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The oriented size Ramsey number of an oriented graph $H$, denoted by $r(H)$, is the minimum $m$ for which there exists an oriented graph $G$ with $m$ edges, such that every $2$-colouring of $G$ contains a monochromatic copy of $H$.\n  In this paper we prove that the oriented size Ramsey number of the directed paths on $n$ vertices satisfies $r(P_n) = \\Omega(n^2 \\log n)$. This improves a lower bound by Ben-Eliezer, Krivelevich and Sudakov. 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