Consider the following premises. For all x_10, if x_10 were a poet, then x_10 is playing a game. For all x_10, x_10 is a mechanic or x_10 will cook. For all x_10, if x_10 writes a letter, then x_10 is a poet. For all x_10, x_10 will write a letter or x_10 will not cook. There is at least one x_10 for which if x_10 were a mechanic, then x_10 is playing a game. Can we infer the following from them? For all x_10, x_10 will not play a game.
 From the fact that for all x_10, x_10 will write a letter or x_10 will not cook we can infer that for all x_10, if x_10 cooks, then x_10 is writing a letter. From the fact that for all x_10, if x_10 cooks, then x_10 is writing a letter, and that for all x_10, if x_10 writes a letter, then x_10 is a poet we can infer that for all x_10, if x_10 cooks, then x_10 is a poet. From the fact that for all x_10, if x_10 cooks, then x_10 is a poet, and that for all x_10, if x_10 were a poet, then x_10 is playing a game we can infer that for all x_10, if x_10 cooks, then x_10 is playing a game. Finally, from the fact that there is at least one x_10 for which if x_10 were a mechanic, then x_10 is playing a game, that for all x_10, if x_10 cooks, then x_10 is playing a game, and that for all x_10, x_10 is a mechanic or x_10 will cook we can infer that there is at least one x_10 for which x_10 will play a game, which contradicts that For all x_10, x_10 will not play a game. Therefore, the answer is no.