TPTP Problem File: CSR153^1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : CSR153^1 : TPTP v8.2.0. Released v4.1.0.
% Domain : Commonsense Reasoning
% Problem : Is there a common relation?
% Version : Especial > Reduced > Especial.
% English : Mary, Sue, Bill and Bob are mutually distinct. Mary is neither a
% sister of Sue nor of Bill. Bob is not a brother of Mary. Sue is a
% sister of Bill and of Bob. Bob is a brother of Bill. Is there a
% relation that holds both between Bob and Bill and between Sue and
% Bob?
% Refs : [PS07] Pease & Sutcliffe (2007), First Order Reasoning on a L
% : [BP10] Benzmueller & Pease (2010), Progress in Automating Hig
% : [Ben10] Benzmueller (2010), Email to Geoff Sutcliffe
% Source : [Ben10]
% Names : paar_9.tq_SUMO_local [Ben10]
% Status : Theorem
% Rating : 0.20 v8.2.0, 0.46 v8.1.0, 0.45 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, 0.60 v4.1.0
% Syntax : Number of formulae : 13 ( 1 unt; 7 typ; 0 def)
% Number of atoms : 22 ( 6 equ; 10 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 47 ( 10 ~; 0 |; 9 &; 28 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 3 ( 0 ^; 2 !; 1 ?; 3 :)
% 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(brother_THFTYPE_IiioI,type,
brother_THFTYPE_IiioI: $i > $i > $o ).
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(sister_THFTYPE_IiioI,type,
sister_THFTYPE_IiioI: $i > $i > $o ).
%----The translated axioms
thf(ax,axiom,
( ( sister_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i )
& ( sister_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBob_THFTYPE_i )
& ( brother_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBill_THFTYPE_i ) ) ).
thf(ax_001,axiom,
( ( (~) @ ( lMary_THFTYPE_i = lSue_THFTYPE_i ) )
& ( (~) @ ( lMary_THFTYPE_i = lBill_THFTYPE_i ) )
& ( (~) @ ( lBob_THFTYPE_i = lMary_THFTYPE_i ) ) ) ).
thf(ax_002,axiom,
( ( (~) @ ( lSue_THFTYPE_i = lBill_THFTYPE_i ) )
& ( (~) @ ( lSue_THFTYPE_i = lBob_THFTYPE_i ) ) ) ).
thf(ax_003,axiom,
( ( (~) @ ( sister_THFTYPE_IiioI @ lMary_THFTYPE_i @ lSue_THFTYPE_i ) )
& ( (~) @ ( sister_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i ) )
& ( (~) @ ( brother_THFTYPE_IiioI @ lBob_THFTYPE_i @ lMary_THFTYPE_i ) ) ) ).
thf(ax_004,axiom,
(~) @ ( lBob_THFTYPE_i = lBill_THFTYPE_i ) ).
%----The translated conjectures
thf(con,conjecture,
? [R: $i > $i > $o] :
( ( R @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
& ( R @ lSue_THFTYPE_i @ lBob_THFTYPE_i )
& ( (~)
@ ! [X: $i,Y: $i] : ( R @ X @ Y ) ) ) ).
%------------------------------------------------------------------------------