%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWB029+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 : 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 08:51:36 AM UTC 2026
% Result : Theorem 3.88s 1.05s
% Output : CNFRefutation 3.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 12 unt; 0 def)
% Number of atoms : 118 ( 0 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 135 ( 50 ~; 46 |; 33 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 14 con; 0-0 aty)
% Number of variables : 61 ( 4 sgn 11 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(owl_bool_complementof_class,axiom,
! [Z,C] :
( iext(uri_owl_complementOf,Z,C)
=> ( ! [X] :
( icext(Z,X)
<=> ~ icext(C,X) )
& ic(C)
& ic(Z) ) ),
file('theBenchmark.p',owl_bool_complementof_class) ).
fof(owl_bool_intersectionof_class_002,axiom,
! [Z,S1,C1,S2,C2] :
( ( iext(uri_rdf_rest,S2,uri_rdf_nil)
& 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(C2,X)
& icext(C1,X) ) )
& ic(C2)
& ic(C1)
& ic(Z) ) ) ),
file('theBenchmark.p',owl_bool_intersectionof_class_002) ).
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_029_Ex_Falso_Quodlibet,axiom,
? [BNODE_x,BNODE_y,BNODE_l1,BNODE_l2] :
( iext(uri_owl_complementOf,BNODE_y,uri_ex_A)
& iext(uri_rdf_rest,BNODE_l2,uri_rdf_nil)
& iext(uri_rdf_first,BNODE_l2,BNODE_y)
& iext(uri_rdf_rest,BNODE_l1,BNODE_l2)
& iext(uri_rdf_first,BNODE_l1,uri_ex_A)
& iext(uri_owl_intersectionOf,BNODE_x,BNODE_l1)
& iext(uri_rdf_type,uri_ex_w,BNODE_x)
& iext(uri_rdf_type,uri_ex_B,uri_owl_Class)
& iext(uri_rdf_type,uri_ex_A,uri_owl_Class) ),
file('theBenchmark.p',testcase_premise_fullish_029_Ex_Falso_Quodlibet) ).
cnf(c_181,plain,
( ~ icext(B,C)
| ~ icext(A,C)
| ~ iext(uri_owl_complementOf,A,B) ),
inference(clausify,[status(thm)],[owl_bool_complementof_class]) ).
cnf(c_197,plain,
( icext(B,F)
| ~ icext(E,F)
| ~ iext(uri_owl_intersectionOf,E,A)
| ~ iext(uri_rdf_rest,C,uri_rdf_nil)
| ~ 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_002]) ).
cnf(c_198,plain,
( icext(D,F)
| ~ icext(E,F)
| ~ iext(uri_owl_intersectionOf,E,A)
| ~ iext(uri_rdf_rest,C,uri_rdf_nil)
| ~ 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_002]) ).
cnf(c_283,plain,
( icext(B,A)
| ~ iext(uri_rdf_type,A,B) ),
inference(clausify,[status(thm)],[rdfs_cext_def]) ).
fof(nnf_36,plain,
? [BNODE_x,BNODE_y,BNODE_l1,BNODE_l2] :
( iext(uri_owl_complementOf,BNODE_y,uri_ex_A)
& iext(uri_rdf_rest,BNODE_l2,uri_rdf_nil)
& iext(uri_rdf_first,BNODE_l2,BNODE_y)
& iext(uri_rdf_rest,BNODE_l1,BNODE_l2)
& iext(uri_rdf_first,BNODE_l1,uri_ex_A)
& iext(uri_owl_intersectionOf,BNODE_x,BNODE_l1)
& iext(uri_rdf_type,uri_ex_w,BNODE_x)
& iext(uri_rdf_type,uri_ex_B,uri_owl_Class)
& iext(uri_rdf_type,uri_ex_A,uri_owl_Class) ),
inference(fof_nnf,[status(thm)],[testcase_premise_fullish_029_Ex_Falso_Quodlibet]) ).
fof(sk_testcase_premise_fullish_029_Ex_Falso_Quodlibet,plain,
( iext(uri_owl_complementOf,sK3,uri_ex_A)
& 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_ex_A)
& iext(uri_owl_intersectionOf,sK0,sK1)
& iext(uri_rdf_type,uri_ex_w,sK0)
& iext(uri_rdf_type,uri_ex_B,uri_owl_Class)
& iext(uri_rdf_type,uri_ex_A,uri_owl_Class) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(BNODE_x,sK0),skolemize(BNODE_y,sK3),skolemize(BNODE_l1,sK1),skolemize(BNODE_l2,sK2)],[nnf_36]) ).
cnf(c_309,plain,
iext(uri_rdf_type,uri_ex_w,sK0),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_029_Ex_Falso_Quodlibet]) ).
cnf(c_310,plain,
iext(uri_owl_intersectionOf,sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_029_Ex_Falso_Quodlibet]) ).
cnf(c_311,plain,
iext(uri_rdf_first,sK1,uri_ex_A),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_029_Ex_Falso_Quodlibet]) ).
cnf(c_312,plain,
iext(uri_rdf_rest,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_029_Ex_Falso_Quodlibet]) ).
cnf(c_313,plain,
iext(uri_rdf_first,sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_029_Ex_Falso_Quodlibet]) ).
