%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWB024+2 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 08:51:34 AM UTC 2026
% Result : Theorem 0.10s 5.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 13 unt; 0 def)
% Number of atoms : 104 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 103 ( 34 ~; 31 |; 31 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-3 aty)
% Number of variables : 51 ( 0 sgn 27 !; 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_mincard_001,axiom,
! [Z,P] :
( ( iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_minCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) )
=> ! [X] :
( icext(Z,X)
<=> ? [Y] : iext(P,X,Y) ) ),
file('theBenchmark.p',owl_restrict_mincard_001) ).
fof(owl_rdfsext_subclassof,axiom,
! [C1,C2] :
( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ! [X] :
( icext(C1,X)
=> icext(C2,X) )
& ic(C2)
& ic(C1) ) ),
file('theBenchmark.p',owl_rdfsext_subclassof) ).
fof(owl_char_transitive,axiom,
! [P] :
( icext(uri_owl_TransitiveProperty,P)
<=> ( ! [X,Y,Z] :
( ( iext(P,Y,Z)
& iext(P,X,Y) )
=> iext(P,X,Z) )
& ip(P) ) ),
file('theBenchmark.p',owl_char_transitive) ).
fof(testcase_premise_fullish_024_Cardinality_Restrictions_on_Complex_Properties,axiom,
? [BNODE_z] :
( iext(uri_ex_hasAncestor,uri_ex_alice,uri_ex_bob)
& iext(uri_rdf_type,uri_ex_bob,uri_ex_Person)
& iext(uri_rdf_type,uri_ex_alice,uri_ex_Person)
& iext(uri_owl_minCardinality,BNODE_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,BNODE_z,uri_ex_hasAncestor)
& iext(uri_rdf_type,BNODE_z,uri_owl_Restriction)
& iext(uri_rdfs_subClassOf,uri_ex_Person,BNODE_z)
& iext(uri_rdf_type,uri_ex_hasAncestor,uri_owl_TransitiveProperty) ),
file('theBenchmark.p',testcase_premise_fullish_024_Cardinality_Restrictions_on_Complex_Properties) ).
fof(testcase_conclusion_fullish_024_Cardinality_Restrictions_on_Complex_Properties,conjecture,
? [BNODE_x] :
( iext(uri_ex_hasAncestor,uri_ex_alice,BNODE_x)
& iext(uri_ex_hasAncestor,uri_ex_bob,BNODE_x) ),
file('theBenchmark.p',testcase_conclusion_fullish_024_Cardinality_Restrictions_on_Complex_Properties) ).
fof(testcase_conclusion_fullish_024_Cardinality_Restrictions_on_Complex_Properties_neg,negated_conjecture,
~ ? [BNODE_x] :
( iext(uri_ex_hasAncestor,uri_ex_alice,BNODE_x)
& iext(uri_ex_hasAncestor,uri_ex_bob,BNODE_x) ),
inference(assume_negation,[status(cth)],[testcase_conclusion_fullish_024_Cardinality_Restrictions_on_Complex_Properties]) ).
cnf(c_11,negated_conjecture,
( ~ iext(uri_ex_hasAncestor,uri_ex_alice,A)
| ~ iext(uri_ex_hasAncestor,uri_ex_bob,A) ),
inference(clausify,[status(thm)],[testcase_conclusion_fullish_024_Cardinality_Restrictions_on_Complex_Properties_neg]) ).
fof(nnf_5,plain,
? [BNODE_z] :
( iext(uri_ex_hasAncestor,uri_ex_alice,uri_ex_bob)
& iext(uri_rdf_type,uri_ex_bob,uri_ex_Person)
& iext(uri_rdf_type,uri_ex_alice,uri_ex_Person)
& iext(uri_owl_minCardinality,BNODE_z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,BNODE_z,uri_ex_hasAncestor)
& iext(uri_rdf_type,BNODE_z,uri_owl_Restriction)
& iext(uri_rdfs_subClassOf,uri_ex_Person,BNODE_z)
& iext(uri_rdf_type,uri_ex_hasAncestor,uri_owl_TransitiveProperty) ),
inference(fof_nnf,[status(thm)],[testcase_premise_fullish_024_Cardinality_Restrictions_on_Complex_Properties]) ).
