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_5 for which if x_5 were a police officer, then x_5 is listening to a song. For all x_5, if x_5 listens to a song, then x_5 is an astronaut. For all x_5, x_5 is curious if and only if x_5 is an astronaut.
There is at least one x_5 for which if x_5 were a police officer, then x_5 is an astronaut can be inferred via the existential transitivity rule. For all x_5, if x_5 were curious, then x_5 is an astronaut can be inferred via the universal biconditional elimination rule. For all x_5, if x_5 were an astronaut, then x_5 is curious can be inferred via the universal biconditional elimination rule.