Consider the following premises. For all y, if y works, then y is drinking water. For all y, if y drinks water, then y is listening to a song. For all y, y will work or y will not listen to a song. Can we infer the following from them? There is at least one y for which the fact that y drinks water does not imply that y is working.
 From the fact that for all y, y will work or y will not listen to a song we can infer that for all y, if y listens to a song, then y is working. From the fact that for all y, if y drinks water, then y is listening to a song, and that for all y, if y listens to a song, then y is working we can infer that for all y, if y drinks water, then y is working. From the fact that for all y, if y works, then y is drinking water, and that for all y, if y drinks water, then y is working we can infer that for all y, y will work if and only if y will drink water. Finally, from the fact that for all y, y will work if and only if y will drink water we can infer that for all y, if y drinks water, then y is working, which contradicts that There is at least one y for which the fact that y drinks water does not imply that y is working. Therefore, the answer is no.