This link does not seem to work. Think you'll find the reference to "DLTR" is a bit out of date now. What used to be DLTR is now ODPM.
An attempted answer to the question is this -
Three of adults in the property are joint owners and are all jointly liable for the CT. The partner is also jointly liable because he is the partner of a liable person. (If I read your post right only 3 of the 5 joint owners reside in the property, the 4th person being the partner of one of them.) The 18-year old son is not liable because the other adults' ownership of the property takes precedence over his mere presence in determining liability. The other two owners are not liable because they don't live there.
Whilst the two SMI people can be ignored for the purposes of assessing a discount this is not significant as there are still two other adult occupiers (well 3 actually including the 18 year-old). I am not clear where the "50% reduction" comes in.
Importantly, their SMI status does NOT mean that they are not liable.
The position re CTB is that the two disabled sisters and the couple could each make claims. In assessing these claims the two disabled sisters would each be allocated one quarter of the CT and the couple the other half (is that where this "50%" comes in?). The relative sizes of the shares held by different owners is not relevant.
The respective "benefit households" are - each of the two disabled sisters would claim for themselves alone, the married couple and their children would constitute another separate household. My own view about the 18 year old is that s/he is a non-dependant of his parents ALONE - he is not a non-dep of all of the liable persons, but another council may disagree on that.
The final point to remember is that although the liability is split like this for CTB purposes, it does not alter there joint and several liability for the whole lot - the Council can enforce debts against any or all of them.
I'm going to get some lunch now......
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