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_9, if x_9 listens to a song, then x_9 is climbing a mountain. For all x_9, if x_9 drinks water, then x_9 is an astronaut. For all x_9, x_9 will listen to a song. For all x_9, if x_9 climbs a mountain, then x_9 is drinking water. There is at least one x_9 for which x_9 is an office clerk.
For all x_9, x_9 will climb a mountain can be inferred via the universal modus ponens rule. For all x_9, if x_9 listens to a song, then x_9 is drinking water can be inferred via the universal transitivity rule. For all x_9, if x_9 climbs a mountain, then x_9 is an astronaut can be inferred via the universal transitivity rule. There is at least one x_9 for which x_9 is an office clerk and x_9 will listen to a song can be inferred via the existential conjunction rule. There is at least one x_9 for which x_9 will listen to a song and x_9 is an office clerk can be inferred via the existential conjunction rule.