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 were an astronaut, then x_2 is poor. There is at least one x_2 for which x_2 is not poor. For all x_2, if x_2 were poor, then x_2 is sleeping. For all x_2, if x_2 sleeps, then x_2 is an astronaut.
There is at least one x_2 for which x_2 is not an astronaut can be inferred via the existential modus tollens rule. For all x_2, if x_2 were an astronaut, then x_2 is sleeping can be inferred via the universal transitivity rule. For all x_2, if x_2 were poor, then x_2 is an astronaut can be inferred via the universal transitivity rule. For all x_2, if x_2 sleeps, then x_2 is poor can be inferred via the universal transitivity rule.