Is there an algorithm for proof of formulas in sequent calculus, like resolution method? I'm especially interested in natural deduction.
UPDATE
Well, we have one scheme of axioms $$\Phi\vdash\Phi$$ and twelve rules of inference: $$ \begin{align} 1.\enspace&\frac{\Gamma\vdash\Phi;\Gamma\vdash\Psi}{\Gamma\vdash\Phi\wedge\Psi} & 7.\enspace&\frac{\Gamma,\Phi\vdash\Psi}{\Gamma\vdash\Phi\to\Psi}\\\\ 2.\enspace&\frac{\Gamma\vdash\Phi\vee\Psi}{\Gamma\vdash\Phi} & 8.\enspace&\frac{\Gamma\vdash\Phi;\Gamma\vdash\Phi\to\Psi}{\Gamma\vdash\Psi}\\\\ 3.\enspace&\frac{\Gamma\vdash\Phi\vee\Psi}{\Gamma\vdash\Psi} & 9.\enspace&\frac{\Gamma,\neg\Phi\vdash}{\Gamma\vdash\Phi}\\\\ 4.\enspace& \frac{\Gamma\vdash\Phi}{\Gamma\vdash\Phi\vee\Psi} & 10.\enspace&\frac{\Gamma\vdash\Phi;\Gamma\vdash\neg\Phi}{\Gamma\vdash}\\\\ 5.\enspace&\frac{\Gamma\vdash\Psi}{\Gamma\vdash\Phi\vee\Psi} & 11.\enspace&\frac{\Gamma,\Phi,\Psi,\Gamma_1\vdash X}{\Gamma,\Psi,\Phi,\Gamma_1\vdash X}\\\\ 6.\enspace&\frac{\Gamma,\Phi\vdash \Psi; \Gamma, X\vdash \Psi; \Gamma\vdash\Phi\vee X}{\Gamma\vdash\Psi} & 12.\enspace&\frac{\Gamma\vdash\Phi}{\Gamma, \Psi\vdash\Phi} \end{align} $$
Is there an algorithm for proof of formulas in this calculus?