Consider the following premises. Patricia is working or John is not listening to a song. Patricia is not driving a car. For all x_12, x_12 will work if and only if x_12 will drive a car. Can we infer the following from them? John is not listening to a song.
 From the fact that for all x_12, x_12 will work if and only if x_12 will drive a car we can infer that Patricia is working if and only if Patricia is driving a car. From the fact that Patricia is working or John is not listening to a song we can infer that if John listens to a song, then Patricia is working. From the fact that Patricia is working if and only if Patricia is driving a car, and that Patricia is not driving a car we can infer that Patricia is not working. Finally, from the fact that if John listens to a song, then Patricia is working, and that Patricia is not working we can infer that John is not listening to a song. Therefore, the answer is yes.