A puzzling inequality involving exp, erf, and log

Question

For $0<y<x<\infty$, I believe the following inequality is true (I've tested it numerically with random values for $x$ and $y$) but have been unable to analytically confirm: \begin{align} s(x,y) = \frac{g(x,y)}{h(x,y)} = \frac{xe^{x^2}\left[\ln \left( \frac{1+{\rm erf}(y)}{1-{\rm erf}(y)}\right)-{\rm erf}(x)\ln \left( \frac{1+{\rm erf}(x){\rm erf}(y)}{1-{\rm erf}(x){\rm erf}(y)}\right)\right]}{ye^{y^2} \left[\ln \left( \frac{1+{\rm erf}(x)}{1-{\rm erf}(x)}\right)-{\rm erf}(y)\ln \left( \frac{1+{\rm erf}(x){\rm erf}(y)}{1-{\rm erf}(x){\rm erf}(y)}\right)\right]} < 1 \end{align} Any help is greatly appreciated.