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 x_10, x_10 is a poet. For all x_10, if x_10 were a soldier, then x_10 is happy. For all x_10, if x_10 were a poet, then x_10 is a politician. For all x_10, if x_10 were a politician, then x_10 is a scientist. For all x_10, x_10 is a soldier.
For all x_10, x_10 is happy can be inferred via the universal modus ponens rule. For all x_10, x_10 is a politician can be inferred via the universal modus ponens rule. For all x_10, if x_10 were a poet, then x_10 is a scientist can be inferred via the universal transitivity rule. For all x_10, x_10 is a poet and x_10 is a soldier can be inferred via the universal conjunction rule. For all x_10, x_10 is a soldier and x_10 is a poet can be inferred via the universal conjunction rule.