TPTP Problem File: SWB038+1.p
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% File : SWB038+1 : TPTP v9.0.0. Released v5.2.0.
% Domain : Semantic Web
% Problem : Class De Morgan
% Version : [Sch11] axioms.
% English : The complement of the union of two classes is an equivalent class
% to the intersection of the complements of the two classes.
% Refs : [Sch11] Schneider, M. (2011), Email to G. Sutcliffe
% Source : [Sch11]
% Names : rdfbased-sem-bool-demorgan [Sch11]
% Status : Theorem
% Rating : 0.91 v9.0.0, 0.89 v8.2.0, 0.92 v8.1.0, 0.94 v7.4.0, 0.93 v7.1.0, 0.87 v7.0.0, 0.93 v6.4.0, 0.92 v6.2.0, 0.88 v6.1.0, 0.90 v6.0.0, 0.96 v5.5.0, 1.00 v5.3.0, 0.96 v5.2.0
% Syntax : Number of formulae : 560 ( 197 unt; 0 def)
% Number of atoms : 1786 ( 90 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 1362 ( 136 ~; 35 |; 770 &)
% ( 126 <=>; 295 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 161 ( 161 usr; 160 con; 0-2 aty)
% Number of variables : 980 ( 911 !; 69 ?)
% SPC : FOF_THM_RFO_SEQ
% Comments :
%------------------------------------------------------------------------------
%----Include OWL 2 Full axioms
include('Axioms/SWB001+0.ax').
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fof(conclusion_rdfbased_sem_bool_demorgan,conjecture,
iext(uri_owl_equivalentClass,uri_ex_c1,uri_ex_c2) ).
fof(premise_rdfbased_sem_bool_demorgan,axiom,
? [X1,X4,X0,X2,X5,X3,X6] :
( iext(uri_owl_intersectionOf,uri_ex_c2,X0)
& iext(uri_owl_complementOf,X1,uri_ex_x)
& iext(uri_rdf_first,X0,X1)
& iext(uri_rdf_rest,X0,X2)
& iext(uri_rdf_first,X3,uri_ex_x)
& iext(uri_rdf_rest,X3,X4)
& iext(uri_owl_complementOf,X5,uri_ex_y)
& iext(uri_owl_complementOf,uri_ex_c1,X6)
& iext(uri_rdf_first,X4,uri_ex_y)
& iext(uri_rdf_rest,X4,uri_rdf_nil)
& iext(uri_owl_unionOf,X6,X3)
& iext(uri_rdf_first,X2,X5)
& iext(uri_rdf_rest,X2,uri_rdf_nil) ) ).
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