An infinite finitely presented residually finite 2-group

We prove that the infinite, ordinarily finitely presented periodic Steinberg group $\Gamma ={\mathrm{St}}_{12}(R)$ of a companion paper is residually finite. Its finite-index subgroup $G=\ker (\Gamma \to {\mathrm{St}}_{12}({\mathbb{F}}_2))$ is infinite, ordinarily finitely presented, and residually finite, and every element of G has finite 2-power order. The orders of its elements are unbounded. Phases of long words in the companion's graded algebra allow finite degree truncations to detect all elements of Γ, including the central kernel.