\dnm,VTdgdNUawB_Ev@U_MR?E "^UWQc_EDK"MnV"ORC[Qc_UadRC[dD EPONMgQcUaKBWT`BMR?BEPONE

QTONEdRMNU_WVTCFUadRdRUWV"K^d{Q\K;eORVTK^bQ\MNMgONUaw^BMRUWV"K^dY`Q\K^eEED_SYVTCFEsQ\K"SYVTC[CFEDK"M{VTKMg?BEdg^w4jLEDSYMY

>@?^U_dvONEPm;V"ONM?^Q\dMRQTcEDKdNV"CEMNUaCEPdFªMR?^EFdRUWMg^QcMRUWV"K£UadC^S]?£VTOgdNEyV"OlMg?BEy¦RwBU_bOREDm,VTORM:§ EYTVTcEPe

UaKKBV\MRExTW_Õ«]`pm^QTONMRWw,EDSDQ\^dREMg?BES]?^Q\OgQ\SYMNEPONU_DQ\MNU_VTKVciVTOgCBaQSYU_OgSY;CFdgSYORUamBMNU_VTK£UaKMR?BE[UaK4¤,KBU_MNE

SDQ\dREQTdFK^V\MsdRVV"w""U_VT;dY`nQ\K^e7E£QTKTMREDe7MNVQ.\VTU_e m^^w^WUadR?^U_KBbMg?BUadsONEPm;V"ONM[@U_MR?BV"BMsdg^S]?7Q

OREDdgB_MY¡>@?4^dY`BdRVTCFEYMRU_CFEPd*E?^Q.TEleBUadRSYV\EDOREDeFUaKMR?^EvOREDSYEDK"M*_UWMREDOgQcMR;ONElQONEPdR^WMMR?^Q\MiE?^QTeb\VTM

w,EV"ONEyU_MRdm;^wB_U_SDQcMNU_VTK6`^MR?BUaK^"UaKBbUWM@nQ\dnKBED{ Q\MR^OgQc__\`BEYTEDKU_KMg?BEDdRE SYQTdNEPdY`4E QcMNMgONUaw^BMRE{MR?BE

SYVTK^SYEDOgKBEDeONEPdR^WM@MRVª(?BVTC EyMg?BU_K;sUad«Mg?BE ONU_bT?"Mnm;EPORdRVTK6

{y

Uad®Mg?BE m^ONV"m;V"dNU_MNU_VTK;Qc_V\bTU_SoSYVTK^dRUaeBEDOREDe¨`?BUaS]? SYVTK"MRQ\U_K^d0m^ONV"m;V"dNU_MNU_VTK;QcdRBCw,V\ad0KBVTMNEPe

/./ /

- 5

UadMR?BEdNEDMVc{Qc_MR?BEm;ONV"m;V"dNU_MNU_VTK^Q\dNBCw;VT_dD0¢ld^dR;Qc9` eBEDK^V\MNEPdsQcadRV

Mg?BEydNEDMV\Qc_ MR?BEVTOgCBaQ\diEBUadNMRU_KBbFUaKsMR?^U_d_V\b\UaSc1¢dEQTONEU_KQm;ONV"m;V"dNU_MNU_VTK^Q\;_V\bTU_S\`"V"^OWVTb\UaS

UadSVTC[m^QTSMnQ\KêSVTC[mB_EYMRE\1¢adRV;`"VTOmÔREEDOREDK"MRU_Q\,EPKTMgQcU__CFEPKTMgdY`4QFONED_Q\MNU_VTKw,EYM:EYEDKCFV4eÊYadC[Q.

w,E Q\dgdRU_CFU__Q\MNEDeMNVQ[OREYaQcMNU_VTKw,EYM:EYEDKSV"C[mBWEDMNE{Mg?BEYV"ONU_EDdD

>@?BE dREYMnV\ - 3 3 & U_d

/

-

5

?BEPONE<- 5

"!# $%!

EYMNMREDOgd&!¯QTKê(' @U_W6eÊDKBVTMNEvVTOgCBaQ\dUaK #)oeBEDK^V\MNEPdnMR?BEyQ\_dREVTOgCBaQ^`^QTKê+*MR?BEyMgORBE

V"ORCBaQ^

,

eBEDK^V\MNEPdvMR?BEdREYMyVcQ\W¡Mg?BE %=3 -3yMg?BEYV"ONU_EDd U_K !.- E^Sa^dRUWTEV"O/0!.- ðVTO

QTK"(!

