Consider the following premises. It is not late. For all x_12, x_12 will climb a mountain if and only if x_12 will work. If Thomas climbs a mountain, then it is late. Can we infer the following from them? If we can, name the inference rule being used: Thomas is not working.
 From the fact that for all x_12, x_12 will climb a mountain if and only if x_12 will work we can infer that Thomas is climbing a mountain if and only if Thomas is working via universal instantiation. From the fact that Thomas is climbing a mountain if and only if Thomas is working we can infer that if Thomas works, then Thomas is climbing a mountain via biconditional elimination. From the fact that if Thomas works, then Thomas is climbing a mountain, and that if Thomas climbs a mountain, then it is late we can infer that if Thomas works, then it is late via transitivity. Finally, from the fact that if Thomas works, then it is late, and that it is not late we can infer that Thomas is not working via modus tollens. Therefore, the answer is yes.