## TPTP Problem File: NLP001^7.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : NLP001^7 : TPTP v7.2.0. Released v5.5.0.
% Domain   : Natural Language Processing
% Problem  : "The old dirty white Chevy" problem
% Version  : [Ben12] axioms.
% English  :

% Refs     : [Bos00] Bos (2000), DORIS: Discourse Oriented Representation an
%          : [Ben12] Benzmueller (2012), Email to Geoff Sutcliffe
% Source   : [Ben12]
% Names    : s4-cumul-NLP001+1 [Ben12]

% Status   : Theorem
% Rating   : 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v5.5.0
% Syntax   : Number of formulae    :   87 (   0 unit;  50 type;  32 defn)
%            Number of atoms       :  445 (  36 equality; 211 variable)
%            Maximal formula depth :   30 (   6 average)
%            Number of connectives :  341 (   5   ~;   5   |;   9   &; 312   @)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :  211 ( 211   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   54 (  50   :;   0   =)
%            Number of variables   :  106 (   2 sgn;  34   !;   7   ?;  65   ^)
%                                         ( 106   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_EQU_NAR

%------------------------------------------------------------------------------
%----Include axioms for Modal logic S4 under cumulative domains
include('Axioms/LCL015^0.ax').
include('Axioms/LCL013^5.ax').
include('Axioms/LCL015^1.ax').
%------------------------------------------------------------------------------
thf(in_type,type,(
in: mu > mu > \$i > \$o )).

thf(down_type,type,(
down: mu > mu > \$i > \$o )).

thf(barrel_type,type,(
barrel: mu > mu > \$i > \$o )).

thf(old_type,type,(
old: mu > \$i > \$o )).

thf(dirty_type,type,(
dirty: mu > \$i > \$o )).

thf(white_type,type,(
white: mu > \$i > \$o )).

thf(car_type,type,(
car: mu > \$i > \$o )).

thf(chevy_type,type,(
chevy: mu > \$i > \$o )).

thf(lonely_type,type,(
lonely: mu > \$i > \$o )).

thf(way_type,type,(
way: mu > \$i > \$o )).

thf(street_type,type,(
street: mu > \$i > \$o )).

thf(event_type,type,(
event: mu > \$i > \$o )).

thf(city_type,type,(
city: mu > \$i > \$o )).

thf(hollywood_type,type,(
hollywood: mu > \$i > \$o )).

thf(co1,conjecture,
( mvalid
@ ( mand
@ ( mimplies
@ ( mexists_ind
@ ^ [U: mu] :
( mexists_ind
@ ^ [V: mu] :
( mexists_ind
@ ^ [W: mu] :
( mexists_ind
@ ^ [X: mu] :
( mand @ ( hollywood @ U ) @ ( mand @ ( city @ U ) @ ( mand @ ( event @ V ) @ ( mand @ ( street @ W ) @ ( mand @ ( way @ W ) @ ( mand @ ( lonely @ W ) @ ( mand @ ( chevy @ X ) @ ( mand @ ( car @ X ) @ ( mand @ ( white @ X ) @ ( mand @ ( dirty @ X ) @ ( mand @ ( old @ X ) @ ( mand @ ( barrel @ V @ X ) @ ( mand @ ( down @ V @ W ) @ ( in @ V @ U ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ ( mexists_ind
@ ^ [Y: mu] :
( mexists_ind
@ ^ [Z: mu] :
( mexists_ind
@ ^ [X1: mu] :
( mexists_ind
@ ^ [X2: mu] :
( mand @ ( hollywood @ Y ) @ ( mand @ ( city @ Y ) @ ( mand @ ( event @ Z ) @ ( mand @ ( chevy @ X1 ) @ ( mand @ ( car @ X1 ) @ ( mand @ ( white @ X1 ) @ ( mand @ ( dirty @ X1 ) @ ( mand @ ( old @ X1 ) @ ( mand @ ( street @ X2 ) @ ( mand @ ( way @ X2 ) @ ( mand @ ( lonely @ X2 ) @ ( mand @ ( barrel @ Z @ X1 ) @ ( mand @ ( down @ Z @ X2 ) @ ( in @ Z @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ ( mimplies
@ ( mexists_ind
@ ^ [X3: mu] :
( mexists_ind
@ ^ [X4: mu] :
( mexists_ind
@ ^ [X5: mu] :
( mexists_ind
@ ^ [X6: mu] :
( mand @ ( hollywood @ X3 ) @ ( mand @ ( city @ X3 ) @ ( mand @ ( event @ X4 ) @ ( mand @ ( chevy @ X5 ) @ ( mand @ ( car @ X5 ) @ ( mand @ ( white @ X5 ) @ ( mand @ ( dirty @ X5 ) @ ( mand @ ( old @ X5 ) @ ( mand @ ( street @ X6 ) @ ( mand @ ( way @ X6 ) @ ( mand @ ( lonely @ X6 ) @ ( mand @ ( barrel @ X4 @ X5 ) @ ( mand @ ( down @ X4 @ X6 ) @ ( in @ X4 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
@ ( mexists_ind
@ ^ [X7: mu] :
( mexists_ind
@ ^ [X8: mu] :
( mexists_ind
@ ^ [X9: mu] :
( mexists_ind
@ ^ [X10: mu] :
( mand @ ( hollywood @ X7 ) @ ( mand @ ( city @ X7 ) @ ( mand @ ( event @ X8 ) @ ( mand @ ( street @ X9 ) @ ( mand @ ( way @ X9 ) @ ( mand @ ( lonely @ X9 ) @ ( mand @ ( chevy @ X10 ) @ ( mand @ ( car @ X10 ) @ ( mand @ ( white @ X10 ) @ ( mand @ ( dirty @ X10 ) @ ( mand @ ( old @ X10 ) @ ( mand @ ( barrel @ X8 @ X10 ) @ ( mand @ ( down @ X8 @ X9 ) @ ( in @ X8 @ X7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

%------------------------------------------------------------------------------
```