Consider the following premises. For all x_9, x_9 is fast if and only if x_9 will listen to a song. There is at least one x_9 for which if x_9 were fast, then x_9 is a server. For all x_9, if x_9 were fast, then x_9 is listening to a song. 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 listens to a song, then x_9 is a server.
 From the fact that for all x_9, x_9 is fast if and only if x_9 will listen to a song we can infer that for all x_9, if x_9 listens to a song, then x_9 is fast via universal biconditional elimination. From the fact that for all x_9, if x_9 listens to a song, then x_9 is fast, and that for all x_9, if x_9 were fast, then x_9 is listening to a song we can infer that for all x_9, x_9 will listen to a song if and only if x_9 is fast via universal biconditional introduction. From the fact that for all x_9, x_9 will listen to a song if and only if x_9 is fast we can infer that for all x_9, if x_9 listens to a song, then x_9 is fast via universal biconditional elimination. Finally, from the fact that for all x_9, if x_9 listens to a song, then x_9 is fast, and that there is at least one x_9 for which if x_9 were fast, then x_9 is a server we can infer that there is at least one x_9 for which if x_9 listens to a song, then x_9 is a server via existential transitivity. Therefore, the answer is yes.