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
Minimize
  C0 + C1
Subject To
 R0: C2 = 1
 R1: C3 = 1
 R2: - C0 - C2 - C4 <= 0
 R3: - C1 - C3 - C4 <= 0
 R4: C4 <= -1
Bounds
 C0 free
 C1 free
 C2 free
 C3 free
 C4 free
End
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GUROBI
Minimize
  X[0] + X[1]
Subject To
 R0: - X[0] - Y[0] + AddExpression_1[0] = 0
 R1: - X[1] - Y[1] + AddExpression_1[1] = 0
 40: min_2 >= 1
 45[0]: Y[0] = 1
 45[1]: Y[1] = 1
Bounds
 X[0] free
 X[1] free
 Y[0] free
 Y[1] free
 AddExpression_1[0] free
 AddExpression_1[1] free
 min_2 free
General Constraints
 GC0: min_2 = MIN ( AddExpression_1[0] , AddExpression_1[1] )
End