Consider the following premises. For all x_10, x_10 is a writer or x_10 will drink water. For all x_10, if x_10 drinks water, then x_10 is climbing a mountain. For all x_10, if x_10 works, then x_10 is climbing a mountain. For all x_10, if x_10 were an office clerk, then x_10 is not climbing a mountain. For all x_10, x_10 is not a writer or x_10 will work. For all x_10, x_10 is a carpenter if and only if x_10 is an office clerk. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_10 for which x_10 is a carpenter.
 From the fact that for all x_10, x_10 is a writer or x_10 will drink water, and that for all x_10, x_10 is not a writer or x_10 will work we can infer that for all x_10, x_10 will drink water or x_10 will work via universal resolution. From the fact that for all x_10, if x_10 drinks water, then x_10 is climbing a mountain, that for all x_10, if x_10 works, then x_10 is climbing a mountain, and that for all x_10, x_10 will drink water or x_10 will work we can infer that for all x_10, x_10 will climb a mountain via universal disjunction elimination. From the fact that for all x_10, if x_10 were an office clerk, then x_10 is not climbing a mountain, and that for all x_10, x_10 will climb a mountain we can infer that for all x_10, x_10 is not an office clerk via universal modus tollens. Finally, from the fact that for all x_10, x_10 is a carpenter if and only if x_10 is an office clerk, and that for all x_10, x_10 is not an office clerk we can infer that for all x_10, x_10 is not a carpenter via universal biconditional elimination, which contradicts that There is at least one x_10 for which x_10 is a carpenter. Therefore, the answer is no.