Consider the following premises. For all x_12, if x_12 listens to a song, then x_12 is a janitor. Mary is listening to a song. If Mary were a janitor, then Mary is listening to a song. Can we infer the following from them? Mary is a janitor.
 From the fact that for all x_12, if x_12 listens to a song, then x_12 is a janitor we can infer that if Mary listens to a song, then Mary is a janitor. From the fact that if Mary were a janitor, then Mary is listening to a song, and that if Mary listens to a song, then Mary is a janitor we can infer that Mary is a janitor if and only if Mary is listening to a song. From the fact that Mary is a janitor if and only if Mary is listening to a song we can infer that if Mary listens to a song, then Mary is a janitor. Finally, from the fact that if Mary listens to a song, then Mary is a janitor, and that Mary is listening to a song we can infer that Mary is a janitor. Therefore, the answer is yes.