%------------------------------------------------------------------------------
% File     : CSR146^1 : TPTP v9.0.0. Released v4.1.0.
% Domain   : Commonsense Reasoning
% Problem  : What is the relation between Chris and Corina during 2009?
% Version  : Especial.
% English  : During 2009 Corina is the wife of Chris. True holds at any time. 
%            What is the relation between Chris and Corina during 2009?

% Refs     : [Ben10] Benzmueller (2010), Email to Geoff Sutcliffe
% Source   : [Ben10]
% Names    : ex_5.tq_SUMO_handselected [Ben10]

% Status   : Theorem
% Rating   : 0.25 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.14 v6.1.0, 0.57 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0
% Syntax   : Number of formulae    :   15 (   1 unt;   9 typ;   0 def)
%            Number of atoms       :   14 (   1 equ;   2 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   29 (   2   ~;   0   |;   1   &;  24   @)
%                                         (   1 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   19 (  19   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :    9 (   2   ^;   5   !;   2   ?;   9   :)
% 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(holdsDuring_THFTYPE_IiooI,type,
    holdsDuring_THFTYPE_IiooI: $i > $o > $o ).

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

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

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

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

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

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

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

thf(ax1,axiom,
    inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI ).

thf(ax2,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(ax3,axiom,
    ! [Z: $i] : ( holdsDuring_THFTYPE_IiooI @ Z @ $true ) ).

thf(ax4,axiom,
    ? [X: $i] : ( (~) @ ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ X ) ) ).

thf(ax5,axiom,
    holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ ( wife_THFTYPE_IiioI @ lCorina_THFTYPE_i @ lChris_THFTYPE_i ) ).

%----The translated conjectures
thf(con,conjecture,
    ? [R: $i > $i > $o] :
      ( ( holdsDuring_THFTYPE_IiooI @ ( lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i ) @ ( R @ lChris_THFTYPE_i @ lCorina_THFTYPE_i ) )
      & ( (~)
        @ ( R
          = ( ^ [X: $i,Y: $i] : $true ) ) ) ) ).

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