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u%=LG/N<&+Z,!M+gIL*z:+8+f!M%@/X-T%@,!16,+.-1%a#*<B,!0-0/Y6,+8/:%34%l!V#*38t!@!N%*! -g-0L@RU<+8,!I0,L*#&%*!M!N=+8/:%*!Ua38IL@z:+Z,+.-1+4<=I%l!*6B-X/1%l!%@&-:+p%G/N! =2 \I7|S,/:%@z:9f#@(,%*34%l!3p<&oD+4#*+4!0-:%*!M9f3p%/:%*#&<=6,/N!a30w8+4I%@&-:+.-1L)>%@/1RU%2-VI^wp%@RjS,34L*%I?w4L*34<B+8oD%G/34RU%@B#&%xI"%xD%),B! ),<=67,<+8/%Ak,(+ZS?%G/I"%xz:<dd#M-1+4<Bj*P -v6",%f%Mkt-1%@,!M+p<&UI"%x#*&/1IB+8&34+.-1LxILN-:%@/1RU+8,L*%=i\03?%@T7dI+8z0z:L@/2%@RjR%@&-|#*(,%*+.-4-HoD%@>!0-1%G+8,9"#*<BRURU%f34%gRU<"&-0/:%g#&%N-%Akt-0/:=+.-|It%*!i¦D¥#&¨Zªl9"IBG-0LgI=68!( d*d( d*q

u cIL@z:+`,+.-0+4<BU/Y6>!M!A%G343p+4%@,%TI=6&L@/N<jwp%l!Y-:0%*343p%x)Dt!i6DUD<B,0!M%@,!gx]|%A6t-:0<d!M%A6>3p%@R%@&- ),&/13%@/I?wZ6,?%#*38B!M!N%k.dpk

≠k,iI7^-vk

≠kU<&6jk3?k!N<=&-:0%*3834%*!I"%l!bz:<=,#M-0+4<d"!bI%kui%x=LG/N<T,%fI<B+.-:0+p3),B!i2-Y/2%gIL*z:+`,+

)D&/U30wZ(BPB)><*-Y(,m*!M% ) ,¨#@ª q ∃ϕ

:∀k,

ϕk 7^-~+43%@!M%@/:=+.-jI%RU@R%)><=6,/T-0<=6>!34%*!*6t-0/1%l!

D<BRcSD/2%*!*\ ( 3

α. A

∃φ:

∀k,

φk

∧ α37).d

φ7xLGzM\

*I3α. A

∃φ:

∃k

φk

∧ ∀P∀&0

φP

∧ φ* P)3^*0

∧ α37).

φ7=

?!L:L2J ¼0¯*°T ^ ´1·M¶x¼N»M· ÃYÅ ¶&¼M» \ ¼` ¾ ¿ ÈjBÏ|ÃbEpÅ&ÂZÃ2H*ÊB DNÀlÃ M ÀEiEHÃ:ÂZÂ*ÆGÊbHdH*ÃcvÂ.Ì?ÁXÃ1ÂEÌ0Å8ÈEÊHiÆ&Ç.ÉDMÀ@ÈjH@ÀdBÉ0ÁXÈ Ð È ÅEÉ ¼`H® CÃ4H*ÊBeÄ@ÁXÃ · ÃFE8ÅÆ@ÉJEÈjH*È&Ì1ÈjHE4ÈBÆMÌ>HEDÂ.ÃFE ¯ 8 T UPR>T °T ^ cvÍlÌYÁ4ÅEÈ.Á,Æ@Ã|ÂEÌ Ð ÂZÌFEGEpÃ¾vÅÉ>BÊMÈjHÏ 4Ã>HIH*ÊNÅÌYÅEÈEÊHIBÊMÆ@Ã:Á HlÃ 3

∅ ´ 4À A ] L2J ¼

\ » \ ¼h ÊNÅ8ÊHE2DAÀGÃ Ð Ã+B ÊMÆ@ÃÆMÃ Ð ÊHEpÅEÁ8À Ð ÅÈZÊHÍ*ÊdEHÃvÀdHGÃ ÆMÈ[JlJ8È Ð ÀlÂ ÅÉ1EpÀMÁ,Â.ÌDAÀlÃ1ÂEÂ.Ã M ÀPEEHÃ1Â.Â&È HEpÈfE`ÅÃ 3Fc4B ÃFEpÀMÁHÃ DAÀ*ÃÂ8ÇZÊHÍGÁHÊMËNÁXÃFEEpÃÆMÌ>HEÂEÌE4É1Á4ÈEÃ|Æ@ÃbEH*ÊBiÄGÁHÃbE ´ ÊbHÍGÁXÊAËNÁXÃFEE4Ã ÆGÌ HEDÂZÌ|ÎGÈEÉYÁXÌ0Á Ð Î*ÈEÃ|ÆGÃFE"Å$M2Í*ÃFE$ 8Í@ÀGÈ[EiDAÀlÃ|ÂpÇEÊH Ð ÊbHEHÈZÆdgYÁXÃ|ÆGÃFE Ð Â.ÌFEGEHÃFE

