%------------------------------------------------------------------------------
% File     : CSR138^1 : TPTP v8.2.0. Released v4.1.0.
% Domain   : Commonsense Reasoning
% Problem  : Feelings from people to Bill and Anna
% Version  : Especial.
% English  : 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    : rv_4.tq_SUMO_local [Ben10]

% Status   : Theorem
% Rating   : 0.20 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0, 0.29 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v6.1.0, 0.57 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0
% Syntax   : Number of formulae    :   19 (   7 unt;   9 typ;   0 def)
%            Number of atoms       :   17 (   2 equ;   4 cnn)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   33 (   4   ~;   0   |;   3   &;  26   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   8 con; 0-2 aty)
%            Number of variables   :   11 (   4   ^;   0   !;   7   ?;  11   :)
% SPC      : TH0_THM_EQU_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.
%------------------------------------------------------------------------------
%----The extracted signature
thf(numbers,type,
    num: $tType ).

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

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

%----The translated axioms
thf(ax,axiom,
    likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i ).

thf(ax_001,axiom,
    likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i ).

thf(ax_002,axiom,
    ? [X: $i,Y: $i] : ( (~) @ ( parent_THFTYPE_IiioI @ X @ Y ) ) ).

thf(ax_003,axiom,
    ? [X: $i,Y: $i] : ( (~) @ ( likes_THFTYPE_IiioI @ X @ Y ) ) ).

thf(ax_004,axiom,
    parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBen_THFTYPE_i ).

thf(ax_005,axiom,
    parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBen_THFTYPE_i ).

thf(ax_006,axiom,
    likes_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBill_THFTYPE_i ).

thf(ax_007,axiom,
    parent_THFTYPE_IiioI @ lSue_THFTYPE_i @ lAnna_THFTYPE_i ).

thf(ax_008,axiom,
    parent_THFTYPE_IiioI @ lMary_THFTYPE_i @ lAnna_THFTYPE_i ).

%----The translated conjecture
thf(con,conjecture,
    ? [Q: $i > $i > $o,R: $i > $i > $o,Y: $i] :
      ( ( R @ Y @ lBill_THFTYPE_i )
      & ( Q @ Y @ lAnna_THFTYPE_i )
      & ( (~)
        @ ( R
          = ( ^ [Z: $i,W: $i] : $true ) ) )
      & ( (~)
        @ ( Q
          = ( ^ [Z: $i,W: $i] : $true ) ) ) ) ).

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