FLC OF AN LTT USED THE WRONG TAXI RTE AFTER TURNING OFF RWY TO PARKING.

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FLT HAD JUST LANDED ON RWY 30R AT STL. CAPT WAS THE PF AND TAXIED THE ACFT OFF THE RWY. FO CONTACTED GND CTLR 121.9 TO RECEIVE TAXI INSTRUCTIONS TO THE AIRLINE GATES. AFTER FO CONTACTED GND; HE INITIATED THE AFTER LNDG CHKLIST AND WAS NOT AWARE OF THE SEQUENCE OF EVENTS UNTIL AFTER THE FACT. THE CAPT WAS SURE HE AND THE GND CTLR INSTRUCTED FLT TO TAXI ON TXWY P TO TXWY B AND HOLD SHORT OF RWY 30R. CAPT HEARD HIS FO REPEAT THE CLRNC AND HAVING NO DOUBT ON THE INSTRUCTIONS; TAXIED THE ACFT TO THE HOLD SHORT POINT AND SET THE PARKING BRAKE. AT THIS POINT; THE FO LOOKED UP AND ASKED THE CAPT WHAT TXWY HE WAS ON. THE CAPT ANSWERED HE WAS ON TXWY B AND THEN THE FO STATED THEY WERE TO HOLD SHORT ON TXWY E AND NOT TXWY B. THE CAPT ASKED THE FO WHY HE DID NOT SPEAK UP SOONER AND THE FO STATED HE WAS TOO BUSY WITH THE AFTER LNDG CHKLIST. AT THIS POINT; THE CAPT WAS NOT SURE IF HE HAD MADE AN ERROR ON THE TAXI INSTRUCTIONS OR IF HIS FO HAD NOT HEARD THE CLRNC CORRECTLY. AFTER SEVERAL MINS; THE GND CTLR ISSUED A CLRNC FOR THE ACFT TO CROSS RWY 30L. THE CTLR MADE NO MENTION OF ANY MISTAKE OR ANY MISINTERP OF THE CLRNC. THE FLT CONCLUDED WITHOUT FURTHER INCIDENT. POSSIBLE FATIGUE MAY BE A FACTOR IN BOTH PLTS NOT BEING ABSOLUTELY CERTAIN OF THE CLRNC. THE CREW HAD COMPLETED ONE ROUND TRIP FROM MKE TO STL AND BACK AND WERE ON THE SECOND HALF OF THEIR SHIFT. DUE TO WX AND TFC; THE FLTS WERE BEHIND SCHEDULE AND BOTH PLTS WERE TRYING TO MAKE UP TIME THROUGHOUT THE DAY. THE TOTAL FLT TIME FOR THE CREW ENDED UP TO BE JUST UNDER 7 HRS.