Consider the following premises. There is at least one z_2 for which if z_2 were excited, then z_2 is sleeping. For all z_2, if z_2 sleeps, then z_2 is playing squash. For all z_2, z_2 is excited if and only if z_2 will play squash. Can we infer the following from them? For all z_2, z_2 is excited if and only if z_2 will play squash.
That is one of the premises. Therefore, the answer is yes.