Consider the following premises. For all x_6, if x_6 were excited, then x_6 is playing squash. For all x_6, if x_6 drinks water, then x_6 is excited. There is at least one x_6 for which x_6 is a writer or x_6 will work. For all x_6, x_6 is not a writer or x_6 will drink water. For all x_6, if x_6 works, then x_6 is playing squash. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 will play squash.
 From the fact that there is at least one x_6 for which x_6 is a writer or x_6 will work, and that for all x_6, x_6 is not a writer or x_6 will drink water we can infer that there is at least one x_6 for which x_6 will work or x_6 will drink water via existential resolution. From the fact that for all x_6, if x_6 drinks water, then x_6 is excited, and that for all x_6, if x_6 were excited, then x_6 is playing squash we can infer that for all x_6, if x_6 drinks water, then x_6 is playing squash via universal transitivity. Finally, from the fact that for all x_6, if x_6 works, then x_6 is playing squash, that for all x_6, if x_6 drinks water, then x_6 is playing squash, and that there is at least one x_6 for which x_6 will work or x_6 will drink water we can infer that there is at least one x_6 for which x_6 will play squash via existential disjunction elimination. Therefore, the answer is yes.