CVXPY
Minimize
  Sum(X, None, False)
Subject To
 28: 1.0 <= min(X, None, False) + min(Y, None, False)
 33: Y == 1.0
Bounds
 X free
 Y free
End
----------------------------------------
AFTER COMPILATION
Minimize
 Obj: +1 x_0 +1 x_1 +1 x_2 +1 x_3
Subject to
 c1: +1 x_5 = +1
 c2: +1 x_6 = +1
 c3: +1 x_7 = +1
 c4: +1 x_8 = +1
 c5: -1 x_0 -1 x_4 <= +0
 c6: -1 x_1 -1 x_4 <= +0
 c7: -1 x_2 -1 x_4 <= +0
 c8: -1 x_3 -1 x_4 <= +0
 c9: -1 x_5 -1 x_9 <= +0
 c10: -1 x_6 -1 x_9 <= +0
 c11: -1 x_7 -1 x_9 <= +0
 c12: -1 x_8 -1 x_9 <= +0
 c13: +1 x_4 +1 x_9 <= -1
Bounds
 x_0 free
 x_1 free
 x_2 free
 x_3 free
 x_4 free
 x_5 free
 x_6 free
 x_7 free
 x_8 free
 x_9 free
End
----------------------------------------
SCIP
Minimize
 Obj: +1 X_0_0 +1 X_0_1 +1 X_1_0 +1 X_1_1
Subject to
 min_1_0_0: +1 X_0_0 -1 min_1 >= +0
 min_1_0_1: +1 X_0_1 -1 min_1 >= +0
 min_1_1_0: +1 X_1_0 -1 min_1 >= +0
 min_1_1_1: +1 X_1_1 -1 min_1 >= +0
 min_2_0_0: +1 Y_0_0 -1 min_2 >= +0
 min_2_0_1: +1 Y_0_1 -1 min_2 >= +0
 min_2_1_0: +1 Y_1_0 -1 min_2 >= +0
 min_2_1_1: +1 Y_1_1 -1 min_2 >= +0
 28: +1 min_1 +1 min_2 >= +1
 33_0_0: +1 Y_0_0 = +1
 33_0_1: +1 Y_0_1 = +1
 33_1_0: +1 Y_1_0 = +1
 33_1_1: +1 Y_1_1 = +1
Bounds
 X_0_0 free
 X_0_1 free
 X_1_0 free
 X_1_1 free
 min_1 free
 Y_0_0 free
 Y_0_1 free
 Y_1_0 free
 Y_1_1 free
 min_2 free
End