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
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]
  [continuous] <x_3>: obj=0, original bounds=[-inf,+inf]
  [continuous] <x_4>: obj=0, original bounds=[-inf,+inf]
CONSTRAINTS
  [linear] <c1>: <x_2>[C] == 1;
  [linear] <c2>: <x_3>[C] == 1;
  [linear] <c3>:  -<x_0>[C] -<x_2>[C] -<x_4>[C] <= 0;
  [linear] <c4>:  -<x_1>[C] -<x_3>[C] -<x_4>[C] <= 0;
  [linear] <c5>: <x_4>[C] <= -1;
END
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SCIP
OBJECTIVE
  Sense            : minimize
VARIABLES
  [continuous] <X_0>: obj=1, original bounds=[-inf,+inf]
  [continuous] <X_1>: obj=1, original bounds=[-inf,+inf]
  [continuous] <Y_0>: obj=0, original bounds=[-inf,+inf]
  [continuous] <Y_1>: obj=0, original bounds=[-inf,+inf]
  [continuous] <min_1>: obj=0, original bounds=[-inf,+inf]
CONSTRAINTS
  [linear] <min_1_0>: <X_0>[C] +<Y_0>[C] -<min_1>[C] >= 0;
  [linear] <min_1_1>: <X_1>[C] +<Y_1>[C] -<min_1>[C] >= 0;
  [linear] <40>: <min_1>[C] >= 1;
  [linear] <45_0>: <Y_0>[C] == 1;
  [linear] <45_1>: <Y_1>[C] == 1;
END