CVXPY
Minimize
  x
Subject To
 33: 1.0 <= minimum(x + 1.0, 2.0)
Bounds
 x free
End
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AFTER COMPILATION
Minimize
 Obj: +1 x_0
Subject to
 c1: -1 x_0 -1 x_1 <= +1
 c2: -1 x_1 <= +2
 c3: +1 x_1 <= -1
Bounds
 x_0 free
 x_1 free
End
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SCIP
Minimize
 Obj: +1 x
Subject to
 minimum_1_0: +1 minimum_1 -1 x <= +1
 minimum_1_1: +1 minimum_1 <= +2
 33: +1 minimum_1 >= +1
Bounds
 x free
 minimum_1 free
End