%------------------------------------------------------------------------------
% File     : CSR145^1 : TPTP v9.0.0. Released v4.1.0.
% Domain   : Commonsense Reasoning
% Problem  : What is the relation between Chris and Corina?
% Version  : Especial.
% English  : Corina is the wife of Chris. There is some person Chris is not 
%            husband of. What is the relationship between Chris and Corina?

% Refs     : [Ben10] Benzmueller (2010), Email to Geoff Sutcliffe
% Source   : [Ben10]
% Names    : ex_4.tq_SUMO_handselected [Ben10]

% Status   : Theorem
% Rating   : 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0, 0.09 v7.5.0, 0.00 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, 0.00 v6.1.0, 0.57 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0
% Syntax   : Number of formulae    :   11 (   2 unt;   6 typ;   0 def)
%            Number of atoms       :   10 (   1 equ;   2 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   21 (   2   ~;   0   |;   1   &;  16   @)
%                                         (   1 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   16 (  16   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :    8 (   2   ^;   4   !;   2   ?;   8   :)
% 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 three modes: handselected,
%            SInE, and local. 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
%            handselected mode contains a hand-selected relevant axioms.
%          : The examples are selected to illustrate the benefits of
%            higher-order reasoning in ontology reasoning.
%------------------------------------------------------------------------------
%----The extracted signature
thf(numbers,type,
    num: $tType ).

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

thf(lChris_THFTYPE_i,type,
    lChris_THFTYPE_i: $i ).

thf(lCorina_THFTYPE_i,type,
    lCorina_THFTYPE_i: $i ).

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

%----The handselected axioms from the knowledge base
thf(inverse_THFTYPE_IIiioIIiioIoI,type,
    inverse_THFTYPE_IIiioIIiioIoI: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).

thf(ax,axiom,
    inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI ).

thf(ax_001,axiom,
    ! [REL2: $i > $i > $o,REL1: $i > $i > $o] :
      ( ( inverse_THFTYPE_IIiioIIiioIoI @ REL1 @ REL2 )
     => ! [INST1: $i,INST2: $i] :
          ( ( REL1 @ INST1 @ INST2 )
        <=> ( REL2 @ INST2 @ INST1 ) ) ) ).

%----The translated axioms
thf(ax_002,axiom,
    ? [X: $i] : ( (~) @ ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ X ) ) ).

thf(ax_003,axiom,
    wife_THFTYPE_IiioI @ lCorina_THFTYPE_i @ lChris_THFTYPE_i ).

%----The translated conjectures
thf(con,conjecture,
    ? [R: $i > $i > $o] :
      ( ( R @ lChris_THFTYPE_i @ lCorina_THFTYPE_i )
      & ( (~)
        @ ( R
          = ( ^ [X: $i,Y: $i] : $true ) ) ) ) ).

%------------------------------------------------------------------------------