Consider the following premises. For all x, x is rich or x is not a writer. For all x, if x were rich, then x is listening to a song. There is at least one x for which if x were a carpenter, then x is a mechanic. For all x, if x listens to a song, then x is a carpenter. Can we infer the following from them? There is at least one x for which if x were a writer, then x is a mechanic.
 From the fact that for all x, if x were rich, then x is listening to a song, and that for all x, if x listens to a song, then x is a carpenter we can infer that for all x, if x were rich, then x is a carpenter. From the fact that for all x, if x were rich, then x is a carpenter, and that there is at least one x for which if x were a carpenter, then x is a mechanic we can infer that there is at least one x for which if x were rich, then x is a mechanic. From the fact that for all x, x is rich or x is not a writer we can infer that for all x, if x were a writer, then x is rich. Finally, from the fact that for all x, if x were a writer, then x is rich, and that there is at least one x for which if x were rich, then x is a mechanic we can infer that there is at least one x for which if x were a writer, then x is a mechanic. Therefore, the answer is yes.