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