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, x will sleep or x is a mechanic. There is at least one x for which x will not sleep or x is a poet. For all x, if x were a poet, then x is taking a plane. For all x, x will take a plane if and only if x is a mechanic.
There is at least one x for which x is a mechanic or x is a poet can be inferred via the existential resolution rule. For all x, if x takes a plane, then x is a mechanic can be inferred via the universal biconditional elimination rule. For all x, if x were a mechanic, then x is taking a plane can be inferred via the universal biconditional elimination rule.