Consider the following premises. John is an astronaut or it is not late. It is late or John is not an astronaut. Can we infer the following from them? If we can, name the inference rule being used: If John were an astronaut, then it is late.
 From the fact that John is an astronaut or it is not late we can infer that if it is late, then John is an astronaut via rewriting. Finally, from the fact that it is late or John is not an astronaut we can infer that if John were an astronaut, then it is late via rewriting. Therefore, the answer is yes.