%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWB016+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 : n002.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 08:51:31 AM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 53 ( 20 unt; 0 def)
% Number of atoms : 169 ( 0 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 194 ( 78 ~; 74 |; 32 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 85 ( 4 sgn 56 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rdf_type_ip,axiom,
! [P] :
( iext(uri_rdf_type,P,uri_rdf_Property)
<=> ip(P) ),
file('theBenchmark.p',rdf_type_ip) ).
fof(rdfs_cext_def,axiom,
! [X,C] :
( iext(uri_rdf_type,X,C)
<=> icext(C,X) ),
file('theBenchmark.p',rdfs_cext_def) ).
fof(rdfs_domain_main,axiom,
! [P,C,X,Y] :
( ( iext(P,X,Y)
& iext(uri_rdfs_domain,P,C) )
=> icext(C,X) ),
file('theBenchmark.p',rdfs_domain_main) ).
fof(owl_prop_equivalentclass_ext,axiom,
! [X,Y] :
( iext(uri_owl_equivalentClass,X,Y)
=> ( ic(Y)
& ic(X) ) ),
file('theBenchmark.p',owl_prop_equivalentclass_ext) ).
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_rdfsext_subpropertyof,axiom,
! [P1,P2] :
( iext(uri_rdfs_subPropertyOf,P1,P2)
<=> ( ! [X,Y] :
( iext(P1,X,Y)
=> iext(P2,X,Y) )
& ip(P2)
& ip(P1) ) ),
file('theBenchmark.p',owl_rdfsext_subpropertyof) ).
fof(owl_eqdis_equivalentclass,axiom,
! [C1,C2] :
( iext(uri_owl_equivalentClass,C1,C2)
<=> ( ! [X] :
( icext(C1,X)
<=> icext(C2,X) )
& ic(C2)
& ic(C1) ) ),
file('theBenchmark.p',owl_eqdis_equivalentclass) ).
fof(testcase_conclusion_fullish_016_Reflective_Tautologies_II,conjecture,
iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,uri_rdfs_subClassOf),
file('theBenchmark.p',testcase_conclusion_fullish_016_Reflective_Tautologies_II) ).
fof(testcase_conclusion_fullish_016_Reflective_Tautologies_II_neg,negated_conjecture,
~ iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,uri_rdfs_subClassOf),
inference(assume_negation,[status(cth)],[testcase_conclusion_fullish_016_Reflective_Tautologies_II]) ).
cnf(c_9,plain,
( ip(A)
| ~ iext(uri_rdf_type,A,uri_rdf_Property) ),
inference(clausify,[status(thm)],[rdf_type_ip]) ).
cnf(c_12,plain,
( ~ icext(B,A)
| iext(uri_rdf_type,A,B) ),
inference(clausify,[status(thm)],[rdfs_cext_def]) ).
cnf(c_13,plain,
( icext(B,C)
| ~ iext(A,C,D)
| ~ iext(uri_rdfs_domain,A,B) ),
inference(clausify,[status(thm)],[rdfs_domain_main]) ).
fof(rdfs_domain_domain,axiom,
iext(uri_rdfs_domain,uri_rdfs_domain,uri_rdf_Property),
file('theBenchmark.p',rdfs_domain_domain) ).
cnf(c_14,plain,
iext(uri_rdfs_domain,uri_rdfs_domain,uri_rdf_Property),
inference(clausify,[status(thm)],[rdfs_domain_domain]) ).
fof(rdfs_subclassof_domain,axiom,
iext(uri_rdfs_domain,uri_rdfs_subClassOf,uri_rdfs_Class),
file('theBenchmark.p',rdfs_subclassof_domain) ).
cnf(c_15,plain,
iext(uri_rdfs_domain,uri_rdfs_subClassOf,uri_rdfs_Class),
inference(clausify,[status(thm)],[rdfs_subclassof_domain]) ).
fof(owl_prop_equivalentclass_type,axiom,
ip(uri_owl_equivalentClass),
file('theBenchmark.p',owl_prop_equivalentclass_type) ).
cnf(c_16,plain,
ip(uri_owl_equivalentClass),
inference(clausify,[status(thm)],[owl_prop_equivalentclass_type]) ).
cnf(c_17,plain,
( ic(A)
| ~ iext(uri_owl_equivalentClass,A,B) ),
inference(clausify,[status(thm)],[owl_prop_equivalentclass_ext]) ).
