Reduce[x4 -
x5 + (x6 x4^2 (x1 + x3 + x5) (x4 + x3) -
x3 x4 x6 (x1 + x3 + x4) (x4 + x5))/((x1 + x3 + x4) (x4 +
x5) (x1 + x3 + x5) (x4 + x3)) < 0 &&
x2 - x3 + (x2^2 x6 (x1 + x3 + x4) (x1 + x2) -
x1 x2 x6 (x1 + x2 + x4) (x2 + x3))/((x1 + x3 + x4) (x1 +
x2) (x1 + x2 + x4) (x2 + x3)) < 0 &&
0 < x5 < x4 < x3 < x2 < x1 && x6 > 0, {x1, x2, x3, x4, x5,
x6}, Reals]

说明还在算。问题确实是有这么复杂的。