Consider the following premises. For all x_2, x_2 is a poet. For all x_2, x_2 will not play a game. For all x_2, x_2 will play a game or x_2 is a police officer. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_2 for which either x_2 is a police officer or x_2 is a poet are not true.
 From the fact that for all x_2, x_2 will play a game or x_2 is a police officer, and that for all x_2, x_2 will not play a game we can infer that for all x_2, x_2 is a police officer via universal disjunctive syllogism. Finally, from the fact that for all x_2, x_2 is a police officer, and that for all x_2, x_2 is a poet we can infer that for all x_2, x_2 is a police officer and x_2 is a poet via universal conjunction, which contradicts that There is at least one x_2 for which either x_2 is a police officer or x_2 is a poet are not true. Therefore, the answer is no.