Consider the following premises. Karen is driving a car or Elisabeth is not a janitor. If Karen drives a car, then Susan is sleeping. Elisabeth is a janitor. Can we infer the following from them? Susan is sleeping.
 From the fact that Karen is driving a car or Elisabeth is not a janitor we can infer that if Elisabeth were a janitor, then Karen is driving a car. From the fact that if Elisabeth were a janitor, then Karen is driving a car, and that if Karen drives a car, then Susan is sleeping we can infer that if Elisabeth were a janitor, then Susan is sleeping. Finally, from the fact that if Elisabeth were a janitor, then Susan is sleeping, and that Elisabeth is a janitor we can infer that Susan is sleeping. Therefore, the answer is yes.