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 drinks water, then x_9 is a mechanic. For all x_9, x_9 will play a game or x_9 is a poet. For all x_9, if x_9 were a mechanic, then x_9 is a poet. There is at least one x_9 for which if x_9 were a poet, then x_9 is a mechanic. For all x_9, x_9 will not play a game or x_9 will drink water.
For all x_9, if x_9 drinks water, then x_9 is a poet can be inferred via the universal transitivity rule. For all x_9, x_9 is a poet or x_9 will drink water can be inferred via the universal resolution rule. There is at least one x_9 for which x_9 is a poet if and only if x_9 is a mechanic can be inferred via the existential biconditional introduction rule. There is at least one x_9 for which x_9 is a mechanic if and only if x_9 is a poet can be inferred via the existential biconditional introduction rule.