Consider the following premises. Susan is running if and only if Barbara is a writer. It is not sunny or Barbara is a writer. If John listens to a song, then Susan is running. It is sunny or John is listening to a song. Can we infer the following from them? Susan is running.
 From the fact that Susan is running if and only if Barbara is a writer we can infer that if Barbara were a writer, then Susan is running. From the fact that it is sunny or John is listening to a song, and that it is not sunny or Barbara is a writer we can infer that John is listening to a song or Barbara is a writer. Finally, from the fact that if John listens to a song, then Susan is running, that if Barbara were a writer, then Susan is running, and that John is listening to a song or Barbara is a writer we can infer that Susan is running. Therefore, the answer is yes.