Consider the following premises. For all x_12, if x_12 were a bartender, then x_12 is a scientist. For all x_12, x_12 is excited or x_12 is a janitor. For all x_12, x_12 is not excited or x_12 will write a letter. For all x_12, x_12 is not a janitor or x_12 is a bartender. For all x_12, x_12 will cook or x_12 is not a scientist. For all x_12, if x_12 writes a letter, then x_12 is a scientist. Can we infer the following from them? There is at least one x_12 for which x_12 will not cook.
 From the fact that for all x_12, x_12 is excited or x_12 is a janitor, and that for all x_12, x_12 is not excited or x_12 will write a letter we can infer that for all x_12, x_12 is a janitor or x_12 will write a letter. From the fact that for all x_12, x_12 will cook or x_12 is not a scientist we can infer that for all x_12, if x_12 were a scientist, then x_12 is cooking. From the fact that for all x_12, x_12 is a janitor or x_12 will write a letter, and that for all x_12, x_12 is not a janitor or x_12 is a bartender we can infer that for all x_12, x_12 will write a letter or x_12 is a bartender. From the fact that for all x_12, if x_12 writes a letter, then x_12 is a scientist, that for all x_12, if x_12 were a bartender, then x_12 is a scientist, and that for all x_12, x_12 will write a letter or x_12 is a bartender we can infer that for all x_12, x_12 is a scientist. Finally, from the fact that for all x_12, if x_12 were a scientist, then x_12 is cooking, and that for all x_12, x_12 is a scientist we can infer that for all x_12, x_12 will cook, which contradicts that There is at least one x_12 for which x_12 will not cook. Therefore, the answer is no.