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% File     : CSR141^1 : TPTP v8.2.0. Released v4.1.0.
% Domain   : Commonsense Reasoning
% Problem  : Reiner and MariaPaola are not connected at the CADE meeting
% Version  : Especial.
% English  : CADE_BM is a Meeting. One agent of this meeting is MariaPaola and
%            one is Reiner. It holds that both agents are not connected during
%            the meeting.

% Refs     : [Ben10] Benzmueller (2010), Email to Geoff Sutcliffe
% Source   : [Ben10]
% Names    : re_1.tq_SUMO_handselected [Ben10]

% Status   : Theorem
% Rating   : 0.08 v8.2.0, 0.09 v8.1.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.2.0, 0.00 v6.1.0, 0.50 v6.0.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.50 v4.1.0
% Syntax   : Number of formulae    :   19 (   3 unt;  12 typ;   0 def)
%            Number of atoms       :   16 (   0 equ;   2 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   39 (   2   ~;   0   |;   2   &;  33   @)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   13 (  11 usr;   7 con; 0-3 aty)
%            Number of variables   :    5 (   0   ^;   5   !;   0   ?;   5   :)
% 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 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(agent_THFTYPE_IiioI,type,
    agent_THFTYPE_IiioI: $i > $i > $o ).

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

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

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

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

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

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

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

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

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

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

%----The translated axioms
thf(ax,axiom,
    agent_THFTYPE_IiioI @ lCADE_BM_THFTYPE_i @ lReiner_THFTYPE_i ).

thf(ax_001,axiom,
    agent_THFTYPE_IiioI @ lCADE_BM_THFTYPE_i @ lMariaPaola_THFTYPE_i ).

thf(ax_002,axiom,
    instance_THFTYPE_IiioI @ lCADE_BM_THFTYPE_i @ lMeeting_THFTYPE_i ).

thf(ax_003,axiom,
    holdsDuring_THFTYPE_IiooI @ ( lWhenFn_THFTYPE_IiiI @ lCADE_BM_THFTYPE_i ) @ $true ).

%----The relevant handselected axioms from SUMO
thf(ax_004,axiom,
    ! [MEET: $i,AGENT2: $i,AGENT1: $i] :
      ( ( ( instance_THFTYPE_IiioI @ MEET @ lMeeting_THFTYPE_i )
        & ( agent_THFTYPE_IiioI @ MEET @ AGENT1 )
        & ( agent_THFTYPE_IiioI @ MEET @ AGENT2 ) )
     => ( holdsDuring_THFTYPE_IiooI @ ( lWhenFn_THFTYPE_IiiI @ MEET ) @ ( orientation_THFTYPE_IiiioI @ AGENT1 @ AGENT2 @ lNear_THFTYPE_i ) ) ) ).

thf(ax_005,axiom,
    ! [OBJ1: $i,OBJ2: $i] :
      ( ( orientation_THFTYPE_IiiioI @ OBJ1 @ OBJ2 @ lNear_THFTYPE_i )
     => ( (~) @ ( connected_THFTYPE_IiioI @ OBJ1 @ OBJ2 ) ) ) ).

%----The translated conjectures
thf(con,conjecture,
    holdsDuring_THFTYPE_IiooI @ ( lWhenFn_THFTYPE_IiiI @ lCADE_BM_THFTYPE_i ) @ ( (~) @ ( connected_THFTYPE_IiioI @ lMariaPaola_THFTYPE_i @ lReiner_THFTYPE_i ) ) ).

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