Consider the following premises. For all x_7, if x_7 were fast, then x_7 is making tea. For all x_7, if x_7 makes tea, then x_7 is listening to a song. For all x_7, x_7 is a janitor if and only if x_7 will listen to a song. For all x_7, x_7 is a janitor or x_7 is fast. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 will listen to a song.
 From the fact that for all x_7, x_7 is a janitor if and only if x_7 will listen to a song we can infer that for all x_7, if x_7 were a janitor, then x_7 is listening to a song via universal biconditional elimination. From the fact that for all x_7, if x_7 were fast, then x_7 is making tea, and that for all x_7, if x_7 makes tea, then x_7 is listening to a song we can infer that for all x_7, if x_7 were fast, then x_7 is listening to a song via universal transitivity. Finally, from the fact that for all x_7, if x_7 were a janitor, then x_7 is listening to a song, that for all x_7, if x_7 were fast, then x_7 is listening to a song, and that for all x_7, x_7 is a janitor or x_7 is fast we can infer that for all x_7, x_7 will listen to a song via universal disjunction elimination. Therefore, the answer is yes.