Consider the following premises. For all x_6, if x_6 were a doctor, then x_6 is a politician. For all x_6, x_6 is a doctor or x_6 is not a server. For all x_6, if x_6 were a politician, then x_6 is a server. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which if is not true that x_6 is a server if and only if x_6 is a doctor.
 From the fact that for all x_6, x_6 is a doctor or x_6 is not a server we can infer that for all x_6, if x_6 were a server, then x_6 is a doctor via universal rewriting. From the fact that for all x_6, if x_6 were a doctor, then x_6 is a politician, and that for all x_6, if x_6 were a politician, then x_6 is a server we can infer that for all x_6, if x_6 were a doctor, then x_6 is a server via universal transitivity. Finally, from the fact that for all x_6, if x_6 were a server, then x_6 is a doctor, and that for all x_6, if x_6 were a doctor, then x_6 is a server we can infer that for all x_6, x_6 is a server if and only if x_6 is a doctor via universal biconditional introduction, which contradicts that There is at least one x_6 for which if is not true that x_6 is a server if and only if x_6 is a doctor. Therefore, the answer is no.