>@?BEWEDMNMREDO6 ª@U_MR?sm,VTdgdRU_wB_Eldg^w^dgSYORU_m^MiVTOidR^m,EDOgdgSYORU_mBM]«¡@U_W eBEPKBV\MREldR;w^dNEDMRdiVc

`"?BEDK oU_d

QMR?ÊYVTOR£ª-«`BMR?Û_d@@U__6w;E{mÔREDSYU_dREDe¨`BQTKê 211ª@U_MR?m;V"dRdRUawBWE{dg^w^dgSYORU_m^M«i@UW_6w,EyOREDdREDOR\EPeMNV

SYVTC[mB_EYMREMg?BEYV"ONU_EDdnª 1 - ,

«]©,VTO1QTKTMR?BEDVTORUWEPd 43Q\K^e.65nUaK

E?^Q.\E 37$ 65nU#238 5c

V\MRU_SYEvMg?^QcMn_EYMRMNEDOgd:9

/; /

QTK^e(<ò@UW_6QcadRVFeBEPKBV\MRE{dNEDMRdVcVTOgCBaQ\dD`Bw^BM@VTK^WUaKSDQ\dREDd?BEPK

SYVTK^dRUaeBEDORU_K^bMg?BE{WVTb\UaSYQ\ SYWV"dR;ONEyw"(Vc¡MR?^EDdREydREYMgd@Uad@KBV\M@UaK"MNEDK;eBEDe¨

(10)

©,VTOlQTK"dg^w^dREYM V\

` - 5 eBEPKBV\MREDdlMR?BEdREYMlVc1MR?BEm^ONV"m;V"dNU_MNU_VTK;Qc6dR4Cw;VT_dlQ\m^m,EDQTONUaKBbUaK

QTK^e

- 5 U_d@Mg?BE aQ\KBb"^QcbTEvdg^S]?MR?;QcM -

- 5 5 - 5 IZ

`;Mg?BEDKE KBVTMNE - 5 VTO

Mg?BE dREYM - 5 Q\K^e - 5 V"O - 5

®?BEPKFE@SV"K^dRU_eBEPO ! -.-5 & V\ -

5

`TE\b; -

./102/43 5

`TECFEPQ\KFQ\d1^dg^Qc

)0 3

% -

5

QTK^e£Mg?BEm^Q\U_OR@UadNE UaK"MNEPORdREDSYMNU_VTK^dQ\ORE EDC[mBM:T` ?^VED\EDOD`,K^V\MNUaSEMR?^Q\MlEQ\W_VEDC[mBM:£dNEDMRdvQ\CFVTK^b

/10/13

E^dREsMR?^EsKBV\MgQcMNU_VTK;d 3 5 - 3 5 5

`<

<-<

5

Q\K^e !

"!

eBEDKBVTMNEPdMR?BEdNEDMsVc Qc_Mg?BESV"C[mBWEDMNEMg?BEYV"ONU_EDds?BU_S]? EPKTMgQcU_ª(U(E\

SYVTK"MRQ\U_K « s1E 4KBV%MR?^Q\M 61

EYMNMREDOgd"!QTKê#eBEPKBV\MREvUaK"MNEPORmÔREYMgQcMRUWV"K^dVTO `!C[Q.sw,E Q\dgdNUaCFUWaQcMREDesMRV[UWMgd@SVTOgOREDdgm;V"KêBUaKBb

SYVTC[mB_EYMRE£MR?BEDVTOR <-! 5 ! ! -

/ ! $ ! ª -$! 5 - ,

«ª(MR?BUadsQTCwBU_bTBV"^dCFEDQTKBU_K^b

V\4$ôQTK^e Vc7U_dSY_QTdRdRU_SDQcnUaK7_V\bTU_SQ\K;e dg?BV"B_e KBVTM[m;ONVTVTcESV"K4^dRUWV"K,« E£@UW_eBEDK^V\MNE

Mg?BE[U_K"MREDOgm^ONEDMRQ\MNU_VTK^dyw"£MR?BEsdg^w^dREYMyV\ -

5 MR?^Q\MyMR?BEDdRQ\MNUadL yE\b;U¥& -

5 / ./ Q\K;e

! .

/7

`BMg?BEDK <-!

