Consider the following premises. For all x_5, if x_5 were a sailor, then x_5 is playing a game. For all x_5, if x_5 listens to a song, then x_5 is a sailor. For all x_5, x_5 will listen to a song. For all x_5, if x_5 plays a game, then x_5 is excited. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 is excited.
 From the fact that for all x_5, if x_5 were a sailor, then x_5 is playing a game, and that for all x_5, if x_5 plays a game, then x_5 is excited we can infer that for all x_5, if x_5 were a sailor, then x_5 is excited via universal transitivity. From the fact that for all x_5, if x_5 listens to a song, then x_5 is a sailor, and that for all x_5, x_5 will listen to a song we can infer that for all x_5, x_5 is a sailor via universal modus ponens. Finally, from the fact that for all x_5, if x_5 were a sailor, then x_5 is excited, and that for all x_5, x_5 is a sailor we can infer that for all x_5, x_5 is excited via universal modus ponens. Therefore, the answer is yes.