Question: How to solve it?

Solving the system

 a1 := 2*x2-x3-x4-x5-x6-x7;
 a2 := -2*x1+2*x3-x4-x5-x6-x7;
 a3 := x1-2*x2+2*x4-x5-x6-x7;
 a4 := x1+x2-2*x3+2*x5-x6-x7;
 a5 := x1+x2+x3-2*x4+2*x6-x7;
 a6 := x1+x2+x3+x4-2*x5+2*x7;
 a7 := x1+x2+x3+x4+x5-2*x6; b := x1+x2+x3+x4+x5+x6+x7;
 solve({x1 >= 0, x2 >= 0, x3 >= 0, x4 >= 0, x5 >= 0, x6 >= 0, x7 >= 0,
 b = 1, a1 <= 0, a2 <= 0, a3 <= 0, a4 <= 0, a5 <= 0, a6 <= 0, a7 <= 0},
 {x1, x2, x3, x4, x5, x6, x7});

 with Maple 13, I obtain only the communication " Warning, solutions may have been lost ". I know that the system under consideration has solutions. Maple 13 solves the reduced system

 solve({x1 >= 0, x2 >= 0, x3 >= 0, x4 >= 0, x5 >= 0, x6 >= 0, x7 >= 0,
 b = 1, a5 <= 0, a6 <= 0, a7 <= 0}, {x1, x2, x3, x4, x5, x6, x7}) .
 
 The output is too long to be cited here.

PS. My attempt to solve this system with the  DirectSearch package was unsuccessful.