If there exists a solution for following system of inequalities, find at least one, else show that there is no solution exists.
$$x_4(x_1+x_7)>x_3(x_2+x_8)$$ $$x_3(x_5+x_8)>x_7(x_4+x_1)$$ $$x_7(x_6+x_4)>x_8(x_5+x_3)$$ $$x_8(x_3+x_2)>x_4(x_6+x_7)$$
for all $i$, $0 < x_i <1$ and $\sum_i x_i=1$