TPTP Problem File: KRS051+1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : KRS051+1 : TPTP v8.2.0. Released v3.1.0.
% Domain : Knowledge Representation (Semantic Web)
% Problem : Integer multiplication in OWL DL
% Version : Especial.
% English : N is 2. M is 3. N times M is 6.
% Refs : [Bec03] Bechhofer (2003), Email to G. Sutcliffe
% : [TR+04] Tsarkov et al. (2004), Using Vampire to Reason with OW
% Source : [Bec03]
% Names : consistent_description-logic-Manifest905 [Bec03]
% Status : Satisfiable
% Rating : 0.20 v8.2.0, 0.33 v8.1.0, 0.25 v7.5.0, 0.33 v7.3.0, 0.00 v7.1.0, 0.75 v7.0.0, 0.00 v6.4.0, 0.60 v6.2.0, 0.50 v6.1.0, 0.60 v6.0.0, 0.50 v5.5.0, 0.33 v5.3.0, 0.67 v5.2.0, 0.33 v5.0.0, 0.67 v4.0.1, 0.75 v3.7.0, 0.67 v3.5.0, 0.33 v3.4.0, 0.80 v3.3.0, 0.67 v3.1.0
% Syntax : Number of formulae : 41 ( 1 unt; 0 def)
% Number of atoms : 177 ( 72 equ)
% Maximal formula atoms : 50 ( 4 avg)
% Number of connectives : 157 ( 21 ~; 27 |; 67 &)
% ( 11 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 0 prp; 1-2 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 114 ( 100 !; 14 ?)
% SPC : FOF_SAT_RFO_SEQ
% Comments : Sean Bechhofer says there are some errors in the encoding of
% datatypes, so this problem may not be perfect. At least it's
% still representative of the type of reasoning required for OWL.
%------------------------------------------------------------------------------
fof(ccardinality_N_substitution_1,axiom,
! [A,B] :
( ( A = B
& ccardinality_N(A) )
=> ccardinality_N(B) ) ).
fof(ccardinality_N_times_M_substitution_1,axiom,
! [A,B] :
( ( A = B
& ccardinality_N_times_M(A) )
=> ccardinality_N_times_M(B) ) ).
fof(conly_d_substitution_1,axiom,
! [A,B] :
( ( A = B
& conly_d(A) )
=> conly_d(B) ) ).
fof(cowlNothing_substitution_1,axiom,
! [A,B] :
( ( A = B
& cowlNothing(A) )
=> cowlNothing(B) ) ).
fof(cowlThing_substitution_1,axiom,
! [A,B] :
( ( A = B
& cowlThing(A) )
=> cowlThing(B) ) ).
fof(rinvP_1_to_N_substitution_1,axiom,
! [A,B,C] :
( ( A = B
& rinvP_1_to_N(A,C) )
=> rinvP_1_to_N(B,C) ) ).
fof(rinvP_1_to_N_substitution_2,axiom,
! [A,B,C] :
( ( A = B
& rinvP_1_to_N(C,A) )
=> rinvP_1_to_N(C,B) ) ).
fof(rinvQ_1_to_M_substitution_1,axiom,
! [A,B,C] :
( ( A = B
& rinvQ_1_to_M(A,C) )
=> rinvQ_1_to_M(B,C) ) ).
fof(rinvQ_1_to_M_substitution_2,axiom,
! [A,B,C] :
( ( A = B
& rinvQ_1_to_M(C,A) )
=> rinvQ_1_to_M(C,B) ) ).
fof(rinvR_N_times_M_to_1_substitution_1,axiom,
! [A,B,C] :
( ( A = B
& rinvR_N_times_M_to_1(A,C) )
=> rinvR_N_times_M_to_1(B,C) ) ).
fof(rinvR_N_times_M_to_1_substitution_2,axiom,
! [A,B,C] :
( ( A = B
& rinvR_N_times_M_to_1(C,A) )
=> rinvR_N_times_M_to_1(C,B) ) ).
fof(rp_N_to_1_substitution_1,axiom,
! [A,B,C] :
( ( A = B
& rp_N_to_1(A,C) )
=> rp_N_to_1(B,C) ) ).
