Consider the following premises. For all x, x is a writer or x will play a game. For all x, x is a mechanic. There is at least one x for which if x were a writer, then x is not a mechanic. Can we infer the following from them? For all x, x will not play a game.
 From the fact that there is at least one x for which if x were a writer, then x is not a mechanic, and that for all x, x is a mechanic we can infer that there is at least one x for which x is not a writer. Finally, from the fact that for all x, x is a writer or x will play a game, and that there is at least one x for which x is not a writer we can infer that there is at least one x for which x will play a game, which contradicts that For all x, x will not play a game. Therefore, the answer is no.