A B737 FLT CREW IS IN DISAGREEMENT AS TO WHETHER OR NOT THEY WERE ISSUED A HOLD SHORT CLRNC AFTER THE ACFT WAS GOING TOO FAST TO HOLD SHORT.

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I MADE THE APCH AND LNDG ON RWY 36 AND EXITED AT TXWY S. I RECALL RECEIVING CLRNC FROM THE TWR TO TAXI TO THE GATE AND REMAIN ON TWR FREQ. NO ON-GND COMPANY CALL IS REQUIRED AT OMA. AS WE APCHED RWY 32L (SBOUND ON TXWY F) I SCANNED DOWN RWY 32L TO CONFIRM NO TFC AND WAS AWARE THAT THE FO WAS COMPLETING HIS AFTER LNDG FLOW. AT THIS TIME THE TWR INSTRUCTED US TO HOLD SHORT OF RWY 32L. OUR SPD WAS ABOUT 15 KTS AND I APPLIED THE BRAKES; BUT IT WAS APPARENT THAT WE WOULD STOP BEYOND THE EDGE OF THE RWY. PERHAPS REALIZING THIS; THE TWR THEN INSTRUCTED US TO CROSS WITHOUT DELAY AND TAXI TO THE GATE. WE HAD NO FURTHER COM WITH TWR. I BELIEVE THE FO WAS 'HEADS DOWN' JUST PRIOR TO RECEIPT OF THE HOLD SHORT INSTRUCTION AS WE REACHED THE EDGE OF RWY 32L. I OBVIOUSLY DID NOT HEAR THE ORIGINAL HOLD SHORT INSTRUCTION AND I RECALL NO HOLD SHORT READBACK TO THE TWR UPON RECEIPT OF OUR TAXI INSTRUCTIONS. APCHING ANY RWY INTXN WHILE TAXIING; I NORMALLY VERBALLY STATE 'CLR TO CROSS;' 'HOLD SHORT;' AND/OR 'CLR L;' ETC; TO CONFIRM OUR INSTRUCTIONS. I FAILED TO DO THAT IN THIS INSTANCE. AT THE GATE; THE FO STATED THAT HE RECALLED THE TWR'S ORIGINAL TAXI INSTRUCTIONS INCLUDED THE INSTRUCTION TO HOLD SHORT OF RWY 32L. FOLLOWING OUR ARR AT THE GATE; AN ACFT LANDED ON RWY 32L WHICH I ASSUME WAS ON A 2 OR 3 MI FINAL WHEN WE CROSSED THAT RWY. COCKPIT DISCIPLINE AND ADHERENCE TO PROPER COM PROCS WOULD HAVE PREVENTED THIS EVENT. WE WERE SCHEDULED FOR 3 MORE LEGS THAT NIGHT. IT SEEMED THAT I WAS DEVELOPING A HEAD COLD AND BECAUSE OF THIS AND MY LACK OF SLEEP FOLLOWING A VERY SHORT 9 HR OVERNIGHT; I CONTACTED SCHEDULING AND REQUESTED THAT I BE REPLACED ON THE NEXT LEG.