Consider the following premises. For all x_13, x_13 is a nurse or x_13 is a server. For all x_13, x_13 is not a nurse or x_13 is a writer. For all x_13, x_13 is a doctor if and only if x_13 is a politician. There is at least one x_13 for which x_13 is a server if and only if x_13 is a politician. For all x_13, x_13 is not a doctor. Can we infer the following from them? If we can, name the inference rule being used: For all x_13, x_13 is not a writer.
 From the fact that for all x_13, x_13 is a doctor if and only if x_13 is a politician, and that for all x_13, x_13 is not a doctor we can infer that for all x_13, x_13 is not a politician via universal biconditional elimination. From the fact that for all x_13, x_13 is a nurse or x_13 is a server, and that for all x_13, x_13 is not a nurse or x_13 is a writer we can infer that for all x_13, x_13 is a server or x_13 is a writer via universal resolution. From the fact that there is at least one x_13 for which x_13 is a server if and only if x_13 is a politician, and that for all x_13, x_13 is not a politician we can infer that there is at least one x_13 for which x_13 is not a server via existential biconditional elimination. Finally, from the fact that for all x_13, x_13 is a server or x_13 is a writer, and that there is at least one x_13 for which x_13 is not a server we can infer that there is at least one x_13 for which x_13 is a writer via existential disjunctive syllogism, which contradicts that For all x_13, x_13 is not a writer. Therefore, the answer is no.