Consider the following premises. Charles is playing squash and Linda is listening to a song. If Thomas sleeps, then Karen is playing tennis. If Karen plays tennis, then Charles is not playing squash. If Karen plays tennis, then Thomas is sleeping. Can we infer the following from them? If we can, name the inference rule being used: Thomas is not sleeping.
 From the fact that Charles is playing squash and Linda is listening to a song we can infer that Charles is playing squash via simplification. From the fact that if Karen plays tennis, then Charles is not playing squash, and that Charles is playing squash we can infer that Karen is not playing tennis via modus tollens. From the fact that if Thomas sleeps, then Karen is playing tennis, and that if Karen plays tennis, then Thomas is sleeping we can infer that Thomas is sleeping if and only if Karen is playing tennis via biconditional introduction. From the fact that Thomas is sleeping if and only if Karen is playing tennis we can infer that if Thomas sleeps, then Karen is playing tennis via biconditional elimination. Finally, from the fact that if Thomas sleeps, then Karen is playing tennis, and that Karen is not playing tennis we can infer that Thomas is not sleeping via modus tollens. Therefore, the answer is yes.