Consider the following premises. For all x, if x plays a game, then x is a poet. For all x, if x were a poet, then x is playing a game. For all x, if x plays a game, then x is a poet. Can we infer the following from them? There is at least one x for which the fact that x plays a game does not imply that x is a poet.
 From the fact that for all x, if x were a poet, then x is playing a game, and that for all x, if x plays a game, then x is a poet we can infer that for all x, x is a poet if and only if x will play a game. From the fact that for all x, x is a poet if and only if x will play a game we can infer that for all x, if x were a poet, then x is playing a game. From the fact that for all x, if x plays a game, then x is a poet, and that for all x, if x were a poet, then x is playing a game we can infer that for all x, x will play a game if and only if x is a poet. Finally, from the fact that for all x, x will play a game if and only if x is a poet we can infer that for all x, if x plays a game, then x is a poet, which contradicts that There is at least one x for which the fact that x plays a game does not imply that x is a poet. Therefore, the answer is no.