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_1, if x_1 makes tea, then x_1 is cooking. For all x_1, if x_1 climbs a mountain, then x_1 is cooking. For all x_1, x_1 is a poet or x_1 will climb a mountain. There is at least one x_1 for which if x_1 were a poet, then x_1 is making tea.
There is at least one x_1 for which if x_1 were a poet, then x_1 is cooking can be inferred via the existential transitivity rule.