Consider the following premises. There is at least one x_15 for which if x_15 were a poet, then x_15 is sleeping. For all x_15, x_15 is a poet if and only if x_15 will make tea. For all x_15, if x_15 were a poet, then x_15 is making tea. For all x_15, if x_15 sleeps, then x_15 is not fast. For all x_15, x_15 is fast. Can we infer the following from them? If we can, name the inference rule being used: For all x_15, x_15 will make tea.
 From the fact that for all x_15, if x_15 sleeps, then x_15 is not fast, and that for all x_15, x_15 is fast we can infer that for all x_15, x_15 will not sleep via universal modus tollens. From the fact that there is at least one x_15 for which if x_15 were a poet, then x_15 is sleeping, and that for all x_15, x_15 will not sleep we can infer that there is at least one x_15 for which x_15 is not a poet via existential modus tollens. From the fact that for all x_15, x_15 is a poet if and only if x_15 will make tea we can infer that for all x_15, if x_15 makes tea, then x_15 is a poet via universal biconditional elimination. From the fact that for all x_15, if x_15 makes tea, then x_15 is a poet, and that for all x_15, if x_15 were a poet, then x_15 is making tea we can infer that for all x_15, x_15 will make tea if and only if x_15 is a poet via universal biconditional introduction. Finally, from the fact that for all x_15, x_15 will make tea if and only if x_15 is a poet, and that there is at least one x_15 for which x_15 is not a poet we can infer that there is at least one x_15 for which x_15 will not make tea via existential biconditional elimination, which contradicts that For all x_15, x_15 will make tea. Therefore, the answer is no.