Consider the following premises. For all x, x will not play squash. For all x, x will play squash. Can we infer the following from them? If we can, name the inference rule being used: For all x, x is a writer.
 From the fact that for all x, x will play squash we can infer that for all x, x will play squash or x is a writer via universal addition. Finally, from the fact that for all x, x will play squash or x is a writer, and that for all x, x will not play squash we can infer that for all x, x is a writer via universal disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.