Consider the following premises. For all x_9, x_9 will cook if and only if x_9 will drink water. For all x_9, if x_9 sleeps, then x_9 is a lawyer. There is at least one x_9 for which x_9 will drink water if and only if x_9 will sleep. For all x_9, x_9 is not a lawyer. Can we infer the following from them? If we can, name the inference rule being used: For all x_9, x_9 will cook.
 From the fact that for all x_9, if x_9 sleeps, then x_9 is a lawyer, and that for all x_9, x_9 is not a lawyer we can infer that for all x_9, x_9 will not sleep via universal modus tollens. From the fact that there is at least one x_9 for which x_9 will drink water if and only if x_9 will sleep, and that for all x_9, x_9 will not sleep we can infer that there is at least one x_9 for which x_9 will not drink water via existential biconditional elimination. Finally, from the fact that for all x_9, x_9 will cook if and only if x_9 will drink water, and that there is at least one x_9 for which x_9 will not drink water we can infer that there is at least one x_9 for which x_9 will not cook via existential biconditional elimination, which contradicts that For all x_9, x_9 will cook. Therefore, the answer is no.