This paper demonstrates both theoretically and numerically that neural networks can detect model-free static arbitrage opportunities in financial markets. The authors consider a market where an agent can statically trade in options and underlying securities, with bid-ask prices and position limits. They define static arbitrage as a trading strategy with non-negative payoff in all scenarios and negative initial cost. The minimal cost to superhedge the zero payoff function is formulated as a convex semi-infinite program (CSIP). The key theoretical result (Theorem 2.5 and 2.6) shows that a single neural network can approximately solve this CSIP for all possible market parameters (strikes and prices), providing an epsilon-optimal superhedging strategy. Consequently, if the market admits arbitrage (i.e., the minimal cost is negative), the neural network outputs a strategy with negative cost, thus detecting arbitrage. The proof relies on the universal approximation theorem and a novel result that a single neural network can uniformly approximate the optimal value and feasible solutions of a class of CSIPs (Theorem 4.5). Numerically, the authors train a neural network offline on real market data and demonstrate that it can detect arbitrage and output trading strategies almost instantaneously when presented with new market conditions. This approach significantly reduces execution risk compared to traditional methods that must be re-run each time market conditions change. The experiments confirm the effectiveness and robustness of the method, making it suitable for high-frequency trading environments.