Consider the following premises. For all x_9, if x_9 climbs a mountain, then x_9 is bored. For all x_9, if x_9 were a police officer, then x_9 is a writer. For all x_9, x_9 will climb a mountain. For all x_9, x_9 is bored or x_9 is not a writer. Can we infer the following from them? If we can, name the inference rule being used: For all x_9, x_9 is bored.
 From the fact that for all x_9, x_9 will climb a mountain we can infer that for all x_9, x_9 will climb a mountain or x_9 is a police officer via universal addition. From the fact that for all x_9, x_9 is bored or x_9 is not a writer we can infer that for all x_9, if x_9 were a writer, then x_9 is bored via universal rewriting. From the fact that for all x_9, if x_9 were a police officer, then x_9 is a writer, and that for all x_9, if x_9 were a writer, then x_9 is bored we can infer that for all x_9, if x_9 were a police officer, then x_9 is bored via universal transitivity. Finally, from the fact that for all x_9, if x_9 climbs a mountain, then x_9 is bored, that for all x_9, if x_9 were a police officer, then x_9 is bored, and that for all x_9, x_9 will climb a mountain or x_9 is a police officer we can infer that for all x_9, x_9 is bored via universal disjunction elimination. Therefore, the answer is yes.