fof(rp_N_to_1_substitution_2,axiom,
! [A,B,C] :
( ( A = B
& rp_N_to_1(C,A) )
=> rp_N_to_1(C,B) ) ).
fof(rq_M_to_1_substitution_1,axiom,
! [A,B,C] :
( ( A = B
& rq_M_to_1(A,C) )
=> rq_M_to_1(B,C) ) ).
fof(rq_M_to_1_substitution_2,axiom,
! [A,B,C] :
( ( A = B
& rq_M_to_1(C,A) )
=> rq_M_to_1(C,B) ) ).
fof(rr_N_times_M_to_1_substitution_1,axiom,
! [A,B,C] :
( ( A = B
& rr_N_times_M_to_1(A,C) )
=> rr_N_times_M_to_1(B,C) ) ).
fof(rr_N_times_M_to_1_substitution_2,axiom,
! [A,B,C] :
( ( A = B
& rr_N_times_M_to_1(C,A) )
=> rr_N_times_M_to_1(C,B) ) ).
fof(xsd_integer_substitution_1,axiom,
! [A,B] :
( ( A = B
& xsd_integer(A) )
=> xsd_integer(B) ) ).
fof(xsd_string_substitution_1,axiom,
! [A,B] :
( ( A = B
& xsd_string(A) )
=> xsd_string(B) ) ).
%----Thing and Nothing
fof(axiom_0,axiom,
! [X] :
( cowlThing(X)
& ~ cowlNothing(X) ) ).
%----String and Integer disjoint
fof(axiom_1,axiom,
! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) ) ).
%----Equality ccardinality_N
fof(axiom_2,axiom,
! [X] :
( ccardinality_N(X)
<=> ( ? [Y0,Y1,Y2] :
( rinvQ_1_to_M(X,Y0)
& rinvQ_1_to_M(X,Y1)
& rinvQ_1_to_M(X,Y2)
& Y0 != Y1
& Y0 != Y2
& Y1 != Y2 )
& ! [Y0,Y1,Y2,Y3] :
( ( rinvQ_1_to_M(X,Y0)
& rinvQ_1_to_M(X,Y1)
& rinvQ_1_to_M(X,Y2)
& rinvQ_1_to_M(X,Y3) )
=> ( Y0 = Y1
| Y0 = Y2
| Y0 = Y3
| Y1 = Y2
| Y1 = Y3
| Y2 = Y3 ) ) ) ) ).
%----Equality ccardinality_N
fof(axiom_3,axiom,
! [X] :
( ccardinality_N(X)
<=> ? [Y] :
( rp_N_to_1(X,Y)
& conly_d(Y) ) ) ).
%----Equality ccardinality_N_times_M
fof(axiom_4,axiom,
! [X] :
( ccardinality_N_times_M(X)
<=> ? [Y] :
( rr_N_times_M_to_1(X,Y)
& conly_d(Y) ) ) ).
%----Equality ccardinality_N_times_M
fof(axiom_5,axiom,
! [X] :
( ccardinality_N_times_M(X)
<=> ? [Y] :
( rq_M_to_1(X,Y)
& ccardinality_N(Y) ) ) ).
%----Equality conly_d
fof(axiom_6,axiom,
! [X] :
( conly_d(X)
<=> ( ? [Y0,Y1,Y2,Y3,Y4,Y5] :
( rinvR_N_times_M_to_1(X,Y0)
& rinvR_N_times_M_to_1(X,Y1)
& rinvR_N_times_M_to_1(X,Y2)
& rinvR_N_times_M_to_1(X,Y3)
& rinvR_N_times_M_to_1(X,Y4)
& rinvR_N_times_M_to_1(X,Y5)
& Y0 != Y1
& Y0 != Y2
& Y0 != Y3
& Y0 != Y4
& Y0 != Y5
& Y1 != Y2
& Y1 != Y3
& Y1 != Y4
& Y1 != Y5
& Y2 != Y3
& Y2 != Y4
& Y2 != Y5
& Y3 != Y4
& Y3 != Y5
& Y4 != Y5 )
& ! [Y0,Y1,Y2,Y3,Y4,Y5,Y6] :
( ( rinvR_N_times_M_to_1(X,Y0)
& rinvR_N_times_M_to_1(X,Y1)
& rinvR_N_times_M_to_1(X,Y2)
& rinvR_N_times_M_to_1(X,Y3)
& rinvR_N_times_M_to_1(X,Y4)
& rinvR_N_times_M_to_1(X,Y5)
& rinvR_N_times_M_to_1(X,Y6) )
=> ( Y0 = Y1
| Y0 = Y2
| Y0 = Y3
| Y0 = Y4
| Y0 = Y5
| Y0 = Y6
| Y1 = Y2
| Y1 = Y3
| Y1 = Y4
| Y1 = Y5
| Y1 = Y6
| Y2 = Y3
| Y2 = Y4
| Y2 = Y5
| Y2 = Y6
| Y3 = Y4
| Y3 = Y5
| Y3 = Y6
| Y4 = Y5
| Y4 = Y6
| Y5 = Y6 ) ) ) ) ).
