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_4, z_4 will work or z_4 will not cook. There is at least one z_4 for which if z_4 were a politician, then z_4 is working. For all z_4, if z_4 reads a book, then z_4 is a politician. For all z_4, if z_4 works, then z_4 is cooking.
There is at least one z_4 for which if z_4 were a politician, then z_4 is cooking can be inferred via the existential transitivity rule. There is at least one z_4 for which if z_4 reads a book, then z_4 is working can be inferred via the existential transitivity rule. For all z_4, if z_4 cooks, then z_4 is working can be inferred via the universal rewriting rule.