TPTP Problem File: PUZ142^1.p

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% File     : PUZ142^1 : TPTP v7.1.0. Released v6.2.0.
% Domain   : Puzzles
% Problem  : Labyrinth2
% Version  : Especial.
% English  : Go around a corner.

% Refs     : [Cam14] Camarero (2014), Email to Geoff Sutcliffe
% Source   : [Cam14]
% Names    : labyrinth2 [Cam14]

% Status   : Theorem
% Rating   : 0.62 v7.1.0, 0.75 v7.0.0, 0.71 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0
% Syntax   : Number of formulae    :   84 (   0 unit;  37 type;  20 defn)
%            Number of atoms       :  243 (  49 equality;  26 variable)
%            Maximal formula depth :   10 (   3 average)
%            Number of connectives :   99 (   1   ~;   0   |;   0   &;  94   @)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   41 (  37   :;   0   =)
%            Number of variables   :   12 (   0 sgn;  11   !;   1   ?;   0   ^)
%                                         (  12   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_EQU_NAR

% Comments :
%------------------------------------------------------------------------------
thf(position_type,type,(
    position: $tType )).

thf(direction_type,type,(
    direction: $tType )).

thf(left_type,type,(
    left: direction )).

thf(right_type,type,(
    right: direction )).

thf(top_type,type,(
    top: direction )).

thf(bottom_type,type,(
    bottom: direction )).

thf(next_type,type,(
    next: position > direction > position )).

thf(next_comm,axiom,(
    ! [D1: direction,D2: direction,P: position] :
      ( ( next @ ( next @ P @ D1 ) @ D2 )
      = ( next @ ( next @ P @ D2 ) @ D1 ) ) )).

thf(left_right,axiom,(
    ! [P: position] :
      ( ( next @ ( next @ P @ left ) @ right )
      = P ) )).

thf(top_bottom,axiom,(
    ! [P: position] :
      ( ( next @ ( next @ P @ top ) @ bottom )
      = P ) )).

thf(wall_type,type,(
    wall: position > $o )).

%----Inductive MoveList. For the moment we do not include the inductive axioms.
thf(movelist_type,type,(
    movelist: $tType )).

thf(nomove_type,type,(
    nomove: movelist )).

thf(movedir_type,type,(
    movedir: movelist > direction > movelist )).

%----The position of the player after a list of movements
thf(playerpos_type,type,(
    playerpos: movelist > position )).

thf(player_move_legal,axiom,(
    ! [PO: position,M: movelist,D: direction] :
      ( ( ( playerpos @ M )
        = PO )
     => ( ~ ( wall @ ( next @ PO @ D ) )
       => ( ( playerpos @ ( movedir @ M @ D ) )
          = ( next @ PO @ D ) ) ) ) )).

thf(player_move_illegal,axiom,(
    ! [PO: position,M: movelist,D: direction] :
      ( ( ( playerpos @ M )
        = PO )
     => ( ( wall @ ( next @ PO @ D ) )
       => ( ( playerpos @ ( movedir @ M @ D ) )
          = PO ) ) ) )).

thf(c00_type,type,(
    c00: position )).

thf(c10_type,type,(
    c10: position )).

thf(c20_type,type,(
    c20: position )).

thf(c30_type,type,(
    c30: position )).

thf(c40_type,type,(
    c40: position )).

thf(c01_type,type,(
    c01: position )).

thf(c11_type,type,(
    c11: position )).

thf(c21_type,type,(
    c21: position )).

thf(c31_type,type,(
    c31: position )).

thf(c41_type,type,(
    c41: position )).

thf(c02_type,type,(
    c02: position )).

thf(c12_type,type,(
    c12: position )).

thf(c22_type,type,(
    c22: position )).

thf(c32_type,type,(
    c32: position )).

thf(c42_type,type,(
    c42: position )).

thf(c03_type,type,(
    c03: position )).

thf(c13_type,type,(
    c13: position )).

thf(c23_type,type,(
    c23: position )).

thf(c33_type,type,(
    c33: position )).

thf(c43_type,type,(
    c43: position )).

thf(c04_type,type,(
    c04: position )).

thf(c14_type,type,(
    c14: position )).

