Consider the following premises. For all x_5, if x_5 sleeps, then x_5 is playing tennis. For all x_5, x_5 will work. For all x_5, x_5 will sleep. For all x_5, if x_5 works, then x_5 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_5 for which either x_5 will play squash or x_5 will play tennis are not true.
 From the fact that for all x_5, if x_5 works, then x_5 is playing squash, and that for all x_5, x_5 will work we can infer that for all x_5, x_5 will play squash via universal modus ponens. From the fact that for all x_5, if x_5 sleeps, then x_5 is playing tennis, and that for all x_5, x_5 will sleep we can infer that for all x_5, x_5 will play tennis via universal modus ponens. Finally, from the fact that for all x_5, x_5 will play squash, and that for all x_5, x_5 will play tennis we can infer that for all x_5, x_5 will play squash and x_5 will play tennis via universal conjunction, which contradicts that There is at least one x_5 for which either x_5 will play squash or x_5 will play tennis are not true. Therefore, the answer is no.