What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? For all x_10, x_10 is happy if and only if x_10 is a soldier. For all x_10, x_10 is a soldier or x_10 will write a letter. There is at least one x_10 for which if x_10 writes a letter, then x_10 is happy. For all x_10, if x_10 were rich, then x_10 is happy. For all x_10, if x_10 were a soldier, then x_10 is rich.
For all x_10, if x_10 were a soldier, then x_10 is happy. For all x_10, if x_10 were happy, then x_10 is a soldier. For all x_10, if x_10 were a soldier, then x_10 is happy.