Consider the following premises. For all x_10, x_10 is not a janitor. It is cloudy if and only if William is a janitor. If it rains, then it is cloudy. Can we infer the following from them? It is not raining.
 From the fact that for all x_10, x_10 is not a janitor we can infer that William is not a janitor. From the fact that it is cloudy if and only if William is a janitor, and that William is not a janitor we can infer that it is not cloudy. Finally, from the fact that if it rains, then it is cloudy, and that it is not cloudy we can infer that it is not raining. Therefore, the answer is yes.