Consider the following premises. If Charles cooks, then John is running. If it rains, then Charles is cooking. If John goes running, then it is raining. John is not running. Can we infer the following from them? If we can, name the inference rule being used: Charles is cooking.
 From the fact that if John goes running, then it is raining, and that if it rains, then Charles is cooking we can infer that if John goes running, then Charles is cooking via transitivity. From the fact that if Charles cooks, then John is running, and that if John goes running, then Charles is cooking we can infer that Charles is cooking if and only if John is running via biconditional introduction. Finally, from the fact that Charles is cooking if and only if John is running, and that John is not running we can infer that Charles is not cooking via biconditional elimination, which contradicts that Charles is cooking. Therefore, the answer is no.