Consider the following premises. If Karen listens to a song, then William is not climbing a mountain. For all y, y will climb a mountain and y will drive a car. Can we infer the following from them? Karen is not listening to a song.
 From the fact that for all y, y will climb a mountain and y will drive a car we can infer that William is climbing a mountain and William is driving a car. From the fact that William is climbing a mountain and William is driving a car we can infer that William is climbing a mountain. Finally, from the fact that if Karen listens to a song, then William is not climbing a mountain, and that William is climbing a mountain we can infer that Karen is not listening to a song. Therefore, the answer is yes.