Consider the following premises. For all x_9, x_9 will drink water or x_9 will not listen to a song. There is at least one x_9 for which if x_9 were excited, then x_9 is listening to a song. For all x_9, if x_9 drinks water, then x_9 is excited. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_9 for which if x_9 drinks water, then x_9 is listening to a song.
 From the fact that for all x_9, x_9 will drink water or x_9 will not listen to a song we can infer that for all x_9, if x_9 listens to a song, then x_9 is drinking water via universal rewriting. Finally, from the fact that for all x_9, if x_9 drinks water, then x_9 is excited, and that there is at least one x_9 for which if x_9 were excited, then x_9 is listening to a song we can infer that there is at least one x_9 for which if x_9 drinks water, then x_9 is listening to a song via existential transitivity. Therefore, the answer is yes.