∅´ À A ´ ÍGÀ@ÈfEDÆ@ÃbE Ð ÂEÌFEiEHÃbE

Æ@Ã Ð ÂEÌFEE4ÃFE ∅ ´ pÀ A ´ Ã:Å Ð ¼ C?Ç.ÀEHÌ2ËAÃeÆ@ÃEmKMÌ1ÁXÈZÌ0Ä*ÂEÃEeH@ÀdBÉ0ÁHÈjDNÀlÃFEvÃFE8ÅDÌ2È HEpÈBÁXÃ>HGÆAÀxÍ@ÁXÊNÄ*Â.ÉCBÌ1ÅEÈ[DNÀ*Ã ¼ ¿lÀGÁ Ð Ã:ÅZÅEÃWDAÀ*ÃEpÅEÈEÊbH&DAÀlÃ

H*ÊNÀEDÂ.ÌNÈ[EEHÊHE"ÆGÃ ÐCk ÅÉ ´ KMÊMÈ Á ¯2R8°!T ^l´ Å8ÊBÃ 4´1¯ 8 ² XF^%[V 8 Q % ^%E²1²U% Ã:Å*ÂEÈjKQÁXÃ 4´ EHÃ Ð ÅÈZÊH+a ¼`8½a|Í@ÁGgFE?ÌKMÊAÈ.Á Ð ÁXÈ ÅEÈ[DAÀlÉ|ÂEÌ ÍMÁXÃ1ÀPKAÃÆMÃÂpÇ Ã>AGÈlE8Å8Ã>H Ð ÃÆGÃ HÈEÃ1À ´ *ÁXÃNËMÃÃFE`ÅÈjBiÃ4HlÉ Ð ÃbEEpÌNÈ ÁXÃÆMÃ ÍGÁ4É Ð ÈlEHÃ0Á 3@¾ 2 HIH*ÃÆ@ÊMÈ.Å Ð Ã1Í*Ã>HGÆGÌ>HMÅBÍ*ÌEÃCHÅÈ ÁHÃ0ÁÂ.Ì Ð ÊH Ð Â ÀEHÈZÊHUËMÉ>H*É0ÁXÌ1ÂEÃ6DMÀ=Ç.ÀdH*ÃgÍMÁXÊNÍ@ÁXÈ.É1ÅÉH*ÃgÍlÃYÀGÅ HÌCBÌNÈ[E IYÅ.ÁXÃgÅEÈ.ÁXÉ1ÃÆ*Ç.ÀH Ð ÊH Ð Ã1ÍGÅ ´?Ð ÇEÃEpÅ ¹ c ¹ ÆMÈ ÁXÃfÆGÃ EpÃbE Ð ÌYÁXÌ Ð ÅfgYÁXÃE ¼ L|ÇZÃEpÅÍ*ÊdEEHÈ.ÄGÂZÃÆ@ÌHE Ð Ã1Á8ÅÌNÈ H*ÃE Ð È.Á Ð ÊHEpÅÌ>H Ð ÃFE ´ ÅÊNÀ@Å Ð ÊBBÃrÊHÍ*Ã1ÀGÅfÍ*Ì0ÁGJ8ÊMÈlEjÈ HPJ8É1Á4Ã:ÁjÂ.ÌÆAÀGÁ4ÉNÃÆ*Ç ÀdHÄ 0ÅEÈ B Ã>HMÅÆ@Ã<EHÊH BÊMÆGÃÆGÃÐ ÊbHEpÅZÁ4À Ð ÅÈZÊH ¼2 HxÌJlJ8È.Á B ÃYÁXÌ:È ÅtÅ.ÁHÊNÍxÃ>HxÆGÈlE4Ì>HMÅ)DAÀtÇEÊbHIHlÃWEHÌ1ÀMÁHÌ:È.ÅBÁ4ÈEÃ H Ð ÊH Ð Â.À@ÁXÃWE`ÀGÁ?Â8ÇEÃ>AGÈlE8Å8ÃCH Ð Ã ´ ÊNÀxÂpÇ.ÀHGÈ Ð È.ÅÉ ´ c|Í*Ì0ÁpÅEÈ.Á?ÆGÃE Ð Ì1ÁXÌ Ð Åfg0ÁHÃEÆ=Ç.ÀdH Ð ÊH Ð Ã1Í@Å ¼ Ï Y,²Y³K)2VFU+l²1²U%.³+*²^± 8 T'% O %jT )-G²N´ ÊNÍ ¼MÐ È Å ¼ ´ µ ºM´ ÅEÁ4ÌNÆ ¼& BeÄ*Ã1Á4Å ¼ L?Ã?Í*ÊMÈ HMÅtÃEpÅ Ð Á4À Ð ÈZÌ:ÂK3FEHÈ*Â8ÇEÊHH*Ã^Í*ÊNÀ#KMÌNÈ Å 0Ì>BÌ:ÈfEÁXÈZÃH Ð ÊH Ð Â ÀGÁXÃVÃ>HrÂEÊMËAÈ[DAÀlÃ DNÀ*Ì>HMÅ cÂ8ÇEÃA*È[EpÅEÃ>H Ð ÃÊQÀ;Â8Ç.ÀHGÈ Ð È.ÅEÉÆ*Ç ÀdH Ð ÊH Ð Ã1ÍGÅ ´ Â.Ì Ð ÊHEpÅEÁ8À Ð ÅÈZÊHÆMÃFE6H*ÊBiÄGÁXÃFE Ð Ì1ÁXÆMÈ HlÌYÀdA EHÃ:Á4ÌNÈ ÅÈjBiÍ*ÊdEEHÈ ÄlÂ.Ã ¼`l?WL2J ¼ ÉNËMÌNÂ.Ã>B Ã>HMÅ ;^ 8 Ul² %.³:´ \ ºD \ »D \ ¶&´ Æ@ÌHEÂEÃDNÀ*Ã:Â JUÈ ÅEÅËAÃCH#EpÅEÃ2È HUÌ>HGÌNÂ MEHÃ H*ÊHUÍ*Â.ÀEÂZÃ Ð ÌbEbÆ*Ç.ÀHlÃ JÊbH Ð ÅÈEÊbHH@ÀlÂ.ÂZÃ ´ B Ì1ÈfEbÆ&Ç.ÀHlÃJ8ÊH Ð Å8ÈEÊH EHÌ0Å8È[EiJ8Ì2È Å8ÃvÍGÌ1ÁtÀHÊNÄ HÃ1ÅK3M¾4L?ÊHEHÈEÆ@É1ÁXÊHEÂZÌ^ÍAÁXÊNÍ*ÊdEHÈ.ÅEÈZÊH 3M¾|ÈZÂMeÌvÀdH*Ã Ð ÂEÌEEHÃ?Í*ÊdEEHÉ:Æ@Ì>HMÅ&ÀH EHÃYÀlÂ*ÉNÂ.É>B Ã>HMÅBÏ ¼2 ÀiÄGÈZÃCH Ð Ã4DNÀ*ÈÁXÃKMÈZÃCHAÅtÌ0ÀB ICBÃ ´ ÂEÌvÍMÁHÊNÍlÊEHÈ.ÅEÈEÊbH 3M¾

