A similar question for put option has been discussed in this question: Finding Arbitrage in two Puts. Basically, the call option payoff is a convex function of the strike. Then the call option price is also a convex function of the strike. Specifically, let $C(K)$ denote the call option price with strike $K$. Then for $ 0 < K_1 < K_2$,
\begin{align*}
C\left(\frac{K_1 + K_2}{2}\right) \le \frac{1}{2}\big(C(K_1) + C(K_2) \big).
\end{align*}
For the example, let $K_1 = 10$ and $K_2 = 30$. Then
\begin{align*}
C(20) &= C\left(\frac{K_1 + K_2}{2}\right)\\
&\le \frac{1}{2}\big(C(K_1) + C(K_2) \big)\\
&= \frac{1}{2} (12 + 1) = 6.5.
\end{align*}
However, $C(20) = 7$, which contradicts to the above. Therefore, there is an arbitrage opportunity.
For an arbitrage strategy, we should short (i.e., sell) the option that is over-priced, and long (i.e., buy) the option that is under-priced.
Specifically, we short two options with strike 20, and long one option with strike 10 and long another option with strike 30. At the start, we have the profit
\begin{align*}
2 \times 7 - 12 - 1 = 1 $.
\end{align*}
At the option maturity, the payoff to us is
\begin{align*}
(S_T-10)^+ + (S_T-30)^+ - 2 (S_T-20)^+ =
\begin{cases}
0, & \mbox{if } S_T \leq 10,\\
S_T-10, & \mbox{if } 10 \le S_T \le 20, \\
30-S_T, & \mbox{if } 20\le S_T \le 30,\\
0 , & \mbox{if } S_T \ge 30,
\end{cases}
\end{align*}
which is always non-negative. Then, we have a guaranteed profit at the start and potential further profit at the option maturity, while without any liabilities.
