What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? For all x_1, if x_1 plays a game, then x_1 is an astronaut. For all x_1, if x_1 were a janitor, then x_1 is playing a game. There is at least one x_1 for which if x_1 were an astronaut, then x_1 is a janitor.
For all x_1, if x_1 were a janitor, then x_1 is an astronaut. There is at least one x_1 for which if x_1 were an astronaut, then x_1 is playing a game. There is at least one x_1 for which if x_1 plays a game, then x_1 is a janitor.