Computer-tested inequalities for triangular ratio metric extremal points

Let $\mathbb{B}^2$ be the unit disk, and let $s_{\mathbb{B}^2}$ and $p_{\mathbb{B}^2}$ denote the triangular ratio and point-pair metrics, respectively. For $x,y\in\mathbb{B}^2$, let $x_i,y_i$, $i=0,\ldots,3$, be the points defined in Definitions and. Extremal-point inequalities. For all $x,y\in\mathbb{B}^2$,

1. $s_{\mathbb{B}^2}(x_2,y_2)\geq s_{\mathbb{B}^2}(x_0,y_0)$,
2. $s_{\mathbb{B}^2}(x_3,y_3)\leq s_{\mathbb{B}^2}(x_1,y_1)$,
3. $s_{\mathbb{B}^2}(x_3,y_3)\leq p_{\mathbb{B}^2}(x,y)$. These inequalities were suggested by numerous computer tests; their validity would compare the triangular ratio metric at the configurations introduced in the cited definitions and relate it to the point-pair metric.