Consider the following premises. For all x_8, if x_8 plays a game, then x_8 is taking a plane. For all x_8, if x_8 were a poet, then x_8 is taking a plane. For all x_8, if x_8 were a server, then x_8 is not taking a plane. There is at least one x_8 for which x_8 is a server or x_8 is sad. For all x_8, x_8 will play a game or x_8 is a poet. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 is not sad.
 From the fact that for all x_8, if x_8 plays a game, then x_8 is taking a plane, that for all x_8, if x_8 were a poet, then x_8 is taking a plane, and that for all x_8, x_8 will play a game or x_8 is a poet we can infer that for all x_8, x_8 will take a plane via universal disjunction elimination. From the fact that for all x_8, if x_8 were a server, then x_8 is not taking a plane, and that for all x_8, x_8 will take a plane we can infer that for all x_8, x_8 is not a server via universal modus tollens. Finally, from the fact that there is at least one x_8 for which x_8 is a server or x_8 is sad, and that for all x_8, x_8 is not a server we can infer that there is at least one x_8 for which x_8 is sad via existential disjunctive syllogism, which contradicts that For all x_8, x_8 is not sad. Therefore, the answer is no.