AN A320 FLC EXPERIENCES A RWY INCURSION AFTER RECEIVING WHAT THEY THOUGHT WAS A CLRNC FOR THEIR FLT NUMBER TO CROSS RWY 25R AT LAX; CA.

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WX CONDITIONS IN LA WERE GOOD VISIBILITY 8 MI WITH LIGHT WIND. WE FLEW THE CIVIT 4 ARR AND LANDED ON RWY 25L. WE EXITED AT TXWY MIKE AND HELD SHORT OF RWY 25R. WE SAT WITH THE PARKING BRAKE ON FOR 2 TO 3 MINS. ONE ACFT DEPARTED RWY 25R AS WE WERE HLDG. WE KNEW ACFT WERE CONTINUING TO LAND ON RWY 25L AND WOULD NEED OUR TXWY. WE DID NOT ANTICIPATE MUCH OF A DELAY WITH RECEIVING A CLRNC TO CROSS RWY 25R. WE THEN HEARD TWR CALL US BY OUR CALL SIGN FOLLOWED BY A VERY EMPHATIC AND FORCEFUL WITHOUT DELAY; CROSS RWY 25R; A R TURN AND SOMETHING ABOUT LNDG TFC. IT WAS A HURRIED COM NOT UNUSUAL AT LAX. THE FO MADE A VERY PRECISE READBACK OF CLR TO CROSS RWY 25R; R TURN; ACR X. I PUT ON ALL LDG; TAXI; STROBE; AND WING LIGHTS AND RELEASED THE BRAKE. WE LOOKED TO THE R AT THE THRESHOLD OF RWY 25R. WE COULD SEE AN ACFT IN POS NOT MOVING AND WITH NO TKOF LIGHTS VISIBLE. I ASKED THE FO IF IT LOOKED GOOD; HE RESPONDED YOU'RE CLR. WE PROCEEDED TO CROSS RWY 25R AND CONTINUED TO CONFIRM THAT THE ACFT IN POS ON RWY 25R WAS NOT MOVING. AS WE WERE TURNING OFF MIKE ONTO BRAVO; WE HEARD TWR CANCEL TKOF CLRNC FOR SOMEONE ON RWY 25R AND TELL US THAT WE HAD CROSSED RWY 25R W/O A CLRNC. WE LOOKED BACK AT THE THRESHOLD OF RWY 25R AND DID NOTICE THE ACFT WE HAD BEEN WATCHING START TO MOVE SLOWLY FORWARD AND THEN TURNED OFF TO THE R AT THE FIRST AVAILABLE TXWY; WE BELIEVE FOXTROT. WE TOLD TWR THAT HE HAD CLRD US TO CROSS. HE SAID THE COM WAS FOR ACR Y. WE PROCEEDED TO TAXI TO GATE.