Consider the following premises. For all z_4, z_4 is a politician or z_4 is a poet. For all z_4, if z_4 were a politician, then z_4 is a server. For all z_4, z_4 is not a server. For all z_4, if z_4 were a server, then z_4 is a politician. 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 neither z_4 is a poet nor z_4 is curious.
 From the fact that for all z_4, if z_4 were a server, then z_4 is a politician, and that for all z_4, if z_4 were a politician, then z_4 is a server we can infer that for all z_4, z_4 is a server if and only if z_4 is a politician via universal biconditional introduction. From the fact that for all z_4, z_4 is a server if and only if z_4 is a politician we can infer that for all z_4, if z_4 were a politician, then z_4 is a server via universal biconditional elimination. From the fact that for all z_4, if z_4 were a politician, then z_4 is a server, and that for all z_4, z_4 is not a server we can infer that for all z_4, z_4 is not a politician via universal modus tollens. From the fact that for all z_4, z_4 is a politician or z_4 is a poet, and that for all z_4, z_4 is not a politician we can infer that for all z_4, z_4 is a poet via universal disjunctive syllogism. Finally, from the fact that for all z_4, z_4 is a poet we can infer that for all z_4, z_4 is a poet or z_4 is curious via universal addition, which contradicts that There is at least one z_4 for which neither z_4 is a poet nor z_4 is curious. Therefore, the answer is no.