cnf(c_18,plain,
( ic(B)
| ~ iext(uri_owl_equivalentClass,A,B) ),
inference(clausify,[status(thm)],[owl_prop_equivalentclass_ext]) ).
fof(nnf_5,plain,
! [C1,C2] :
( ( ? [X] :
( ~ icext(C2,X)
& icext(C1,X) )
| ~ ic(C2)
| ~ ic(C1)
| iext(uri_rdfs_subClassOf,C1,C2) )
& ( ( ! [X0] :
( icext(C2,X0)
| ~ icext(C1,X0) )
& ic(C2)
& ic(C1) )
| ~ iext(uri_rdfs_subClassOf,C1,C2) ) ),
inference(fof_nnf,[status(thm)],[owl_rdfsext_subclassof]) ).
fof(sk_owl_rdfsext_subclassof_sk,plain,
! [C1,C2] :
( ( ( ~ icext(C2,sK0(C1,C2))
& icext(C1,sK0(C1,C2)) )
| ~ ic(C2)
| ~ ic(C1)
| iext(uri_rdfs_subClassOf,C1,C2) )
& ( ( ! [X0] :
( icext(C2,X0)
| ~ icext(C1,X0) )
& ic(C2)
& ic(C1) )
| ~ iext(uri_rdfs_subClassOf,C1,C2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0(C1,C2))],[nnf_5]) ).
fof(sk_owl_rdfsext_subclassof,plain,
( ! [VAR_0,VAR_1] :
( ~ icext(VAR_1,sK0(VAR_0,VAR_1))
| ~ ic(VAR_1)
| ~ ic(VAR_0)
| iext(uri_rdfs_subClassOf,VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( icext(VAR_0,sK0(VAR_0,VAR_1))
| ~ ic(VAR_1)
| ~ ic(VAR_0)
| iext(uri_rdfs_subClassOf,VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( icext(VAR_1,VAR_2)
| ~ icext(VAR_0,VAR_2)
| ~ iext(uri_rdfs_subClassOf,VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( ic(VAR_1)
| ~ iext(uri_rdfs_subClassOf,VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( ic(VAR_0)
| ~ iext(uri_rdfs_subClassOf,VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_owl_rdfsext_subclassof_sk]) ).
cnf(c_22,plain,
( icext(A,sK0(A,B))
| ~ ic(B)
| ~ ic(A)
| iext(uri_rdfs_subClassOf,A,B) ),
inference(split_conjunct,[status(thm)],[sk_owl_rdfsext_subclassof]) ).
cnf(c_23,plain,
( ~ icext(B,sK0(A,B))
| ~ ic(B)
| ~ ic(A)
| iext(uri_rdfs_subClassOf,A,B) ),
inference(split_conjunct,[status(thm)],[sk_owl_rdfsext_subclassof]) ).
fof(nnf_6,plain,
! [P1,P2] :
( ( ? [X,Y] :
( ~ iext(P2,X,Y)
& iext(P1,X,Y) )
| ~ ip(P2)
| ~ ip(P1)
| iext(uri_rdfs_subPropertyOf,P1,P2) )
& ( ( ! [X0,X1] :
( iext(P2,X0,X1)
| ~ iext(P1,X0,X1) )
& ip(P2)
& ip(P1) )
| ~ iext(uri_rdfs_subPropertyOf,P1,P2) ) ),
inference(fof_nnf,[status(thm)],[owl_rdfsext_subpropertyof]) ).
fof(sk_owl_rdfsext_subpropertyof_sk,plain,
! [P1,P2] :
( ( ( ~ iext(P2,sK1(P1,P2),sK2(P1,P2))
& iext(P1,sK1(P1,P2),sK2(P1,P2)) )
| ~ ip(P2)
| ~ ip(P1)
| iext(uri_rdfs_subPropertyOf,P1,P2) )
& ( ( ! [X0,X1] :
( iext(P2,X0,X1)
| ~ iext(P1,X0,X1) )
& ip(P2)
& ip(P1) )
| ~ iext(uri_rdfs_subPropertyOf,P1,P2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X,sK1(P1,P2)),skolemize(Y,sK2(P1,P2))],[nnf_6]) ).
