The k Satisfiability logic representation (kSAT) contains valuable information that can be represented in terms of variables. This paper investigates the use of a particular non-systematic logical rule namely Random k Satisfiability (RANkSAT). RANkSAT contains a series of satisfiable clauses but the structure of the formula is determined randomly by the user. In the present study, RANkSAT representation is successfully implemented in Hopfield Neural Network (HNN) by obtaining the optimal synaptic weights. We focus on the different regimes for k ≤ 2 by taking advantage of the non-redundant logical structure, thus obtaining the final neuron state that minimizes the cost function. We also simulate the performances of RANkSAT logical rule using several performance metrics. The simulated results suggest that the RANkSAT representation can be embedded optimally in HNN and that the proposed method can retrieve the optimal final state.