The artificial immune system (AIS) algorithm is a heuristic technique inspired by the biological immune system. The biological immune system has been proven to be a robust system that defends our body from any pathogen attacks. This paper presents a hybrid paradigm by implementing the Hopfield neural network integrated with enhanced AIS for solving a 3-Satisfiability (3-SAT) problem. Fundamentally, a 3-Satisfiability problem is used as an ideal optimisation problem by neural network practitioners in their research. The core impetus of this study was to compare the performance of artificial immune system (AIS) algorithm and brute-force search (BFS) algorithm in doing 3-SAT logic programming. Microsoft Visual C++ 2013 was used as a dynamic platform for training, simulating and testing of the network. We restricted our analysis to 3-Satisfiability (3-SAT) clauses. The performances of both paradigms were analysed according to the following measures, namely, global minima ratio, global Hamming distance, fitness landscape value and computational time. The experimental results successfully depicted the robustness of the AIS compared to the BFS algorithm. The work presented here has profound implications for future studies of AIS to solve more complicated NP problems.