Consider the following premises. For all x_16, if x_16 were fast, then x_16 is climbing a mountain. There is at least one x_16 for which x_16 is fast or x_16 will not cook. For all x_16, x_16 will climb a mountain or x_16 is not a lawyer. For all x_16, x_16 will drink water or x_16 will cook. For all x_16, x_16 will not drink water or x_16 is a lawyer. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_16 for which x_16 will climb a mountain.
 From the fact that for all x_16, x_16 will drink water or x_16 will cook, and that for all x_16, x_16 will not drink water or x_16 is a lawyer we can infer that for all x_16, x_16 will cook or x_16 is a lawyer via universal resolution. From the fact that there is at least one x_16 for which x_16 is fast or x_16 will not cook we can infer that there is at least one x_16 for which if x_16 cooks, then x_16 is fast via existential rewriting. From the fact that there is at least one x_16 for which if x_16 cooks, then x_16 is fast, and that for all x_16, if x_16 were fast, then x_16 is climbing a mountain we can infer that there is at least one x_16 for which if x_16 cooks, then x_16 is climbing a mountain via existential transitivity. From the fact that for all x_16, x_16 will climb a mountain or x_16 is not a lawyer we can infer that for all x_16, if x_16 were a lawyer, then x_16 is climbing a mountain via universal rewriting. Finally, from the fact that there is at least one x_16 for which if x_16 cooks, then x_16 is climbing a mountain, that for all x_16, if x_16 were a lawyer, then x_16 is climbing a mountain, and that for all x_16, x_16 will cook or x_16 is a lawyer we can infer that there is at least one x_16 for which x_16 will climb a mountain via existential disjunction elimination. Therefore, the answer is yes.