Consider the following premises. If Charles climbs a mountain, then it is cold. If Richard were fast, then Charles is climbing a mountain. For all x_10, x_10 is not a lawyer or x_10 will drink water. If Richard drinks water, then it is cold. For all x_10, x_10 is a lawyer or x_10 is fast. Can we infer the following from them? If we can, name the inference rule being used: It is not cold.
 From the fact that for all x_10, x_10 is a lawyer or x_10 is fast, and that for all x_10, x_10 is not a lawyer or x_10 will drink water we can infer that for all x_10, x_10 is fast or x_10 will drink water via universal resolution. From the fact that for all x_10, x_10 is fast or x_10 will drink water we can infer that Richard is fast or Richard is drinking water via universal instantiation. From the fact that if Richard were fast, then Charles is climbing a mountain, and that if Charles climbs a mountain, then it is cold we can infer that if Richard were fast, then it is cold via transitivity. Finally, from the fact that if Richard were fast, then it is cold, that if Richard drinks water, then it is cold, and that Richard is fast or Richard is drinking water we can infer that it is cold via disjunction elimination, which contradicts that It is not cold. Therefore, the answer is no.