A Satisfiability algorithm based on Simple Spinors of the Clifford algebra of ${\mathbb{R}}^{n,n}$

We refine the formulation of the Boolean satisfiability problem with $n$ Boolean variables in Clifford algebra $\mathcal{C}\mathrm{\ell }({\mathbb{R}}^{n,n})$ [3] and exploit this continuous setting to outline a new unsatisfiability test. This algorithm is not combinatorial and can prove unsatisfiability in polynomial time.