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, if x were a poet, then x is running. There is at least one x for which x will go running if and only if x will write a letter. For all x, if x goes running, then x is a poet. For all x, x will not write a letter.
For all x, x is a poet if and only if x will go running can be inferred via the universal biconditional introduction rule. For all x, x will go running if and only if x is a poet can be inferred via the universal biconditional introduction rule. There is at least one x for which if x goes running, then x is writing a letter can be inferred via the existential biconditional elimination rule. There is at least one x for which if x writes a letter, then x is running can be inferred via the existential biconditional elimination rule. There is at least one x for which x will not go running can be inferred via the existential biconditional elimination rule.