Consider the following premises. If William were a scientist, then Robert is listening to a song. If Robert listens to a song, then William is a scientist. If William were a scientist, then it is not cold. It is cold. Can we infer the following from them? Robert is not listening to a song.
 From the fact that if William were a scientist, then it is not cold, and that it is cold we can infer that William is not a scientist. From the fact that if Robert listens to a song, then William is a scientist, and that if William were a scientist, then Robert is listening to a song we can infer that Robert is listening to a song if and only if William is a scientist. Finally, from the fact that Robert is listening to a song if and only if William is a scientist, and that William is not a scientist we can infer that Robert is not listening to a song. Therefore, the answer is yes.