Let's define $S(x) = \vartheta(x) - x$, where $\vartheta(x)$ is the Chebyshev function. We prove that the Riemann Hypothesis is false when $\int_{x}^{\infty} \frac{S(y) \times (1 + \log y)}{y^{2} \times \log^{2} y} dy \geq \frac{S(x)^{2}}{x^{2} \times \log x}$ is satisfied for some number $x \geq 121$. In addition, we demonstrate that the previous inequality is satisfied when $S(x) \geq 0$ for some number $x \geq 121$. It is known that $S(x)$ changes sign infinitely often. In this way, we show that the Riemann Hypothesis is indeed false.