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_2, if x_2 cooks, then x_2 is listening to a song. There is at least one x_2 for which if x_2 were a poet, then x_2 is cooking. For all x_2, if x_2 were a carpenter, then x_2 is a poet.
There is at least one x_2 for which if x_2 were a poet, then x_2 is listening to a song can be inferred via the existential transitivity rule. There is at least one x_2 for which if x_2 were a carpenter, then x_2 is cooking can be inferred via the existential transitivity rule.