Consider the following premises. William is cooking or Sarah is a lawyer. Sarah is not a lawyer or Patricia is a mechanic. If Elisabeth were a bartender, then James is reading a book. William is not cooking or Elisabeth is a bartender. If Patricia were a mechanic, 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 reading a book.
 From the fact that William is cooking or Sarah is a lawyer, and that William is not cooking or Elisabeth is a bartender we can infer that Sarah is a lawyer or Elisabeth is a bartender via resolution. From the fact that Sarah is a lawyer or Elisabeth is a bartender, and that Sarah is not a lawyer or Patricia is a mechanic we can infer that Elisabeth is a bartender or Patricia is a mechanic via resolution. Finally, from the fact that if Elisabeth were a bartender, then James is reading a book, that if Patricia were a mechanic, then James is reading a book, and that Elisabeth is a bartender or Patricia is a mechanic we can infer that James is reading a book via disjunction elimination, which contradicts that James is not reading a book. Therefore, the answer is no.