Consider the following premises. Jennifer is a cashier or David is not happy. If David were not happy, then Barbara is sleeping. Barbara is sleeping if and only if Richard is running. Jennifer is not a cashier. Can we infer the following from them? Richard is running.
 From the fact that Barbara is sleeping if and only if Richard is running we can infer that if Barbara sleeps, then Richard is running. From the fact that Jennifer is a cashier or David is not happy we can infer that if David were happy, then Jennifer is a cashier. From the fact that if David were happy, then Jennifer is a cashier, and that Jennifer is not a cashier we can infer that David is not happy. From the fact that if David were not happy, then Barbara is sleeping, and that if Barbara sleeps, then Richard is running we can infer that if David were not happy, then Richard is running. Finally, from the fact that if David were not happy, then Richard is running, and that David is not happy we can infer that Richard is running. Therefore, the answer is yes.