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 is a writer. There is at least one x_12 for which if x_12 climbs a mountain, then x_12 is listening to a song. For all x_12, if x_12 were a writer, then x_12 is climbing a mountain. For all x_12, x_12 is a janitor.
For all x_12, x_12 will climb a mountain can be inferred via the universal modus ponens rule. There is at least one x_12 for which if x_12 were a writer, then x_12 is listening to a song can be inferred via the existential transitivity rule. For all x_12, x_12 is a writer and x_12 is a janitor can be inferred via the universal conjunction rule. For all x_12, x_12 is a janitor and x_12 is a writer can be inferred via the universal conjunction rule.