Consider the following premises. For all x_10, x_10 is a poet or x_10 is fast. There is at least one x_10 for which x_10 is a police officer. For all x_10, x_10 will not play tennis. For all x_10, x_10 is fast if and only if x_10 will play tennis. For all x_10, x_10 is not a poet or x_10 is a sailor. Can we infer the following from them? If we can, name the inference rule being used: For all x_10, either x_10 is a police officer or x_10 is a sailor are not true.
 From the fact that for all x_10, x_10 is fast if and only if x_10 will play tennis, and that for all x_10, x_10 will not play tennis we can infer that for all x_10, x_10 is not fast via universal biconditional elimination. From the fact that for all x_10, x_10 is a poet or x_10 is fast, and that for all x_10, x_10 is not a poet or x_10 is a sailor we can infer that for all x_10, x_10 is fast or x_10 is a sailor via universal resolution. From the fact that for all x_10, x_10 is fast or x_10 is a sailor, and that for all x_10, x_10 is not fast we can infer that for all x_10, x_10 is a sailor via universal disjunctive syllogism. Finally, from the fact that there is at least one x_10 for which x_10 is a police officer, and that for all x_10, x_10 is a sailor we can infer that there is at least one x_10 for which x_10 is a police officer and x_10 is a sailor via existential conjunction, which contradicts that For all x_10, either x_10 is a police officer or x_10 is a sailor are not true. Therefore, the answer is no.