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: There is at least one x_8 for which x_8 is a doctor or x_8 will not play a game. For all x_8, if x_8 were a doctor, then x_8 is an artist. For all x_8, if x_8 were an artist, then x_8 is playing a game.
For all x_8, if x_8 were a doctor, then x_8 is playing a game can be inferred via the universal transitivity rule. There is at least one x_8 for which if x_8 plays a game, then x_8 is a doctor can be inferred via the existential rewriting rule.