ACFT EQUIP PROB -- ACR FLC AND MAINT MISREAD THE MEL AND PERFORMED TKOF WITH A HYD PUMP INOP.

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TAXIING OUT AT FRA #2 GREEN HYD PUMP SHOWED LOW PRESSURE WITH ECAM ACTION. WE TRIED TO TROUBLE-SHOOT; BUT COULD NOT CORRECT THE SIT. FRA MAINT WAS THEN CONTACTED BY RADIO; THEY ASKED US TO FEATHER #1 GREEN PUMP AND THE GREEN HYD PRESSURE WENT TO ZERO. MAINT THEN STATED THAT WE HAD A BAD PUMP; BUT WERE OK TO GO AS PER MEL 29-29-11- 01 AND THEY WOULD BE READY TO CHANGE THE PUMP WHEN WE RETURNED THE FOLLOWING DAY. WE WERE ALREADY LOOKING AT THE MEL ITEM REFED AND AGREED. HOWEVER; THIS ITEM REFED THE PRESSURE SWITCH ONLY. I THEN QUESTIONED MAINT ABOUT THE MENTALITY OF FLYING 4 LEGS -- FRA; VIE; OTP; VIE; FRA -- IN THIS CONDITION AND MAINT'S REPLY WAS THAT IT WAS LEGAL TO DO SO; BUT THEY WOULD WIRE VIE AND ASK THEM TO CHK THE SIT. THE FO AND I THEN DISCUSSED THE SIT BTWN OURSELVES AND DECIDED TO GO. I DEFINITELY BELIEVE THAT HUMAN FACTORS IS A CONSIDERATION HERE. AT THE TIME OF MY DECISION TO TAKE THE ACFT IN THIS CONDITION I HAD 9 HRS OF SLEEP IN THE PREVIOUS 71 HRS BECAUSE OF A LATE LCL DEP FROM JFK AND MY ARR IN WAW WAS 13 HRS AFTER RPTING FOR DUTY AND OVER 25 HRS AFTER I LEFT MY BED THE PREVIOUS MORNING. I WAS OVER TIRED AND COULD NOT SLEEP PROPERLY IN WAW. ON MY RETURN TO FRA THE DAY AFTER ACCEPTING THE ACFT WITH THE BAD PUMP I SPOKE WITH THE MAINT SUPVR WHO TOLD ME TO GO IN THIS SIT AND HE TOLD ME THAT HE TOO WAS UNDER A LOT OF JOB STRESS THAT DAY AND WAS NOT AS SHARP AS HE SHOULD HAVE BEEN.