Applying the compact constraint calculation method of S-box based on Mixed Integer Linear Programming （MILP） model can solve the low efficiency of differential path search of SPONGENT in differential cryptanalysis. To find the best description of S box， a compactness verification algorithm was proposed to verify the inequality constraints in S-box from the perspective of the necessity of the existence of constraints. Firstly， the MILP model was introduced to analyze the inequality constraints of SPONGENT S-box， and the constraint composed of 23 inequalities was obtained. Then， an index for evaluating the existence necessity of constraint inequality was proposed， and a compactness verification algorithm for verifying the compactness of group of constraint inequalities was proposed based on this index. Finally， the compactness of the obtained SPONGENT S-box constraint was verified by using the proposed algorithm. Calculation analysis show that the 23 inequalities have a unique impossible difference mode that can be excluded， that is， each inequality has the necessity of existence. Furthermore， for the same case， the number of inequalities was reduced by 20% compared to that screened by using the greedy algorithm principle. Therefore， the obtained inequality constraint of S-box in SPONGENT is compact， and the proposed compactness verification algorithm outperforms the greedy algorithm.