Consider the following premises. If Joseph were rich, then Susan is sleeping. If Susan sleeps, then Joseph is rich. Joseph is rich. Can we infer the following from them? Susan is not sleeping.
 From the fact that if Joseph were rich, then Susan is sleeping, and that if Susan sleeps, then Joseph is rich we can infer that Joseph is rich if and only if Susan is sleeping. From the fact that Joseph is rich if and only if Susan is sleeping we can infer that if Joseph were rich, then Susan is sleeping. Finally, from the fact that if Joseph were rich, then Susan is sleeping, and that Joseph is rich we can infer that Susan is sleeping, which contradicts that Susan is not sleeping. Therefore, the answer is no.