fof(sk_testcase_premise_fullish_024_Cardinality_Restrictions_on_Complex_Properties,plain,
( iext(uri_ex_hasAncestor,uri_ex_alice,uri_ex_bob)
& iext(uri_rdf_type,uri_ex_bob,uri_ex_Person)
& iext(uri_rdf_type,uri_ex_alice,uri_ex_Person)
& iext(uri_owl_minCardinality,sK0,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,sK0,uri_ex_hasAncestor)
& iext(uri_rdf_type,sK0,uri_owl_Restriction)
& iext(uri_rdfs_subClassOf,uri_ex_Person,sK0)
& iext(uri_rdf_type,uri_ex_hasAncestor,uri_owl_TransitiveProperty) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(BNODE_z,sK0)],[nnf_5]) ).
cnf(c_12,plain,
iext(uri_ex_hasAncestor,uri_ex_alice,uri_ex_bob),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_024_Cardinality_Restrictions_on_Complex_Properties]) ).
cnf(c_13,plain,
iext(uri_rdf_type,uri_ex_bob,uri_ex_Person),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_024_Cardinality_Restrictions_on_Complex_Properties]) ).
cnf(c_15,plain,
iext(uri_owl_minCardinality,sK0,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_024_Cardinality_Restrictions_on_Complex_Properties]) ).
cnf(c_16,plain,
iext(uri_owl_onProperty,sK0,uri_ex_hasAncestor),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_024_Cardinality_Restrictions_on_Complex_Properties]) ).
cnf(c_18,plain,
iext(uri_rdfs_subClassOf,uri_ex_Person,sK0),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_024_Cardinality_Restrictions_on_Complex_Properties]) ).
cnf(c_19,plain,
iext(uri_rdf_type,uri_ex_hasAncestor,uri_owl_TransitiveProperty),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_024_Cardinality_Restrictions_on_Complex_Properties]) ).
cnf(c_20,plain,
( iext(A,B,D)
| ~ iext(A,C,D)
| ~ iext(A,B,C)
| ~ icext(uri_owl_TransitiveProperty,A) ),
inference(clausify,[status(thm)],[owl_char_transitive]) ).
cnf(c_23,plain,
( icext(B,C)
| ~ icext(A,C)
| ~ iext(uri_rdfs_subClassOf,A,B) ),
inference(clausify,[status(thm)],[owl_rdfsext_subclassof]) ).
fof(nnf_2,plain,
! [Z,P] :
( ! [X] :
( ( ! [Y] : ~ iext(P,X,Y)
| icext(Z,X) )
& ( ? [X0] : iext(P,X,X0)
| ~ icext(Z,X) ) )
| ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_minCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ),
inference(fof_nnf,[status(thm)],[owl_restrict_mincard_001]) ).
fof(sk_owl_restrict_mincard_001_sk,plain,
! [Z,P] :
( ! [X] :
( ( ! [Y] : ~ iext(P,X,Y)
| icext(Z,X) )
& ( iext(P,X,sK1(Z,P,X))
| ~ icext(Z,X) ) )
| ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_minCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1(Z,P,X))],[nnf_2]) ).
fof(sk_owl_restrict_mincard_001,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ iext(VAR_1,VAR_2,VAR_3)
| icext(VAR_0,VAR_2)
| ~ iext(uri_owl_onProperty,VAR_0,VAR_1)
| ~ iext(uri_owl_minCardinality,VAR_0,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) )
& ! [VAR_0,VAR_1,VAR_2] :
( iext(VAR_1,VAR_2,sK1(VAR_0,VAR_1,VAR_2))
| ~ icext(VAR_0,VAR_2)
| ~ iext(uri_owl_onProperty,VAR_0,VAR_1)
| ~ iext(uri_owl_minCardinality,VAR_0,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ) ),
inference(cnf_transformation,[status(thm)],[sk_owl_restrict_mincard_001_sk]) ).
