Consider the following premises. For all x_10, if x_10 plays a game, then x_10 is a doctor. For all x_10, if x_10 were a lawyer, then x_10 is playing a game. For all x_10, x_10 is a lawyer if and only if x_10 will play a game. For all x_10, x_10 is not a doctor. Can we infer the following from them? There is at least one x_10 for which x_10 is a lawyer.
 From the fact that for all x_10, if x_10 plays a game, then x_10 is a doctor, and that for all x_10, x_10 is not a doctor we can infer that for all x_10, x_10 will not play a game. From the fact that for all x_10, x_10 is a lawyer if and only if x_10 will play a game we can infer that for all x_10, if x_10 plays a game, then x_10 is a lawyer. From the fact that for all x_10, if x_10 were a lawyer, then x_10 is playing a game, and that for all x_10, if x_10 plays a game, then x_10 is a lawyer we can infer that for all x_10, x_10 is a lawyer if and only if x_10 will play a game. From the fact that for all x_10, x_10 is a lawyer if and only if x_10 will play a game we can infer that for all x_10, if x_10 were a lawyer, then x_10 is playing a game. Finally, from the fact that for all x_10, if x_10 were a lawyer, then x_10 is playing a game, and that for all x_10, x_10 will not play a game we can infer that for all x_10, x_10 is not a lawyer, which contradicts that There is at least one x_10 for which x_10 is a lawyer. Therefore, the answer is no.