Adding equality to semantic tableaux

An extension to the system of semantic tableaux to deal with first-order logic with equality is introduced and proved sound and complete. This involves the use of partial unification, an operation which is based on unification without the presence of variables. We show, further, that semantic tableaux with partial unification provide a sound and complete proof method without needing the functionally reflexive axioms. We also give an example of an ordering rule which allows us to provide less complex proofs in the ground case.