Consider the following premises. For all x_10, if x_10 plays a game, then x_10 is a mechanic. For all x_10, if x_10 listens to a song, then x_10 is playing a game. For all x_10, x_10 is a mechanic if and only if x_10 will listen to a song. For all x_10, x_10 will listen to a song or x_10 will write a letter. There is at least one x_10 for which if x_10 writes a letter, then x_10 is a mechanic. Can we infer the following from them? For all x_10, x_10 is not a mechanic.
 From the fact that for all x_10, if x_10 listens to a song, then x_10 is playing a game, and that for all x_10, if x_10 plays a game, then x_10 is a mechanic we can infer that for all x_10, if x_10 listens to a song, then x_10 is a mechanic. From the fact that for all x_10, x_10 is a mechanic if and only if x_10 will listen to a song we can infer that for all x_10, if x_10 were a mechanic, then x_10 is listening to a song. From the fact that for all x_10, if x_10 were a mechanic, then x_10 is listening to a song, and that for all x_10, if x_10 listens to a song, then x_10 is a mechanic we can infer that for all x_10, x_10 is a mechanic if and only if x_10 will listen to a song. From the fact that for all x_10, x_10 is a mechanic if and only if x_10 will listen to a song we can infer that for all x_10, if x_10 listens to a song, then x_10 is a mechanic. Finally, from the fact that for all x_10, if x_10 listens to a song, then x_10 is a mechanic, that there is at least one x_10 for which if x_10 writes a letter, then x_10 is a mechanic, and that for all x_10, x_10 will listen to a song or x_10 will write a letter we can infer that there is at least one x_10 for which x_10 is a mechanic, which contradicts that For all x_10, x_10 is not a mechanic. Therefore, the answer is no.