This paper investigates reasoning support for the semantic Web based on the first-order logic. The key reasoning tasks of the semantic Web can be reduced to deciding the satisfiability of formulas. The first-order logic theorem prover is efficient and complete for unsatisfiability, while finite model searcher finds models for satisfiable formula. This paper proposes to use a theorem prover and a finite model searcher concurrently in the semantic Web reasoning. The experiments show that the method can make up the deficiencies of the description logic reasoner and complement the theorem prover for satisfiable formulas.