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 is a mechanic if and only if z is happy. For all z, if z were a mechanic, then z is cooking. There is at least one z for which z will not cook.
There is at least one z for which z is not a mechanic can be inferred via the existential modus tollens rule. For all z, if z were a mechanic, then z is happy can be inferred via the universal biconditional elimination rule. For all z, if z were happy, then z is a mechanic can be inferred via the universal biconditional elimination rule.