  Khabibullin's conjecture for integral inequalities has two numeric parameters
$n$ and $\alpha$ in its statement, $n$ being a positive integer and $\alpha$
being a positive real number. This conjecture is already proved in the case
where $n>0$ and $0<\alpha\leq 1/2$. However, for $\alpha>1/2$ it is not always
valid. In this paper a counterexample is constructed for $n=2$ and $\alpha=2$.
Then Khabibullin's conjecture is reformulated in a way suitable for all
$\alpha>0$.
