= Solution
Buy half a call at each neighboring strike and sell one call at the middle strike. Its cost is
$$
\frac12C(K_{i-1})+\frac12C(K_{i+1})-C(K_i)<0.
$$
For fixed terminal <stock> price $s$, the function $K\mapsto(s-K)^+$ is <convex>. Since $K_i$ is the midpoint, the payoff
$$
\frac12(s-K_{i-1})^++\frac12(s-K_{i+1})^+-(s-K_i)^+
$$
is nonnegative for every $s$. More explicitly, it is zero outside $[K_{i-1},K_{i+1}]$, equals $(s-K_{i-1})/2$ on $[K_{i-1},K_i]$, and equals $(K_{i+1}-s)/2$ on $[K_i,K_{i+1}]$. The negative cost and nonnegative payoff produce an <arbitrage>. This is the <butterfly-spread arbitrage for nonconvex call prices>.
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