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_1 for which if x_1 were a musician, then x_1 is playing tennis. For all x_1, if x_1 plays tennis, then x_1 is a writer. For all x_1, if x_1 were a writer, then x_1 is a politician. For all x_1, if x_1 were a politician, then x_1 is a writer. For all x_1, x_1 is not a politician. For all x_1, if x_1 were a writer, then x_1 is a musician.
For all x_1, x_1 is not a writer can be inferred via the universal modus tollens rule. For all x_1, if x_1 plays tennis, then x_1 is a politician can be inferred via the universal transitivity rule. For all x_1, if x_1 plays tennis, then x_1 is a musician can be inferred via the universal transitivity rule. For all x_1, if x_1 were a politician, then x_1 is a musician can be inferred via the universal transitivity rule. There is at least one x_1 for which if x_1 were a musician, then x_1 is a writer can be inferred via the existential transitivity rule. There is at least one x_1 for which if x_1 were a writer, then x_1 is playing tennis can be inferred via the existential transitivity rule. For all x_1, x_1 is a writer if and only if x_1 is a politician can be inferred via the universal biconditional introduction rule. For all x_1, x_1 is a politician if and only if x_1 is a writer can be inferred via the universal biconditional introduction rule.