Consider the following premises. It is cloudy. If Michael goes running, then Elisabeth is making tea. If Elisabeth makes tea, then it is not cloudy. If Elisabeth makes tea, then Michael is running. Can we infer the following from them? If we can, name the inference rule being used: Michael is running.
 From the fact that if Elisabeth makes tea, then it is not cloudy, and that it is cloudy we can infer that Elisabeth is not making tea via modus tollens. From the fact that if Elisabeth makes tea, then Michael is running, and that if Michael goes running, then Elisabeth is making tea we can infer that Elisabeth is making tea if and only if Michael is running via biconditional introduction. Finally, from the fact that Elisabeth is making tea if and only if Michael is running, and that Elisabeth is not making tea we can infer that Michael is not running via biconditional elimination, which contradicts that Michael is running. Therefore, the answer is no.