Consider the following premises. It is cloudy. William is fast or it is not cloudy. William is not fast. Can we infer the following from them? If we can, name the inference rule being used: It is sunny.
 From the fact that William is fast or it is not cloudy we can infer that if it is cloudy, then William is fast via rewriting. From the fact that if it is cloudy, then William is fast, and that William is not fast we can infer that it is not cloudy via modus tollens. From the fact that it is cloudy we can infer that it is cloudy or it is sunny via addition. Finally, from the fact that it is cloudy or it is sunny, and that it is not cloudy we can infer that it is sunny via disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.