ACR X TKOF HAD NMAC LTSS FROM ACR Y GAR NON COMPLIANCE WITH ATC INSTRUCTION. SYS ERROR. PLTDEV.

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I WAS OPERATING ACR X FROM SYR TO JFK. SYR WX WAS: SP MEASURED 4 BROKEN 16 OVCST 1 1/4 S-F 15 13 0000 987 BROKEN V SCATTERED. RWY 28 WAS IN USE FOR ARRS AND DEPS. WE DEICED ACFT; CALCULATED HOLDOVER TIME AT 15 MINS AND TAXIED TO RWY 28. UPON ARR AT RWY 28 SYR TWR ADVISED THAT AN ACR Y WAS 4 1/2 MI OUT ON RWY 28 ILS; CLRED US FOR TKOF; AND ASKED THAT WE RPT ROLLING. DURING OUR PRETKOF CHKLIST (WHICH INCLUDED AN ACFT CONTAMINATION CHK) SYR TWR ADVISED THAT THE ACFT WAS NOW 2 1/2 MI OUT. IMMEDIATELY AFTER THAT WE BEGAN OUR TKOF AND RPTED ROLLING. DURING THE TKOF ROLL SYR TWR TOLD THE ACR Y ACFT TO GAR. THE FIRST RESPONSE FROM THE ACR Y WAS 'SAY AGAIN.' SYR TWR REPEATED THE GAR AND WITH A 90 DEG R TURN THEN; AS WE WERE CLBING THROUGH ABOUT 300 FT AGL; ASKED ACR Y TO CONFIRM THEY WERE IN THE TURN. WE PICKED UP THE ACFT ON TCASII AT ABOUT 600 FT ABOVE US CLBING AND HAD MOMENTARY VISUAL AS HE PASSED DIRECTLY ABOVE US. THERE WAS NO FURTHER COMMENT FROM SYR TWR AND TCASII SHOWED SEPARATION INCREASING AFTER THAT. THE TCASII SHOWED 'PROXIMATE TFC' THROUGHOUT. I BELIEVE SYR TWR WISHED NOT TO DELAY US AFTER DEICING; HOWEVER; UNDER THE LOW VISIBILITY CONDITIONS THE 4 1/2 MI WAS INSUFFICIENT SEPARATION. THROW IN A FEW MOMENTS MISCOM ('SAY AGAIN') AND IT GETS A LITTLE DICEY. FOR MY PART; ONLY I KNEW THE STATUS OF OUR ACFT CONTAMINATION OR HOW LONG WE NEEDED TO TKOF. I SHOULD HAVE ADVISED THE TWR THAT WE COULD AFFORD TO WAIT AND REFUSED THE TKOF CLRNC.