## TPTP Problem File: CSR131^1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : CSR131^1 : TPTP v7.1.0. Released v4.1.0.
% Domain   : Commonsense Reasoning
% Problem  : In 2009, what's the feeling for Bill and Anna?
% Version  : Especial.
% English  : In the context of year 2009: Do there exist relations ?R and ?Q
%            so that ?R holds between a person ?Y and Bill and ?Q between ?Y
%            and Anna.

% Refs     : [Ben10] Benzmueller (2010), Email to Geoff Sutcliffe
% Source   : [Ben10]
% Names    : ef_rv_3.tq_SUMO_local [Ben10]

% Status   : Theorem
% Rating   : 0.38 v7.1.0, 0.43 v7.0.0, 0.50 v6.4.0, 0.57 v6.3.0, 0.67 v6.2.0, 0.50 v6.1.0, 0.83 v6.0.0, 0.67 v5.5.0, 0.60 v5.4.0, 0.50 v5.1.0, 0.75 v5.0.0, 0.50 v4.1.0
% Syntax   : Number of formulae    :   23 (   0 unit;  12 type;   0 defn)
%            Number of atoms       :   80 (   0 equality;  10 variable)
%            Maximal formula depth :   13 (   4 average)
%            Number of connectives :   69 (   0   ~;   0   |;   3   &;  66   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  :   11 (  11   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   16 (  12   :;   0   =)
%            Number of variables   :    7 (   0 sgn;   4   !;   3   ?;   0   ^)
%                                         (   7   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_NEQ_NAR

% Comments : This is a simple test problem for reasoning in/about SUMO.
%            Initally the problem has been hand generated in KIF syntax in
%            SigmaKEE and then automatically translated by Benzmueller's
%            KIF2TH0 translator into THF syntax.
%          : The translation has been applied in two modes: local and SInE.
%            The local mode only translates the local assumptions and the
%            query. The SInE mode additionally translates the SInE-extract
%            of the loaded knowledge base (usually SUMO).
%          : The examples are selected to illustrate the benefits of
%            higher-order reasoning in ontology reasoning.
%          : Note that the universal predicates is excluded for ?R and Q? with
%            the second and third conjuncts in the query.
%------------------------------------------------------------------------------
%----The extracted signature
thf(numbers,type,(
num: \$tType )).

thf(holdsDuring_THFTYPE_IiooI,type,(
holdsDuring_THFTYPE_IiooI: \$i > \$o > \$o )).

thf(lAnna_THFTYPE_i,type,(
lAnna_THFTYPE_i: \$i )).

thf(lBen_THFTYPE_i,type,(
lBen_THFTYPE_i: \$i )).

thf(lBill_THFTYPE_i,type,(
lBill_THFTYPE_i: \$i )).

thf(lBob_THFTYPE_i,type,(
lBob_THFTYPE_i: \$i )).

thf(lMary_THFTYPE_i,type,(
lMary_THFTYPE_i: \$i )).

thf(lSue_THFTYPE_i,type,(
lSue_THFTYPE_i: \$i )).

thf(lYearFn_THFTYPE_IiiI,type,(
lYearFn_THFTYPE_IiiI: \$i > \$i )).

thf(likes_THFTYPE_IiioI,type,(
likes_THFTYPE_IiioI: \$i > \$i > \$o )).

thf(n2009_THFTYPE_i,type,(
n2009_THFTYPE_i: \$i )).

thf(parent_THFTYPE_IiioI,type,(
parent_THFTYPE_IiioI: \$i > \$i > \$o )).

%----The translated axioms
thf(ax,axiom,
( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ ( parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i ) )).

thf(ax_001,axiom,
( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ ( parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBen_THFTYPE_i ) )).

thf(ax_002,axiom,
( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ ( (~) @ ( parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lAnna_THFTYPE_i ) ) )).

thf(ax_003,axiom,
( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ ( likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i ) )).

thf(ax_004,axiom,
( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ ( likes_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBill_THFTYPE_i ) )).

thf(ax_005,axiom,
( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ ( (~) @ ( parent_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBen_THFTYPE_i ) ) )).

thf(ax_006,axiom,
( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ ( likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i ) )).

thf(ax_007,axiom,
( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ ( parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lAnna_THFTYPE_i ) )).

thf(ax_008,axiom,
( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ ( parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBen_THFTYPE_i ) )).

thf(ax_009,axiom,
( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ ( (~) @ ( likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lMary_THFTYPE_i ) ) )).

%----The translated conjecture
thf(con,conjecture,(
? [Q: \$i > \$i > \$o,R: \$i > \$i > \$o,Y: \$i] :
( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i )
@ ( ( R @ Y @ lBill_THFTYPE_i )
& ( Q @ Y @ lAnna_THFTYPE_i )
& ( (~)
@ ! [A: \$i,B: \$i] :
( R @ A @ B ) )
& ( (~)
@ ! [A: \$i,B: \$i] :
( Q @ A @ B ) ) ) ) )).

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