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: There is at least one x_12 for which x_12 is not an office clerk. For all x_12, x_12 is a mechanic if and only if x_12 is an office clerk. For all x_12, x_12 is a mechanic if and only if x_12 is a poet.
For all x_12, if x_12 were a mechanic, then x_12 is an office clerk can be inferred via the universal biconditional elimination rule. For all x_12, if x_12 were a mechanic, then x_12 is a poet can be inferred via the universal biconditional elimination rule. For all x_12, if x_12 were an office clerk, then x_12 is a mechanic can be inferred via the universal biconditional elimination rule. For all x_12, if x_12 were a poet, then x_12 is a mechanic can be inferred via the universal biconditional elimination rule. There is at least one x_12 for which x_12 is not a mechanic can be inferred via the existential biconditional elimination rule.