Consider the following premises. For all y, y will go running if and only if y will drive a car. For all y, if y were a mechanic, then y is listening to a song. There is at least one y for which y is a mechanic if and only if y will go running. For all y, y will not listen to a song. Can we infer the following from them? There is at least one y for which y will not drive a car.
 From the fact that for all y, if y were a mechanic, then y is listening to a song, and that for all y, y will not listen to a song we can infer that for all y, y is not a mechanic. From the fact that there is at least one y for which y is a mechanic if and only if y will go running, and that for all y, y is not a mechanic we can infer that there is at least one y for which y will not go running. Finally, from the fact that for all y, y will go running if and only if y will drive a car, and that there is at least one y for which y will not go running we can infer that there is at least one y for which y will not drive a car. Therefore, the answer is yes.