Consider the following premises. For all x_1, x_1 is happy if and only if x_1 will cook. James is not happy. Can we infer the following from them? If we can, name the inference rule being used: James is cooking.
 From the fact that for all x_1, x_1 is happy if and only if x_1 will cook we can infer that James is happy if and only if James is cooking via universal instantiation. Finally, from the fact that James is happy if and only if James is cooking, and that James is not happy we can infer that James is not cooking via biconditional elimination, which contradicts that James is cooking. Therefore, the answer is no.