Consider the following premises. For all x, x will play a game or x is not a sailor. For all x, x is a sailor. For all x, x will play a game or x will not play squash. Can we infer the following from them? If we can, name the inference rule being used: For all x, x will play a game.
 From the fact that for all x, x will play a game or x is not a sailor we can infer that for all x, if x were a sailor, then x is playing a game via universal rewriting. From the fact that for all x, x will play a game or x will not play squash we can infer that for all x, if x plays squash, then x is playing a game via universal rewriting. From the fact that for all x, x is a sailor we can infer that for all x, x is a sailor or x will play squash via universal addition. Finally, from the fact that for all x, if x were a sailor, then x is playing a game, that for all x, if x plays squash, then x is playing a game, and that for all x, x is a sailor or x will play squash we can infer that for all x, x will play a game via universal disjunction elimination. Therefore, the answer is yes.