The 4x4 example.

Maximize
  Obj: 0
Subject to
  x3 = 1
  x3 + x4 + x9 = 1
  x2 + x3 + x4 + x6 + x9 + x11 + x14 = 1
  x2 + x3 + x4 + x5 + x6 + x7 + x11 + x13 = 1
  x2 + x4 + x6 + x7 + x10 + x12 + x13 + x15 = 1
  x1 + x7 + x12 = 1
  x2 + x8 + x9 + x14 = 1
  x1 + x5 + x8 + x10 + x11 + x13 + x14 = 1
  x1 + x5 + x6 + x8 + x10 + x15 = 1
  x1 + x5 + x12 + x15 = 1
  x1 + x2 + x3 + x4 + x5 + x6 = 1
  x7 + x8 + x9 = 1
  x10 + x11 + x12 + x13 + x14 + x15 = 1
  4 x1 + 4 x2 + 4 x3 + 4 x4 + 4 x5 + 4 x6 + 3 x7 + 3 x8 + 3 x9 + 3 x10 + 3 x11 + 3 x12 + 3 x13 + 3 x14 + 3 x15 = 10
Binary
  x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15
End