5

%<-&%+/

% 5

'

eBEPKBV\MREDdMR?ÊvdREYMVcQ\W MR?ÊvUaK"MNEPORmÔREYMgQcMRUWV"K^d1V"O `4U9EvMR?ÊvdREYMVcQ\W Mg?BEvdg^w^dREYMgdVc)( -

5

' 1

Vc

'

` EFKBV\MRE -' 15 V"OlMg?BE[dNEDM *

'

<-! 5 ! !%-

/ ! $

!°VTO@QTKT+! - ' 1

¢KEY^m^ONEPdRdRU_VTKsdg^S]?Q\d1¦:V"OnQ\K" !p§v@U_W6CFEDQTKF¦LVTOnQTKT[V"ORCBaQ!¯U_K

§`^dRUaCU_aQ\ORW¦LVTOnQ\K"

y§{@U__CFEDQTKs¦:V"OQ\K"dR;w^dNEDMVc

§Q\K;e¦:V"OQ\K"! § @UW_CFEDQTK¦LVTOQTKTUaKTMREDOgm^OREYMRQ\MNU_VTK!VTO

§]`;Q\K;edRU_CFU__QTON_s?BEPK¦:V"OQTK"\§yU_d@OREDm^_QTSEDew"¦NMR?BEPONEyEBUadNMgd@dNV"CFE]§]

' - 5

e^EDKBVTMNEDdvMg?BEdNEDMV\Qc_¡MR?BECFVBeBEYadvVc s

' - 5 ,!-

'

-!%$

>@?4^dvE

?;Q.\E.! - ' - 5

U$# <-!

5

-/ - 5

EKBVTMNE -! 5

U_K^dRMNEPQ\eyV\ - !

5 Q\K;e

' -! 5

UaK^dRMNEDQTeyVc

' - !

5

`Q\K;e{QcadNV

-! 5

VTO

- ! 5

`

-! 5

V"O& - "!

%5

¢dyE[VTOgU_KmÔRVTm,VTdRUWMRUWV"K^QcWVTb\UaSc`6Mg?BEDOREFEBU_dRMRd{QTKV"w""U_VT;dSYVTOgONEPdRm,VTKêÊDK^SYEw,EYM:EYEDK

'

QTK^e

, ` ' - 5

QTK^e0 - 5

`)!Q\K^e <-!

5

QTK^edNVV"K¨ ;lVEYTEDOD`BE{_U_\E w;EDMNMREDOMNVscEDEDmMg?BE M:V

"UaKê^d@V\*KBV\MgQcMNU_VTK;dY`;QTddRVTCFEYMRU_CFEDdlUWMlU_d@EPQ\dRUWEPO@MNVsSYVTK^dRUaeBEDO@Mg?BE UaK"MNEDOgmÔREYMgQcMNU_VTK;dY`;QTKêdNV"CFEYMNUaCFEDd

U_MC[Q.w,E{EDQ\dRU_EDOMNVSV"K^dRU_eBEPOnMR?BE SYVTC[mB_EYMREvMg?BEYV"ONU_EDdD

&.- 5 eBEPKBV\MREDdnMg?BE SaQ\dgdNUaSYQ\ MNVTm,V\_V\bTU_SDQc S_VTdg^ORE\VTO@QTKTdNEDM1 ,

`^EyK^V\MNE &.-1 5 VTO

Mg?BEyS_VTdg^ONEVc6Mg?BE{dNEDM"1n`4U9ET0 &.-21 5 3 -4-65 615 *>@?^QTK^4diMRVMg?BEySVTOgOREDdgm;V"K^eBEDK;SElw,EYM:EYEPK

,

Q\K^e

'

`¨VTOyQ\K"dREYM

' 1 '

`6E@U_W*Q\_dRVe^EDKBVTMNE4 &.-

' 15 V"OvMR?BES_VTdg^OREV\

' 1

`pU(E\

&.-

' 15 '

-<- ' 15 5

(11)

Uad1MR?BEdNEDM1Vc MR?BE -3 * !-5 # 3 - 3 3 & V\

- U$#Mg?BEDORE@EBUadNMgd1dNV"CE:!dR;S]?

Mg?^QcM %<-! 5 ¡IZ -2`BE{@U__6Q\d@^dg^QcSYQc_! -3 *< !-5 # 3lU# - 5 -

ª@U_MR?BV"BMQ\K"dg^w^dgSYORUamBM«iUadQ[CEDMRQ[dR4Cw;VT6CFEDQ\K^U_KBb ¦NE4BU_Qc_EDK"MnMNV§]

>@?BEMNEPORC ! @UW_b\EDK^EDOgQc_Ww;E^dNEPeUaKQ\SYMMNVeBEDKBVTMNEMR?BE "^V\MNU_EDK"MVc@MR?BUadFKBV\MRUWV"K

w"_V\b\UaSYQ\E 4BUWQ\WEPK^SETEF@U_W1KBVTMNE4! ' VTO!

