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