Consider the following premises. For all x_9, if x_9 were a nurse, then x_9 is not a police officer. For all x_9, x_9 is bored or x_9 is a nurse. For all x_9, x_9 is not a carpenter. There is at least one x_9 for which x_9 is not bored or x_9 is a writer. For all x_9, x_9 is a carpenter or x_9 is a police officer. Can we infer the following from them? If we can, name the inference rule being used: For all x_9, x_9 is not a writer.
 From the fact that for all x_9, x_9 is a carpenter or x_9 is a police officer, and that for all x_9, x_9 is not a carpenter we can infer that for all x_9, x_9 is a police officer via universal disjunctive syllogism. From the fact that for all x_9, x_9 is bored or x_9 is a nurse, and that there is at least one x_9 for which x_9 is not bored or x_9 is a writer we can infer that there is at least one x_9 for which x_9 is a nurse or x_9 is a writer via existential resolution. From the fact that for all x_9, if x_9 were a nurse, then x_9 is not a police officer, and that for all x_9, x_9 is a police officer we can infer that for all x_9, x_9 is not a nurse via universal modus tollens. Finally, from the fact that there is at least one x_9 for which x_9 is a nurse or x_9 is a writer, and that for all x_9, x_9 is not a nurse we can infer that there is at least one x_9 for which x_9 is a writer via existential disjunctive syllogism, which contradicts that For all x_9, x_9 is not a writer. Therefore, the answer is no.