Consider the following premises. For all x_11, x_11 is not a doctor. There is at least one x_11 for which x_11 is a doctor or x_11 is poor. For all x_11, x_11 is a writer or x_11 is not poor. Can we infer the following from them? If we can, name the inference rule being used: For all x_11, x_11 is not a writer.
 From the fact that for all x_11, x_11 is a writer or x_11 is not poor we can infer that for all x_11, if x_11 were poor, then x_11 is a writer via universal rewriting. From the fact that there is at least one x_11 for which x_11 is a doctor or x_11 is poor, and that for all x_11, x_11 is not a doctor we can infer that there is at least one x_11 for which x_11 is poor via existential disjunctive syllogism. Finally, from the fact that for all x_11, if x_11 were poor, then x_11 is a writer, and that there is at least one x_11 for which x_11 is poor we can infer that there is at least one x_11 for which x_11 is a writer via existential modus ponens, which contradicts that For all x_11, x_11 is not a writer. Therefore, the answer is no.