CVXPY
Minimize
  Sum(X, None, False)
Subject To
 59: 0.0 <= minimum(X, z, 1.0)
 63: z == 1.0
Bounds
 X free
 z free
End
----------------------------------------
AFTER COMPILATION
Minimize
  C0 + C1
Subject To
 R0: C4 = 1
 R1: - C0 - C2 <= 0
 R2: - C1 - C3 <= 0
 R3: - C2 - C4 <= 0
 R4: - C3 - C4 <= 0
 R5: - C2 <= 1
 R6: - C3 <= 1
 R7: C2 <= 0
 R8: C3 <= 0
Bounds
 C0 free
 C1 free
 C2 free
 C3 free
 C4 free
End
----------------------------------------
GUROBI
Minimize
  X[0] + X[1]
Subject To
 59[0]: minimum_1 >= 0
 59[1]: minimum_2 >= 0
 63: z = 1
Bounds
 X[0] free
 X[1] free
 z free
 minimum_1 free
 minimum_2 free
General Constraints
 GC0: minimum_1 = MIN ( X[0] , z , 1 )
 GC1: minimum_2 = MIN ( X[1] , z , 1 )
End