Consider the following premises. For all x_22, x_22 will drink water if and only if x_22 will make tea. For all x_22, x_22 is a poet or x_22 is an office clerk. For all x_22, if x_22 were an office clerk, then x_22 is driving a car. For all x_22, if x_22 drives a car, then x_22 is drinking water. There is at least one x_22 for which x_22 is not a poet. Can we infer the following from them? If we can, name the inference rule being used: For all x_22, x_22 will not make tea.
 From the fact that for all x_22, x_22 is a poet or x_22 is an office clerk, and that there is at least one x_22 for which x_22 is not a poet we can infer that there is at least one x_22 for which x_22 is an office clerk via existential disjunctive syllogism. From the fact that for all x_22, if x_22 were an office clerk, then x_22 is driving a car, and that for all x_22, if x_22 drives a car, then x_22 is drinking water we can infer that for all x_22, if x_22 were an office clerk, then x_22 is drinking water via universal transitivity. From the fact that for all x_22, x_22 will drink water if and only if x_22 will make tea we can infer that for all x_22, if x_22 drinks water, then x_22 is making tea via universal biconditional elimination. From the fact that for all x_22, if x_22 were an office clerk, then x_22 is drinking water, and that there is at least one x_22 for which x_22 is an office clerk we can infer that there is at least one x_22 for which x_22 will drink water via existential modus ponens. Finally, from the fact that for all x_22, if x_22 drinks water, then x_22 is making tea, and that there is at least one x_22 for which x_22 will drink water we can infer that there is at least one x_22 for which x_22 will make tea via existential modus ponens, which contradicts that For all x_22, x_22 will not make tea. Therefore, the answer is no.