  We settle the Ramsey problem $R(K_6 - e, K_4)$, also known as $R(J_6, K_4)$
and $R(K_6^-, K_4)$. Previously, the best bounds were $30 \leq R(K_6 - e, K4)
\leq 32$. We prove that $R(K_6 - e, K_4) = 30$. Our technique is based on the
recent approach of Angeltveit and McKay and on older algorithms of McKay and
Radziszowski.
