Who is fighting whom in Libya?

An astute Libyan student who lives in Tripoli explained to me: who is fighting whom in Libya? On the one side, there are the armies of Al-Qa`idah and the Muslim Brothers. They work side-by-side with support from Qatar.  On the other side, there is the army of US covert operations (Khalifah Haftar), the forces loyal to Qadhdhafi (kid you not) and other tribal forces which get support from Western governments and Saudi Arabia.  Memorably, both sides stopped the fighting briefly to allow the evacuation of US staff from the embassy.  Kid you not.