Consider the following premises. There is at least one y for which if y goes running, then y is listening to a song. For all y, y will go running or y will not make tea. For all y, if y listens to a song, then y is making tea. Can we infer the following from them? For all y, if is not true that y will make tea if and only if y will listen to a song.
 From the fact that for all y, y will go running or y will not make tea we can infer that for all y, if y makes tea, then y is running. From the fact that for all y, if y makes tea, then y is running, and that there is at least one y for which if y goes running, then y is listening to a song we can infer that there is at least one y for which if y makes tea, then y is listening to a song. Finally, from the fact that there is at least one y for which if y makes tea, then y is listening to a song, and that for all y, if y listens to a song, then y is making tea we can infer that there is at least one y for which y will make tea if and only if y will listen to a song, which contradicts that For all y, if is not true that y will make tea if and only if y will listen to a song. Therefore, the answer is no.