Consider the following premises. Susan is sleeping or it is not cloudy. It is cloudy or Susan is not sleeping. Can we infer the following from them? If we can, name the inference rule being used: The fact that Susan sleeps does not imply that it is cloudy.
 From the fact that Susan is sleeping or it is not cloudy we can infer that if it is cloudy, then Susan is sleeping via rewriting. Finally, from the fact that it is cloudy or Susan is not sleeping we can infer that if Susan sleeps, then it is cloudy via rewriting, which contradicts that The fact that Susan sleeps does not imply that it is cloudy. Therefore, the answer is no.