I cannot reach a meaningful solution from the given information. To prove that S was always true, you would have to prove that N was always false. To prove that N was always false you would have to prove that L was always false. For the statement (L ^ T) -> K to be true, you only need K to be true, so L can be either true or false.
Therefore, because of the aforementioned knowledge, I do not believe that you can prove S to be true.
