Consider the following premises. If John were poor, then Joseph is running. If David were a cashier, then Joseph is running. David is a cashier or John is poor. If Joseph goes running, then John is poor. Can we infer the following from them? Joseph is not running.
 From the fact that if John were poor, then Joseph is running, and that if Joseph goes running, then John is poor we can infer that John is poor if and only if Joseph is running. From the fact that John is poor if and only if Joseph is running we can infer that if John were poor, then Joseph is running. Finally, from the fact that if David were a cashier, then Joseph is running, that if John were poor, then Joseph is running, and that David is a cashier or John is poor we can infer that Joseph is running, which contradicts that Joseph is not running. Therefore, the answer is no.