How to compare two lists in Prolog?

I am trying to write a program which takes a list containing lists, and then compares the lists inside. If any two lists contain the same information, such as them both containing X, then I want to remove X from both lists. How could I go about this?

Solution

This seems to do it:

dedupe(Lists, Result) :-
    append(Lists, Flat),
    findall(E, (select(E, Flat, FlatNoE), \+ memberchk(E, FlatNoE)), Uniques),
    subtract(Flat, Uniques, Unwanted),
    findall(Rs, (member(Ls, Lists), subtract(Ls, Unwanted, Rs)), Result).

e.g.

?- dedupe([[1,2,3], [1,2,5,6,1], [4,1,2,1]], R).
R = [[3], [5, 6], [4]]

The design is:

we need to remove duplicates from each sublist
duplicates are found by finding all the elements, finding the unique elements, and removing those from all leaving the duplicate elements.
All elements are found by flattening the nested lists with append/2.
Unique elements are found by taking one element out at a time with select and seeing if that element still exists in the rest of the values with memeberchk.
subtract does a list-from-list subtraction to remove the unique elements from all the elements, leaving the Unwanted duplicate elements.
The last findall then runs subtract over the sublists, removing the duplicaates from each one.

It's possible in SWI Prolog to rewrite the last line as:

maplist({Unwanted}/[Ls, Ls_]>>subtract(Ls, Unwanted, Ls_), Lists, Result).

fwiw. In small testing they have almost identical timing/inferences to solve.