Consider the following premises. For all x_5, x_5 is a taxi driver or x_5 will play squash. There is at least one x_5 for which x_5 is not a taxi driver. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_5 for which x_5 will play squash or x_5 will write a letter.
 From the fact that for all x_5, x_5 is a taxi driver or x_5 will play squash, and that there is at least one x_5 for which x_5 is not a taxi driver we can infer that there is at least one x_5 for which x_5 will play squash via existential disjunctive syllogism. Finally, from the fact that there is at least one x_5 for which x_5 will play squash we can infer that there is at least one x_5 for which x_5 will play squash or x_5 will write a letter via existential addition. Therefore, the answer is yes.