Consider the following premises. Charles is sleeping if and only if James is cooking. Charles is sleeping or John is climbing a mountain. James is not cooking. Can we infer the following from them? If we can, name the inference rule being used: Karen is a musician or John is climbing a mountain.
 From the fact that Charles is sleeping if and only if James is cooking we can infer that if Charles sleeps, then James is cooking via biconditional elimination. From the fact that if Charles sleeps, then James is cooking, and that James is not cooking we can infer that Charles is not sleeping via modus tollens. From the fact that Charles is not sleeping we can infer that Charles is not sleeping or Karen is a musician via addition. Finally, from the fact that Charles is not sleeping or Karen is a musician, and that Charles is sleeping or John is climbing a mountain we can infer that Karen is a musician or John is climbing a mountain via resolution. Therefore, the answer is yes.