Consider the following premises. For all x_12, if x_12 plays a game, then x_12 is an astronaut. For all x_12, x_12 will play a game if and only if x_12 is an astronaut. For all x_12, x_12 will play a game if and only if x_12 is a musician. For all x_12, x_12 is not a sailor. For all x_12, x_12 is a sailor if and only if x_12 is a musician. Can we infer the following from them? There is at least one x_12 for which x_12 is an astronaut.
 From the fact that for all x_12, x_12 is a sailor if and only if x_12 is a musician, and that for all x_12, x_12 is not a sailor we can infer that for all x_12, x_12 is not a musician. From the fact that for all x_12, x_12 will play a game if and only if x_12 is an astronaut we can infer that for all x_12, if x_12 were an astronaut, then x_12 is playing a game. From the fact that for all x_12, if x_12 were an astronaut, then x_12 is playing a game, and that for all x_12, if x_12 plays a game, then x_12 is an astronaut we can infer that for all x_12, x_12 is an astronaut if and only if x_12 will play a game. From the fact that for all x_12, x_12 will play a game if and only if x_12 is a musician, and that for all x_12, x_12 is not a musician we can infer that for all x_12, x_12 will not play a game. Finally, from the fact that for all x_12, x_12 is an astronaut if and only if x_12 will play a game, and that for all x_12, x_12 will not play a game we can infer that for all x_12, x_12 is not an astronaut, which contradicts that There is at least one x_12 for which x_12 is an astronaut. Therefore, the answer is no.