exact cover set problem
To convert to MaxSAT:


For each set $ S $ introduce a fresh variable $ X_S $.
If two sets $ S $ and $ D $ intersect, produce the hard clause $\lnot X_S\lor \lnot X_D$.
For each element $e$ produce the hard clause $\bigvee_{e\in S} X_S$, making sure that at least one set that contains $ e $ is selected.
For each set $ S$ with weight $W$ produce the soft clause $\lnot X_S$ with weight $W$, to minimize the total weight of selected sets.


I wrote a Python script for this (http://sat.inesc-id.pt/~mikolas/excover). This is the most naïve encoding. I believe there are ways how to make it smaller.