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, if z were curious, then z is reading a book. For all z, z will not work. For all z, z will work if and only if z is curious. For all z, if z reads a book, then z is curious. There is at least one z for which z will read a book if and only if z will climb a mountain.
For all z, z is curious if and only if z will read a book can be inferred via the universal biconditional introduction rule. For all z, z will read a book if and only if z is curious can be inferred via the universal biconditional introduction rule. For all z, if z works, then z is curious can be inferred via the universal biconditional elimination rule. There is at least one z for which if z reads a book, then z is climbing a mountain can be inferred via the existential biconditional elimination rule. For all z, if z were curious, then z is working can be inferred via the universal biconditional elimination rule. There is at least one z for which if z climbs a mountain, then z is reading a book can be inferred via the existential biconditional elimination rule. For all z, z is not curious can be inferred via the universal biconditional elimination rule.