Consider the following premises. If Charles were a janitor, then Susan is sad. If Susan writes a letter, then Charles is a janitor. For all x_12, if x_12 were sad, then x_12 is writing a letter. Susan is not writing a letter. Can we infer the following from them? Charles is not a janitor.
 From the fact that for all x_12, if x_12 were sad, then x_12 is writing a letter we can infer that if Susan were sad, then Susan is writing a letter. From the fact that if Charles were a janitor, then Susan is sad, and that if Susan were sad, then Susan is writing a letter we can infer that if Charles were a janitor, then Susan is writing a letter. From the fact that if Charles were a janitor, then Susan is writing a letter, and that if Susan writes a letter, then Charles is a janitor we can infer that Charles is a janitor if and only if Susan is writing a letter. Finally, from the fact that Charles is a janitor if and only if Susan is writing a letter, and that Susan is not writing a letter we can infer that Charles is not a janitor. Therefore, the answer is yes.