Consider the following premises. If Charles climbs a mountain, then it is cloudy. It is raining. If it is cloudy, then it is cold. If it rains, then Charles is climbing a mountain. 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 rains, then Charles is climbing a mountain, and that it is raining we can infer that Charles is climbing a mountain via modus ponens. From the fact that if Charles climbs a mountain, then it is cloudy, and that if it is cloudy, then it is cold we can infer that if Charles climbs a mountain, then it is cold via transitivity. Finally, from the fact that if Charles climbs a mountain, then it is cold, and that Charles is climbing a mountain we can infer that it is cold via modus ponens, which contradicts that It is not cold. Therefore, the answer is no.