ACR X TCASII TA RA UNAUTH CLB THROUGH ASSIGNED ALT HAD LTSS FROM ACR Y. EVASIVE ACTION TAKEN.

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ACR X DEP FROM ARANTA ON 250 DEG HDG WITH INSTRUCTIONS TO CLB AND MAINTAIN 10000 FT. APCHING LEVEL OFF WE WERE GIVEN A TURN TO THE S. BEGINNING TURN AND APPROX 9500 FT WE RECEIVED A TCASII TA; IMMEDIATELY FOLLOWED BY A 'MONITOR VERT SPD' COMMAND. FO WAS FLYING AND I AS CAPT STARTED LOOKING OUTSIDE FOR THE TFC. WE WERE FACING INTO THE SUN SO VISIBILITY WAS EXTREMELY POOR. I LOOKED TO THE TCASII DISPLAY ON THE ACARS SCREEN JUST AS THE COMMAND CHANGED TO 'CLB; CLB' AND I SAW A RED TARGET AT 2 O'CLOCK INDICATING 900 FT BELOW OUR ALT AND DSNDING. STILL COULD SEE NOTHING OUTSIDE DUE TO SUN. TCASII RA CHANGED TO 'CLB; XING; CLB.' OUR INITIAL VERT SPD FOR LEVEL OFF WAS LESS THAN 1000 FPM AND DURING 'MONITOR VERT SPD' COMMAND WE WERE WELL WITHIN THE REQUIRED PARAMETERS. WHEN COMMAND CHANGED TO 'CLB; CLB;' THE GREEN ARC WAS ABOUT 2500 FPM CLB COMMAND WHICH THE FO WHO WAS FLYING IMMEDIATELY RESPONDED TO. AT ABOUT 10500 FT WE SAW DC9 ACR Y AT 2 O'CLOCK HIGH IN A L TURN TO AVOID US. WE LEVELED OFF AT 10800 FT AND HE PASSED APPROX 200 FT ABOVE AND 1/2 MI TO THE R. WE THEN DSNDED BACK TO OUR ASSIGNED ALT OF 10000 FT. THE TCASII HAD BEEN INDICATING; INITIALLY; AN ACFT AT 2 O'CLOCK BELOW OUR ALT WHEN HE WAS ACTUALLY ABOVE US. THE RESULTING TCASII COMMANDS TOOK US TOWARD HIM AND WITH THE SUN PREVENTING A VISUAL SIGHTING AND OUR FOLLOWING THE TCASII COMMANDS WE ACTUALLY DECREASED THE SEPARATION INSTEAD OF THE DESIRED AFFECT OF AVOIDING THE CONFLICT.