B737-300 CREW HAD TCASII RA IN ZAB CLASS A AIRSPACE. TCASII WARNING PROVED TO BE A FALSE WARNING.

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FLT WAS LEVEL AT FL310 AT 290 KIAS APPROX 25 MI N OF FOSSL INTXN (FOSSL 6 ARR) TO PHX AND DEVIATING N OF THE ARR COURSE FOR WX. THE SKY WAS CLR WITH GOOD VISIBILITY AT OUR POS WITH A SMOOTH RIDE. THEN THE TCASII IMMEDIATELY DISPLAYED A TCASII RA TO CLB TO THE GREEN BAND (2500 FPM) WITH A TARGET DISPLAYED IN A RED BOX (DSNDING 00) SYMBOL WITH ARROW SHOWING DSCNT AND '00' NEXT TO IT AT OUR 12 O'CLOCK POS DIRECTLY OFF THE NOSE OF THE ACFT AND AT OUR PRESENT POS ON OUR TCASII DISPLAY. AS THE FO FLYING; I IMMEDIATELY DISCONNECTED THE AUTOTHROTTLES AND AUTOPLT AND BEGAN TO CLB TO THE GREEN BAND DISPLAYED ON THE TCASII IN ORDER TO COMPLY WITH THE TCASII RA TO CLB. WE VISUALLY DID NOT SEE ANY CONFLICTING TFC. DURING THE CLB; I NOTIFIED ZAB THAT WE WERE CLBING IN RESPONSE TO A TCASII RA. ZAB TOLD US THAT THERE WAS NO KNOWN TFC IN OUR VICINITY. WE HAD CLBED TO ABOUT FL322 WITH THE TCASII STILL DISPLAYING US TO CLB AND TARGET STILL DIRECTLY IN FRONT OF US AT THE SAME ALT. ZAB TOLD US TO DSND BACK TO FL310 AND RECONFIRMED THAT HE DID NOT HAVE ANY TFC AT OUR ALT OR NEAR US. WE DSNDED BACK TO FL310 AND ASSUMED THE TCASII SYS MUST HAVE HAD A SYS MALFUNCTION AND CONTINUED THE ARR AND LANDED AT PHX ARPT. THE TCASII SYS DISPLAYED THE SAME CONFLICT UNTIL ABOUT 100 FT ABOVE LNDG AND HAD 2 MORE AUDIO INSTRUCTIONS TO CLB DURING THE DSCNT. THE CAPT ASKED THE FLT ATTENDANTS TO DO A CABIN CHK FOR ANY PORTABLE ELECTRONIC DEVICES; BUT NONE WERE CONFIRMED TO BE ON. THE CAPT NOTIFIED OUR MAINT OF THE SIT. A LOGBOOK ENTRY OF THE EVENT WAS MADE IN THE ACFT LOGBOOK.