Consider the following premises. For all z_4, if z_4 drinks water, then z_4 is a doctor. For all z_4, if z_4 were a doctor, then z_4 is a server. For all z_4, if z_4 were a server, then z_4 is drinking water. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z_4 for which the fact that z_4 were a server does not imply that z_4 is a doctor.
 From the fact that for all z_4, if z_4 were a server, then z_4 is drinking water, and that for all z_4, if z_4 drinks water, then z_4 is a doctor we can infer that for all z_4, if z_4 were a server, then z_4 is a doctor via universal transitivity. From the fact that for all z_4, if z_4 were a doctor, then z_4 is a server, and that for all z_4, if z_4 were a server, then z_4 is a doctor we can infer that for all z_4, z_4 is a doctor if and only if z_4 is a server via universal biconditional introduction. Finally, from the fact that for all z_4, z_4 is a doctor if and only if z_4 is a server we can infer that for all z_4, if z_4 were a server, then z_4 is a doctor via universal biconditional elimination, which contradicts that There is at least one z_4 for which the fact that z_4 were a server does not imply that z_4 is a doctor. Therefore, the answer is no.