Consider the following premises. It is cold or Charles is a mechanic. If it rains, then James is a writer. If Charles were a mechanic, then it is raining. If James reads a book, then James is a writer. If it is cold, then James is reading a book. Can we infer the following from them? If we can, name the inference rule being used: James is not a writer.
 From the fact that if it is cold, then James is reading a book, and that if James reads a book, then James is a writer we can infer that if it is cold, then James is a writer via transitivity. From the fact that if Charles were a mechanic, then it is raining, and that if it rains, then James is a writer we can infer that if Charles were a mechanic, then James is a writer via transitivity. Finally, from the fact that if it is cold, then James is a writer, that if Charles were a mechanic, then James is a writer, and that it is cold or Charles is a mechanic we can infer that James is a writer via disjunction elimination, which contradicts that James is not a writer. Therefore, the answer is no.