Consider the following premises. William is not playing squash. For all z_4, z_4 will play squash if and only if z_4 is a cashier. Can we infer the following from them? William is not a cashier.
 From the fact that for all z_4, z_4 will play squash if and only if z_4 is a cashier we can infer that for all z_4, if z_4 were a cashier, then z_4 is playing squash. From the fact that for all z_4, if z_4 were a cashier, then z_4 is playing squash we can infer that if William were a cashier, then William is playing squash. Finally, from the fact that if William were a cashier, then William is playing squash, and that William is not playing squash we can infer that William is not a cashier. Therefore, the answer is yes.