Consider the following premises. For all x_6, x_6 is a bartender or x_6 is a police officer. For all x_6, x_6 will listen to a song or x_6 is not a bartender. For all x_6, if x_6 were a police officer, then x_6 is listening to a song. For all x_6, x_6 will drink water. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 will drink water and x_6 will listen to a song.
 From the fact that for all x_6, x_6 will listen to a song or x_6 is not a bartender we can infer that for all x_6, if x_6 were a bartender, then x_6 is listening to a song via universal rewriting. From the fact that for all x_6, if x_6 were a bartender, then x_6 is listening to a song, that for all x_6, if x_6 were a police officer, then x_6 is listening to a song, and that for all x_6, x_6 is a bartender or x_6 is a police officer we can infer that for all x_6, x_6 will listen to a song via universal disjunction elimination. Finally, from the fact that for all x_6, x_6 will drink water, and that for all x_6, x_6 will listen to a song we can infer that for all x_6, x_6 will drink water and x_6 will listen to a song via universal conjunction. Therefore, the answer is yes.