Cross-posting from math.stackexchange, since there might be people here familiar with this topic.
Assume working in floating point arithmetic with finite precision, bounded exponent and rounding to nearest.
Let $x,y$ be positive. It is not hard to find examples such that
$$(x+y)-x > y$$
In order to construct a test for a software I wanted to find an example or prove that such example doesn't exist of following:
Let $s(x)$ be the successor of $x$.
Is it possible to have both $$\begin{align}(x+y)-x&>y\\(x+y)-s(x)&>y\end{align}$$
It is easy to write a program that searches for such an example, but also it is unfeasible to test all possibilities and show that the example doesn't exist in this manner. So far my code hasn't got any example.
Example: In case seeing an example of $(x+y)-x>y$ helps somehow, take $$ \begin{align} x&=1.1234567891234568\\ y&=1e-5\text{ ( denoting }10^{-5}) \end{align} $$ Then $(x+y)-x=1.0000000000065512e-05 > y$. Examples of the first inequality there are many.