Consider the following premises. For all x_10, x_10 will climb a mountain or x_10 is a carpenter. For all x_10, x_10 will not climb a mountain or x_10 is a cashier. For all x_10, x_10 is not fast. For all x_10, x_10 is a carpenter if and only if x_10 is fast. Can we infer the following from them? If we can, name the inference rule being used: For all x_10, x_10 is a cashier or x_10 will drink water.
 From the fact that for all x_10, x_10 will climb a mountain or x_10 is a carpenter, and that for all x_10, x_10 will not climb a mountain or x_10 is a cashier we can infer that for all x_10, x_10 is a carpenter or x_10 is a cashier via universal resolution. From the fact that for all x_10, x_10 is a carpenter if and only if x_10 is fast, and that for all x_10, x_10 is not fast we can infer that for all x_10, x_10 is not a carpenter via universal biconditional elimination. From the fact that for all x_10, x_10 is a carpenter or x_10 is a cashier, and that for all x_10, x_10 is not a carpenter we can infer that for all x_10, x_10 is a cashier via universal disjunctive syllogism. Finally, from the fact that for all x_10, x_10 is a cashier we can infer that for all x_10, x_10 is a cashier or x_10 will drink water via universal addition. Therefore, the answer is yes.