Consider the following premises. For all x_11, x_11 is a soldier if and only if x_11 is a carpenter. For all x_11, if x_11 were sad, then x_11 is a police officer. For all x_11, x_11 is a police officer if and only if x_11 is a soldier. For all x_11, x_11 is a carpenter or x_11 is sad. Can we infer the following from them? If we can, name the inference rule being used: For all x_11, x_11 is a soldier.
 From the fact that for all x_11, x_11 is a police officer if and only if x_11 is a soldier we can infer that for all x_11, if x_11 were a police officer, then x_11 is a soldier via universal biconditional elimination. From the fact that for all x_11, x_11 is a soldier if and only if x_11 is a carpenter we can infer that for all x_11, if x_11 were a carpenter, then x_11 is a soldier via universal biconditional elimination. From the fact that for all x_11, if x_11 were sad, then x_11 is a police officer, and that for all x_11, if x_11 were a police officer, then x_11 is a soldier we can infer that for all x_11, if x_11 were sad, then x_11 is a soldier via universal transitivity. Finally, from the fact that for all x_11, if x_11 were a carpenter, then x_11 is a soldier, that for all x_11, if x_11 were sad, then x_11 is a soldier, and that for all x_11, x_11 is a carpenter or x_11 is sad we can infer that for all x_11, x_11 is a soldier via universal disjunction elimination. Therefore, the answer is yes.