Consider the following premises. Joseph is a bartender. Elisabeth is a janitor or Joseph is not a bartender. If Elisabeth were a janitor, then Joseph is a bartender. Can we infer the following from them? Elisabeth is not a janitor.
 From the fact that Elisabeth is a janitor or Joseph is not a bartender we can infer that if Joseph were a bartender, then Elisabeth is a janitor. From the fact that if Elisabeth were a janitor, then Joseph is a bartender, and that if Joseph were a bartender, then Elisabeth is a janitor we can infer that Elisabeth is a janitor if and only if Joseph is a bartender. From the fact that Elisabeth is a janitor if and only if Joseph is a bartender we can infer that if Joseph were a bartender, then Elisabeth is a janitor. Finally, from the fact that if Joseph were a bartender, then Elisabeth is a janitor, and that Joseph is a bartender we can infer that Elisabeth is a janitor, which contradicts that Elisabeth is not a janitor. Therefore, the answer is no.