# Solving the five-house riddle
#
# House positions connect nationalities, colors, drinks, pets, and smoking
# brands. N3 rules combine the puzzle's constraints to derive the complete
# arrangement and identify who owns the fish.

@prefix : <http://eulersharp.sourceforge.net/2005/11swap/zebra#> .
@prefix list: <http://www.w3.org/2000/10/swap/list#> .
@prefix math: <http://www.w3.org/2000/10/swap/math#> .
@prefix log: <http://www.w3.org/2000/10/swap/log#> .

{

    # Green is immediately left of white. The green house drinks coffee.
    (1 2 3 4) list:member ?Green .
    (?Green 1) math:sum ?White .
    ?Green log:notEqualTo 2, 3 .
    ?White log:notEqualTo 2 .

    # The Brit lives in red; the Norwegian lives in house 1.
    (1 2 3 4 5) list:member ?Red .
    ?Red log:notEqualTo 1, 2, ?Green, ?White .
    (1 2 3 4 5) list:member ?Yellow .
    ?Yellow log:notEqualTo 2, ?Green, ?White, ?Red .

    # The Dane drinks tea, the Swede keeps dogs, the German smokes Prince.
    (1 2 3 4 5) list:member ?Dane .
    ?Dane log:notEqualTo 1, ?Red, 3, ?Green .
    (1 2 3 4 5) list:member ?Swede .
    ?Swede log:notEqualTo 1, ?Red, ?Dane .
    (1 2 3 4 5) list:member ?German .
    ?German log:notEqualTo 1, ?Red, ?Dane, ?Swede, ?Yellow .

    # Yellow smokes Dunhill; its neighbour keeps horses.
    (1 2 3 4 5) list:member ?Horse .
    (?Horse ?Yellow) math:difference ?HorseDelta .
    ?HorseDelta math:absoluteValue 1 .
    ?Horse log:notEqualTo ?Swede .

    # Pall Mall smokers keep birds; Blue Masters smokers drink beer.
    (1 2 3 4 5) list:member ?Birds .
    ?Birds log:notEqualTo ?Yellow, ?German, ?Horse, ?Swede .
    (1 2 3 4 5) list:member ?Beer .
    ?Beer log:notEqualTo ?Yellow, ?German, ?Birds, 3, ?Green, ?Dane .
    (1 2 3 4 5) list:member ?Blends .
    ?Blends log:notEqualTo ?Yellow, ?German, ?Birds, ?Beer .

    # Blends has a neighbour with cats and a neighbour who drinks water.
    (1 2 3 4 5) list:member ?Cats .
    ?Cats log:notEqualTo ?Horse, ?Swede, ?Birds .
    (?Blends ?Cats) math:difference ?CatDelta .
    ?CatDelta math:absoluteValue 1 .
    (1 2 3 4 5) list:member ?Water .
    ?Water log:notEqualTo 3, ?Green, ?Dane, ?Beer .
    (?Blends ?Water) math:difference ?WaterDelta .
    ?WaterDelta math:absoluteValue 1 .

    # The fifth pet is the fish. Find the nationality at that position.
    (1 2 3 4 5) list:member ?Fish .
    ?Fish log:notEqualTo ?Horse, ?Swede, ?Birds, ?Cats .
    ((1 :norwegian) (?Red :brit) (?Swede :swede) (?Dane :dane) (?German :german)) list:member (
        ?Fish ?Owner
    ) .
} => {
    ?Owner :eats :fish .
    :solution :positions (
        ((?Yellow :yellow) (2 :blue) (?Red :red) (?Green :green) (?White :white))
        ((1 :norwegian) (?Red :brit) (?Swede :swede) (?Dane :dane) (?German :german))
        ((?Horse :horse) (?Swede :dogs) (?Birds :birds) (?Cats :cats) (?Fish :fish))
        ((3 :milk) (?Green :coffee) (?Dane :tea) (?Beer :beer) (?Water :water))
        (
            (?Yellow :dunhill)
            (?German :prince)
            (?Birds :pallmall)
            (?Beer :bluemasters)
            (?Blends :blends)
        )
    ) .
} .

# Present the five houses in their left-to-right order.
{
    :solution :positions (?Colours ?Nationalities ?Pets ?Drinks ?Cigars) .
    (1 2 3 4 5) list:member ?Position .
    ?Colours list:member (?Position ?Colour) .
    ?Nationalities list:member (?Position ?Nationality) .
    ?Pets list:member (?Position ?Pet) .
    ?Drinks list:member (?Position ?Drink) .
    ?Cigars list:member (?Position ?Cigar) .
} => {
    :solution :house (?Position ?Colour ?Nationality ?Pet ?Drink ?Cigar) .
} .

{
    ?Owner :eats :fish
} log:query {
    ?Owner :eats :fish
} .

{
    :solution :house ?House
} log:query {
    :solution :house ?House
} .