%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWB009+2 : 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 : n003.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 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 7 unt; 0 def)
% Number of atoms : 95 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 116 ( 49 ~; 39 |; 25 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 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 : 51 ( 0 sgn 29 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdfs_cext_def,axiom,
! [X,C] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
file('theBenchmark.p',rdfs_cext_def) ).
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(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]) ).
cnf(c_5,plain,
( icext(B,A)
| ~ iext(uri_rdf_type,A,B) ),
inference(clausify,[status(thm)],[rdfs_cext_def]) ).
cnf(c_6,plain,
( ~ icext(B,A)
| iext(uri_rdf_type,A,B) ),
inference(clausify,[status(thm)],[rdfs_cext_def]) ).
fof(nnf_2,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_2]) ).
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_7,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_8,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]) ).
fof(nnf_3,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_3]) ).
cnf(c_12,plain,
iext(uri_rdf_type,uri_ex_s,sK1),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_009_Existential_Restriction_Entailments]) ).
cnf(c_14,plain,
iext(uri_owl_onProperty,sK1,uri_ex_p),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_009_Existential_Restriction_Entailments]) ).
cnf(c_15,plain,
iext(uri_owl_someValuesFrom,sK1,uri_ex_c),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_009_Existential_Restriction_Entailments]) ).
cnf(c_16,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_19,plain,
icext(sK1,uri_ex_s),
inference(resolve,[status(thm)],[c_5,c_12]) ).
cnf(c_22,plain,
( ~ icext(uri_ex_c,A)
| ~ iext(uri_ex_p,uri_ex_s,A) ),
inference(resolve,[status(thm)],[c_16,c_6]) ).
cnf(c_23,plain,
( ~ icext(A,uri_ex_s)
| ~ iext(uri_owl_onProperty,A,uri_ex_p)
| ~ iext(uri_owl_someValuesFrom,A,B)
| ~ icext(uri_ex_c,sK0(A,uri_ex_p,B,uri_ex_s)) ),
inference(resolve,[status(thm)],[c_22,c_7]) ).
cnf(c_35,plain,
( ~ icext(sK1,uri_ex_s)
| ~ iext(uri_owl_onProperty,sK1,uri_ex_p)
| ~ icext(uri_ex_c,sK0(sK1,uri_ex_p,uri_ex_c,uri_ex_s)) ),
inference(resolve,[status(thm)],[c_23,c_15]) ).
cnf(c_36,plain,
( ~ icext(sK1,uri_ex_s)
| ~ icext(uri_ex_c,sK0(sK1,uri_ex_p,uri_ex_c,uri_ex_s)) ),
inference(resolve,[status(thm)],[c_14,c_35]) ).
cnf(c_28,plain,
~ icext(uri_ex_c,sK0(sK1,uri_ex_p,uri_ex_c,uri_ex_s)),
inference(resolve,[status(thm)],[c_19,c_36]) ).
cnf(c_37,plain,
( ~ icext(sK1,uri_ex_s)
| ~ iext(uri_owl_onProperty,sK1,uri_ex_p)
| ~ iext(uri_owl_someValuesFrom,sK1,uri_ex_c) ),
inference(resolve,[status(thm)],[c_28,c_8]) ).
cnf(c_38,plain,
( ~ icext(sK1,uri_ex_s)
| ~ iext(uri_owl_onProperty,sK1,uri_ex_p) ),
inference(resolve,[status(thm)],[c_15,c_37]) ).
cnf(c_39,plain,
~ icext(sK1,uri_ex_s),
inference(resolve,[status(thm)],[c_14,c_38]) ).
cnf(c_34,plain,
$false,
inference(resolve,[status(thm)],[c_19,c_39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWB009+2 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 11:43:40 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 2791002 was started by sandbox on n003,
% 0.10/0.36 % Sat Sep 26 11:43:40 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.38
% 0.10/0.38 % SZS status Theorem for theBenchmark
% 0.10/0.38
% 0.10/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.38 % Length of proof is 17.
% 0.10/0.38 % Level of proof is 5.
% 0.10/0.38 % Maximum clause weight is 19.000.
% 0.10/0.38 % Given clauses 16.
% 0.10/0.38
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------