%------------------------------------------------------------------------------
% File     : PUZ135_2 : TPTP v8.2.0. Released v5.1.0.
% Domain   : Puzzles
% Problem  : The Knowheyan Art Fair Puzzle - Order
% Version  : Especial.
% English  : Knowheyans are not negative by nature; it is just that their way
%            of expressing themselves, using negative sentences, makes it 
%            appear that way. Several fortunate visitors have an opportunity
%            to attend the Midseason Art Fair, in which they are able to 
%            observe a variety of Knowheyans art forms. An artists' competition
%            was held as part of the fair and awards were given for the top
%            four entries, which were collage painting, holography, laser
%            etchings, and reconstituted materials sculpture. The interpreter
%            is explaining the results of the competition to the visitors:
%            1. A, who was not the first-place winner, did not enter a 
%               holograph.
%            2. The fourth-place winner did not enter a sculpture or a 
%               holograph.
%            3. The one who entered the collage painting, who was neither A
%               nor C, did not win first or second place.
%            4. Neither B, nor the one who entered the laser etching, was the
%               fourth-place winner.
%            5. The third-place winner was neither B nor C.
%            6. The one who entered the laser etching, who was not A, was not
%               the second place winner.
%            In what order did they finish?

% Refs     : [WS+06] Willis et al. (2006), The World's Biggest Book of Brai
% Source   : [TPTP]
% Names    :

% Status   : Theorem
% Rating   : 0.00 v6.0.0, 0.60 v5.5.0, 0.25 v5.4.0, 0.33 v5.3.0, 0.00 v5.2.0, 0.33 v5.1.0
% Syntax   : Number of formulae    :   47 (  18 unt;  17 typ;   0 def)
%            Number of atoms       :   57 (  57 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :   64 (  37   ~;   9   |;  12   &)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    3 (   3 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    1 (   0 usr;   0 prp; 2-2 aty)
%            Number of functors    :   14 (  14 usr;  12 con; 0-1 aty)
%            Number of variables   :   11 (  11   !;   0   ?;  11   :)
% SPC      : TF0_THM_EQU_NAR

% Comments :
%------------------------------------------------------------------------------
tff(knowheyan_type,type,
    knowheyan: $tType ).

tff(place_type,type,
    place: $tType ).

tff(entry_type,type,
    entry: $tType ).

tff(entry_of_type,type,
    entry_of: knowheyan > entry ).

tff(place_of_type,type,
    place_of: knowheyan > place ).

tff(a_knowheyan,type,
    a: knowheyan ).

tff(b_knowheyan,type,
    b: knowheyan ).

tff(c_knowheyan,type,
    c: knowheyan ).

tff(d_knowheyan,type,
    d: knowheyan ).

tff(a_not_b,axiom,
    a != b ).

tff(a_not_c,axiom,
    a != c ).

tff(a_not_d,axiom,
    a != d ).

tff(b_not_c,axiom,
    b != c ).

tff(b_not_d,axiom,
    b != d ).

tff(c_not_d,axiom,
    c != d ).

tff(collage_painting_entry,type,
    collage_painting: entry ).

tff(holography_entry,type,
    holography: entry ).

tff(laser_etching_entry,type,
    laser_etching: entry ).

tff(reconstituted_materials_sculpture_entry,type,
    reconstituted_materials_sculpture: entry ).

tff(collage_painting_not_holography,axiom,
    collage_painting != holography ).

tff(collage_painting_not_laser_etching,axiom,
    collage_painting != laser_etching ).

tff(collage_painting_not_reconstituted_materials_sculpture,axiom,
    collage_painting != reconstituted_materials_sculpture ).

tff(holography_not_laser_etching,axiom,
    holography != laser_etching ).

tff(holography_not_reconstituted_materials_sculpture,axiom,
    holography != reconstituted_materials_sculpture ).

tff(laser_etching_not_reconstituted_materials_sculpture,axiom,
    laser_etching != reconstituted_materials_sculpture ).

tff(first_place,type,
    first: place ).

tff(second_place,type,
    second: place ).

tff(third_place,type,
    third: place ).

tff(fourth_place,type,
    fourth: place ).

tff(first_not_second,axiom,
    first != second ).

tff(first_not_third,axiom,
    first != third ).

tff(first_not_fourth,axiom,
    first != fourth ).

tff(second_not_third,axiom,
    second != third ).

tff(second_not_fourth,axiom,
    second != fourth ).

tff(third_not_fourth,axiom,
    third != fourth ).

tff(only_knowheyans,axiom,
    ! [X: knowheyan] :
      ( ( X = a )
      | ( X = b )
      | ( X = c )
      | ( X = d ) ) ).

tff(only_entries,axiom,
    ! [X: entry] :
      ( ( X = collage_painting )
      | ( X = holography )
      | ( X = laser_etching )
      | ( X = reconstituted_materials_sculpture ) ) ).

tff(only_places,axiom,
    ! [X: place] :
      ( ( X = first )
      | ( X = second )
      | ( X = third )
      | ( X = fourth ) ) ).

tff(unique_entrys,axiom,
    ! [X: knowheyan,Y: knowheyan] :
      ( ( X != Y )
     => ( entry_of(X) != entry_of(Y) ) ) ).

tff(unique_places,axiom,
    ! [X: knowheyan,Y: knowheyan] :
      ( ( X != Y )
     => ( place_of(X) != place_of(Y) ) ) ).

tff(a_info,axiom,
    ( ( place_of(a) != first )
    & ( entry_of(a) != holography ) ) ).

tff(fourth_info,axiom,
    ! [X: knowheyan] :
      ( ( place_of(X) = fourth )
     => ( ( entry_of(X) != reconstituted_materials_sculpture )
        & ( entry_of(X) != holography ) ) ) ).

tff(collage_info,axiom,
    ! [X: knowheyan] :
      ( ( entry_of(X) = collage_painting )
     => ( ( X != a )
        & ( X != c )
        & ( place_of(X) != first )
        & ( place_of(X) != second ) ) ) ).

tff(fourth_info2,axiom,
    ( ( place_of(b) != fourth )
    & ! [X: knowheyan] :
        ( ( entry_of(X) = laser_etching )
       => ( place_of(X) != fourth ) ) ) ).

tff(third_info,axiom,
    ( ( place_of(b) != third )
    & ( place_of(c) != third ) ) ).

tff(laser_etching_info,axiom,
    ( ( entry_of(b) != laser_etching )
    & ! [X: knowheyan] :
        ( ( entry_of(X) = laser_etching )
       => ( ( X != a )
          & ( place_of(X) != second ) ) ) ) ).

tff(places,conjecture,
    ( ( place_of(a) = third )
    & ( place_of(b) = second )
    & ( place_of(c) = first )
    & ( place_of(d) = fourth ) ) ).

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