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_9, if x_9 cooks, then x_9 is a politician. There is at least one x_9 for which if x_9 were a politician, then x_9 is cooking. For all x_9, x_9 is a scientist. For all x_9, x_9 will take a plane if and only if x_9 is a politician. For all x_9, if x_9 takes a plane, then x_9 is not a scientist.
For all x_9, x_9 will not take a plane can be inferred via the universal modus tollens rule. There is at least one x_9 for which x_9 is a politician if and only if x_9 will cook can be inferred via the existential biconditional introduction rule. There is at least one x_9 for which x_9 will cook if and only if x_9 is a politician can be inferred via the existential biconditional introduction rule. For all x_9, if x_9 takes a plane, then x_9 is a politician can be inferred via the universal biconditional elimination rule. For all x_9, if x_9 were a politician, then x_9 is taking a plane can be inferred via the universal biconditional elimination rule.