CVXPY
Minimize
  Sum(X + Y, None, False)
Subject To
 31: -2.0 <= minimum(X, Y, [[1.00 -2.00]
 [3.00 4.00]])
Bounds
 X free
 Y free
End
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AFTER COMPILATION
Minimize
 Obj: +1 x_0 +1 x_1 +1 x_2 +1 x_3 +1 x_4 +1 x_5 +1 x_6 +1 x_7
Subject to
 c1: -1 x_0 -1 x_8 <= +0
 c2: -1 x_1 -1 x_9 <= +0
 c3: -1 x_2 -1 x_10 <= +0
 c4: -1 x_3 -1 x_11 <= +0
 c5: -1 x_4 -1 x_8 <= +0
 c6: -1 x_5 -1 x_9 <= +0
 c7: -1 x_6 -1 x_10 <= +0
 c8: -1 x_7 -1 x_11 <= +0
 c9: -1 x_8 <= +1
 c10: -1 x_9 <= +3
 c11: -1 x_10 <= -2
 c12: -1 x_11 <= +4
 c13: +1 x_8 <= +2
 c14: +1 x_9 <= +2
 c15: +1 x_10 <= +2
 c16: +1 x_11 <= +2
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
 x_10 free
 x_11 free
End
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SCIP
Minimize
 Obj: +1 X_0_0 +1 X_0_1 +1 X_1_0 +1 X_1_1 +1 Y_0_0 +1 Y_0_1 +1 Y_1_0 +1 Y_1_1
Subject to
 minimum_1_0_0_0: +1 minimum_1_0_0 -1 X_0_0 <= +0
 minimum_1_0_0_1: +1 minimum_1_0_1 -1 X_0_1 <= +0
 minimum_1_0_1_0: +1 minimum_1_1_0 -1 X_1_0 <= +0
 minimum_1_0_1_1: +1 minimum_1_1_1 -1 X_1_1 <= +0
 minimum_1_1_0_0: +1 minimum_1_0_0 -1 Y_0_0 <= +0
 minimum_1_1_0_1: +1 minimum_1_0_1 -1 Y_0_1 <= +0
 minimum_1_1_1_0: +1 minimum_1_1_0 -1 Y_1_0 <= +0
 minimum_1_1_1_1: +1 minimum_1_1_1 -1 Y_1_1 <= +0
 minimum_1_2_0_0: +1 minimum_1_0_0 <= +1
 minimum_1_2_0_1: +1 minimum_1_0_1 <= -2
 minimum_1_2_1_0: +1 minimum_1_1_0 <= +3
 minimum_1_2_1_1: +1 minimum_1_1_1 <= +4
 31_0_0: +1 minimum_1_0_0 >= -2
 31_0_1: +1 minimum_1_0_1 >= -2
 31_1_0: +1 minimum_1_1_0 >= -2
 31_1_1: +1 minimum_1_1_1 >= -2
Bounds
 X_0_0 free
 X_0_1 free
 X_1_0 free
 X_1_1 free
 Y_0_0 free
 Y_0_1 free
 Y_1_0 free
 Y_1_1 free
 minimum_1_0_0 free
 minimum_1_0_1 free
 minimum_1_1_0 free
 minimum_1_1_1 free
End