A conventional systematic satisfiability logic suffers from a nonflexible logical structure that leads to a lack of interpretation. To resolve this problem, the advantage of introducing nonsystematic satisfiability logic is important to improve the flexibility of the logical structure. This paper proposes Random 3 Satisfiability ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RAN3SAT</i> ) with three types of logical combinations ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k = 1, 3, k =2, 3$ </tex-math></inline-formula> , and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k =1$ </tex-math></inline-formula> , 2, 3) to report the behaviors of multiple logical structures. The different types of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RAN3SAT</i> enforced with Discrete Hopfield Neural Network (DHNN) are included with benchmark searching techniques, such as Exhaustive Search algorithm. Additionally, to strengthen and certify the behavior of the proposed model, we extensively conducted several performance evaluation metrics with a specific number of neurons. In particular, the experimental results revealed that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RAN3SAT</i> was able to be implemented in DHNN, and each logical combination has its characteristics. Nonetheless, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RAN3SAT</i> provides more neuron variations in the whole solution space. The proposed model can also be applied in real-world applications such as the logic mining approach since <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RAN3SAT</i> consists of various logic combinat...