First Order Logic in Semantic Tableau and VAMPIRE

Semantic tableau is a proof system used to prove the validity of a formula using Prolog, it can also be used to prove if a formula is a logic consequence of a set of formulas. Semantic tableau is used in both propositional and predicate logic. Tableau is a disjunction normal form. VAMPIRE is a high-performance theorem prover for first-order logic with or without equality. In this paper, a modified version of semantic tableau is presented, experimental results proved the validity of modified tableau. Also, it is shown how Tableau proof system and VAMPIRE can be used in predicate logic.