Consider the following premises. For all x_11, if x_11 were a janitor, then x_11 is a scientist. For all x_11, x_11 is happy if and only if x_11 is a soldier. For all x_11, x_11 is a soldier or x_11 is a janitor. For all x_11, x_11 is a scientist if and only if x_11 is happy. Can we infer the following from them? For all x_11, x_11 is happy.
 From the fact that for all x_11, x_11 is a scientist if and only if x_11 is happy we can infer that for all x_11, if x_11 were a scientist, then x_11 is happy. From the fact that for all x_11, x_11 is happy if and only if x_11 is a soldier we can infer that for all x_11, if x_11 were a soldier, then x_11 is happy. From the fact that for all x_11, if x_11 were a janitor, then x_11 is a scientist, and that for all x_11, if x_11 were a scientist, then x_11 is happy we can infer that for all x_11, if x_11 were a janitor, then x_11 is happy. Finally, from the fact that for all x_11, if x_11 were a soldier, then x_11 is happy, that for all x_11, if x_11 were a janitor, then x_11 is happy, and that for all x_11, x_11 is a soldier or x_11 is a janitor we can infer that for all x_11, x_11 is happy. Therefore, the answer is yes.