Consider the following premises. If Linda were a soldier, then Elisabeth is writing a letter. For all x_10, if x_10 writes a letter, then x_10 is an artist. Elisabeth is an artist or Linda is a soldier. For all x_10, if x_10 were an artist, then x_10 is writing a letter. Can we infer the following from them? Elisabeth is not writing a letter.
 From the fact that for all x_10, if x_10 writes a letter, then x_10 is an artist, and that for all x_10, if x_10 were an artist, then x_10 is writing a letter we can infer that for all x_10, x_10 will write a letter if and only if x_10 is an artist. From the fact that for all x_10, x_10 will write a letter if and only if x_10 is an artist we can infer that for all x_10, if x_10 were an artist, then x_10 is writing a letter. From the fact that for all x_10, if x_10 were an artist, then x_10 is writing a letter we can infer that if Elisabeth were an artist, then Elisabeth is writing a letter. Finally, from the fact that if Elisabeth were an artist, then Elisabeth is writing a letter, that if Linda were a soldier, then Elisabeth is writing a letter, and that Elisabeth is an artist or Linda is a soldier we can infer that Elisabeth is writing a letter, which contradicts that Elisabeth is not writing a letter. Therefore, the answer is no.