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_3, if x_3 cooks, then x_3 is playing a game. For all x_3, if x_3 were a taxi driver, then x_3 is playing a game. For all x_3, x_3 is a taxi driver. There is at least one x_3 for which if x_3 were fast, then x_3 is cooking.
For all x_3, x_3 will play a game can be inferred via the universal modus ponens rule. There is at least one x_3 for which if x_3 were fast, then x_3 is playing a game can be inferred via the existential transitivity rule.