Inequality testing using numerical substitution

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I am seeing that CASs might fail in inequality testing, so a vague approach can be to test them for very large number of values sampled at some interval and it might give at least some approximation. But it can't be a water-tight approach.

I want to know if someone has some examples to share where such a scenario will fail.

Example, On maxima, for $k>1$ and $k\in\mathbb{Z}$

$:is(k^2>k)$ is true

$:is(k^2+1>k);$ is unknown

$:is(k^2+1>k+1);$ is true

From the definition of inequality testing, if $a>b$ then,$a+c>b+c$ is fine, but $k^2+anything$ will keep it still great, for $k^2$ is even function.

This can be tested for numerical values. Can someone give some examples where numerical testing is certain to fail.