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_15, x_15 will cook if and only if x_15 is excited. There is at least one x_15 for which if x_15 cooks, then x_15 is excited. For all x_15, x_15 is excited or x_15 is not an astronaut.
For all x_15, if x_15 were an astronaut, then x_15 is excited can be inferred via the universal rewriting rule. For all x_15, if x_15 cooks, then x_15 is excited can be inferred via the universal biconditional elimination rule. For all x_15, if x_15 were excited, then x_15 is cooking can be inferred via the universal biconditional elimination rule.