Consider the following premises. Karen is climbing a mountain or Jessica is not a doctor. Jessica is a doctor or it is not sunny. Can we infer the following from them? If we can, name the inference rule being used: The fact that it is sunny does not imply that Karen is climbing a mountain.
 From the fact that Karen is climbing a mountain or Jessica is not a doctor we can infer that if Jessica were a doctor, then Karen is climbing a mountain via rewriting. From the fact that Jessica is a doctor or it is not sunny we can infer that if it is sunny, then Jessica is a doctor via rewriting. Finally, from the fact that if it is sunny, then Jessica is a doctor, and that if Jessica were a doctor, then Karen is climbing a mountain we can infer that if it is sunny, then Karen is climbing a mountain via transitivity, which contradicts that The fact that it is sunny does not imply that Karen is climbing a mountain. Therefore, the answer is no.