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: For all z, z will play a game if and only if z will take a plane. For all z, if z takes a plane, then z is excited. For all z, z is not excited.
For all z, z will not take a plane can be inferred via the universal modus tollens rule. For all z, if z plays a game, then z is taking a plane can be inferred via the universal biconditional elimination rule. For all z, if z takes a plane, then z is playing a game can be inferred via the universal biconditional elimination rule.