CVXPY
Minimize
  Sum(X, None, False)
Subject To
 40: 1.0 <= min(X + Y, None, False)
 45: Y == 1.0
Bounds
 X free
 Y free
End
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AFTER COMPILATION
Minimize
 Obj: +1 x_0 +1 x_1
Subject to
 c1: +1 x_2 = +1
 c2: +1 x_3 = +1
 c3: -1 x_0 -1 x_2 -1 x_4 <= +0
 c4: -1 x_1 -1 x_3 -1 x_4 <= +0
 c5: +1 x_4 <= -1
Bounds
 x_0 free
 x_1 free
 x_2 free
 x_3 free
 x_4 free
End
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SCIP
Minimize
 Obj: +1 X_0 +1 X_1
Subject to
 min_1_0: +1 X_0 +1 Y_0 -1 min_1 >= +0
 min_1_1: +1 X_1 +1 Y_1 -1 min_1 >= +0
 40: +1 min_1 >= +1
 45_0: +1 Y_0 = +1
 45_1: +1 Y_1 = +1
Bounds
 X_0 free
 X_1 free
 Y_0 free
 Y_1 free
 min_1 free
End