CVXPY
Minimize
  Sum(X, None, False)
Subject To
 28: 1.0 <= min(X, None, False) + min(Y, None, False)
 33: Y == 1.0
Bounds
 X free
 Y free
End
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AFTER COMPILATION
Minimize
  C0 + C1
Subject To
 R0: C3 = 1
 R1: C4 = 1
 R2: - C0 - C2 <= 0
 R3: - C1 - C2 <= 0
 R4: - C3 - C5 <= 0
 R5: - C4 - C5 <= 0
 R6: C2 + C5 <= -1
Bounds
 C0 free
 C1 free
 C2 free
 C3 free
 C4 free
 C5 free
End
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GUROBI
Minimize
  X[0] + X[1]
Subject To
 28: min_1 + min_2 >= 1
 33[0]: Y[0] = 1
 33[1]: Y[1] = 1
Bounds
 X[0] free
 X[1] free
 min_1 free
 Y[0] free
 Y[1] free
 min_2 free
General Constraints
 GC0: min_1 = MIN ( X[0] , X[1] )
 GC1: min_2 = MIN ( Y[0] , Y[1] )
End