/**

%% Popology > An object can be human like > 24

logic_ff0([
[[[a, true], [b,  false],[c,true],[d,false]], [true]],
[[[a, true], [b,  false],[c,false],[d,false]], [true]],
[[[a, false], [b,  false],[c,true],[d,false]], [true]],
[[[a, true], [b,  true],[c,true],[d,false]], [true]],
[[[a, false], [b,  false],[c,false],[d,false]], [true]]
],F).

F=[[not,d],[not,[a,and,[d,and,[b,and,c]]]],[not,[a,and,[d,and,[b,or,c]]]],[not,[a,and,[d,and,[c,and,b]]]],[not,[a,and,[d,and,[c,or,b]]]],[not,[a,and,[d,and,[not,[b,and,c]]]]],[not,[a,and,[d,and,[not,[b,or,c]]]]],[not,[a,and,[d,and,[not,[c,and,b]]]]],[not,[a,and,[d,and,[not,[c,or,b]]]]],[not,[a,and,[[d,and,b],and,c]]],[not,[a,and,[[d,and,c],and,b]]],[not,[a,and,[[not,[d,or,c]],and,b]]],[not,[b,and,[d,and,[a,and,c]]]],[not,[b,and,[d,and,[a,or,c]]]],[not,[b,and,[d,and,[c,and,a]]]],[not,[b,and,[d,and,[c,or,a]]]],...

logic_ff0([                                                         [[[a, true]], [false]],[[[a,false]], [true]]],F).
F = [[not, a]].

logic_ff0([                                                         [[[a, true]], [true]],[[[a,false]], [false]]],F).
F = [[a]].

logic_ff0([                                                         [[[a, true],[b, true]], [false]],[[[a,false],[b, false]], [true]]],F).
F=[[not,a],[not,b],[not,[a,and,b]],[not,[a,or,b]],[not,[b,and,a]],[not,[b,or,a]]]


logic_ff0([                                                         [[[a, true],[b, false]], [false]],[[[a,false],[b, true]], [true]]],F).
F = [[not, a]].
**/
 
logic_ff0(Specs,Formula0) :-
	Specs=[[A1,A2]|A3],
	findall(B,logic_ff1(A1,A1,A2,B),C),
	logic_ff01(A3,C,Formula0),
	writeln(Formula0).
	
logic_ff01([],Formula,Formula) :- !.
logic_ff01(Specs,Formula1,Formula2) :-
	Specs=[[A1,A2]|A3],
	findall(B,logic_ff1(A1,A1,A2,B),C),
	intersection(Formula1,C,Formula4),
	sort(Formula4,Formula5),
	logic_ff01(A3,Formula5,Formula2).

	
logic_ff1(Columns1,Columns2,Result,Formula1) :-
        member(Column,Columns1),
        Column=[Name|_Rest],
        delete(Columns2,Column,Columns3),
	Formula2=Name,
        logic_ff2(Columns1,Columns3,Result,Formula2,Formula3),
	list(Formula3,Formula1).
logic_ff2([[A, true]],[],[false],A,[not,A]):-!.
logic_ff2([[A, false]],[],[true],A,[not,A]):-!.
logic_ff2(_Columns1,[],_Result,Formula,Formula).
logic_ff2(Columns1,Columns2,Result,Formula1,Formula2) :-
	member(Column,Columns2),
	Column=[Name|_Rest],
	delete(Columns2,Column,Columns3),
	appendlogic(Formula1,Name,Formula3),
        logic_ff3(Columns1,Result,Formula3),
	logic_ff2(Columns1,Columns3,Result,Formula3,Formula2).


logic_ff2(Columns1,Columns2,Result,_Formula1,Formula2) :-
	member(Column,Columns2),
	Column=[Name|_Rest],
	delete(Columns2,Column,Columns3),
	appendlogic(%%Formula1,
	Name,
	Formula3),
        logic_ff3(Columns1,Result,Formula3),
	logic_ff2(Columns1,Columns3,Result,Formula3,Formula2).


logic_ff3(Columns1,Result1,[not,Formula2]) :-
        logic_ff3(Columns1,Result3,Formula2),
        not(Result3,[],Result1).


logic_ff3(Columns1,Result1,[Formula1,and,Formula2]) :-
        logic_ff3(Columns1,Result2,Formula1),
        logic_ff3(Columns1,Result3,Formula2),
        and1(Result2,Result3,[],Result1).
logic_ff3(Columns1,Result1,[Formula1,or,Formula2]) :-
        logic_ff3(Columns1,Result2,Formula1),
        logic_ff3(Columns1,Result3,Formula2),
        or(Result2,Result3,Result1).
logic_ff3(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([Operator,Formula2],Name2,Formula3) :-

        appendlogic(Formula2,Name2,Formula4),
        Formula3=[Operator,Formula4].


appendlogic(Formula1,Name,Formula2) :-
	atom(Formula1),append([Formula1],[and,Name],Formula2).
appendlogic(Formula1,Name,Formula2) :-
	atom(Formula1), append([Formula1],[or,Name],Formula2).

appendlogic(Formula1,Name,Formula2) :-
	atom(Formula1),append([Formula1],[and,Name],Formula3),
	Formula2=[not,Formula3].
appendlogic(Formula1,Name,Formula2) :-
	atom(Formula1), append([Formula1],[or,Name],Formula3),
	Formula2=[not,Formula3].


appendlogic(F,
%%Name,
Formula2) :-
%%writeln([f,F]),
	%%atom(Formula1), 
	append([],[not,F],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)).
	
and1([true],[true],[],[true]):-!.
and1([false],[true],[],[false]):-!.
and1([true],[false],[],[false]):-!.
and1([false],[false],[],[false]):-!.
or([false],[false],[false]):-!.
or([true],[false],[true]):-!.
or([false],[true],[true]):-!.
or([true],[true],[true]):-!.
not([true],[],[false]):-!.
not([false],[],[true]):-!.