Consider the following premises. It is cloudy or it is not cold. If it rains, then William is fast. If William were fast, then it is cold. It is not cloudy. Can we infer the following from them? It is not raining.
 From the fact that it is cloudy or it is not cold we can infer that if it is cold, then it is cloudy. From the fact that if William were fast, then it is cold, and that if it is cold, then it is cloudy we can infer that if William were fast, then it is cloudy. From the fact that if William were fast, then it is cloudy, and that it is not cloudy we can infer that William is not fast. Finally, from the fact that if it rains, then William is fast, and that William is not fast we can infer that it is not raining. Therefore, the answer is yes.