Well, it can. Suppose when we have a door that is unlocked, we'll take our equation to be ( u | -v) & (-u | v).

When our door will be locked, we'll take it (u | v) & (-u | -v)

Submission #24941604

PS :- I got accepted using this only in the contest.

Or you can say that this problem is reducable to 2-SAT Problem.