A social law is a set of restrictions on the available actions of agents to establish some target properties in a multiagent system. In the strategic case, where the agents have individual rationality and private information, the social law synthesizing problem should be modeled as an algorithmic mechanism design problem instead of a common optimization problem. Minimal side effect is usually a basic requirement for social laws. From the perspective of game theory, minimal side effect closely relates to the concept of maximum social welfare, and synthesizing a social law with minimal side effect can be modeled as an efficient mechanism design problem. Therefore, this study not only needs to find out the efficient social laws with maximum social welfare for the given target property but also pays for the agents to induce incentive compatibility and individual rationality. The study first designs an efficient mechanism based on the VCG mechanism, namely VCG-SLM, and proves that it satisfies all the required formal properties. However, as the computation of VCG-SLM is an FP^NP-complete problem, the study proposes an ILP-based implementation of this mechanism (VCG-SLM-ILP), transforms the computation of allocation and payment to ILPs based on the semantics of ATL, and strictly proves its correction, so as to effectively utilize the currently mature industrial-grade integer programming solver and successfully solve the intractable mechanism computing problems.