'l`¨U9ET -! 5 -'

5

>@?BUadyCFEDQ\K;dMg?^QcM

EyVcMREDKQ\dgdNUaCFUWaQcMREMg?BE dNEDMnVcQ\W¨Mg?BEyVTOgC^_QTd MNV[MR?^E 4BVTMNU_EDK"MnVc w"s_V\bTU_SDQc E4BU_.Q\WEPK^SE

ª UaKêBEPK"w;Q\^CóQc_b\EPwÔRQ4«);lVEY\EPOY`BU_MUadlKBVTMlQc_nQ.4dnm,VTdgdNUawB_E MNVCFQTcEyMR?Û_dvQ\dgdNUaCFUWaQcMRUWV"KïmÔREDSYU¥X

dREY_\`¨?^EDKE[SVTK;dNUaeBEDO -! 5

ªVTO - 5

«`6E[SYQ\K;KBV\MyQ\dgdNUaCFUWaQcMRE!=MRVU_MRdvE "^UWQc_EDK;SE[SaQ\dgdw"

_V\bTU_SDQc E4BU_Qc_EDK^SYE\1>@?BE{SV"K"MNEBM@dg?BVTBaeCFQTcEyS_EDQTO?;QcMnU_dnUaK"MNEPKêBEDew"Q ! ` Q\KêMR?Û_d

QTw^^dRUWTEvm;Q\ORMNUaQc Q\dgdNUaCFUWaQcMRUWV"K¨`4?BU_S]?dRU_C[mB_U¥¤,EDd@SV"K^dRU_eBEPORQTwB_FMg?BEyE^mÔREDdgdNU_VTKQ\KêmÔRV"V\pVc¡dNV"CFE

OREDdgB_MRdD`^dR?^VTBaeK^V\Mm^ORV\V"cESYVTK4;dNU_VTK¨

@ Y

! #"$%'&(*),+'".-/+!0-1 23+4-/56*7)8:9*)5,;-/9<%'),%=6(&>"

?²A@

¶ 6B

¢ 3DC

& -5FE

ª(U_K «FUadsQ\K EY4MREDK^dRU_\EªU9ET

E - 5 8 V"OsQ\K"

E - 5 E -<- 5 5G

1E ^dRE{QcadNV[Mg?BE KBV\MgQcMRUWV"K E -! 5

V"O E - !

5

E - -! 5 5

¢ 3DC & -5 & 3 &9-5 -3 -H U_dMg?BE ONEPdNMgONUaSMRUWV"K MRV H Vc Qñm^OREX

SYU_OgSY;CFdgSYORUamBMNU_VTK E

>@?BE ! IE 3 E 5Q\K;eMR?BE - 3 9& 3 -.JE 3 E 5V\M:Vm^ONEYXZSYU_OgSY;CFdgSYORUamBMNU_VTK^d E 3sQTK^e E 5

QTONEFMR?^Esm^ONEYXZSYU_OgSY;CFdgSYORUamBMNU_VTK^dveBEY¤,KBEDew" -E 3 .E 5 5 - 5 E 3- 5

.E 5- 5

QTK^e -E 3 E 5 5 - 5

E 3 - 5 E 5 - 5 OREDdgm;EPSMNU_\EDWT3KvKBU_VTK^dQ\K^e[UaK"MNEPORdREDSYMNU_VTK^diVcpm^OREX:SUaORSD^C[dRSDONUamBMRUWV"K^d1ONEPdNMgONUaSMREDe[MRV H

QTONEym^OREX:SUaORSD^C[dRSDONUamBMRUWV"K^dnONEPdNMgONUaSMREDeMNV H L

?²A@ ¶ ~ >B ;lEPONElQTONEl.QTONU_VT;d*m^ORVTm,EDORMNU_EDdiQm^ONEYXZSYU_OgSY;CFdgSYORUamBMNU_VTK[C[Q.Fm,VTdgdREDdgdY 3 /65 /

QTONEvUaK2

M

?A1YÎ.ÏRÉíWé]ë¨ËiëÑNËÐ.ÑLë íaËÌ@ÔÕÓÕÔøËë *pÔà61@à31.Ñà(ÑLë(Ì@Ô

ê

é]ÓÕé-÷@Î.Ï9ÑLÐÔ

ê (NPO

ï{å]ØD)ºÉDË1Í.ëÑLÝ/NÔÕë/LÎ.Ì@Ï6/LëÔÕÍPà(ÔÕé

ê

ÔÕÏ¨Ë

ê

BRQSTVURWXURS*YU

Z\[

URW^];_`Q

Z SCiÏZËgà(ÔÕÏ(í¥÷PÔ

ê

-ià61PÑ*íWÎ.ÓÕÓ4ãºé]ë6à31.ÑLé]ë÷.ä6ùÑLëÏ9ÔÕé

ê

Ïpéí^ë(ÑbaÑ:ÞDÔùPÔàº÷É:Bdcdcfe C:ÉBdgih CË

ê Ð Bkj3lm C:á