%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWB012+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 : n010.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 08:51:29 AM UTC 2026
% Result : Theorem 15.27s 2.33s
% Output : CNFRefutation 15.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 53 ( 20 unt; 0 def)
% Number of atoms : 195 ( 0 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 231 ( 89 ~; 84 |; 51 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 21 con; 0-1 aty)
% Number of variables : 109 ( 21 sgn 18 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
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_bool_intersectionof_class_003,axiom,
! [Z,S1,C1,S2,C2,S3,C3] :
( ( iext(uri_rdf_rest,S3,uri_rdf_nil)
& iext(uri_rdf_first,S3,C3)
& iext(uri_rdf_rest,S2,S3)
& iext(uri_rdf_first,S2,C2)
& iext(uri_rdf_rest,S1,S2)
& iext(uri_rdf_first,S1,C1) )
=> ( iext(uri_owl_intersectionOf,Z,S1)
<=> ( ! [X] :
( icext(Z,X)
<=> ( icext(C3,X)
& icext(C2,X)
& icext(C1,X) ) )
& ic(C3)
& ic(C2)
& ic(C1)
& ic(Z) ) ) ),
file('theBenchmark.p',owl_bool_intersectionof_class_003) ).
fof(owl_restrict_hasvalue,axiom,
! [Z,P,A] :
( ( iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_hasValue,Z,A) )
=> ! [X] :
( icext(Z,X)
<=> iext(P,X,A) ) ),
file('theBenchmark.p',owl_restrict_hasvalue) ).
fof(testcase_premise_fullish_012_Template_Class,axiom,
? [BNODE_l1,BNODE_l2,BNODE_l3,BNODE_r] :
( iext(uri_ex_name,uri_ex_alice,literal_plain(dat_str_alice))
& iext(uri_rdf_type,uri_ex_name,uri_ex_PersonAttribute)
& iext(uri_owl_hasValue,BNODE_r,uri_foaf_Person)
& iext(uri_owl_onProperty,BNODE_r,uri_rdfs_domain)
& iext(uri_rdf_type,BNODE_r,uri_owl_Restriction)
& iext(uri_rdf_rest,BNODE_l3,uri_rdf_nil)
& iext(uri_rdf_first,BNODE_l3,BNODE_r)
& iext(uri_rdf_rest,BNODE_l2,BNODE_l3)
& iext(uri_rdf_first,BNODE_l2,uri_owl_FunctionalProperty)
& iext(uri_rdf_rest,BNODE_l1,BNODE_l2)
& iext(uri_rdf_first,BNODE_l1,uri_owl_DatatypeProperty)
& iext(uri_owl_intersectionOf,uri_ex_PersonAttribute,BNODE_l1)
& iext(uri_rdf_type,uri_foaf_Person,uri_owl_Class) ),
file('theBenchmark.p',testcase_premise_fullish_012_Template_Class) ).
fof(testcase_conclusion_fullish_012_Template_Class,conjecture,
( iext(uri_rdf_type,uri_ex_alice,uri_foaf_Person)
& iext(uri_rdf_type,uri_ex_name,uri_owl_FunctionalProperty) ),
file('theBenchmark.p',testcase_conclusion_fullish_012_Template_Class) ).
fof(testcase_conclusion_fullish_012_Template_Class_neg,negated_conjecture,
~ ( iext(uri_rdf_type,uri_ex_alice,uri_foaf_Person)
& iext(uri_rdf_type,uri_ex_name,uri_owl_FunctionalProperty) ),
inference(assume_negation,[status(cth)],[testcase_conclusion_fullish_012_Template_Class]) ).
cnf(c_7,plain,
( icext(B,A)
| ~ iext(uri_rdf_type,A,B) ),
inference(clausify,[status(thm)],[rdfs_cext_def]) ).
cnf(c_8,plain,
( ~ icext(B,A)
| iext(uri_rdf_type,A,B) ),
inference(clausify,[status(thm)],[rdfs_cext_def]) ).
cnf(c_9,plain,
( icext(B,C)
| ~ iext(A,C,D)
| ~ iext(uri_rdfs_domain,A,B) ),
inference(clausify,[status(thm)],[rdfs_domain_main]) ).
cnf(c_15,plain,
( icext(D,V7)
| ~ icext(V6,V7)
| ~ iext(uri_owl_intersectionOf,V6,A)
| ~ iext(uri_rdf_rest,E,uri_rdf_nil)
| ~ iext(uri_rdf_first,E,F)
| ~ iext(uri_rdf_rest,C,E)
| ~ iext(uri_rdf_first,C,D)
| ~ iext(uri_rdf_rest,A,C)
| ~ iext(uri_rdf_first,A,B) ),
inference(clausify,[status(thm)],[owl_bool_intersectionof_class_003]) ).
