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 cooks, then x_2 is drinking water. For all x_2, if x_2 drinks water, then x_2 is a writer. For all x_2, if x_2 were a writer, then x_2 is cooking. There is at least one x_2 for which x_2 will not drink water.
There is at least one x_2 for which x_2 will not cook can be inferred via the existential modus tollens rule. For all x_2, if x_2 cooks, then x_2 is a writer can be inferred via the universal transitivity rule. For all x_2, if x_2 drinks water, then x_2 is cooking can be inferred via the universal transitivity rule. For all x_2, if x_2 were a writer, then x_2 is drinking water can be inferred via the universal transitivity rule.