Consider the following premises. For all x_11, if x_11 listens to a song, then x_11 is a bartender. For all x_11, x_11 will not go running. For all x_11, x_11 will go running if and only if x_11 is bored. For all x_11, x_11 is curious if and only if x_11 is bored. For all x_11, if x_11 were a bartender, then x_11 is curious. Can we infer the following from them? If we can, name the inference rule being used: For all x_11, x_11 will not listen to a song.
 From the fact that for all x_11, x_11 will go running if and only if x_11 is bored, and that for all x_11, x_11 will not go running we can infer that for all x_11, x_11 is not bored via universal biconditional elimination. From the fact that for all x_11, x_11 is curious if and only if x_11 is bored, and that for all x_11, x_11 is not bored we can infer that for all x_11, x_11 is not curious via universal biconditional elimination. From the fact that for all x_11, if x_11 were a bartender, then x_11 is curious, and that for all x_11, x_11 is not curious we can infer that for all x_11, x_11 is not a bartender via universal modus tollens. Finally, from the fact that for all x_11, if x_11 listens to a song, then x_11 is a bartender, and that for all x_11, x_11 is not a bartender we can infer that for all x_11, x_11 will not listen to a song via universal modus tollens. Therefore, the answer is yes.