Consider the following premises. It is raining or it is not cloudy. If it rains, then Linda is a carpenter. If it is late, then it is cloudy. Can we infer the following from them? If we can, name the inference rule being used: The fact that it is late does not imply that Linda is a carpenter.
 From the fact that it is raining or it is not cloudy we can infer that if it is cloudy, then it is raining via rewriting. From the fact that if it is cloudy, then it is raining, and that if it rains, then Linda is a carpenter we can infer that if it is cloudy, then Linda is a carpenter via transitivity. Finally, from the fact that if it is late, then it is cloudy, and that if it is cloudy, then Linda is a carpenter we can infer that if it is late, then Linda is a carpenter via transitivity, which contradicts that The fact that it is late does not imply that Linda is a carpenter. Therefore, the answer is no.