cnf(c_16,plain,
( icext(F,V7)
| ~ icext(V6,V7)
| ~ iext(uri_owl_intersectionOf,V6,A)
| ~ iext(uri_rdf_rest,E,uri_rdf_nil)
| ~ iext(uri_rdf_first,E,F)
| ~ iext(uri_rdf_rest,C,E)
| ~ iext(uri_rdf_first,C,D)
| ~ iext(uri_rdf_rest,A,C)
| ~ iext(uri_rdf_first,A,B) ),
inference(clausify,[status(thm)],[owl_bool_intersectionof_class_003]) ).
cnf(c_22,plain,
( iext(C,D,B)
| ~ icext(A,D)
| ~ iext(uri_owl_onProperty,A,C)
| ~ iext(uri_owl_hasValue,A,B) ),
inference(clausify,[status(thm)],[owl_restrict_hasvalue]) ).
fof(nnf_5,plain,
? [BNODE_l1,BNODE_l2,BNODE_l3,BNODE_r] :
( iext(uri_ex_name,uri_ex_alice,literal_plain(dat_str_alice))
& iext(uri_rdf_type,uri_ex_name,uri_ex_PersonAttribute)
& iext(uri_owl_hasValue,BNODE_r,uri_foaf_Person)
& iext(uri_owl_onProperty,BNODE_r,uri_rdfs_domain)
& iext(uri_rdf_type,BNODE_r,uri_owl_Restriction)
& iext(uri_rdf_rest,BNODE_l3,uri_rdf_nil)
& iext(uri_rdf_first,BNODE_l3,BNODE_r)
& iext(uri_rdf_rest,BNODE_l2,BNODE_l3)
& iext(uri_rdf_first,BNODE_l2,uri_owl_FunctionalProperty)
& iext(uri_rdf_rest,BNODE_l1,BNODE_l2)
& iext(uri_rdf_first,BNODE_l1,uri_owl_DatatypeProperty)
& iext(uri_owl_intersectionOf,uri_ex_PersonAttribute,BNODE_l1)
& iext(uri_rdf_type,uri_foaf_Person,uri_owl_Class) ),
inference(fof_nnf,[status(thm)],[testcase_premise_fullish_012_Template_Class]) ).
fof(sk_testcase_premise_fullish_012_Template_Class,plain,
( iext(uri_ex_name,uri_ex_alice,literal_plain(dat_str_alice))
& iext(uri_rdf_type,uri_ex_name,uri_ex_PersonAttribute)
& iext(uri_owl_hasValue,sK3,uri_foaf_Person)
& iext(uri_owl_onProperty,sK3,uri_rdfs_domain)
& iext(uri_rdf_type,sK3,uri_owl_Restriction)
& iext(uri_rdf_rest,sK2,uri_rdf_nil)
& iext(uri_rdf_first,sK2,sK3)
& iext(uri_rdf_rest,sK1,sK2)
& iext(uri_rdf_first,sK1,uri_owl_FunctionalProperty)
& iext(uri_rdf_rest,sK0,sK1)
& iext(uri_rdf_first,sK0,uri_owl_DatatypeProperty)
& iext(uri_owl_intersectionOf,uri_ex_PersonAttribute,sK0)
& iext(uri_rdf_type,uri_foaf_Person,uri_owl_Class) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(BNODE_l1,sK0),skolemize(BNODE_l2,sK1),skolemize(BNODE_l3,sK2),skolemize(BNODE_r,sK3)],[nnf_5]) ).
cnf(c_25,plain,
iext(uri_owl_intersectionOf,uri_ex_PersonAttribute,sK0),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_012_Template_Class]) ).
cnf(c_26,plain,
iext(uri_rdf_first,sK0,uri_owl_DatatypeProperty),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_012_Template_Class]) ).
cnf(c_27,plain,
iext(uri_rdf_rest,sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_012_Template_Class]) ).
cnf(c_28,plain,
iext(uri_rdf_first,sK1,uri_owl_FunctionalProperty),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_012_Template_Class]) ).
cnf(c_29,plain,
iext(uri_rdf_rest,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_012_Template_Class]) ).
cnf(c_30,plain,
iext(uri_rdf_first,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_012_Template_Class]) ).
cnf(c_31,plain,
iext(uri_rdf_rest,sK2,uri_rdf_nil),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_012_Template_Class]) ).
cnf(c_33,plain,
iext(uri_owl_onProperty,sK3,uri_rdfs_domain),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_012_Template_Class]) ).
