Consider the following premises. There is at least one x_12 for which x_12 is a sailor or x_12 is not a janitor. For all x_12, x_12 is a janitor. For all x_12, if x_12 were sad, then x_12 is not a sailor. Can we infer the following from them? If we can, name the inference rule being used: For all x_12, x_12 is sad.
 From the fact that there is at least one x_12 for which x_12 is a sailor or x_12 is not a janitor we can infer that there is at least one x_12 for which if x_12 were a janitor, then x_12 is a sailor via existential rewriting. From the fact that there is at least one x_12 for which if x_12 were a janitor, then x_12 is a sailor, and that for all x_12, x_12 is a janitor we can infer that there is at least one x_12 for which x_12 is a sailor via existential modus ponens. Finally, from the fact that for all x_12, if x_12 were sad, then x_12 is not a sailor, and that there is at least one x_12 for which x_12 is a sailor we can infer that there is at least one x_12 for which x_12 is not sad via existential modus tollens, which contradicts that For all x_12, x_12 is sad. Therefore, the answer is no.