%----Equality conly_d
fof(axiom_7,axiom,
! [X] :
( conly_d(X)
<=> ( ? [Y0,Y1] :
( rinvP_1_to_N(X,Y0)
& rinvP_1_to_N(X,Y1)
& Y0 != Y1 )
& ! [Y0,Y1,Y2] :
( ( rinvP_1_to_N(X,Y0)
& rinvP_1_to_N(X,Y1)
& rinvP_1_to_N(X,Y2) )
=> ( Y0 = Y1
| Y0 = Y2
| Y1 = Y2 ) ) ) ) ).
%----Enumeration conly_d
fof(axiom_8,axiom,
! [X] :
( conly_d(X)
<=> X = id ) ).
%----Functional: rp_N_to_1
fof(axiom_9,axiom,
! [X,Y,Z] :
( ( rp_N_to_1(X,Y)
& rp_N_to_1(X,Z) )
=> Y = Z ) ).
%----Domain: rp_N_to_1
fof(axiom_10,axiom,
! [X,Y] :
( rp_N_to_1(X,Y)
=> ccardinality_N(X) ) ).
%----Range: rp_N_to_1
fof(axiom_11,axiom,
! [X,Y] :
( rp_N_to_1(X,Y)
=> conly_d(Y) ) ).
%----Inverse: rp_N_to_1
fof(axiom_12,axiom,
! [X,Y] :
( rp_N_to_1(X,Y)
<=> rinvP_1_to_N(Y,X) ) ).
%----Functional: rq_M_to_1
fof(axiom_13,axiom,
! [X,Y,Z] :
( ( rq_M_to_1(X,Y)
& rq_M_to_1(X,Z) )
=> Y = Z ) ).
%----Domain: rq_M_to_1
fof(axiom_14,axiom,
! [X,Y] :
( rq_M_to_1(X,Y)
=> ccardinality_N_times_M(X) ) ).
%----Range: rq_M_to_1
fof(axiom_15,axiom,
! [X,Y] :
( rq_M_to_1(X,Y)
=> ccardinality_N(Y) ) ).
%----Inverse: rq_M_to_1
fof(axiom_16,axiom,
! [X,Y] :
( rq_M_to_1(X,Y)
<=> rinvQ_1_to_M(Y,X) ) ).
%----Functional: rr_N_times_M_to_1
fof(axiom_17,axiom,
! [X,Y,Z] :
( ( rr_N_times_M_to_1(X,Y)
& rr_N_times_M_to_1(X,Z) )
=> Y = Z ) ).
%----Domain: rr_N_times_M_to_1
fof(axiom_18,axiom,
! [X,Y] :
( rr_N_times_M_to_1(X,Y)
=> ccardinality_N_times_M(X) ) ).
%----Range: rr_N_times_M_to_1
fof(axiom_19,axiom,
! [X,Y] :
( rr_N_times_M_to_1(X,Y)
=> conly_d(Y) ) ).
%----Inverse: rr_N_times_M_to_1
fof(axiom_20,axiom,
! [X,Y] :
( rr_N_times_M_to_1(X,Y)
<=> rinvR_N_times_M_to_1(Y,X) ) ).
%----id
fof(axiom_21,axiom,
cowlThing(id) ).
%------------------------------------------------------------------------------