cnf(c_34,plain,
iext(uri_owl_hasValue,sK3,uri_foaf_Person),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_012_Template_Class]) ).
cnf(c_35,plain,
iext(uri_rdf_type,uri_ex_name,uri_ex_PersonAttribute),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_012_Template_Class]) ).
cnf(c_36,plain,
iext(uri_ex_name,uri_ex_alice,literal_plain(dat_str_alice)),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_012_Template_Class]) ).
cnf(c_37,negated_conjecture,
( ~ iext(uri_rdf_type,uri_ex_alice,uri_foaf_Person)
| ~ iext(uri_rdf_type,uri_ex_name,uri_owl_FunctionalProperty) ),
inference(clausify,[status(thm)],[testcase_conclusion_fullish_012_Template_Class_neg]) ).
cnf(c_1414,plain,
( icext(D,F)
| ~ icext(E,F)
| ~ iext(uri_owl_intersectionOf,E,A)
| ~ iext(uri_rdf_rest,sK2,uri_rdf_nil)
| ~ iext(uri_rdf_first,sK2,D)
| ~ iext(uri_rdf_first,sK1,C)
| ~ iext(uri_rdf_rest,A,sK1)
| ~ iext(uri_rdf_first,A,B) ),
inference(resolve,[status(thm)],[c_29,c_16]) ).
cnf(c_466,plain,
( icext(D,F)
| ~ icext(E,F)
| ~ iext(uri_owl_intersectionOf,E,A)
| ~ iext(uri_rdf_first,sK2,D)
| ~ iext(uri_rdf_first,sK1,C)
| ~ iext(uri_rdf_rest,A,sK1)
| ~ iext(uri_rdf_first,A,B) ),
inference(resolve,[status(thm)],[c_31,c_1414]) ).
cnf(c_1415,plain,
( icext(D,F)
| ~ icext(E,F)
| ~ iext(uri_owl_intersectionOf,E,A)
| ~ iext(uri_rdf_rest,sK2,uri_rdf_nil)
| ~ iext(uri_rdf_rest,C,sK2)
| ~ iext(uri_rdf_first,C,D)
| ~ iext(uri_rdf_rest,A,C)
| ~ iext(uri_rdf_first,A,B) ),
inference(resolve,[status(thm)],[c_30,c_15]) ).
cnf(c_496,plain,
( icext(D,F)
| ~ icext(E,F)
| ~ iext(uri_owl_intersectionOf,E,A)
| ~ iext(uri_rdf_rest,C,sK2)
| ~ iext(uri_rdf_first,C,D)
| ~ iext(uri_rdf_rest,A,C)
| ~ iext(uri_rdf_first,A,B) ),
inference(resolve,[status(thm)],[c_31,c_1415]) ).
cnf(c_560,plain,
( iext(uri_rdfs_domain,B,A)
| ~ icext(sK3,B)
| ~ iext(uri_owl_hasValue,sK3,A) ),
inference(resolve,[status(thm)],[c_33,c_22]) ).
cnf(c_568,plain,
icext(uri_ex_PersonAttribute,uri_ex_name),
inference(resolve,[status(thm)],[c_35,c_7]) ).
cnf(c_570,plain,
( icext(A,uri_ex_alice)
| ~ iext(uri_rdfs_domain,uri_ex_name,A) ),
inference(resolve,[status(thm)],[c_36,c_9]) ).
cnf(c_932,plain,
( iext(uri_rdfs_domain,A,uri_foaf_Person)
| ~ icext(sK3,A) ),
inference(resolve,[status(thm)],[c_560,c_34]) ).
cnf(c_1416,plain,
( icext(B,D)
| ~ icext(C,D)
| ~ iext(uri_owl_intersectionOf,C,sK0)
| ~ iext(uri_rdf_first,sK2,B)
| ~ iext(uri_rdf_first,sK1,A)
| ~ iext(uri_rdf_rest,sK0,sK1) ),
inference(resolve,[status(thm)],[c_466,c_26]) ).
cnf(c_1103,plain,
( icext(B,D)
| ~ icext(C,D)
| ~ iext(uri_owl_intersectionOf,C,sK0)
| ~ iext(uri_rdf_first,sK2,B)
| ~ iext(uri_rdf_first,sK1,A) ),
inference(resolve,[status(thm)],[c_27,c_1416]) ).
cnf(c_1417,plain,
( icext(B,uri_ex_name)
| ~ iext(uri_owl_intersectionOf,uri_ex_PersonAttribute,sK0)
| ~ iext(uri_rdf_first,sK2,B)
| ~ iext(uri_rdf_first,sK1,A) ),
inference(resolve,[status(thm)],[c_1103,c_568]) ).
