TPTP Problem File: PUZ142^1.p
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% File : PUZ142^1 : TPTP v9.0.0. 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 : 0.50 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.57 v7.4.0, 0.67 v7.2.0, 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 ( 45 unt; 37 typ; 20 def)
% Number of atoms : 91 ( 49 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 99 ( 1 ~; 0 |; 0 &; 94 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 1 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 34 usr; 32 con; 0-2 aty)
% Number of variables : 12 ( 0 ^; 11 !; 1 ?; 12 :)
% SPC : TH0_THM_EQU_NAR
% Comments :
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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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