Consider the following premises. For all x_11, x_11 is happy if and only if x_11 will listen to a song. For all x_11, if x_11 plays tennis, then x_11 is a janitor. For all x_11, if x_11 listens to a song, then x_11 is sad. For all x_11, x_11 will play tennis or x_11 is happy. For all x_11, if x_11 were sad, then x_11 is a janitor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_11 for which x_11 is not a janitor.
 From the fact that for all x_11, x_11 is happy if and only if x_11 will listen to a song we can infer that for all x_11, if x_11 were happy, then x_11 is listening to a song via universal biconditional elimination. From the fact that for all x_11, if x_11 listens to a song, then x_11 is sad, and that for all x_11, if x_11 were sad, then x_11 is a janitor we can infer that for all x_11, if x_11 listens to a song, then x_11 is a janitor via universal transitivity. From the fact that for all x_11, if x_11 were happy, then x_11 is listening to a song, and that for all x_11, if x_11 listens to a song, then x_11 is a janitor we can infer that for all x_11, if x_11 were happy, then x_11 is a janitor via universal transitivity. Finally, from the fact that for all x_11, if x_11 plays tennis, then x_11 is a janitor, that for all x_11, if x_11 were happy, then x_11 is a janitor, and that for all x_11, x_11 will play tennis or x_11 is happy we can infer that for all x_11, x_11 is a janitor via universal disjunction elimination, which contradicts that There is at least one x_11 for which x_11 is not a janitor. Therefore, the answer is no.