Consider the following premises. There is at least one x_1 for which if x_1 were a politician, then x_1 is listening to a song. For all x_1, x_1 is a mechanic or x_1 is a politician. For all x_1, if x_1 listens to a song, then x_1 is a police officer. For all x_1, if x_1 were a mechanic, then x_1 is a police officer. Can we infer the following from them? For all x_1, x_1 is not a police officer.
 From the fact that there is at least one x_1 for which if x_1 were a politician, then x_1 is listening to a song, and that for all x_1, if x_1 listens to a song, then x_1 is a police officer we can infer that there is at least one x_1 for which if x_1 were a politician, then x_1 is a police officer. Finally, from the fact that for all x_1, if x_1 were a mechanic, then x_1 is a police officer, that there is at least one x_1 for which if x_1 were a politician, then x_1 is a police officer, and that for all x_1, x_1 is a mechanic or x_1 is a politician we can infer that there is at least one x_1 for which x_1 is a police officer, which contradicts that For all x_1, x_1 is not a police officer. Therefore, the answer is no.