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_12, if x_12 plays tennis, then x_12 is not a doctor. For all x_12, x_12 will play tennis or x_12 will not take a plane. For all x_12, if x_12 were a scientist, then x_12 is a doctor. For all x_12, if x_12 cooks, then x_12 is a doctor. For all x_12, x_12 is a scientist or x_12 will cook.
For all x_12, if x_12 takes a plane, then x_12 is playing tennis can be inferred via the universal rewriting rule. For all x_12, x_12 is a doctor can be inferred via the universal disjunction elimination rule.