cnf(c_314,plain,
iext(uri_rdf_rest,sK2,uri_rdf_nil),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_029_Ex_Falso_Quodlibet]) ).
cnf(c_315,plain,
iext(uri_owl_complementOf,sK3,uri_ex_A),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_029_Ex_Falso_Quodlibet]) ).
cnf(c_948,plain,
( ~ icext(uri_ex_A,A)
| ~ icext(sK3,A) ),
inference(resolve,[status(thm)],[c_315,c_181]) ).
cnf(c_1249,plain,
icext(sK0,uri_ex_w),
inference(resolve,[status(thm)],[c_283,c_309]) ).
cnf(c_1345,plain,
( icext(B,D)
| ~ icext(C,D)
| ~ iext(uri_owl_intersectionOf,C,sK1)
| ~ iext(uri_rdf_rest,A,uri_rdf_nil)
| ~ iext(uri_rdf_first,A,B)
| ~ iext(uri_rdf_rest,sK1,A) ),
inference(resolve,[status(thm)],[c_198,c_311]) ).
cnf(c_1346,plain,
( icext(A,C)
| ~ icext(B,C)
| ~ iext(uri_owl_intersectionOf,B,sK1)
| ~ iext(uri_rdf_rest,sK2,uri_rdf_nil)
| ~ iext(uri_rdf_first,sK2,A) ),
inference(resolve,[status(thm)],[c_1345,c_312]) ).
cnf(c_1347,plain,
( icext(sK3,B)
| ~ icext(A,B)
| ~ iext(uri_owl_intersectionOf,A,sK1)
| ~ iext(uri_rdf_rest,sK2,uri_rdf_nil) ),
inference(resolve,[status(thm)],[c_1346,c_313]) ).
cnf(c_1348,plain,
( icext(sK3,B)
| ~ icext(A,B)
| ~ iext(uri_owl_intersectionOf,A,sK1) ),
inference(resolve,[status(thm)],[c_1347,c_314]) ).
cnf(c_1349,plain,
( icext(sK3,A)
| ~ icext(sK0,A) ),
inference(resolve,[status(thm)],[c_1348,c_310]) ).
cnf(c_1268,plain,
icext(sK3,uri_ex_w),
inference(resolve,[status(thm)],[c_1349,c_1249]) ).
cnf(c_1350,plain,
( icext(uri_ex_A,D)
| ~ icext(C,D)
| ~ iext(uri_owl_intersectionOf,C,sK1)
| ~ iext(uri_rdf_rest,A,uri_rdf_nil)
| ~ iext(uri_rdf_first,A,B)
| ~ iext(uri_rdf_rest,sK1,A) ),
inference(resolve,[status(thm)],[c_197,c_311]) ).
cnf(c_1351,plain,
( icext(uri_ex_A,C)
| ~ icext(B,C)
| ~ iext(uri_owl_intersectionOf,B,sK1)
| ~ iext(uri_rdf_rest,sK2,uri_rdf_nil)
| ~ iext(uri_rdf_first,sK2,A) ),
inference(resolve,[status(thm)],[c_1350,c_312]) ).
cnf(c_1352,plain,
( icext(uri_ex_A,B)
| ~ icext(A,B)
| ~ iext(uri_owl_intersectionOf,A,sK1)
| ~ iext(uri_rdf_rest,sK2,uri_rdf_nil) ),
inference(resolve,[status(thm)],[c_1351,c_313]) ).
cnf(c_1353,plain,
( icext(uri_ex_A,B)
| ~ icext(A,B)
| ~ iext(uri_owl_intersectionOf,A,sK1) ),
inference(resolve,[status(thm)],[c_1352,c_314]) ).
cnf(c_1354,plain,
( icext(uri_ex_A,A)
| ~ icext(sK0,A) ),
inference(resolve,[status(thm)],[c_1353,c_310]) ).
cnf(c_1269,plain,
icext(uri_ex_A,uri_ex_w),
inference(resolve,[status(thm)],[c_1354,c_1249]) ).
cnf(c_1355,plain,
~ icext(uri_ex_A,uri_ex_w),
inference(resolve,[status(thm)],[c_1268,c_948]) ).
cnf(c_1344,plain,
$false,
inference(resolve,[status(thm)],[c_1269,c_1355]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWB029+3 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03 % 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 11:54:08 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.37 % Process 2801853 was started by sandbox on n003,
% 0.14/0.37 % Sat Sep 26 11:54:08 2026
% 0.14/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.39
% 0.14/0.39 % From the command line: assign(max_seconds, 300).
% 0.14/0.39
% 0.14/0.39 % SInE: 57 to sos, 82 to usable, of 139 axioms (tolerance 2.00, depth 0 fixpoint).
% 3.88/1.05
% 3.88/1.05 % SZS status Theorem for theBenchmark
% 3.88/1.05
% 3.88/1.05 % Proof 1 at 0.56 (+ 0.08) seconds.
% 3.88/1.05 % Length of proof is 20.
% 3.88/1.05 % Level of proof is 4.
% 3.88/1.05 % Maximum clause weight is 131.000.
% 3.88/1.05 % Given clauses 120.
% 3.88/1.05
% 3.88/1.05 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------