Consider the following premises. James is writing a letter if and only if it is cloudy. For all x_16, x_16 is a nurse or x_16 is happy. James is writing a letter or Barbara is not happy. Barbara is not a nurse or it is cloudy. Can we infer the following from them? If we can, name the inference rule being used: James is writing a letter.
 From the fact that for all x_16, x_16 is a nurse or x_16 is happy we can infer that Barbara is a nurse or Barbara is happy via universal instantiation. From the fact that James is writing a letter or Barbara is not happy we can infer that if Barbara were happy, then James is writing a letter via rewriting. From the fact that Barbara is a nurse or Barbara is happy, and that Barbara is not a nurse or it is cloudy we can infer that Barbara is happy or it is cloudy via resolution. From the fact that James is writing a letter if and only if it is cloudy we can infer that if it is cloudy, then James is writing a letter via biconditional elimination. Finally, from the fact that if Barbara were happy, then James is writing a letter, that if it is cloudy, then James is writing a letter, and that Barbara is happy or it is cloudy we can infer that James is writing a letter via disjunction elimination. Therefore, the answer is yes.