%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWB009+3 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:51:28 AM UTC 2026
% Result : Theorem 9.79s 2.08s
% Output : CNFRefutation 9.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 9 unt; 0 def)
% Number of atoms : 91 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 101 ( 38 ~; 35 |; 25 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 10 con; 0-4 aty)
% Number of variables : 54 ( 0 sgn 29 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(owl_restrict_somevaluesfrom,axiom,
! [Z,P,C] :
( ( iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_someValuesFrom,Z,C) )
=> ! [X] :
( icext(Z,X)
<=> ? [Y] :
( icext(C,Y)
& iext(P,X,Y) ) ) ),
file('theBenchmark.p',owl_restrict_somevaluesfrom) ).
fof(rdfs_cext_def,axiom,
! [X,C] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
file('theBenchmark.p',rdfs_cext_def) ).
fof(testcase_premise_fullish_009_Existential_Restriction_Entailments,axiom,
? [BNODE_z] :
( iext(uri_owl_someValuesFrom,BNODE_z,uri_ex_c)
& iext(uri_owl_onProperty,BNODE_z,uri_ex_p)
& iext(uri_rdf_type,BNODE_z,uri_owl_Restriction)
& iext(uri_rdf_type,uri_ex_s,BNODE_z)
& iext(uri_rdf_type,uri_ex_c,uri_owl_Class)
& iext(uri_rdf_type,uri_ex_p,uri_owl_ObjectProperty) ),
file('theBenchmark.p',testcase_premise_fullish_009_Existential_Restriction_Entailments) ).
fof(testcase_conclusion_fullish_009_Existential_Restriction_Entailments,conjecture,
? [BNODE_x] :
( iext(uri_rdf_type,BNODE_x,uri_ex_c)
& iext(uri_ex_p,uri_ex_s,BNODE_x) ),
file('theBenchmark.p',testcase_conclusion_fullish_009_Existential_Restriction_Entailments) ).
fof(testcase_conclusion_fullish_009_Existential_Restriction_Entailments_neg,negated_conjecture,
~ ? [BNODE_x] :
( iext(uri_rdf_type,BNODE_x,uri_ex_c)
& iext(uri_ex_p,uri_ex_s,BNODE_x) ),
inference(assume_negation,[status(cth)],[testcase_conclusion_fullish_009_Existential_Restriction_Entailments]) ).
fof(nnf_28,plain,
! [Z,P,C] :
( ! [X] :
( ( ! [Y] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) )
| icext(Z,X) )
& ( ? [X0] :
( icext(C,X0)
& iext(P,X,X0) )
| ~ icext(Z,X) ) )
| ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_someValuesFrom,Z,C) ),
inference(fof_nnf,[status(thm)],[owl_restrict_somevaluesfrom]) ).
fof(sk_owl_restrict_somevaluesfrom_sk,plain,
! [Z,P,C] :
( ! [X] :
( ( ! [Y] :
( ~ icext(C,Y)
| ~ iext(P,X,Y) )
| icext(Z,X) )
& ( ( icext(C,sK0(Z,P,C,X))
& iext(P,X,sK0(Z,P,C,X)) )
| ~ icext(Z,X) ) )
| ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_someValuesFrom,Z,C) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0(Z,P,C,X))],[nnf_28]) ).
fof(sk_owl_restrict_somevaluesfrom,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ icext(VAR_1,VAR_4)
| ~ iext(VAR_2,VAR_3,VAR_4)
| icext(VAR_0,VAR_3)
| ~ iext(uri_owl_onProperty,VAR_0,VAR_2)
| ~ iext(uri_owl_someValuesFrom,VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( icext(VAR_1,sK0(VAR_0,VAR_2,VAR_1,VAR_3))
| ~ icext(VAR_0,VAR_3)
| ~ iext(uri_owl_onProperty,VAR_0,VAR_2)
| ~ iext(uri_owl_someValuesFrom,VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( iext(VAR_2,VAR_3,sK0(VAR_0,VAR_2,VAR_1,VAR_3))
| ~ icext(VAR_0,VAR_3)
| ~ iext(uri_owl_onProperty,VAR_0,VAR_2)
| ~ iext(uri_owl_someValuesFrom,VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_owl_restrict_somevaluesfrom_sk]) ).
