Consider the following premises. For all x_12, x_12 will go running if and only if x_12 is a poet. There is at least one x_12 for which x_12 will play a game or x_12 will not go running. For all x_12, if x_12 plays a game, then x_12 is a poet. Can we infer the following from them? If we can, name the inference rule being used: For all x_12, if is not true that x_12 is a poet if and only if x_12 will go running.
That contradicts the premises. Therefore the answer is no.