AIR CARRIER FIRST OFFICER NOTICES THE SHIFTY RNAV ARRIVAL INTO RSW CONFLICTS WITH A CURRENT NOTAM.

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WE WERE CLRED ON THE SHIFTY 1 ARR INTO RSW. RWY 24 WAS IN USE AT RSW. THE ARR HAS A NOTE WHICH STATES IF LNDG RWY 24 AT RSW FROM OVER MOEMO; TURN TO A 220 DEG HDG. THERE IS A NOTAM OUT FOR THE SHIFTY 1 ARR WHICH STATES; 'LNDG RSW RWY 24 AND FMY: FROM OVER LBV VIA 190 DEG HDG. EXPECT RADAR VECTORS.' WE QUERIED THE CTLR ABOUT WHAT WE'RE TO DO OVER MOEMO. WE WERE PROGRAMMED TO FOLLOW THE 220 DEG HDG OUT OF MOEMO AS THE ARR STATES. THE CTLR SAID NO; WE WERE TO GO TO LBV. HE THEN GAVE US A 180 DEG HDG TO FOLLOW. THE CTLR ASKED US TO RPT THIS SITUATION SINCE TOO MANY ACFT QUESTION THIS ARR AND NOTAM OR FLY IT INCORRECTLY. THE NOTAM WAS NOT ON ATIS INFO THAT WE INITIALLY ACQUIRED BUT AFTER WE QUERIED THE CTLR; IT WAS ON THE FOLLOWING HOUR'S ATIS INFO. THE MAIN PROB WITH THIS NOTAM AND THE ARR IS LBV IS S OF MOEMO. THEREFORE; WITH CURRENT PROGRAMMING AND SETUP WITH RWY 24 IN USE; THE ACFT NEVER GETS TO LBV TO FOLLOW THE NOTAM. A 220 DEG HDG WOULD BE EXECUTED AT MOEMO. EITHER THE ARR OR THE NOTAM HAS TO BE CHANGED.