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 x_2, x_2 will not play a game. For all x_2, if x_2 were happy, then x_2 is a carpenter. For all x_2, if x_2 were a carpenter, then x_2 is fast. There is at least one x_2 for which x_2 will play a game if and only if x_2 is fast.
For all x_2, if x_2 were happy, then x_2 is fast can be inferred via the universal transitivity rule. There is at least one x_2 for which if x_2 plays a game, then x_2 is fast can be inferred via the existential biconditional elimination rule. There is at least one x_2 for which if x_2 were fast, then x_2 is playing a game can be inferred via the existential biconditional elimination rule. There is at least one x_2 for which x_2 is not fast can be inferred via the existential biconditional elimination rule.