cnf(c_278,plain,
( iext(C,D,sK0(A,C,B,D))
| ~ icext(A,D)
| ~ iext(uri_owl_onProperty,A,C)
| ~ iext(uri_owl_someValuesFrom,A,B) ),
inference(split_conjunct,[status(thm)],[sk_owl_restrict_somevaluesfrom]) ).
cnf(c_279,plain,
( icext(B,sK0(A,C,B,D))
| ~ icext(A,D)
| ~ iext(uri_owl_onProperty,A,C)
| ~ iext(uri_owl_someValuesFrom,A,B) ),
inference(split_conjunct,[status(thm)],[sk_owl_restrict_somevaluesfrom]) ).
cnf(c_285,plain,
( icext(B,A)
| ~ iext(uri_rdf_type,A,B) ),
inference(clausify,[status(thm)],[rdfs_cext_def]) ).
cnf(c_286,plain,
( ~ icext(B,A)
| iext(uri_rdf_type,A,B) ),
inference(clausify,[status(thm)],[rdfs_cext_def]) ).
fof(nnf_41,plain,
? [BNODE_z] :
( iext(uri_owl_someValuesFrom,BNODE_z,uri_ex_c)
& iext(uri_owl_onProperty,BNODE_z,uri_ex_p)
& iext(uri_rdf_type,BNODE_z,uri_owl_Restriction)
& iext(uri_rdf_type,uri_ex_s,BNODE_z)
& iext(uri_rdf_type,uri_ex_c,uri_owl_Class)
& iext(uri_rdf_type,uri_ex_p,uri_owl_ObjectProperty) ),
inference(fof_nnf,[status(thm)],[testcase_premise_fullish_009_Existential_Restriction_Entailments]) ).
fof(sk_testcase_premise_fullish_009_Existential_Restriction_Entailments,plain,
( iext(uri_owl_someValuesFrom,sK1,uri_ex_c)
& iext(uri_owl_onProperty,sK1,uri_ex_p)
& iext(uri_rdf_type,sK1,uri_owl_Restriction)
& iext(uri_rdf_type,uri_ex_s,sK1)
& iext(uri_rdf_type,uri_ex_c,uri_owl_Class)
& iext(uri_rdf_type,uri_ex_p,uri_owl_ObjectProperty) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(BNODE_z,sK1)],[nnf_41]) ).
cnf(c_311,plain,
iext(uri_rdf_type,uri_ex_s,sK1),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_009_Existential_Restriction_Entailments]) ).
cnf(c_313,plain,
iext(uri_owl_onProperty,sK1,uri_ex_p),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_009_Existential_Restriction_Entailments]) ).
cnf(c_314,plain,
iext(uri_owl_someValuesFrom,sK1,uri_ex_c),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_009_Existential_Restriction_Entailments]) ).
cnf(c_315,negated_conjecture,
( ~ iext(uri_rdf_type,A,uri_ex_c)
| ~ iext(uri_ex_p,uri_ex_s,A) ),
inference(clausify,[status(thm)],[testcase_conclusion_fullish_009_Existential_Restriction_Entailments_neg]) ).
cnf(c_1027,plain,
icext(sK1,uri_ex_s),
inference(resolve,[status(thm)],[c_285,c_311]) ).
cnf(c_7954,plain,
( iext(A,B,sK0(sK1,A,uri_ex_c,B))
| ~ icext(sK1,B)
| ~ iext(uri_owl_onProperty,sK1,A) ),
inference(resolve,[status(thm)],[c_278,c_314]) ).
cnf(c_7955,plain,
( iext(uri_ex_p,A,sK0(sK1,uri_ex_p,uri_ex_c,A))
| ~ icext(sK1,A) ),
inference(resolve,[status(thm)],[c_7954,c_313]) ).
cnf(c_4502,plain,
iext(uri_ex_p,uri_ex_s,sK0(sK1,uri_ex_p,uri_ex_c,uri_ex_s)),
inference(resolve,[status(thm)],[c_7955,c_1027]) ).
