What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? Name the inference rule being used: If Joseph plays a game, then Robert is an astronaut. If Robert sleeps, then Joseph is playing a game. For all x_12, x_12 is an astronaut if and only if x_12 will sleep.
If Robert sleeps, then Robert is an astronaut can be inferred via the transitivity rule. For all x_12, if x_12 were an astronaut, then x_12 is sleeping can be inferred via the universal biconditional elimination rule. For all x_12, if x_12 sleeps, then x_12 is an astronaut can be inferred via the universal biconditional elimination rule.