Consider the following premises. Elisabeth is a bartender or it is not cold. If Elisabeth were a bartender, then it is late. Can we infer the following from them? If we can, name the inference rule being used: The fact that it is cold does not imply that it is late.
 From the fact that Elisabeth is a bartender or it is not cold we can infer that if it is cold, then Elisabeth is a bartender via rewriting. Finally, from the fact that if it is cold, then Elisabeth is a bartender, and that if Elisabeth were a bartender, then it is late we can infer that if it is cold, then it is late via transitivity, which contradicts that The fact that it is cold does not imply that it is late. Therefore, the answer is no.