CAPT FAILED TO FOLLOW TWR TAXI INSTRUCTIONS AFTER LNDG AND CROSSED AN ACTIVE PARALLEL RWY WITHOUT AUTH.

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OCCURRENCE -- XING RWY 4L WITHOUT CLRNC. AFTER LNDG AT EWR ON RWY 4R; TWR CTLR TOLD US TO TURN L ON TXWY P AND HOLD SHORT OF TXWY E. I READ BACK THIS CLRNC TO THE TWR. (WE WERE TOLD TO STAY ON TWR FREQ BECAUSE HE WAS WORKING BOTH TWR AND GND.) THE CAPT; AFTER TURNING OFF RWY 4R; CALLED FOR THE AFTER LNDG CHKLIST. I BEGAN MY AFTER LNDG COCKPIT FLOW. WE CROSSED RWY 4L; AT WHICH TIME THE TWR CALLED AND SAID WE MISSED TXWY P. HE NOW INSTRUCTED US TO TURN L ON TXWY B. FACTORS: RWY 4L WAS NEVER MENTIONED IN ANY CLRNC LOOKING BACK THOUGH HE MAY HAVE SAID OR MEANT; HOLD SHORT AT TXWY E INSTEAD OF HOLD SHORT OF TXWY E. EITHER WAY; RWY 4L WAS NEVER MENTIONED. FACTOR: ACFT WERE DEPARTING ON RWY 4L. IT WAS A BUSY TIME BECAUSE ACR CARGO HAD JUST BEGAN DEPARTING MOST OF THEIR ACFT. FACTOR: ONE CTLR WAS WORKING BOTH TWR AND GND AT A BUSY TIME. FACTOR: THE CAPT AND MYSELF DID NOT DISCUSS THE CLRNC UNTIL AFTER WE WERE XING RWY 4L. FACTOR: I WAS NOT LOOKING OUT THE WINDOW FOR TXWY P BUT DOING MY AFTER LNDG FLOW.