The SAT/SMT by Example has couple of examples, about how to find safe cells in Minesweeper (that can be clicked safely) (Ctrl-F "Minesweeper").
Now here is a bruteforce solver I wrote for fun. I doesn't use any external library or solver. However, it's painfully slow, it takes several minutes to find safe cells on 9*9 field. Still, it can serve as a demonstration.
This is where SAT/SMT solvers excels: they can find faster ways than bruteforce...
→ [list of blog posts]Please drop me email about any bug(s) and suggestion(s): dennis(@)yurichev.com.