CVXPY
Minimize
  x + y
Subject To
 12: 1.0 <= minimum(x, y)
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_0 -1 x_2 <= +0
 c2: -1 x_1 -1 x_2 <= +0
 c3: +1 x_2 <= -1
Bounds
 x_0 free
 x_1 free
 x_2 free
End
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SCIP
Minimize
 Obj: +1 x +1 y
Subject to
 minimum_1_0: +1 minimum_1 -1 x <= +0
 minimum_1_1: +1 minimum_1 -1 y <= +0
 12: +1 minimum_1 >= +1
Bounds
 x free
 y free
 minimum_1 free
End