cnf(c_1279,plain,
( icext(B,uri_ex_name)
| ~ iext(uri_rdf_first,sK2,B)
| ~ iext(uri_rdf_first,sK1,A) ),
inference(resolve,[status(thm)],[c_25,c_1417]) ).
cnf(c_1282,plain,
( icext(A,uri_ex_name)
| ~ iext(uri_rdf_first,sK2,A) ),
inference(resolve,[status(thm)],[c_1279,c_28]) ).
cnf(c_1284,plain,
icext(sK3,uri_ex_name),
inference(resolve,[status(thm)],[c_1282,c_30]) ).
cnf(c_1292,plain,
iext(uri_rdfs_domain,uri_ex_name,uri_foaf_Person),
inference(resolve,[status(thm)],[c_1284,c_932]) ).
cnf(c_1331,plain,
icext(uri_foaf_Person,uri_ex_alice),
inference(resolve,[status(thm)],[c_1292,c_570]) ).
cnf(c_1382,plain,
iext(uri_rdf_type,uri_ex_alice,uri_foaf_Person),
inference(resolve,[status(thm)],[c_1331,c_8]) ).
cnf(c_1385,negated_conjecture,
~ iext(uri_rdf_type,uri_ex_name,uri_owl_FunctionalProperty),
inference(resolve,[status(thm)],[c_1382,c_37]) ).
cnf(c_1402,negated_conjecture,
~ icext(uri_owl_FunctionalProperty,uri_ex_name),
inference(resolve,[status(thm)],[c_8,c_1385]) ).
cnf(c_1418,plain,
( icext(B,D)
| ~ icext(C,D)
| ~ iext(uri_owl_intersectionOf,C,sK0)
| ~ iext(uri_rdf_rest,sK1,sK2)
| ~ iext(uri_rdf_first,sK1,B)
| ~ iext(uri_rdf_first,sK0,A) ),
inference(resolve,[status(thm)],[c_496,c_27]) ).
cnf(c_1419,plain,
( icext(uri_owl_FunctionalProperty,C)
| ~ icext(B,C)
| ~ iext(uri_owl_intersectionOf,B,sK0)
| ~ iext(uri_rdf_rest,sK1,sK2)
| ~ iext(uri_rdf_first,sK0,A) ),
inference(resolve,[status(thm)],[c_1418,c_28]) ).
cnf(c_1420,plain,
( icext(uri_owl_FunctionalProperty,C)
| ~ icext(B,C)
| ~ iext(uri_owl_intersectionOf,B,sK0)
| ~ iext(uri_rdf_first,sK0,A) ),
inference(resolve,[status(thm)],[c_1419,c_29]) ).
cnf(c_1421,plain,
( icext(uri_owl_FunctionalProperty,B)
| ~ icext(uri_ex_PersonAttribute,B)
| ~ iext(uri_rdf_first,sK0,A) ),
inference(resolve,[status(thm)],[c_1420,c_25]) ).
cnf(c_1422,plain,
( icext(uri_owl_FunctionalProperty,uri_ex_name)
| ~ iext(uri_rdf_first,sK0,A) ),
inference(resolve,[status(thm)],[c_1421,c_568]) ).
cnf(c_1412,plain,
~ iext(uri_rdf_first,sK0,A),
inference(resolve,[status(thm)],[c_1422,c_1402]) ).
cnf(c_1413,plain,
$false,
inference(resolve,[status(thm)],[c_1412,c_26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWB012+2 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n010.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 11:43:15 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 3200858 was started by sandbox2 on n010,
% 0.09/0.35 % Sat Sep 26 11:43:15 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 15.27/2.33
% 15.27/2.33 % given #500 (T,wt=20): 713 -iext(uri_rdf_rest,c1,c1) | -iext(uri_rdf_rest,c1,uri_rdf_nil) | -iext(uri_owl_intersectionOf,A,c1) | icext(A,B) | -icext(uri_owl_DatatypeProperty,B). [resolve(133,a,26,a)].
% 15.27/2.33
% 15.27/2.33 % SZS status Theorem for theBenchmark
% 15.27/2.33
% 15.27/2.33 % Proof 1 at 1.69 (+ 0.15) seconds.
% 15.27/2.33 % Length of proof is 41.
% 15.27/2.33 % Level of proof is 13.
% 15.27/2.33 % Maximum clause weight is 36.000.
% 15.27/2.33 % Given clauses 562.
% 15.27/2.33
% 15.27/2.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------