cnf(c_7956,plain,
( icext(uri_ex_c,sK0(sK1,A,uri_ex_c,B))
| ~ icext(sK1,B)
| ~ iext(uri_owl_onProperty,sK1,A) ),
inference(resolve,[status(thm)],[c_279,c_314]) ).
cnf(c_7957,plain,
( icext(uri_ex_c,sK0(sK1,uri_ex_p,uri_ex_c,A))
| ~ icext(sK1,A) ),
inference(resolve,[status(thm)],[c_7956,c_313]) ).
cnf(c_4523,plain,
icext(uri_ex_c,sK0(sK1,uri_ex_p,uri_ex_c,uri_ex_s)),
inference(resolve,[status(thm)],[c_7957,c_1027]) ).
cnf(c_7206,plain,
iext(uri_rdf_type,sK0(sK1,uri_ex_p,uri_ex_c,uri_ex_s),uri_ex_c),
inference(resolve,[status(thm)],[c_4523,c_286]) ).
cnf(c_7958,negated_conjecture,
~ iext(uri_rdf_type,sK0(sK1,uri_ex_p,uri_ex_c,uri_ex_s),uri_ex_c),
inference(resolve,[status(thm)],[c_4502,c_315]) ).
cnf(c_7953,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_7206,c_7958]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWB009+3 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.60 % Computer : n014.cluster.edu
% 0.10/0.60 % Model : x86_64 x86_64
% 0.10/0.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.60 % Memory : 8046.5625MB
% 0.10/0.60 % OS : Linux 6.8.0-71-generic
% 0.10/0.60 % CPULimit : 300
% 0.10/0.60 % WCLimit : 300
% 0.10/0.60 % DateTime : Sat Sep 26 11:41:48 UTC 2026
% 0.10/0.60 % CPUTime :
% 0.10/0.60 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.60 % Process 3067658 was started by sandbox on n014,
% 0.10/0.60 % Sat Sep 26 11:41:48 2026
% 0.10/0.60 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.63
% 0.10/0.63 % From the command line: assign(max_seconds, 300).
% 0.10/0.63
% 0.10/0.63 % SInE: 65 to sos, 74 to usable, of 139 axioms (tolerance 2.00, depth 0 fixpoint).
% 9.79/2.08
% 9.79/2.08 % given #500 (T,wt=8): 2162 icext(uri_rdf_Property,uri_rdfs_isDefinedBy). [hyper(260,a,156,a,b,123,a)].
% 9.79/2.08
% 9.79/2.08 % given #1000 (T,wt=11): 3704 iext(uri_rdfs_subClassOf,uri_owl_Nothing,A) | -ic(A). [resolve(271,b,76,a),unit_del(c,75)].
% 9.79/2.08
% 9.79/2.08 % given #1500 (A,wt=56): 473 -iext(uri_rdf_first,A,B) | -iext(uri_rdf_rest,A,A) | -iext(uri_rdf_first,A,C) | -iext(uri_rdf_rest,A,uri_rdf_nil) | iext(uri_owl_intersectionOf,D,A) | -ic(D) | -ic(B) | -ic(C) | icext(D,f4(D,A,B,A,C,A,B)) | icext(B,f4(D,A,B,A,C,A,B)). [factor(339,b,d)].
% 9.79/2.08
% 9.79/2.08 % given #2000 (T,wt=16): 6896 -iext(uri_owl_hasValue,A,uri_rdfs_Class) | -iext(uri_owl_onProperty,A,uri_rdfs_subClassOf) | icext(A,uri_rdfs_Class). [resolve(6272,a,277,d)].
% 9.79/2.08
% 9.79/2.08 % SZS status Theorem for theBenchmark
% 9.79/2.08
% 9.79/2.08 % Proof 1 at 1.23 (+ 0.19) seconds.
% 9.79/2.08 % Length of proof is 17.
% 9.79/2.08 % Level of proof is 5.
% 9.79/2.08 % Maximum clause weight is 129.000.
% 9.79/2.08 % Given clauses 2139.
% 9.79/2.08
% 9.79/2.08 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------