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 were a poet, then x_12 is sleeping. For all x_12, if x_12 sleeps, then x_12 is a poet. For all x_12, if x_12 sleeps, then x_12 is fast. There is at least one x_12 for which if x_12 were fast, then x_12 is sleeping.
For all x_12, if x_12 were a poet, then x_12 is fast can be inferred via the universal transitivity rule. There is at least one x_12 for which if x_12 were fast, then x_12 is a poet can be inferred via the existential transitivity rule. For all x_12, x_12 is a poet if and only if x_12 will sleep can be inferred via the universal biconditional introduction rule. For all x_12, x_12 will sleep if and only if x_12 is a poet can be inferred via the universal biconditional introduction rule. There is at least one x_12 for which x_12 is fast if and only if x_12 will sleep can be inferred via the existential biconditional introduction rule. There is at least one x_12 for which x_12 will sleep if and only if x_12 is fast can be inferred via the existential biconditional introduction rule.