CVXPY
Minimize
  x + y
Subject To
 12: 1.0 <= minimum(x, y)
Bounds
 x free
 y free
End
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AFTER COMPILATION
OBJECTIVE
  Sense            : minimize
VARIABLES
  [continuous] <x_0>: obj=1, original bounds=[-inf,+inf]
  [continuous] <x_1>: obj=1, original bounds=[-inf,+inf]
  [continuous] <x_2>: obj=0, original bounds=[-inf,+inf]
CONSTRAINTS
  [linear] <c1>:  -<x_0>[C] -<x_2>[C] <= 0;
  [linear] <c2>:  -<x_1>[C] -<x_2>[C] <= 0;
  [linear] <c3>: <x_2>[C] <= -1;
END
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SCIP
OBJECTIVE
  Sense            : minimize
VARIABLES
  [continuous] <x>: obj=1, original bounds=[-inf,+inf]
  [continuous] <y>: obj=1, original bounds=[-inf,+inf]
  [continuous] <minimum_1>: obj=0, original bounds=[-inf,+inf]
CONSTRAINTS
  [linear] <minimum_1_0>: <minimum_1>[C] -<x>[C] <= 0;
  [linear] <minimum_1_1>: <minimum_1>[C] -<y>[C] <= 0;
  [linear] <12>: <minimum_1>[C] >= 1;
END