Consider the following premises. For all x_18, if x_18 were a writer, then x_18 is playing a game. For all x_18, x_18 is a mechanic or x_18 is a poet. For all x_18, if x_18 were a mechanic, then x_18 is writing a letter. For all x_18, if x_18 were a writer, then x_18 is not writing a letter. There is at least one x_18 for which if x_18 were a poet, then x_18 is writing a letter. For all x_18, if x_18 plays a game, then x_18 is a writer. Can we infer the following from them? There is at least one x_18 for which x_18 will not play a game.
 From the fact that for all x_18, if x_18 plays a game, then x_18 is a writer, and that for all x_18, if x_18 were a writer, then x_18 is playing a game we can infer that for all x_18, x_18 will play a game if and only if x_18 is a writer. From the fact that for all x_18, if x_18 were a mechanic, then x_18 is writing a letter, that there is at least one x_18 for which if x_18 were a poet, then x_18 is writing a letter, and that for all x_18, x_18 is a mechanic or x_18 is a poet we can infer that there is at least one x_18 for which x_18 will write a letter. From the fact that for all x_18, if x_18 were a writer, then x_18 is not writing a letter, and that there is at least one x_18 for which x_18 will write a letter we can infer that there is at least one x_18 for which x_18 is not a writer. Finally, from the fact that for all x_18, x_18 will play a game if and only if x_18 is a writer, and that there is at least one x_18 for which x_18 is not a writer we can infer that there is at least one x_18 for which x_18 will not play a game. Therefore, the answer is yes.