%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWB023+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 : n009.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 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 16 unt; 0 def)
% Number of atoms : 87 ( 16 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 79 ( 28 ~; 20 |; 24 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 13 con; 0-0 aty)
% Number of variables : 36 ( 0 sgn 12 !; 4 ?)
% 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_enum_class_001,axiom,
! [Z,S1,A1] :
( ( iext(uri_rdf_rest,S1,uri_rdf_nil)
& iext(uri_rdf_first,S1,A1) )
=> ( iext(uri_owl_oneOf,Z,S1)
<=> ( ! [X] :
( icext(Z,X)
<=> X = A1 )
& ic(Z) ) ) ),
file('theBenchmark.p',owl_enum_class_001) ).
fof(owl_char_functional,axiom,
! [P] :
( icext(uri_owl_FunctionalProperty,P)
<=> ( ! [X,Y1,Y2] :
( ( iext(P,X,Y2)
& iext(P,X,Y1) )
=> Y1 = Y2 )
& ip(P) ) ),
file('theBenchmark.p',owl_char_functional) ).
fof(owl_eqdis_sameas,axiom,
! [X,Y] :
( iext(uri_owl_sameAs,X,Y)
<=> X = Y ),
file('theBenchmark.p',owl_eqdis_sameas) ).
fof(testcase_premise_fullish_023_Unique_List_Components,axiom,
? [BNODE_o,BNODE_l] :
( iext(uri_rdf_rest,BNODE_l,uri_rdf_nil)
& iext(uri_rdf_first,BNODE_l,uri_ex_v)
& iext(uri_rdf_first,BNODE_l,uri_ex_u)
& iext(uri_owl_oneOf,BNODE_o,BNODE_l)
& iext(uri_rdf_type,BNODE_o,uri_owl_Class)
& iext(uri_rdf_type,uri_ex_w,BNODE_o)
& iext(uri_rdf_type,uri_rdf_first,uri_owl_FunctionalProperty) ),
file('theBenchmark.p',testcase_premise_fullish_023_Unique_List_Components) ).
fof(testcase_conclusion_fullish_023_Unique_List_Components,conjecture,
( iext(uri_owl_sameAs,uri_ex_w,uri_ex_v)
& iext(uri_owl_sameAs,uri_ex_w,uri_ex_u) ),
file('theBenchmark.p',testcase_conclusion_fullish_023_Unique_List_Components) ).
fof(testcase_conclusion_fullish_023_Unique_List_Components_neg,negated_conjecture,
~ ( iext(uri_owl_sameAs,uri_ex_w,uri_ex_v)
& iext(uri_owl_sameAs,uri_ex_w,uri_ex_u) ),
inference(assume_negation,[status(cth)],[testcase_conclusion_fullish_023_Unique_List_Components]) ).
cnf(c_14,plain,
( icext(B,A)
| ~ iext(uri_rdf_type,A,B) ),
inference(clausify,[status(thm)],[rdfs_cext_def]) ).
cnf(c_16,plain,
( B = D
| ~ icext(C,D)
| ~ iext(uri_owl_oneOf,C,A)
| ~ iext(uri_rdf_rest,A,uri_rdf_nil)
| ~ iext(uri_rdf_first,A,B) ),
inference(clausify,[status(thm)],[owl_enum_class_001]) ).
cnf(c_18,plain,
( D = C
| ~ iext(A,B,D)
| ~ iext(A,B,C)
| ~ icext(uri_owl_FunctionalProperty,A) ),
inference(clausify,[status(thm)],[owl_char_functional]) ).
cnf(c_20,plain,
( B != A
| iext(uri_owl_sameAs,A,B) ),
inference(clausify,[status(thm)],[owl_eqdis_sameas]) ).
