Consider the following premises. John is climbing a mountain or it is cold. Robert is not a server. If it is late, then Robert is a server. If John climbs a mountain, then it is late. Can we infer the following from them? If we can, name the inference rule being used: It is not cold.
 From the fact that if it is late, then Robert is a server, and that Robert is not a server we can infer that it is not late via modus tollens. From the fact that if John climbs a mountain, then it is late, and that it is not late we can infer that John is not climbing a mountain via modus tollens. Finally, from the fact that John is climbing a mountain or it is cold, and that John is not climbing a mountain we can infer that it is cold via disjunctive syllogism, which contradicts that It is not cold. Therefore, the answer is no.