Consider the following premises. For all x_10, x_10 will not work. For all x_10, if x_10 were a soldier, then x_10 is a police officer. For all x_10, if x_10 listens to a song, then x_10 is a soldier. For all x_10, x_10 will work or x_10 is not a police officer. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_10 for which x_10 will listen to a song.
 From the fact that for all x_10, x_10 will work or x_10 is not a police officer we can infer that for all x_10, if x_10 were a police officer, then x_10 is working via universal rewriting. From the fact that for all x_10, if x_10 were a police officer, then x_10 is working, and that for all x_10, x_10 will not work we can infer that for all x_10, x_10 is not a police officer via universal modus tollens. From the fact that for all x_10, if x_10 were a soldier, then x_10 is a police officer, and that for all x_10, x_10 is not a police officer we can infer that for all x_10, x_10 is not a soldier via universal modus tollens. Finally, from the fact that for all x_10, if x_10 listens to a song, then x_10 is a soldier, and that for all x_10, x_10 is not a soldier we can infer that for all x_10, x_10 will not listen to a song via universal modus tollens, which contradicts that There is at least one x_10 for which x_10 will listen to a song. Therefore, the answer is no.