> 3. Yet another description (as pointed out by Erwin and Michael)
> 
>    z >= x
> 
>    z >= y
> 
>    z <= x+y
> 
>    It is a good description, because all inequalities are facet-defined
>    (until the mip instance includes other constraints).
> 

This case is a CNF description, because

z >= x     can be written as   z + (1 - x) >= 1    
z >= y     can be written as   z + (1 - y) >= 1    
z <= x+y   can be written as   x + y + (1 - z) >= 1

so it is equivalent to the case 1, where one of the constriants is
redundant.


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