AN MD11 WAS DISPATCHED IN NON COMPLIANCE WITH AN AIR SYS MALFUNCTION NOT ADDRESSED IN THE MEL. INCORRECT OP PROCS GIVEN CREW.

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PRIOR TO DEP FROM ZZZ ON NOV/SUN/03; WE WERE ADVISED BY MAINT THAT AN AIR SYS WRITE-UP IN THE ACFT MAINT LOG (WHICH WOULD HAVE REQUIRED CREW TO OPERATE THE AIR SYS IN THE MANUAL MODE) WAS ENTERED IN ERROR. THEY ADVISED US THAT THE MEL DID NOT ADDRESS THE TRUE PROB ON BOARD THE ACFT; AND THAT A COMPLETE DESCRIPTION OF THE ACFT PROB WOULD BE DISCUSSED WITH THE CREW IN ZZZ BY THE MECH WHO HAD INITIATED THE MEL IN QUESTION. UNTIL THEN; WE WERE ADVISED BY MAINT TO OPERATE THE ACFT WITH THE AIR SYS IN THE AUTOMATIC MODE (AGAINST THE PROCS CALLED FOR IN THE MEL); LIKE 'ALL THE OTHER CREWS HAD OPERATED.' WE DEPARTED ZZZZ AND PROCEEDED TO ZZZ AND DURING DSCNT TO LNDG; WE ENCOUNTERED ICING CONDITIONS. AFTER SELECTING THE WING ANTI-ICE SYS ON; THE L WING ANTI-ICE DISAGREE LIGHT CAME ON. WE SELECTED THE SYS OFF; AND TRIED TO AVOID ANY ICING CONDITIONS; AND MADE AN UNEVENTFUL LNDG ON RWY 6R AT ZZZ. AFTER ENG SHUTDOWN; A WRITE-UP WAS MADE IN THE ACFT MAINT LOG DESCRIBING THE EVENT. THE MECH IN DESCRIBING THE CORRECTIVE ACTION TAKEN; STATED THE AIR SYS WAS OPERATED IN AUTOMATIC MODE AGAINST THE PROCS CALLED FOR IN THE MEL; AND SIGNED OFF THE WRITE-UP. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED THE DEFERRED ITEM WAS ACTUALLY A L WING ANTI-ICE DISAGREE PROB WITH A LONG MAINT HISTORY. THE RPTR SAID THE INSTRUCTIONS GIVEN TO THE CREW BY THE ZZZ TECHNICIAN WERE TO OPERATE THE AIR SYS IN THE AUTO-MODE WHICH WAS NOT THE PROC CALLED FOR IN THE MEL. THE RPTR STATED THE INBOUND TRIP TO ZZZ1 DID ENCOUNTER ICING AND WHEN THE WING ANTI-ICE WAS SWITCHED ON THE L WING 'DISAGREE' LIGHT CAME ON. THE RPTR SAID ON LNDG THE ITEM WAS WRITTEN UP IN THE MAINT LOG AND THE ZZZ1 TECHNICIAN CLRED THE ITEM. THE RPTR STATED THE CORRECTIVE ACTION WAS THE AIR SYS WAS OPERATED IN AUTO IN CONFLICT WITH THE MEL.