Consider the following premises. If Thomas drives a car, then it is sunny. Thomas is driving a car or Karen is not writing a letter. If it is sunny, then it is cloudy. Can we infer the following from them? If we can, name the inference rule being used: The fact that Karen writes a letter does not imply that it is cloudy.
 From the fact that Thomas is driving a car or Karen is not writing a letter we can infer that if Karen writes a letter, then Thomas is driving a car via rewriting. From the fact that if Karen writes a letter, then Thomas is driving a car, and that if Thomas drives a car, then it is sunny we can infer that if Karen writes a letter, then it is sunny via transitivity. Finally, from the fact that if Karen writes a letter, then it is sunny, and that if it is sunny, then it is cloudy we can infer that if Karen writes a letter, then it is cloudy via transitivity, which contradicts that The fact that Karen writes a letter does not imply that it is cloudy. Therefore, the answer is no.