Consider the following premises. For all x_8, if x_8 were a janitor, then x_8 is a soldier. For all x_8, if x_8 were a soldier, then x_8 is listening to a song. There is at least one x_8 for which if x_8 listens to a song, then x_8 is a janitor. For all x_8, x_8 will listen 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_8 for which x_8 is a soldier.
 From the fact that there is at least one x_8 for which if x_8 listens to a song, then x_8 is a janitor, and that for all x_8, if x_8 were a janitor, then x_8 is a soldier we can infer that there is at least one x_8 for which if x_8 listens to a song, then x_8 is a soldier via existential transitivity. From the fact that for all x_8, if x_8 were a soldier, then x_8 is listening to a song, and that there is at least one x_8 for which if x_8 listens to a song, then x_8 is a soldier we can infer that there is at least one x_8 for which x_8 is a soldier if and only if x_8 will listen to a song via existential biconditional introduction. From the fact that there is at least one x_8 for which x_8 is a soldier if and only if x_8 will listen to a song we can infer that there is at least one x_8 for which if x_8 listens to a song, then x_8 is a soldier via existential biconditional elimination. Finally, from the fact that there is at least one x_8 for which if x_8 listens to a song, then x_8 is a soldier, and that for all x_8, x_8 will listen to a song we can infer that there is at least one x_8 for which x_8 is a soldier via existential modus ponens. Therefore, the answer is yes.