Consider the following premises. For all x_8, x_8 will sleep or x_8 will drink water. There is at least one x_8 for which if x_8 drinks water, then x_8 is a server. For all x_8, if x_8 sleeps, then x_8 is a server. For all x_8, x_8 will write a letter. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, either x_8 will write a letter or x_8 is a server are not true.
 From the fact that for all x_8, if x_8 sleeps, then x_8 is a server, that there is at least one x_8 for which if x_8 drinks water, then x_8 is a server, and that for all x_8, x_8 will sleep or x_8 will drink water we can infer that there is at least one x_8 for which x_8 is a server via existential disjunction elimination. Finally, from the fact that for all x_8, x_8 will write a letter, and that there is at least one x_8 for which x_8 is a server we can infer that there is at least one x_8 for which x_8 will write a letter and x_8 is a server via existential conjunction, which contradicts that For all x_8, either x_8 will write a letter or x_8 is a server are not true. Therefore, the answer is no.