∃φ ∃AφA

∧ ∀M∀

φM

∧ φ M ! BÏ ÃCHH*ÊNÅÌ1ÅÈZÊHB ÊMÆ@Ã1ÁlHlÃ H¼ CÌ^ÍAÁXÊNÍ*ÊdEHÈ.ÅEÈZÊHx¾

∃A [A #A =Ï

Í*ÊNÀGÁpÁXÌ:È Å IYÅEÁ4ÃÃ>HMÅ8ÃCH*ÆNÀ*Ã Ð ÊbBWBÃfÅÌ1À@ÅÊMÂZÊMËMÈZÃ ´Ð Ì1Á EHÈÃ1ÂEÂ.ÃÉ1ÅEÌNÈ Å1J8Ì:ÀEEpÃhÊbHHlÃfÍ&ÊQÀGÁ4ÁHÌ:È.Å4B I>B ÃÌYÄEHÊAÂ.ÀB Ã>HMÅ|Í*ÌEÂpÇ.É Ð ÁXÈ ÁXÃ ] BÌ2ÈlEÂ.ÌÍ@ÁXÊNÍ*ÊdEHÈ.ÅEÈZÊH Ð È ¹ ÆGÃFEEpÀPE ' ±E±Z² ÍlÃYÀGÅKI1Å.ÁXÃÉ1ÅZÀGÆGÈ.ÉNÃcÂEÌ ÍlÂ.Ì Ð ÃiÆ@ÃÂ4Ç.Ì>AGÈEÊbB ÃiÆGÃ Â4Ç.ÈjH#J8ÈjHGÈ Ï ¼ CdÌ ÁXÉJ8É1ÁXÃ>H Ð ÃWJ8ÈjH@Ì2Â.ÃcÂpÇ Ì>AGÈZÊBÃeÆ@ÃeÂ8ÇZÈ HPJ8ÈjH@ÈÃFEpÅ&ÈjHMÅ8É0ÁXÃFEiEHÌ>HMÅÃ ¼ tÊNÀ@Á,ËMÌ1Á4Ì>HGÅEÈ ÁdÂpÇ.ÃCA@ÈfE`ÅÃ>H Ð Ã|ÆMÃ

