CVXPY
Minimize
  Sum(X, None, False)
Subject To
 70: 0.0 <= minimum(X, z, 1.0)
 74: z == 1.0
Bounds
 X free
 z free
End
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AFTER COMPILATION
Minimize
  C0 + C1 + C2 + C3
Subject To
 R0: C8 = 1
 R1: - C0 - C4 <= 0
 R2: - C1 - C5 <= 0
 R3: - C2 - C6 <= 0
 R4: - C3 - C7 <= 0
 R5: - C4 - C8 <= 0
 R6: - C5 - C8 <= 0
 R7: - C6 - C8 <= 0
 R8: - C7 - C8 <= 0
 R9: - C4 <= 1
 R10: - C5 <= 1
 R11: - C6 <= 1
 R12: - C7 <= 1
 R13: C4 <= 0
 R14: C5 <= 0
 R15: C6 <= 0
 R16: C7 <= 0
Bounds
 C0 free
 C1 free
 C2 free
 C3 free
 C4 free
 C5 free
 C6 free
 C7 free
 C8 free
End
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GUROBI
Minimize
  X[0,0] + X[0,1] + X[1,0] + X[1,1]
Subject To
 70[0,0]: minimum_1 >= 0
 70[0,1]: minimum_2 >= 0
 70[1,0]: minimum_3 >= 0
 70[1,1]: minimum_4 >= 0
 74: z = 1
Bounds
 X[0,0] free
 X[0,1] free
 X[1,0] free
 X[1,1] free
 z free
 minimum_1 free
 minimum_2 free
 minimum_3 free
 minimum_4 free
General Constraints
 GC0: minimum_1 = MIN ( X[0,0] , z , 1 )
 GC1: minimum_2 = MIN ( X[0,1] , z , 1 )
 GC2: minimum_3 = MIN ( X[1,0] , z , 1 )
 GC3: minimum_4 = MIN ( X[1,1] , z , 1 )
End