Consider the following premises. Richard is not an astronaut. It is windy if and only if Richard is an astronaut. It is not late or Charles is climbing a mountain. Thomas is cooking or it is late. Thomas is not cooking or it is windy. Can we infer the following from them? If we can, name the inference rule being used: Charles is climbing a mountain.
 From the fact that Thomas is cooking or it is late, and that Thomas is not cooking or it is windy we can infer that it is late or it is windy via resolution. From the fact that it is late or it is windy, and that it is not late or Charles is climbing a mountain we can infer that it is windy or Charles is climbing a mountain via resolution. From the fact that it is windy if and only if Richard is an astronaut, and that Richard is not an astronaut we can infer that it is not windy via biconditional elimination. Finally, from the fact that it is windy or Charles is climbing a mountain, and that it is not windy we can infer that Charles is climbing a mountain via disjunctive syllogism. Therefore, the answer is yes.