Consider the following premises. For all x, x is a janitor or x is sad. For all x, if x takes a plane, then x is playing a game. For all x, if x were sad, then x is playing a game. For all x, if x were a janitor, then x is taking a plane. For all x, if x takes a plane, then x is a janitor. Can we infer the following from them? There is at least one x for which x will not play a game.
 From the fact that for all x, if x takes a plane, then x is a janitor, and that for all x, if x were a janitor, then x is taking a plane we can infer that for all x, x will take a plane if and only if x is a janitor. From the fact that for all x, x will take a plane if and only if x is a janitor we can infer that for all x, if x were a janitor, then x is taking a plane. From the fact that for all x, if x were a janitor, then x is taking a plane, and that for all x, if x takes a plane, then x is playing a game we can infer that for all x, if x were a janitor, then x is playing a game. Finally, from the fact that for all x, if x were a janitor, then x is playing a game, that for all x, if x were sad, then x is playing a game, and that for all x, x is a janitor or x is sad we can infer that for all x, x will play a game, which contradicts that There is at least one x for which x will not play a game. Therefore, the answer is no.