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_4 for which x_4 will play tennis or x_4 is not a carpenter. For all x_4, if x_4 were a writer, then x_4 is a carpenter. For all x_4, if x_4 were a carpenter, then x_4 is a scientist. For all x_4, if x_4 were a scientist, then x_4 is a writer.
For all x_4, if x_4 were a writer, then x_4 is a scientist can be inferred via the universal transitivity rule. For all x_4, if x_4 were a carpenter, then x_4 is a writer can be inferred via the universal transitivity rule. For all x_4, if x_4 were a scientist, then x_4 is a carpenter can be inferred via the universal transitivity rule. There is at least one x_4 for which if x_4 were a carpenter, then x_4 is playing tennis can be inferred via the existential rewriting rule.