fof(sk_owl_rdfsext_subpropertyof,plain,
( ! [VAR_0,VAR_1] :
( ~ iext(VAR_1,sK1(VAR_0,VAR_1),sK2(VAR_0,VAR_1))
| ~ ip(VAR_1)
| ~ ip(VAR_0)
| iext(uri_rdfs_subPropertyOf,VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( iext(VAR_0,sK1(VAR_0,VAR_1),sK2(VAR_0,VAR_1))
| ~ ip(VAR_1)
| ~ ip(VAR_0)
| iext(uri_rdfs_subPropertyOf,VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( iext(VAR_1,VAR_2,VAR_3)
| ~ iext(VAR_0,VAR_2,VAR_3)
| ~ iext(uri_rdfs_subPropertyOf,VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( ip(VAR_1)
| ~ iext(uri_rdfs_subPropertyOf,VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( ip(VAR_0)
| ~ iext(uri_rdfs_subPropertyOf,VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_owl_rdfsext_subpropertyof_sk]) ).
cnf(c_27,plain,
( iext(A,sK1(A,B),sK2(A,B))
| ~ ip(B)
| ~ ip(A)
| iext(uri_rdfs_subPropertyOf,A,B) ),
inference(split_conjunct,[status(thm)],[sk_owl_rdfsext_subpropertyof]) ).
cnf(c_28,plain,
( ~ iext(B,sK1(A,B),sK2(A,B))
| ~ ip(B)
| ~ ip(A)
| iext(uri_rdfs_subPropertyOf,A,B) ),
inference(split_conjunct,[status(thm)],[sk_owl_rdfsext_subpropertyof]) ).
cnf(c_29,plain,
( icext(B,C)
| ~ icext(A,C)
| ~ iext(uri_owl_equivalentClass,A,B) ),
inference(clausify,[status(thm)],[owl_eqdis_equivalentclass]) ).
cnf(c_33,negated_conjecture,
~ iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,uri_rdfs_subClassOf),
inference(clausify,[status(thm)],[testcase_conclusion_fullish_016_Reflective_Tautologies_II_neg]) ).
cnf(c_42,plain,
( icext(uri_rdf_Property,A)
| ~ iext(uri_rdfs_domain,A,B) ),
inference(resolve,[status(thm)],[c_14,c_13]) ).
cnf(c_48,plain,
( iext(uri_owl_equivalentClass,sK1(uri_owl_equivalentClass,A),sK2(uri_owl_equivalentClass,A))
| ~ ip(A)
| iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,A) ),
inference(resolve,[status(thm)],[c_27,c_16]) ).
cnf(c_52,plain,
icext(uri_rdf_Property,uri_rdfs_subClassOf),
inference(resolve,[status(thm)],[c_42,c_15]) ).
cnf(c_54,plain,
iext(uri_rdf_type,uri_rdfs_subClassOf,uri_rdf_Property),
inference(resolve,[status(thm)],[c_52,c_12]) ).
cnf(c_66,plain,
ip(uri_rdfs_subClassOf),
inference(resolve,[status(thm)],[c_54,c_9]) ).
cnf(c_99,negated_conjecture,
( ~ iext(uri_rdfs_subClassOf,sK1(uri_owl_equivalentClass,uri_rdfs_subClassOf),sK2(uri_owl_equivalentClass,uri_rdfs_subClassOf))
| ~ ip(uri_rdfs_subClassOf)
| ~ ip(uri_owl_equivalentClass) ),
inference(resolve,[status(thm)],[c_28,c_33]) ).
cnf(c_100,negated_conjecture,
( ~ iext(uri_rdfs_subClassOf,sK1(uri_owl_equivalentClass,uri_rdfs_subClassOf),sK2(uri_owl_equivalentClass,uri_rdfs_subClassOf))
| ~ ip(uri_rdfs_subClassOf) ),
inference(resolve,[status(thm)],[c_99,c_16]) ).
cnf(c_70,negated_conjecture,
~ iext(uri_rdfs_subClassOf,sK1(uri_owl_equivalentClass,uri_rdfs_subClassOf),sK2(uri_owl_equivalentClass,uri_rdfs_subClassOf)),
inference(resolve,[status(thm)],[c_100,c_66]) ).
cnf(c_101,plain,
( iext(uri_owl_equivalentClass,sK1(uri_owl_equivalentClass,uri_rdfs_subClassOf),sK2(uri_owl_equivalentClass,uri_rdfs_subClassOf))
| iext(uri_rdfs_subPropertyOf,uri_owl_equivalentClass,uri_rdfs_subClassOf) ),
inference(resolve,[status(thm)],[c_48,c_66]) ).
