Consider the following premises. There is at least one x_20 for which if x_20 were a taxi driver, then x_20 is fast. For all x_20, x_20 is a carpenter or x_20 will play squash. For all x_20, x_20 is a taxi driver or x_20 will not play squash. For all x_20, x_20 is not a carpenter. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_20 for which x_20 is fast or x_20 is a mechanic.
 From the fact that for all x_20, x_20 is a taxi driver or x_20 will not play squash we can infer that for all x_20, if x_20 plays squash, then x_20 is a taxi driver via universal rewriting. From the fact that for all x_20, if x_20 plays squash, then x_20 is a taxi driver, and that there is at least one x_20 for which if x_20 were a taxi driver, then x_20 is fast we can infer that there is at least one x_20 for which if x_20 plays squash, then x_20 is fast via existential transitivity. From the fact that for all x_20, x_20 is a carpenter or x_20 will play squash, and that for all x_20, x_20 is not a carpenter we can infer that for all x_20, x_20 will play squash via universal disjunctive syllogism. From the fact that there is at least one x_20 for which if x_20 plays squash, then x_20 is fast, and that for all x_20, x_20 will play squash we can infer that there is at least one x_20 for which x_20 is fast via existential modus ponens. Finally, from the fact that there is at least one x_20 for which x_20 is fast we can infer that there is at least one x_20 for which x_20 is fast or x_20 is a mechanic via existential addition. Therefore, the answer is yes.