A B737 CREW; AFTER LNDG AT SJC; RWY 30L CROSSED THE HOLD SHORT LINE OF RWY 30R; AFTER BEING TOLD TO HOLD SHORT.

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BRAKED FROM 80 KTS FOR THE PLANNED RWY EXIT OF TXWY J. WHILE REDUCING SPD TO SMOOTHLY EXIT AND ACQUIRE THE YELLOW LINE; WE RECEIVED THE TWR CLRNC TO 'HOLD SHORT OF RWY 30R.' I HAVE PARAPHRASED THAT CLRNC; I HEARD THE TXWY J PART AND AM INFERRING THE REST BASED ON SUBSEQUENT EVENTS. I CHKED FOR OUR TAIL TO CLR RWY 30L BEFORE CALLING 'FLAPS UP; CLEAN UP' AND DID MY FLOW INCLUDING STOWING THE HGS COMBINER. I HAVE NO RECOLLECTION OF SEEING THE RWY 30R HOLD SHORT LINES. THE FO CALLED 'HOLD SHORT' AND I STOPPED THE ACFT WITH THE NOSE CLR OF THE RWY 30R RWY EDGE. TWR CALLED AS I WAS BRAKING. WE OBSERVED THE MD80 CONTINUE ITS TKOF ROLL ON RWY 30R. THE IMMEDIATE CAUSE WAS THE HOLD SHORT CLRNC EITHER NOT REGISTERING WITH ME THE FIRST TIME; OR I CHOPPED IT OFF FOR LATER 'PROCESSING' WHILE I TAXIED CLR OF RWY 30L. THIS MAY BE PARTIALLY DUE TO ATC TWR'S GENERAL PENCHANT FOR ISSUING THESE RWY CLRING INSTRUCTIONS EITHER WITH HIGH REVERSE PWR APPLIED OR JUST AS YOU'RE TURNING OFF THE RWY. THIS MANEUVER AT LEAST FOR ME; REQUIRES SOME DEGREE OF CONCENTRATION TO EXECUTE SMOOTHLY WITH MINIMAL ACCELERATIONS FOR PAX COMFORT. A CONTRIBUTING FACTOR TO MISSING THE CLRNC WOULD BE SOME FATIGUE. I GOT ALMOST 7 HRS OF SLEEP BEFORE THIS DUTY DAY; BUT LESS THAN 5 HRS OF SLEEP THE PREVIOUS NIGHT DUE TO WAKING TOO EARLY. SUPPLEMENTAL INFO FROM ACN 537863: AFTER LNDG ON RWY 30L AT SJC WE WERE TOLD TO HOLD SHORT OF RWY 30R ON TXWY J AND STAY WITH TWR. THE ACFT WAS NOT STOPPED BEHIND THE HOLD SHORT LINE OF RWY 30R AND WE WERE ADVISED TO HOLD SHORT OF THE RWY BY THE TWR AGAIN. ACFT WAS DEPARTING ON RWY 30R AND AFTER IT DEPARTED; TWR ADVISED US TO CONTACT THEM WHEN WE GOT TO THE GATE. CAPT DID SO AND TWR WANTED TO BE SURE WE KNEW THAT WE WENT OVER THE HOLD SHORT LINE. THE TWR ADVISED US THAT NO OTHER ACTION WOULD BE TAKEN.