Consider the following premises. For all x, if x listens to a song, then x is excited. For all x, if x were excited, then x is a mechanic. For all x, if x were a mechanic, then x is listening to a song. For all x, if x were a mechanic, then x is listening to a song. Can we infer the following from them? There is at least one x for which the fact that x listens to a song does not imply that x is a mechanic.
 From the fact that for all x, if x listens to a song, then x is excited, and that for all x, if x were excited, then x is a mechanic we can infer that for all x, if x listens to a song, then x is a mechanic. From the fact that for all x, if x were a mechanic, then x is listening to a song, and that for all x, if x listens to a song, then x is a mechanic we can infer that for all x, x is a mechanic if and only if x will listen to a song. From the fact that for all x, x is a mechanic if and only if x will listen to a song we can infer that for all x, if x listens to a song, then x is a mechanic. From the fact that for all x, if x listens to a song, then x is a mechanic, and that for all x, if x were a mechanic, then x is listening to a song we can infer that for all x, x will listen to a song if and only if x is a mechanic. Finally, from the fact that for all x, x will listen to a song if and only if x is a mechanic we can infer that for all x, if x listens to a song, then x is a mechanic, which contradicts that There is at least one x for which the fact that x listens to a song does not imply that x is a mechanic. Therefore, the answer is no.