Consider the following premises. Karen is not sleeping. For all z, if z sleeps, then z is playing tennis. For all z, z will play tennis if and only if z will sleep. If William were excited, then Karen is playing tennis. Can we infer the following from them? If we can, name the inference rule being used: William is not excited.
 From the fact that for all z, z will play tennis if and only if z will sleep we can infer that for all z, if z plays tennis, then z is sleeping via universal biconditional elimination. From the fact that for all z, if z sleeps, then z is playing tennis, and that for all z, if z plays tennis, then z is sleeping we can infer that for all z, z will sleep if and only if z will play tennis via universal biconditional introduction. From the fact that for all z, z will sleep if and only if z will play tennis we can infer that Karen is sleeping if and only if Karen is playing tennis via universal instantiation. From the fact that Karen is sleeping if and only if Karen is playing tennis, and that Karen is not sleeping we can infer that Karen is not playing tennis via biconditional elimination. Finally, from the fact that if William were excited, then Karen is playing tennis, and that Karen is not playing tennis we can infer that William is not excited via modus tollens. Therefore, the answer is yes.