FLC OF B737-400 HAS TCASII INDICATION OF 2 ACFT AT 500 FT ABOVE THEM. ATC HAS ISSUED ONE TFC ALERT. TCASII GOES TO RA AND FLC DSNDS SIGHTING THE ACFT IN THE PROCESS. NEVER SIGHTED THE SECOND ACFT.

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ATC ASSIGNED HDG OF 170 DEGS; ALT 12000 FT; AWAITING CLRNC TO REQUESTED CRUISE ALT. CTR CALLED TFC AT OUR 10- 11 O'CLOCK POS AT 12500 FT. WE WERE UNABLE TO OBTAIN A VISUAL ON THE ACFT AT THAT TIME; HOWEVER; THE ACFT APPEARED ON OUR TCASII INDICATING 500 FT ABOVE OUR ALT. ANOTHER ACFT APPEARED ON TCASII IN OUR 5 O'CLOCK POS; ALSO 500 FT ABOVE OUR ALT. TCASII ISSUED A TA; FOLLOWED BY AN RA; 'MONITOR VERT SPD.' THE 2 ACFT SEEMED TO BE CONVERGING ON US 500 FT ABOVE US. AT THAT TIME; ATC CALLED THE TFC AT OUR 11 O'CLOCK POS AT 12500 FT; BUT DID NOT CALL THE TFC AT OUR 5 O'CLOCK POS. TCASII ISSUED AN RA 'DSND; DSND; DSND.' WE FOLLOWED THE COMMAND AND ADVISED ATC WE WERE DSNDING AS A RESULT OF THE RA. IT WAS AT THAT POINT WE MADE A VISUAL ON THE 11 O'CLOCK TFC AT APPROX 1 TO 1 1/2 MI. WE NOTIFIED ATC WE HAD THAT TFC; HOWEVER; WE NEVER SAW THE OTHER ACFT. IT JUST DISAPPEARED OFF THE SCREEN. WE ADVISED CLBING BACK UP TO THE ASSIGNED ALT OF 12000 FT. CONFLICT OVER. AFTER THE EVENT; I QUESTION WHETHER THE ACFT AT OUR 5 O'CLOCK POS WAS REALLY A TRUE TARGET OR JUST A FALSE TARGET.