Consider the following premises. Michael is a carpenter or William is not listening to a song. William is listening to a song or Michael is not a carpenter. Can we infer the following from them? If we can, name the inference rule being used: The fact that Michael were a carpenter does not imply that William is listening to a song.
 From the fact that Michael is a carpenter or William is not listening to a song we can infer that if William listens to a song, then Michael is a carpenter via rewriting. Finally, from the fact that William is listening to a song or Michael is not a carpenter we can infer that if Michael were a carpenter, then William is listening to a song via rewriting, which contradicts that The fact that Michael were a carpenter does not imply that William is listening to a song. Therefore, the answer is no.