## TPTP Problem File: SWB021+2.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : SWB021+2 : TPTP v7.5.0. Released v5.2.0.
% Domain   : Semantic Web
% Problem  : Composite Enumerations
% Version  : [Sch11] axioms : Reduced > Incomplete.
% English  :

% Refs     : [Sch11] Schneider, M. (2011), Email to G. Sutcliffe
% Source   : [Sch11]
% Names    : 021_Composite_Enumerations [Sch11]

% Status   : Theorem
% Rating   : 0.39 v7.5.0, 0.38 v7.4.0, 0.37 v7.3.0, 0.38 v7.1.0, 0.26 v7.0.0, 0.37 v6.4.0, 0.42 v6.3.0, 0.38 v6.2.0, 0.52 v6.1.0, 0.57 v6.0.0, 0.61 v5.5.0, 0.56 v5.4.0, 0.61 v5.3.0, 0.67 v5.2.0
% Syntax   : Number of formulae    :    8 (   1 unit)
%            Number of atoms       :   66 (   5 equality)
%            Maximal formula depth :   31 (  11 average)
%            Number of connectives :   58 (   0   ~;   4   |;  41   &)
%                                         (   8 <=>;   5  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of predicates  :    4 (   0 propositional; 1-3 arity)
%            Number of functors    :   14 (  14 constant; 0-0 arity)
%            Number of variables   :   36 (   0 sgn;  27   !;   9   ?)
%            Maximal term depth    :    1 (   1 average)
% SPC      : FOF_THM_RFO_SEQ

%------------------------------------------------------------------------------
fof(owl_prop_oneof_ext,axiom,(
! [X,Y] :
( iext(uri_owl_oneOf,X,Y)
=> ( ic(X)
& icext(uri_rdf_List,Y) ) ) )).

fof(owl_prop_unionof_ext,axiom,(
! [X,Y] :
( iext(uri_owl_unionOf,X,Y)
=> ( ic(X)
& icext(uri_rdf_List,Y) ) ) )).

fof(owl_bool_unionof_class_002,axiom,(
! [Z,S1,C1,S2,C2] :
( ( iext(uri_rdf_first,S1,C1)
& iext(uri_rdf_rest,S1,S2)
& iext(uri_rdf_first,S2,C2)
& iext(uri_rdf_rest,S2,uri_rdf_nil) )
=> ( iext(uri_owl_unionOf,Z,S1)
<=> ( ic(Z)
& ic(C1)
& ic(C2)
& ! [X] :
( icext(Z,X)
<=> ( icext(C1,X)
| icext(C2,X) ) ) ) ) ) )).

fof(owl_enum_class_002,axiom,(
! [Z,S1,A1,S2,A2] :
( ( iext(uri_rdf_first,S1,A1)
& iext(uri_rdf_rest,S1,S2)
& iext(uri_rdf_first,S2,A2)
& iext(uri_rdf_rest,S2,uri_rdf_nil) )
=> ( iext(uri_owl_oneOf,Z,S1)
<=> ( ic(Z)
& ! [X] :
( icext(Z,X)
<=> ( X = A1
| X = A2 ) ) ) ) ) )).

fof(owl_enum_class_003,axiom,(
! [Z,S1,A1,S2,A2,S3,A3] :
( ( iext(uri_rdf_first,S1,A1)
& iext(uri_rdf_rest,S1,S2)
& iext(uri_rdf_first,S2,A2)
& iext(uri_rdf_rest,S2,S3)
& iext(uri_rdf_first,S3,A3)
& iext(uri_rdf_rest,S3,uri_rdf_nil) )
=> ( iext(uri_owl_oneOf,Z,S1)
<=> ( ic(Z)
& ! [X] :
( icext(Z,X)
<=> ( X = A1
| X = A2
| X = A3 ) ) ) ) ) )).

fof(owl_eqdis_equivalentclass,axiom,(
! [C1,C2] :
( iext(uri_owl_equivalentClass,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X] :
( icext(C1,X)
<=> icext(C2,X) ) ) ) )).

fof(testcase_conclusion_fullish_021_Composite_Enumerations,conjecture,(
iext(uri_owl_equivalentClass,uri_ex_c3,uri_ex_c4) )).

fof(testcase_premise_fullish_021_Composite_Enumerations,axiom,(
? [BNODE_l11,BNODE_l12,BNODE_l21,BNODE_l22,BNODE_l31,BNODE_l32,BNODE_l33,BNODE_l41,BNODE_l42] :
( iext(uri_owl_oneOf,uri_ex_c1,BNODE_l11)
& iext(uri_rdf_first,BNODE_l11,uri_ex_w1)
& iext(uri_rdf_rest,BNODE_l11,BNODE_l12)
& iext(uri_rdf_first,BNODE_l12,uri_ex_w2)
& iext(uri_rdf_rest,BNODE_l12,uri_rdf_nil)
& iext(uri_owl_oneOf,uri_ex_c2,BNODE_l21)
& iext(uri_rdf_first,BNODE_l21,uri_ex_w2)
& iext(uri_rdf_rest,BNODE_l21,BNODE_l22)
& iext(uri_rdf_first,BNODE_l22,uri_ex_w3)
& iext(uri_rdf_rest,BNODE_l22,uri_rdf_nil)
& iext(uri_owl_oneOf,uri_ex_c3,BNODE_l31)
& iext(uri_rdf_first,BNODE_l31,uri_ex_w1)
& iext(uri_rdf_rest,BNODE_l31,BNODE_l32)
& iext(uri_rdf_first,BNODE_l32,uri_ex_w2)
& iext(uri_rdf_rest,BNODE_l32,BNODE_l33)
& iext(uri_rdf_first,BNODE_l33,uri_ex_w3)
& iext(uri_rdf_rest,BNODE_l33,uri_rdf_nil)
& iext(uri_owl_unionOf,uri_ex_c4,BNODE_l41)
& iext(uri_rdf_first,BNODE_l41,uri_ex_c1)
& iext(uri_rdf_rest,BNODE_l41,BNODE_l42)
& iext(uri_rdf_first,BNODE_l42,uri_ex_c2)
& iext(uri_rdf_rest,BNODE_l42,uri_rdf_nil) ) )).

%------------------------------------------------------------------------------
```