Butterfly-spread arbitrage for nonconvex call prices ($C(K_2)\le \frac{1}{2}[C(K_1)+C(K_3)](K_2=(K_1+K_3)/2)$)

The midpoint butterfly buys half a call at each outer strike and sells one at the middle strike. Convexity of $K\mapsto (S-K{)}^{+}$ makes its terminal payoff nonnegative. A violation of the displayed price inequality makes its cost negative and creates arbitrage. The payoff is triangular between the outer strikes and zero elsewhere.