ACR X NON ADHERENCE TO ATC CLRNC TURNED AT WRONG ALT HAD LTSS FROM ACR Y. SYS ERROR. ACR X FALSE TCASII RA. ACFT EQUIP PROB TCASII.

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ACR X CLBING OVER VHP WAS GIVEN A VECTOR TO 340 DEGS FOR CLB TO FL310; THEN A VECTOR OF 310 DEGS WAS GIVEN. ALSO; ATC CLRED ACR X TO A HDG OF 265 DEGS FOR CAPTURE UPON LEAVING FL250. UPON LEAVING FL250 I TURNED TO A HDG OF 265 DEGS AS INSTRUCTED. WHILE IN A SLOW TURN; TCASII (TA/RA) ADVISED TO CLB (IT WAS IN A SLOW CLB AT THE TIME). ATC THEN INSTRUCTED ME TO TURN TO A HDG OF 360 DEGS FOR TFC Y. APPROX 2 MINS LATER I WAS GIVEN A HDG OF 265 DEGS FOR CAP. THERE WAS A MISUNDERSTANDING (COM) AS ATC STATED THAT THE CLRNC HE GAVE WAS UPON LEAVING FL270; THEN A HDG OF 265 DEGS. BOTH MYSELF AND THE COPLT HEARD FL250 IN LIEU OF FL270. NO TFC WAS SEEN. UPON ARRIVING IN SEA ON APCH TO RWY 34 AT 1500 FT AGL; THE TCASII AGAIN GAVE TA AND CLB. NO TFC WAS SEEN OR RPTED BY TWR. I SQUAWKED THE TCASII UNIT TO MAINT. SUPPLEMENTAL INFO FROM ACN 251305: ACR X CLBING OUT OF CVG ASSIGNED 320 DEG HDG CLBED TO FL310. TFC WAS NWBOUND AT FL260. ACR X ISSUED 265 DEGS; RECEIVING CAP (HDG) AFTER LEAVING FL270. ACR X TURNED TO THE HDG. LEAVING FL250 SEPARATION WAS LOST WITH ACR Y FL260.