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