No, Obama is fighting against a faction of ISIS, not against the movement, itself. What Obama wants is to replace the leadership of ISIS with the Muslim Brotherhood without sacrificing any of the gains that they have made toward the caliphate.
My point was that I don’t think he is doing any REAL fighting against anyone or anything. I think he is just wasting ammunition in the form of missiles so that we won’t have them when we really need them. It is probably what George W. Bush said he would NOT do, “...fire a two million dollar missile at a ten dollar empty tent and hit a camel in the butt.”