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dbff(Columns1,Result,Formula1) :-
dbff1(Columns1,Columns1,Result,Formula1).
dbff1(Columns1,Columns2,Result,Formula1) :-
member(Column,Columns1),
Column=[Name|_Rest],
delete(Columns2,Column,Columns3),
Formula2=Name,
dbff2(Columns1,Columns3,Result,Formula2,Formula3),
list(Formula3,Formula1).
dbff2(_Columns1,[],_Result,Formula,Formula).
dbff2(Columns1,Columns2,Result,Formula1,Formula2) :-
member(Column,Columns2),
Column=[Name|_Rest],
delete(Columns2,Column,Columns3),
appendlogic(Formula1,Name,Formula3),
dbff3(Columns1,Result,Formula3),
dbff2(Columns1,Columns3,Result,Formula3,Formula2).
dbff3(Columns1,Result1,[Formula1,and,Formula2]) :-
dbff3(Columns1,Result2,Formula1),
dbff3(Columns1,Result3,Formula2),
intersection1(Result2,Result3,[],Result1).
dbff3(Columns1,Result1,[Formula1,or,Formula2]) :-
dbff3(Columns1,Result2,Formula1),
dbff3(Columns1,Result3,Formula2),
union(Result2,Result3,Result1).
dbff3(Columns,Result1,Formula1) :-
member([Formula1|Result1],Columns).
appendlogic([Formula1,Operator,Formula2],Name2,Formula3) :-
appendlogic(Formula1,Name2,Formula4),
Formula3=[Formula4,Operator,Formula2].
appendlogic([Formula1,Operator,Formula2],Name2,Formula3) :-
appendlogic(Formula2,Name2,Formula4),
Formula3=[Formula1,Operator,Formula4].
appendlogic(Formula1,Name,Formula2) :-
atom(Formula1),append([Formula1],[and,Name],Formula2).
appendlogic(Formula1,Name,Formula2) :-
atom(Formula1), append([Formula1],[or,Name],Formula2).
unique1(_Remainders,[],UniqueRemainders,UniqueRemainders) :- !.
unique1(Remainders1,Remainder,UniqueRemainders1,UniqueRemainders2) :-
delete(Remainders1,Remainder,Remainders2),
append([Remainder],Remainders2,Remainders3),
unique2(Remainders3,Remainders4,Remainders5,UniqueRemainders1,UniqueRemainders3),
unique1(Remainders5,Remainders4,UniqueRemainders3,UniqueRemainders2).
unique2(Remainders1,Remainder1,Remainders2,UniqueRemainders1,UniqueRemainders2) :-
Remainders1=[Remainder2,Remainder1|Remainders2],
append(UniqueRemainders1,[Remainder2],UniqueRemainders2).
unique2(Remainders1,_Remainder1,Remainder2,UniqueRemainders1,UniqueRemainders2) :-
Remainders1=[Remainder2],
append(UniqueRemainders1,[Remainder2],UniqueRemainders2).
intersection1([],_Result1,Result2,Result2).
intersection1(Result1,Result2,Result3,Result4) :-
Result1=[Result6|Results1],
intersection2(Result6,Result2,Result3,Result5),
intersection1(Results1,Result2,Result5,Result4).
intersection2(Result1,Result2,Result7,Result3) :-
member(Result1,Result2),
append(Result7,[Result1],Result3).
intersection2(Result1,Result2,Result7,Result7) :-
not(member(Result1,Result2)).
union(Result1,Result2,Result3) :-
append(Result1,Result2,Result4),
Result4=[Result5|Results],
unique1(Results,Result5,[],Result3).
list(Formula1,Formula2) :-
atom(Formula1),Formula2=[Formula1].
list(Formula,Formula) :-
not(atom(Formula)).
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