thf(c24_type,type,(
    c24: position )).

thf(c34_type,type,(
    c34: position )).

thf(c44_type,type,(
    c44: position )).

thf(c10_defin,definition,
    ( c10
    = ( next @ c00 @ right ) )).

thf(c20_defin,definition,
    ( c20
    = ( next @ c10 @ right ) )).

thf(c30_defin,definition,
    ( c30
    = ( next @ c20 @ right ) )).

thf(c40_defin,definition,
    ( c40
    = ( next @ c30 @ right ) )).

thf(c01_defin,definition,
    ( c01
    = ( next @ c00 @ top ) )).

thf(c02_defin,definition,
    ( c02
    = ( next @ c01 @ top ) )).

thf(c03_defin,definition,
    ( c03
    = ( next @ c02 @ top ) )).

thf(c04_defin,definition,
    ( c04
    = ( next @ c03 @ top ) )).

thf(c11_defin,definition,
    ( c11
    = ( next @ c10 @ top ) )).

thf(c12_defin,definition,
    ( c12
    = ( next @ c11 @ top ) )).

thf(c13_defin,definition,
    ( c13
    = ( next @ c12 @ top ) )).

thf(c14_defin,definition,
    ( c14
    = ( next @ c13 @ top ) )).

thf(c21_defin,definition,
    ( c21
    = ( next @ c20 @ top ) )).

thf(c22_defin,definition,
    ( c22
    = ( next @ c21 @ top ) )).

thf(c23_defin,definition,
    ( c23
    = ( next @ c22 @ top ) )).

thf(c24_defin,definition,
    ( c24
    = ( next @ c23 @ top ) )).

thf(c31_defin,definition,
    ( c31
    = ( next @ c30 @ top ) )).

thf(c32_defin,definition,
    ( c32
    = ( next @ c31 @ top ) )).

thf(c33_defin,definition,
    ( c33
    = ( next @ c32 @ top ) )).

thf(c34_defin,definition,
    ( c34
    = ( next @ c33 @ top ) )).

%----Exercise 2
%----Go from * to +
%----#####
%----#   #
%----#*#+#
%----#####
thf(c00_axiom,axiom,
    ( ( wall @ c00 )
    = $true )).

thf(c10_axiom,axiom,
    ( ( wall @ c10 )
    = $true )).

thf(c20_axiom,axiom,
    ( ( wall @ c20 )
    = $true )).

thf(c30_axiom,axiom,
    ( ( wall @ c30 )
    = $true )).

thf(c40_axiom,axiom,
    ( ( wall @ c40 )
    = $true )).

thf(c01_axiom,axiom,
    ( ( wall @ c01 )
    = $true )).

thf(c11_axiom,axiom,
    ( ( wall @ c11 )
    = $false )).

thf(c21_axiom,axiom,
    ( ( wall @ c21 )
    = $true )).

thf(c31_axiom,axiom,
    ( ( wall @ c31 )
    = $false )).

thf(c41_axiom,axiom,
    ( ( wall @ c41 )
    = $true )).

thf(c02_axiom,axiom,
    ( ( wall @ c02 )
    = $true )).

thf(c12_axiom,axiom,
    ( ( wall @ c12 )
    = $false )).

thf(c22_axiom,axiom,
    ( ( wall @ c22 )
    = $false )).

thf(c32_axiom,axiom,
    ( ( wall @ c32 )
    = $false )).

thf(c42_axiom,axiom,
    ( ( wall @ c42 )
    = $true )).

thf(c03_axiom,axiom,
    ( ( wall @ c03 )
    = $true )).

thf(c13_axiom,axiom,
    ( ( wall @ c13 )
    = $true )).

thf(c23_axiom,axiom,
    ( ( wall @ c23 )
    = $true )).

thf(c33_axiom,axiom,
    ( ( wall @ c33 )
    = $true )).

thf(c43_axiom,axiom,
    ( ( wall @ c43 )
    = $true )).

thf(start_axiom,axiom,
    ( ( playerpos @ nomove )
    = c11 )).

thf(exercise,conjecture,(
    ? [M: movelist] :
      ( ( playerpos @ M )
      = c31 ) )).

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