Consider the following premises. If David cooks, then it is cloudy. Sarah is not sleeping or David is cooking. If it is windy, then it is cloudy. Sarah is sleeping or it is windy. Can we infer the following from them? If we can, name the inference rule being used: It is not cloudy.
 From the fact that Sarah is sleeping or it is windy, and that Sarah is not sleeping or David is cooking we can infer that it is windy or David is cooking via resolution. Finally, from the fact that if it is windy, then it is cloudy, that if David cooks, then it is cloudy, and that it is windy or David is cooking we can infer that it is cloudy via disjunction elimination, which contradicts that It is not cloudy. Therefore, the answer is no.