Consider the following premises. There is at least one x_1 for which x_1 will write a letter. For all x_1, if x_1 makes tea, then x_1 is a scientist. For all x_1, if x_1 writes a letter, then x_1 is making tea. Can we infer the following from them? For all x_1, x_1 is not a scientist.
 From the fact that for all x_1, if x_1 writes a letter, then x_1 is making tea, and that for all x_1, if x_1 makes tea, then x_1 is a scientist we can infer that for all x_1, if x_1 writes a letter, then x_1 is a scientist. Finally, from the fact that for all x_1, if x_1 writes a letter, then x_1 is a scientist, and that there is at least one x_1 for which x_1 will write a letter we can infer that there is at least one x_1 for which x_1 is a scientist, which contradicts that For all x_1, x_1 is not a scientist. Therefore, the answer is no.