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_6, if x_6 takes a plane, then x_6 is an artist. For all x_6, if x_6 were an artist, then x_6 is playing a game. There is at least one x_6 for which if x_6 were a poet, then x_6 is taking a plane. For all x_6, if x_6 plays a game, then x_6 is a poet.
For all x_6, if x_6 takes a plane, then x_6 is playing a game can be inferred via the universal transitivity rule. For all x_6, if x_6 were an artist, then x_6 is a poet can be inferred via the universal transitivity rule. There is at least one x_6 for which if x_6 were a poet, then x_6 is an artist can be inferred via the existential transitivity rule. There is at least one x_6 for which if x_6 plays a game, then x_6 is taking a plane can be inferred via the existential transitivity rule.