cnf(c_27,plain,
( iext(B,C,sK1(A,B,C))
| ~ icext(A,C)
| ~ iext(uri_owl_onProperty,A,B)
| ~ iext(uri_owl_minCardinality,A,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ),
inference(split_conjunct,[status(thm)],[sk_owl_restrict_mincard_001]) ).
cnf(c_29,plain,
( icext(B,A)
| ~ iext(uri_rdf_type,A,B) ),
inference(clausify,[status(thm)],[rdfs_cext_def]) ).
cnf(c_42,plain,
( iext(uri_ex_hasAncestor,uri_ex_alice,A)
| ~ iext(uri_ex_hasAncestor,uri_ex_bob,A)
| ~ icext(uri_owl_TransitiveProperty,uri_ex_hasAncestor) ),
inference(resolve,[status(thm)],[c_20,c_12]) ).
cnf(c_51,plain,
( icext(sK0,A)
| ~ icext(uri_ex_Person,A) ),
inference(resolve,[status(thm)],[c_23,c_18]) ).
cnf(c_96,plain,
( iext(uri_ex_hasAncestor,A,sK1(sK0,uri_ex_hasAncestor,A))
| ~ icext(sK0,A)
| ~ iext(uri_owl_minCardinality,sK0,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ),
inference(resolve,[status(thm)],[c_27,c_16]) ).
cnf(c_63,plain,
( iext(uri_ex_hasAncestor,A,sK1(sK0,uri_ex_hasAncestor,A))
| ~ icext(sK0,A) ),
inference(resolve,[status(thm)],[c_15,c_96]) ).
cnf(c_64,plain,
icext(uri_owl_TransitiveProperty,uri_ex_hasAncestor),
inference(resolve,[status(thm)],[c_29,c_19]) ).
cnf(c_67,plain,
icext(uri_ex_Person,uri_ex_bob),
inference(resolve,[status(thm)],[c_29,c_13]) ).
cnf(c_69,plain,
( iext(uri_ex_hasAncestor,uri_ex_alice,A)
| ~ iext(uri_ex_hasAncestor,uri_ex_bob,A) ),
inference(resolve,[status(thm)],[c_64,c_42]) ).
cnf(c_77,plain,
icext(sK0,uri_ex_bob),
inference(resolve,[status(thm)],[c_51,c_67]) ).
cnf(c_87,plain,
iext(uri_ex_hasAncestor,uri_ex_bob,sK1(sK0,uri_ex_hasAncestor,uri_ex_bob)),
inference(resolve,[status(thm)],[c_63,c_77]) ).
cnf(c_91,plain,
iext(uri_ex_hasAncestor,uri_ex_alice,sK1(sK0,uri_ex_hasAncestor,uri_ex_bob)),
inference(resolve,[status(thm)],[c_87,c_69]) ).
cnf(c_97,negated_conjecture,
~ iext(uri_ex_hasAncestor,uri_ex_alice,sK1(sK0,uri_ex_hasAncestor,uri_ex_bob)),
inference(resolve,[status(thm)],[c_87,c_11]) ).
cnf(c_95,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_91,c_97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWB024+2 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n026.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sat Sep 26 11:52:46 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.37 % Process 910596 was started by sandbox2 on n026,
% 0.10/5.37 % Sat Sep 26 11:52:46 2026
% 0.10/5.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/5.38
% 0.10/5.38 % From the command line: assign(max_seconds, 300).
% 0.10/5.39
% 0.10/5.39 % SZS status Theorem for theBenchmark
% 0.10/5.39
% 0.10/5.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.10/5.39 % Length of proof is 27.
% 0.10/5.39 % Level of proof is 6.
% 0.10/5.39 % Maximum clause weight is 20.000.
% 0.10/5.39 % Given clauses 48.
% 0.10/5.39
% 0.10/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------