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_12, x_12 will take a plane. There is at least one x_12 for which if x_12 were a musician, then x_12 is a police officer. For all x_12, if x_12 writes a letter, then x_12 is a police officer. For all x_12, if x_12 takes a plane, then x_12 is playing a game. For all x_12, x_12 will write a letter or x_12 is a musician.
For all x_12, x_12 will play a game can be inferred via the universal modus ponens rule. There is at least one x_12 for which x_12 is a police officer can be inferred via the existential disjunction elimination rule.