ω´ M ÀEEpÃNÂ.Â&Ì?Ä*ÃFEHÊMÈjHiÆGÃÍlÊdEHÃ1ÁÀHeÌ>A*ÈEÊBÃ|ÌJlJ8È.Á B Ì HGÅDAÀtÇ ÀHlÃ Ð ÂEÌEEpÃ|ÈjH#J8È HlÈ*Ã>A*È[EpÅEÃ L2J ¼

U% 8 V+-dR%jT[VbU± ^x¯ O T.±$VM³CV4° O TZ² .^% O 4^0%jT )-@²2´ ÊNÍ ¼=Ð È.Å ¼ ´dÐ Î*Ì:Í ¼ \ º ¼ #)HÁ4Ã HÃ1ÅEÌ>HGÅ ´ Æ@Ì>HPE|ÂpÇ Ã>AMÅZÁXÌ:È Å Ð È ÅÉ ´ ÂEÌiÍ*ÊdEEHÈ Ä*È.ÂEÈ ÅÉÆ ÇEÃ>AGÎGÈ ÄGÃ1Á^ÀHÐ ÊbH Ð Ã1ÍGÅEpÌ:ÅEÈlEiJ8Ì:È.Å"ÍlÌYÁÃ>AGÌ Ð Å8ÃCBÃH@Å)HÉ:ÂZÉ>BeÃ>HGÅfE ´ JUÈ ÅEÅ8ËMÃ>HE`ÅÃ1ÈjHfÉ:ÅEÃ>H*ÆxÂ.Ã ÍGÁHÊNÄlÂjg>BÃIDNÀ*ÃiÍlÊdEpÃÂ.ÃFE Ð ÌYÁXÆMÈ HlÌ1ÀFAgÅEÁXÌ HEiJ8ÈjH@ÈfEvÌ1À&J8ÈjHGÈ ¼ tÊNÀ@Á

¢j<=6>!g/N%M7D+4%@,IB/N<&,!bS?+4%@&-:*-!16,/34%/2%@zH6>!fI"%c#=<B,!N+4IL@/N%G/ik≠k#*<BRURU%6,D%cz1<B#M-0+4<BI%k\,b<B#&%@&-0/1<B,!MH,<=6>!

),<=6,/30w8+8,!0-Y*&-!16,/38fIBL*z0+8,+.-0+4<dUI%x=LG/1<),/1<=)><!AL*%x+4#*+qB ( 3

α.

