Consider the following premises. Thomas is an astronaut. Mary is not listening to a song. Mary is listening to a song or it is not raining. Can we infer the following from them? If we can, name the inference rule being used: It is raining.
 From the fact that Mary is listening to a song or it is not raining we can infer that if it rains, then Mary is listening to a song via rewriting. Finally, from the fact that if it rains, then Mary is listening to a song, and that Mary is not listening to a song we can infer that it is not raining via modus tollens, which contradicts that It is raining. Therefore, the answer is no.