Consider the following premises. Jessica is reading a book if and only if Susan is a writer. Robert is running if and only if Jessica is reading a book. For all x_12, x_12 will go running if and only if x_12 is a scientist. Robert is not a scientist. Can we infer the following from them? If we can, name the inference rule being used: Susan is a writer.
 From the fact that for all x_12, x_12 will go running if and only if x_12 is a scientist we can infer that Robert is running if and only if Robert is a scientist via universal instantiation. From the fact that Robert is running if and only if Robert is a scientist, and that Robert is not a scientist we can infer that Robert is not running via biconditional elimination. From the fact that Robert is running if and only if Jessica is reading a book, and that Robert is not running we can infer that Jessica is not reading a book via biconditional elimination. Finally, from the fact that Jessica is reading a book if and only if Susan is a writer, and that Jessica is not reading a book we can infer that Susan is not a writer via biconditional elimination, which contradicts that Susan is a writer. Therefore, the answer is no.