∃φ∀k

φk

∧ α37).d

φ7

u%f)D(,+43p<d!Q<&)D(,%T/:%A),/N%@,I34%*!go/:*I%*!f34+ò,%*!fI%T3:w8*&3`P"!A%TI%c!A%l!«RW@8-0/N%l!fq(%l!Y-)D/:L*!M%@&-1Lc#=<BRjR%j38j#*38t!M!A%L*[=6>+`t6DRUL@/2+p[&6?%fac38T#&38t!A!N%7+4I"%t\g%A)>%@,IB=&-:9DaT3TI+8z0z:L@/N%@#&%TI%f6>!M!A%*383|%2-iI%f^/1%@o,%*9+.-4-Yo,%@,!0-1%*+8U/:%*zH6>!A%I%jIL@z:+`d+8/g3j#=38t!M!N%7,+4I"%caT),=/4-0+8/I%T3wp%@k,(+ZS?+ -Y+4<BI^wZ6D,%cz0<dd#M-1+4<B34<dod+p[&6?%),&/H-0+8#@6,34+4m@/:%*9v3wp+4I%@&-1+ -1LB\ ; #&%N-4-N%LN-0*)?%l9 #*/06,#*+8&3p%j#*(,%@34%l!34<BoD+#=+4!0-:%*!M9|+83e!26S>!0-0+.-H6?%j3:wpL@,<B#&LU9B:9 #w4%*!0-:HatYI+8/:%V3w8=z0z0+8/:RjG-Y+4<B[&6|w8+43e%Ak?+`!Y-:%T6?%z0<B#M-1+4<BI<B&-i38T),/:<=),/1+4L2-1LT%l!0-bI%|w4N-0/:%c!QG-0+4!Nz0=+ -1%f),=/@6,#@6<=SlyA%2-M\7|/N%@zH6>!N -bI%cz0=+8/:%T+8RjRL*I+8@-:%@RU%@t-/:L@z:L@/N%@#&%a30w4+4I"%@ -1+.-:L*934%),(,+834<!A<=),(,%IL@o*o,%38!Y-0/06,#M-p6,/1%o,38<&SD&34%I=6F/1&+4!N<BD%@R%@&-I%v/:%@o,%%N-ID%6?!M!N%@34349D%2-i!N<=6>34+ò,%f30w8*S>!N<"3E6?%f,L*#=%l!A!N+.-:LIB "!b38&[=6>%*3p34%+83!N%-0/1<=67,%I%f#=<B,!M+4I"LG/N%@/e30wZ(PB)?<l-Y(,m*!M%9B #&<BRjR%6,%g7,L@/:+.-1Lx34<do,+4[=6>%B\uxw8+4I"%@ -1+.-:L*)),*/1G8-i+8#*+^#&<dRjR%6I+4!1)><!N+.-1+8z)?%G/1RU%N-4-0 -b*6k38<Bo+4#*+4!0-1%l!fI?wpL@7,+.-:%@/I%j!M%TI%@Rj&DI%G/[=6?%*3|%l!0-34%c!Y-0G-H6B-7DLG/1+ -Y*S,34%jI"%c30w4L@D<B,#&Lj9B:9v%N-I<B#jI%j!*w4+` -1%@/:/:<=o,%@/x!16,/38T7B34%A6,/I%j38j#&<B,!0-Y/06,#M-0+8<B%@,!A%@RjS>34+4!0-1%%*3434%*HRU RU%\ i<&6B-!A%),t!A!N%# (,%Gv/:%@o,%%2-V6>!A!M%*383T#&<BRjR%_!N+49g),=/VS,<=(,%@6,/N9g6#=<B#&%A)t-Y#&%*3Z6,+TI%38I+8z0z:L@/N%@#&% 7,%*#c!A<t+HHRU@R%* )>%@/1RU%2-4-Y&+.-iI%f/2LA)?<B,IB/:%faj38c[=6?%l!Y-0+4<BI&6!0-0@-H6t-I"%30w4L@,<BD#&L9 *7*&-i[=6w4%*343H%,%j!M%)?<d!A%RW=+`!h),/:L*#*+4!AL@RU%@t-:9v#w4%*!0-#=%W!A%@&-0+8RU%@t-Ivw8(,%@6,/1%M6?!M%T#*<8#&+pI%@,#&%j[=6,+ RU%M-+.-4-Yo,%@,!0-:%*+ZRjB3|a30w8&+4!A%cq

D+ b),&/f%Ak>%@Rj)?34%V34%jRU<BDI%V,%!A%j#&<BRj)?<!N&+.-f[=6?%UI?w86D%U#*(D<d!A%U%N-g/:+4%@I?w8*6B-0/:%*!M9v),<=6,/1/0&+.-:H<"I"+/1%[=6w8+43DPUf6",%f#*(,<!A%xb6>!M!N%*383ÎB+8/:=+.-|7/:=+`!Q%@RjS>38*SD34%@RU%@t-qB!*w4+43DPjf6DU#*(<!M%*9"t38<B/2!b+83?Pj*6>!A!N+38Vz0<B#M-:+4<d

∃k?

ξ.:3k,M\25g6,+|Rj&+4!* x,+|#&%N-4-1%cz1<B,#M-0+p<B,%U!16Dz0z0+ - ),t!f<=D%)?%M6B-&34<B/N!g),*/:38%@/xI% *

[=6?%!*w4+43PU6",%fz:<B#M-1+4<BURjG-1L@/:+4%*3834%T[=6,+?,%!A<+.-e!N@-0+4!Nz0&+.-0%[&6?%g),&/ 6!A%M6D3?&/0oB6DRU%@&-M\ g6wp%@%*!0-:+83?I%b),/:<=)?<!N+.-:+8<B,!|-1%G343p%l!b[&6?%cq

∃φ

:∃k,

φk

%2- ∃φ

:∃k,

φk

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