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_17, x_17 is a doctor or x_17 is fast. For all x_17, if x_17 were a carpenter, then x_17 is a doctor. For all x_17, if x_17 were a doctor, then x_17 is a carpenter. For all x_17, if x_17 were a carpenter, then x_17 is cooking. There is at least one x_17 for which x_17 will not cook.
There is at least one x_17 for which x_17 is not a carpenter can be inferred via the existential modus tollens rule. For all x_17, if x_17 were a doctor, then x_17 is cooking can be inferred via the universal transitivity rule. For all x_17, x_17 is a carpenter if and only if x_17 is a doctor can be inferred via the universal biconditional introduction rule. For all x_17, x_17 is a doctor if and only if x_17 is a carpenter can be inferred via the universal biconditional introduction rule.