Consider the following premises. For all z_3, z_3 will play squash or z_3 will not sleep. For all z_3, if z_3 plays squash, then z_3 is sleeping. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z_3 for which if is not true that z_3 will sleep if and only if z_3 will play squash.
 From the fact that for all z_3, z_3 will play squash or z_3 will not sleep we can infer that for all z_3, if z_3 sleeps, then z_3 is playing squash via universal rewriting. Finally, from the fact that for all z_3, if z_3 sleeps, then z_3 is playing squash, and that for all z_3, if z_3 plays squash, then z_3 is sleeping we can infer that for all z_3, z_3 will sleep if and only if z_3 will play squash via universal biconditional introduction, which contradicts that There is at least one z_3 for which if is not true that z_3 will sleep if and only if z_3 will play squash. Therefore, the answer is no.