cnf(c_73,negated_conjecture,
iext(uri_owl_equivalentClass,sK1(uri_owl_equivalentClass,uri_rdfs_subClassOf),sK2(uri_owl_equivalentClass,uri_rdfs_subClassOf)),
inference(resolve,[status(thm)],[c_33,c_101]) ).
cnf(c_78,plain,
ic(sK2(uri_owl_equivalentClass,uri_rdfs_subClassOf)),
inference(resolve,[status(thm)],[c_73,c_18]) ).
cnf(c_79,plain,
ic(sK1(uri_owl_equivalentClass,uri_rdfs_subClassOf)),
inference(resolve,[status(thm)],[c_73,c_17]) ).
cnf(c_102,plain,
( ~ icext(sK2(uri_owl_equivalentClass,uri_rdfs_subClassOf),sK0(sK1(uri_owl_equivalentClass,uri_rdfs_subClassOf),sK2(uri_owl_equivalentClass,uri_rdfs_subClassOf)))
| ~ ic(sK2(uri_owl_equivalentClass,uri_rdfs_subClassOf))
| ~ ic(sK1(uri_owl_equivalentClass,uri_rdfs_subClassOf)) ),
inference(resolve,[status(thm)],[c_23,c_70]) ).
cnf(c_103,plain,
( ~ icext(sK2(uri_owl_equivalentClass,uri_rdfs_subClassOf),sK0(sK1(uri_owl_equivalentClass,uri_rdfs_subClassOf),sK2(uri_owl_equivalentClass,uri_rdfs_subClassOf)))
| ~ ic(sK2(uri_owl_equivalentClass,uri_rdfs_subClassOf)) ),
inference(resolve,[status(thm)],[c_102,c_79]) ).
cnf(c_93,plain,
~ icext(sK2(uri_owl_equivalentClass,uri_rdfs_subClassOf),sK0(sK1(uri_owl_equivalentClass,uri_rdfs_subClassOf),sK2(uri_owl_equivalentClass,uri_rdfs_subClassOf))),
inference(resolve,[status(thm)],[c_103,c_78]) ).
cnf(c_104,plain,
( icext(sK2(uri_owl_equivalentClass,uri_rdfs_subClassOf),A)
| ~ icext(sK1(uri_owl_equivalentClass,uri_rdfs_subClassOf),A) ),
inference(resolve,[status(thm)],[c_29,c_73]) ).
cnf(c_96,plain,
~ icext(sK1(uri_owl_equivalentClass,uri_rdfs_subClassOf),sK0(sK1(uri_owl_equivalentClass,uri_rdfs_subClassOf),sK2(uri_owl_equivalentClass,uri_rdfs_subClassOf))),
inference(resolve,[status(thm)],[c_104,c_93]) ).
cnf(c_105,plain,
( icext(sK1(uri_owl_equivalentClass,uri_rdfs_subClassOf),sK0(sK1(uri_owl_equivalentClass,uri_rdfs_subClassOf),sK2(uri_owl_equivalentClass,uri_rdfs_subClassOf)))
| ~ ic(sK2(uri_owl_equivalentClass,uri_rdfs_subClassOf))
| ~ ic(sK1(uri_owl_equivalentClass,uri_rdfs_subClassOf)) ),
inference(resolve,[status(thm)],[c_22,c_70]) ).
cnf(c_106,plain,
( icext(sK1(uri_owl_equivalentClass,uri_rdfs_subClassOf),sK0(sK1(uri_owl_equivalentClass,uri_rdfs_subClassOf),sK2(uri_owl_equivalentClass,uri_rdfs_subClassOf)))
| ~ ic(sK1(uri_owl_equivalentClass,uri_rdfs_subClassOf)) ),
inference(resolve,[status(thm)],[c_105,c_78]) ).
cnf(c_107,plain,
~ ic(sK1(uri_owl_equivalentClass,uri_rdfs_subClassOf)),
inference(resolve,[status(thm)],[c_106,c_96]) ).
cnf(c_98,plain,
$false,
inference(resolve,[status(thm)],[c_79,c_107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWB016+2 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n002.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 11:48:05 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 1635960 was started by sandbox2 on n002,
% 0.08/0.36 % Sat Sep 26 11:48:05 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 34.
% 0.13/0.38 % Level of proof is 10.
% 0.13/0.38 % Maximum clause weight is 16.000.
% 0.13/0.38 % Given clauses 62.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------