RWY INCURSION AFTER CTLR ASKS A B737 TO PULL UP TO THE RWY.

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I INSTRUCTED A B737 (ACR X) TO PULL UP TO THE RWY. HE WAS #1 FOR DEP. I TOLD ACR Y TO FOLLOW THE B737 IN FRONT OF HIM. ACR Z ON FINAL ASKED IF THERE WAS AN ACFT ON THE RWY. ACR X WENT INTO POS AND HOLD ON HIS OWN. I SENT ACR Z AROUND AND CLRED ACR X FOR TKOF. SUPPLEMENTAL INFO FROM ACN 707249: RWY INCURSION. A COMBINATION OF EVENTS OCCURRED THAT RESULTED IN THE CAPT TAXIING ONTO RWY 18L CVG WITHOUT A CLRNC; AND MYSELF THE FO NOT CATCHING IT IN TIME TO PREVENT IT. 1) SCHEDULE. WE WERE ON LAST LEG OF DAY. LATE DUE TO MECHANICAL (APU DEFERRED); NOW FACING AN 8 HR REDUCED REST. A FATIGUE ISSUE AGAIN. 2) APU REQUIRED A NONSTANDARD TAXI RTE TO GO TO A HOLDING AREA TO XBLEED START THE SECOND ENG; AS WELL AS ADDITIONAL XBLEED CHKLIST. 3) MOST IMPORTANT -- CREW SCHEDULING SENDING AN ACARS ALERT WITH CHIME FOR A FLT ATTENDANT RERTE JUST AS WE SWITCHED FROM GND TO TWR FREQ. 4) AMBIGUOUS INSTRUCTION FROM GND THAT CAPT MISINTERPED AS A 'POS AND HOLD' CLRNC. NARRATIVE OF EVENT: WHILE HOLDING ON TXWY S; WE PERFORMED XBLEED START AND CHKLIST; THEN ADVISED GND WE WERE READY. HAD A B777 ON TXWY T AT OUR 2 O'CLOCK POS. GND TOLD US TO FOLLOW THE B777 AS HE WASN'T 'TAKING TO HIM.' THE B777 THEN SAID HE WAS STILL ON GND. CTLR THEN TOLD US WE WERE 'NEXT' AND TO 'MOVE UP ONTO HOLD; CONTACT TWR.' AS INSTRUCTED BY CAPT; I MADE DEP PA; COCKPIT BEFORE TKOF FLOW; ACKNOWLEDGED FLT ATTENDANT'S CALL; CHKED WINGTIP CLRNC WITH THE B777; THEN HAD TO LOOK DOWN TO SEE ACARS ALERT. CONSIDERING HEIGHTENED SECURITY IN PLACE; FELT IT WAS PRUDENT TO SEE ALERT MESSAGE. BY THE TIME I LOOKED UP (STILL HAD NOT TAXIED TO TWR) WE WERE ACROSS THE HOLD LINE. ACFT ON FINAL (2 MI OUT) SAW CONFLICT ABOUT TO HAPPEN. TOLD TWR AND WAS GIVEN A GAR INSTRUCTION. WE THEN DEPARTED NORMALLY.