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 z, z will go running or z will write a letter. For all z, if z were a poet, then z is making tea. For all z, if z makes tea, then z is writing a letter. There is at least one z for which if z writes a letter, then z is making tea. For all z, z will not go running or z is a poet.
For all z, if z were a poet, then z is writing a letter can be inferred via the universal transitivity rule. For all z, z will write a letter or z is a poet can be inferred via the universal resolution rule. There is at least one z for which z will write a letter if and only if z will make tea can be inferred via the existential biconditional introduction rule. There is at least one z for which z will make tea if and only if z will write a letter can be inferred via the existential biconditional introduction rule.