Consider the following premises. For all x_9, x_9 will climb a mountain if and only if x_9 will make tea. There is at least one x_9 for which if x_9 drinks water, then x_9 is a taxi driver. For all x_9, x_9 will drink water if and only if x_9 will climb a mountain. For all x_9, x_9 is not a taxi driver. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_9 for which x_9 will not make tea.
 From the fact that there is at least one x_9 for which if x_9 drinks water, then x_9 is a taxi driver, and that for all x_9, x_9 is not a taxi driver we can infer that there is at least one x_9 for which x_9 will not drink water via existential modus tollens. From the fact that for all x_9, x_9 will drink water if and only if x_9 will climb a mountain, 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 climb a mountain via existential biconditional elimination. Finally, from the fact that for all x_9, x_9 will climb a mountain if and only if x_9 will make tea, and that there is at least one x_9 for which x_9 will not climb a mountain we can infer that there is at least one x_9 for which x_9 will not make tea via existential biconditional elimination. Therefore, the answer is yes.