The artificial neural network system's dynamical behaviors are greatly dependent on the construction of the network. Artificial Neural Network's outputs suffered from a shortage of interpretability and variation lead to severely limited the practical usability of artificial neural networks for doing the logical program. The goal for implementing a logical program in Hopfield neural network rotates rounding minimizing the energy function of the network to reaching the best global solution which ordinarily fetches local minimum solution also. Nevertheless, this problem can be overcome by utilizing the hyperbolic tangent activation function and the Boltzmann Machine in the Hopfield neural network. The foremost purpose of this article is to explore the solution quality obtained from the Hopfield neural network to solve 2 Satisfiability logic (2SAT) by using the Mean-Field Theory algorithm. We want for replacing the real unstable prompt local field for the separate neurons into the network by its average local field utility. By using the solution to the deterministic Mean-Field Theory (MFT) equation, the system will derive the training algorithms in which time-consuming stochastic measures of collections are rearranged. By evaluating the outputs of global minima ratio (zM), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE) with computer processing unit (CPU) time as benchmarks, we find that the MFT theory successfully captures the best global solutions by relaxation effects energy function.