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_4, z_4 will play a game and z_4 will go running. There is at least one z_4 for which z_4 is a poet if and only if z_4 will play a game.
For all z_4, z_4 will play a game can be inferred via the universal simplification rule. For all z_4, z_4 will go running can be inferred via the universal simplification rule. There is at least one z_4 for which if z_4 were a poet, then z_4 is playing a game can be inferred via the existential biconditional elimination rule. There is at least one z_4 for which if z_4 plays a game, then z_4 is a poet can be inferred via the existential biconditional elimination rule.