Consider the following premises. Sarah is playing tennis. If Sarah plays tennis, then it is sunny. Elisabeth is climbing a mountain or it is not sunny. Can we infer the following from them? If we can, name the inference rule being used: Elisabeth is not climbing a mountain.
 From the fact that Elisabeth is climbing a mountain or it is not sunny we can infer that if it is sunny, then Elisabeth is climbing a mountain via rewriting. From the fact that if Sarah plays tennis, then it is sunny, and that Sarah is playing tennis we can infer that it is sunny via modus ponens. Finally, from the fact that if it is sunny, then Elisabeth is climbing a mountain, and that it is sunny we can infer that Elisabeth is climbing a mountain via modus ponens, which contradicts that Elisabeth is not climbing a mountain. Therefore, the answer is no.