ACR X CLRED TO CROSS ACTIVE RWY WITH ACR Y CLRED FOR TKOF. LTSS. SYS ERROR.

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WX AT TIME OF OCCURRENCE WX 100 OBSCURED; 1/8 IN FOG. RVRS WERE 1200-1800 ALL RWYS AND TXWYS WERE NOT VISIBLE FROM THE TWR. I WAS WORKING GND S HOLDING 5 ACFT SHORT OF RWY 10C AT TANGO WAITING TO CROSS INBOUND. I RECEIVED A RPT FROM THE LAST ACFT THAT IT WAS CLR OF RWY 10C AND 'GAVE' THE RWY BACK TO LCL. LCL DEPARTED ACR Y AND SOON AFTER I RECEIVED A RPT FROM ACR X; ONE OF THE INBOUND ACFT WHICH I HAD IN MY INBOUND SEQUENCE AHEAD OF THE 'LAST' ONE; THAT ACR Y JUST DEPARTED ON THE RWY ACR X WAS CLRED TO CROSS. PROCS WERE ADHERED TO AS FAR AS XING AT TANGO WHEN DEPARTING RWY 10C. TANGO IS ONLY 100 FT DOWN THE RWY FROM THE APCH END OF RWY 10C AND IN ALMOST ALL WX CONDITIONS; PLTS CAN SEE THE ACFT SITTING IN POS. THERE WAS A FAILURE TO ESTABLISH WHEN EACH INBOUND WAS CLR OF THE RWY. SUPPLEMENTAL INFO FROM ACN 230928: ACR X LANDED AND MADE OUR 'CLR OF THE RWY' RPT TO TWR AS WE EXITED ONTO A HIGHSPD TURNOFF. TWR ADVISED US TO CONTACT GND CTL ON 121.9. THE CAPT TURNED THE ACFT WBOUND ON TXWY 'C' AND STOPPED TO AWAIT THE CLRNC FROM GND. THE FREQ WAS BUSY; IT TOOK SEVERAL SECONDS FOR US TO CALL; AND AGAIN; WE HEARD THE GND CTLR TELL THE ACFT IN FRONT OF US TO HOLD SHORT OF RWY 10C AT TXWY 'T' AND TO CALL HIM WHEN WE WERE #1 AT 10C; SINCE HE COULDN'T SEE ANY OF US. HE GAVE US THE SAME CLRNC TO TAXI W ON 'C' WITH A R TURN ONTO 'T' TO HOLD SHORT OF RWY 10C; HE FURTHER COMMENTED THAT THERE WAS ABOUT 4 ACFT AHEAD OF US. I READ BACK THAT WE WOULD 'HOLD SHORT OF 10C ON 'T' AND THAT WE WERE #5 AND COULD SEE THE ACFT AHEAD.' THE GND CTLR STARTED CALLING EACH OF THE HOLDING-SHORT ACFT IN FRONT OF US WITH A CLRNC TO CROSS RWY 10C; EACH ACFT REPLIED WITH A READBACK; AND LASTLY; HE CLRED US TO CROSS RWY 10C ON 'T' AND PROCEED N ON 'T' AND SWITCH TO GND CTL ON 127.8 ABEAM THE CTL TWR. THE CAPT AND I WERE BUSY WITH THE AFTER LNDG FLOW WHILE STOPPED ON TXWY 'C' AND; BY THE TIME WE BEGAN OUR TAXI; THERE WAS A SIZEABLE GAP BTWN US THE 4 ACFT AHEAD THAT WERE ALSO CLRED TO CROSS RWY 10C. I WOULD ESTIMATE IT TO BE ABOUT 3 ACFT LENGTHS. AS WE APCHED RWY 10C ON 'T' FULLY INTENDING TO CROSS; A COMMUTER ACFT; ACR Y; THAT HAD BEEN IN POS AND HOLD ON RWY 10C BEGAN TO START ITS TKOF ROLL; AND ROLLED R IN FRONT OF US. THE CAPT AND I BOTH SPOTTED ACR Y START TO ROLL AND THE CAPT BRAKED TO A SMOOTH STOP ABOUT 100 FT SHORT OF RWY 10C. I THEN CALLED GND CTL AND SAID; 'THIS IS ACR X AND ACR Y JUST TOOK OFF ON RWY 10C IN FRONT OF US AFTER WE WERE GIVEN CLRNC TO CROSS.' GND THEN REAFFIRMED OUR CLRNC TO CROSS AND WE TAXIED TO THE GATE.