Consider the following premises. For all y_3, y_3 is a cashier or y_3 is excited. If James were excited, then Karen is running. For all y_3, y_3 is not a cashier. Can we infer the following from them? If we can, name the inference rule being used: Karen is not running.
 From the fact that for all y_3, y_3 is a cashier or y_3 is excited, and that for all y_3, y_3 is not a cashier we can infer that for all y_3, y_3 is excited via universal disjunctive syllogism. From the fact that for all y_3, y_3 is excited we can infer that James is excited via universal instantiation. Finally, from the fact that if James were excited, then Karen is running, and that James is excited we can infer that Karen is running via modus ponens, which contradicts that Karen is not running. Therefore, the answer is no.