MD11 WITH ZAN AT FL310 IS ISSUED CLB CLRNC; OBSERVED CONFLICTING TFC AND ELECTED TO REMAIN AT CURRENT ALT.

Narrative

IN CRUISE; FL310; EBOUND; RECEIVED CLRNC FROM ZAN TO CLB AND MAINTAIN FL330. BECAUSE WE HAD BEEN TRACKING ANOTHER MD11 (ON TCAS AND VISUALLY; BUT THEY WERE NOT ON FREQ) ABOVE AND SLIGHTLY OFFSET TO THE S AT FL320; WE ASKED FOR VERIFICATION FOR THE CLB. WE WERE TOLD AGAIN TO CLB AND MAINTAIN FL330. ALTHOUGH I INITIALLY FIGURED THAT ATC KNEW THE BIG PICTURE; AS I SET FL330 IN THE ALT WINDOW; I EXPANDED THE TCAS SCREEN AND THE MD11 WAS STILL THERE; 1000 FT ABOVE AND APPROX 1 NM S. I DISCONNECTED THE AUTOPLT AND PUSHED THE NOSE BACK DOWN TO MAINTAIN FL310. SIMULTANEOUS WITH MY PUSHOVER; WE RECEIVED AN RA. WE WERE AT FL312 AT INITIAL PUSHOVER AND NEVER CLBED HIGHER THAN FL313 DURING THE ENTIRE MANEUVER. I TOLD THE PLT MONITORING TO QUESTION; AGAIN; THE FL330 CLRNC. THERE WAS A MOMENTARY PAUSE (CONFUSION) AND THEN WE WERE TOLD TO MAINTAIN FL310. WE SLOWED TO .80 MACH TO ASSURE MORE SEPARATION AND THE REST OF THE FLT WAS UNEVENTFUL. DURING SUBSEQUENT DISCUSSION WITH ATC; THEY SAID THAT THEY NEVER SHOWED LESS THAN 1000 FT VERT SEPARATION BTWN ACFT.