Consider the following premises. If David sleeps, then Sarah is a doctor. Barbara is driving a car or James is not fast. If Sarah were a doctor, then James is fast. Can we infer the following from them? If we can, name the inference rule being used: The fact that David sleeps does not imply that Barbara is driving a car.
 From the fact that Barbara is driving a car or James is not fast we can infer that if James were fast, then Barbara is driving a car via rewriting. From the fact that if Sarah were a doctor, then James is fast, and that if James were fast, then Barbara is driving a car we can infer that if Sarah were a doctor, then Barbara is driving a car via transitivity. Finally, from the fact that if David sleeps, then Sarah is a doctor, and that if Sarah were a doctor, then Barbara is driving a car we can infer that if David sleeps, then Barbara is driving a car via transitivity, which contradicts that The fact that David sleeps does not imply that Barbara is driving a car. Therefore, the answer is no.