Consider the following premises. Barbara is making tea or James is not excited. If Barbara makes tea, then it is overcast. James is excited. Can we infer the following from them? If we can, name the inference rule being used: It is not overcast.
 From the fact that Barbara is making tea or James is not excited we can infer that if James were excited, then Barbara is making tea via rewriting. From the fact that if James were excited, then Barbara is making tea, and that James is excited we can infer that Barbara is making tea via modus ponens. Finally, from the fact that if Barbara makes tea, then it is overcast, and that Barbara is making tea we can infer that it is overcast via modus ponens, which contradicts that It is not overcast. Therefore, the answer is no.