What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? For all x_12, x_12 is not happy. For all x_12, x_12 is an astronaut if and only if x_12 will write a letter. For all x_12, x_12 is an astronaut if and only if x_12 is a soldier. For all x_12, if x_12 were an astronaut, then x_12 is writing a letter. For all x_12, x_12 is happy if and only if x_12 is a soldier.
For all x_12, if x_12 were an astronaut, then x_12 is writing a letter. For all x_12, if x_12 were an astronaut, then x_12 is a soldier. For all x_12, if x_12 were happy, then x_12 is a soldier. For all x_12, if x_12 writes a letter, then x_12 is an astronaut. For all x_12, if x_12 were a soldier, then x_12 is an astronaut. For all x_12, if x_12 were a soldier, then x_12 is happy. For all x_12, x_12 is not a soldier.