Consider the following premises. There is at least one x_12 for which if x_12 were a politician, then x_12 is playing a game. For all x_12, if x_12 were an office clerk, then x_12 is a politician. For all x_12, x_12 is a soldier if and only if x_12 will climb a mountain. For all x_12, if x_12 climbs a mountain, then x_12 is an office clerk. Can we infer the following from them? There is at least one x_12 for which if x_12 were a soldier, then x_12 is playing a game.
 From the fact that for all x_12, x_12 is a soldier if and only if x_12 will climb a mountain we can infer that for all x_12, if x_12 were a soldier, then x_12 is climbing a mountain. From the fact that for all x_12, if x_12 climbs a mountain, then x_12 is an office clerk, and that for all x_12, if x_12 were an office clerk, then x_12 is a politician we can infer that for all x_12, if x_12 climbs a mountain, then x_12 is a politician. From the fact that for all x_12, if x_12 climbs a mountain, then x_12 is a politician, and that there is at least one x_12 for which if x_12 were a politician, then x_12 is playing a game we can infer that there is at least one x_12 for which if x_12 climbs a mountain, then x_12 is playing a game. Finally, from the fact that for all x_12, if x_12 were a soldier, then x_12 is climbing a mountain, and that there is at least one x_12 for which if x_12 climbs a mountain, then x_12 is playing a game we can infer that there is at least one x_12 for which if x_12 were a soldier, then x_12 is playing a game. Therefore, the answer is yes.