Consider the following premises. It is not raining or Thomas is a politician. It is raining or Mary is reading a book. If Mary reads a book, then John is a janitor. John is a janitor or Thomas is not a politician. Can we infer the following from them? If we can, name the inference rule being used: John is not a janitor.
 From the fact that it is raining or Mary is reading a book, and that it is not raining or Thomas is a politician we can infer that Mary is reading a book or Thomas is a politician via resolution. From the fact that John is a janitor or Thomas is not a politician we can infer that if Thomas were a politician, then John is a janitor via rewriting. Finally, from the fact that if Mary reads a book, then John is a janitor, that if Thomas were a politician, then John is a janitor, and that Mary is reading a book or Thomas is a politician we can infer that John is a janitor via disjunction elimination, which contradicts that John is not a janitor. Therefore, the answer is no.