Consider the following premises. It is not raining or Sarah is excited. If it is cloudy, then it is windy. It is not windy. It is cloudy or it is not windy. It is raining or it is cloudy. Can we infer the following from them? If we can, name the inference rule being used: Sarah is excited.
 From the fact that it is raining or it is cloudy, and that it is not raining or Sarah is excited we can infer that it is cloudy or Sarah is excited via resolution. From the fact that it is cloudy or it is not windy we can infer that if it is windy, then it is cloudy via rewriting. From the fact that if it is windy, then it is cloudy, and that if it is cloudy, then it is windy we can infer that it is windy if and only if it is cloudy via biconditional introduction. From the fact that it is windy if and only if it is cloudy, and that it is not windy we can infer that it is not cloudy via biconditional elimination. Finally, from the fact that it is cloudy or Sarah is excited, and that it is not cloudy we can infer that Sarah is excited via disjunctive syllogism. Therefore, the answer is yes.