Consider the following premises. For all x_7, x_7 is a poet or x_7 will not play a game. There is at least one x_7 for which if x_7 were a poet, then x_7 is climbing a mountain. For all x_7, if x_7 climbs a mountain, then x_7 is playing a game. Can we infer the following from them? For all x_7, if is not true that x_7 will play a game if and only if x_7 is a poet.
 From the fact that for all x_7, x_7 is a poet or x_7 will not play a game we can infer that for all x_7, if x_7 plays a game, then x_7 is a poet. From the fact that there is at least one x_7 for which if x_7 were a poet, then x_7 is climbing a mountain, and that for all x_7, if x_7 climbs a mountain, then x_7 is playing a game we can infer that there is at least one x_7 for which if x_7 were a poet, then x_7 is playing a game. Finally, from the fact that for all x_7, if x_7 plays a game, then x_7 is a poet, and that there is at least one x_7 for which if x_7 were a poet, then x_7 is playing a game we can infer that there is at least one x_7 for which x_7 will play a game if and only if x_7 is a poet, which contradicts that For all x_7, if is not true that x_7 will play a game if and only if x_7 is a poet. Therefore, the answer is no.