What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? There is at least one z for which if z sleeps, then z is playing a game. For all z, if z sleeps, then z is taking a plane. For all z, if z plays a game, then z is sleeping. For all z, z will not take a plane.
For all z, z will not sleep. For all z, if z plays a game, then z is taking a plane. There is at least one z for which z will sleep if and only if z will play a game. There is at least one z for which z will play a game if and only if z will sleep.