A counterexample to Khabibullin's conjecture for integral inequalities

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 was already proved for the case where $n>0$ and $0<\alpha\leq1/2$. However, it is not always valid for $\alpha>1/2$. In this paper a counterexample is constructed for $n=2$ and $\alpha=2$. Thus Khabibullin's conjecture is reformulated so that it holds for all $\alpha>0$.