Consider the following premises. For all x_14, x_14 will not climb a mountain. There is at least one x_14 for which x_14 will climb a mountain or x_14 is not a taxi driver. For all x_14, x_14 is a taxi driver if and only if x_14 will make tea. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_14 for which x_14 will not make tea.
 From the fact that for all x_14, x_14 is a taxi driver if and only if x_14 will make tea we can infer that for all x_14, if x_14 makes tea, then x_14 is a taxi driver via universal biconditional elimination. From the fact that there is at least one x_14 for which x_14 will climb a mountain or x_14 is not a taxi driver we can infer that there is at least one x_14 for which if x_14 were a taxi driver, then x_14 is climbing a mountain via existential rewriting. From the fact that for all x_14, if x_14 makes tea, then x_14 is a taxi driver, and that there is at least one x_14 for which if x_14 were a taxi driver, then x_14 is climbing a mountain we can infer that there is at least one x_14 for which if x_14 makes tea, then x_14 is climbing a mountain via existential transitivity. Finally, from the fact that there is at least one x_14 for which if x_14 makes tea, then x_14 is climbing a mountain, and that for all x_14, x_14 will not climb a mountain we can infer that there is at least one x_14 for which x_14 will not make tea via existential modus tollens. Therefore, the answer is yes.