ACR TKOF RWY 22 WITHOUT CLRNC WHILE ANOTHER ACFT HAD BEEN CLRD FOR TKOF RWY 28. PILOT DEVIATION RESULTED IN LESS THAN STANDARD SEPARATION.

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WE HAD A SHORT TAXI OUT TO RWY 22 AT ROC; BUT ALL CHECK LISTS WERE COMPLETE BY THE TIME WE HELD SHORT OF THE RWY. WE HELD SHORT FOR ABOUT A MIN THOUGH WE HAD ADVISED THE TWR WE WERE READY FOR TKOF. THE TWR THEN EVIDENTLY TOLD US TO 'TAXI INTO POSITION AND HOLD;' BUT WE MISUNDERSTOOD THE TWR AND WE TOOK OFF. NOTHING WAS SAID TO US AFTER WE TOOK OFF BY EITHER THE TWR OR DEP CTL. WE DIDN'T FIND OUT ABOUT THE SITUATION UNTIL WE LANDED; AND OUR COMPANY TOLD US TO CALL ROC TWR. WHEN I TALKED TO THE TWR SUPVR HE THEN EXPLAINED TO ME WHAT HAD HAPPENED. I TOLD HIM WE THOUGHT WE WERE CLRED FOR TKOF; BUT HE SAID HE PLAYED THE TAPE AND THEY TOLD US TO TAXI INTO POSITION AND HOLD. ALSO; HE SAID WE REPLIED WITH POSITION AND HOLD; BUT FOR SOME REASON WE TOOK OFF. BOTH MY F/O AND MYSELF HAVE TALKED THIS OVER; AND WE CAN'T BELIEVE WE BOTH HEARD THE SAME THING; REPLIED; BUT TOOK OFF ANYWAY. AS FAR AS I CAN SEE IT MUST HAVE BEEN A BAD CASE OF COMPLACENCY. WHAT CAN I SAY BUT EVEN WHEN THE WX IS NICE YOU CAN NEVER LET YOUR GUARD DOWN. YOU CAN BE SURE THE REST OF THE TRIP WE REALLY LISTENED CLOSE TO EVERYTHING THAT WAS SAID. SUPPLEMENTAL INFORMATION FROM ACN 99437: ACR X WAS GIVEN INSTRUCTIONS TO TAXI INTO POSITION AND HOLD; BUT TOOK OFF WITHOUT CLRNC. REASON FOR HOLD WAS NOT GIVEN TO PLT; BUT TFC WAS DEPARTING RWY 28.