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, if x_2 plays a game, then x_2 is a sailor. For all x_2, if x_2 were a sailor, then x_2 is playing tennis. For all x_2, if x_2 plays tennis, then x_2 is playing a game. There is at least one x_2 for which x_2 is not a sailor.
There is at least one x_2 for which x_2 will not play a game can be inferred via the existential modus tollens rule. For all x_2, if x_2 plays a game, then x_2 is playing tennis can be inferred via the universal transitivity rule. For all x_2, if x_2 were a sailor, then x_2 is playing a game can be inferred via the universal transitivity rule. For all x_2, if x_2 plays tennis, then x_2 is a sailor can be inferred via the universal transitivity rule.