fof(nnf_5,plain,
? [BNODE_o,BNODE_l] :
( iext(uri_rdf_rest,BNODE_l,uri_rdf_nil)
& iext(uri_rdf_first,BNODE_l,uri_ex_v)
& iext(uri_rdf_first,BNODE_l,uri_ex_u)
& iext(uri_owl_oneOf,BNODE_o,BNODE_l)
& iext(uri_rdf_type,BNODE_o,uri_owl_Class)
& iext(uri_rdf_type,uri_ex_w,BNODE_o)
& iext(uri_rdf_type,uri_rdf_first,uri_owl_FunctionalProperty) ),
inference(fof_nnf,[status(thm)],[testcase_premise_fullish_023_Unique_List_Components]) ).
fof(sk_testcase_premise_fullish_023_Unique_List_Components,plain,
( iext(uri_rdf_rest,sK1,uri_rdf_nil)
& iext(uri_rdf_first,sK1,uri_ex_v)
& iext(uri_rdf_first,sK1,uri_ex_u)
& iext(uri_owl_oneOf,sK0,sK1)
& iext(uri_rdf_type,sK0,uri_owl_Class)
& iext(uri_rdf_type,uri_ex_w,sK0)
& iext(uri_rdf_type,uri_rdf_first,uri_owl_FunctionalProperty) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(BNODE_o,sK0),skolemize(BNODE_l,sK1)],[nnf_5]) ).
cnf(c_21,plain,
iext(uri_rdf_type,uri_rdf_first,uri_owl_FunctionalProperty),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_023_Unique_List_Components]) ).
cnf(c_22,plain,
iext(uri_rdf_type,uri_ex_w,sK0),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_023_Unique_List_Components]) ).
cnf(c_24,plain,
iext(uri_owl_oneOf,sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_023_Unique_List_Components]) ).
cnf(c_25,plain,
iext(uri_rdf_first,sK1,uri_ex_u),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_023_Unique_List_Components]) ).
cnf(c_26,plain,
iext(uri_rdf_first,sK1,uri_ex_v),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_023_Unique_List_Components]) ).
cnf(c_27,plain,
iext(uri_rdf_rest,sK1,uri_rdf_nil),
inference(split_conjunct,[status(thm)],[sk_testcase_premise_fullish_023_Unique_List_Components]) ).
cnf(c_28,negated_conjecture,
( ~ iext(uri_owl_sameAs,uri_ex_w,uri_ex_v)
| ~ iext(uri_owl_sameAs,uri_ex_w,uri_ex_u) ),
inference(clausify,[status(thm)],[testcase_conclusion_fullish_023_Unique_List_Components_neg]) ).
cnf(c_35,plain,
icext(uri_owl_FunctionalProperty,uri_rdf_first),
inference(resolve,[status(thm)],[c_21,c_14]) ).
cnf(c_37,plain,
icext(sK0,uri_ex_w),
inference(resolve,[status(thm)],[c_22,c_14]) ).
cnf(c_69,plain,
( uri_ex_u = A
| ~ iext(uri_rdf_first,sK1,A)
| ~ icext(uri_owl_FunctionalProperty,uri_rdf_first) ),
inference(resolve,[status(thm)],[c_25,c_18]) ).
cnf(c_43,plain,
( uri_ex_u = A
| ~ iext(uri_rdf_first,sK1,A) ),
inference(resolve,[status(thm)],[c_35,c_69]) ).
cnf(c_70,plain,
uri_ex_u = uri_ex_v,
inference(resolve,[status(thm)],[c_43,c_26]) ).
cnf(c_63,plain,
uri_ex_v = uri_ex_u,
inference(copy,[status(thm)],[c_70]) ).
cnf(c_71,negated_conjecture,
( ~ iext(uri_owl_sameAs,uri_ex_w,uri_ex_u)
| ~ iext(uri_owl_sameAs,uri_ex_w,uri_ex_u) ),
inference(paramod,[status(thm)],[c_63,c_28]) ).
cnf(c_64,negated_conjecture,
~ iext(uri_owl_sameAs,uri_ex_w,uri_ex_u),
inference(copy,[status(thm)],[c_71]) ).
cnf(c_72,negated_conjecture,
uri_ex_u != uri_ex_w,
inference(resolve,[status(thm)],[c_20,c_64]) ).
cnf(c_65,negated_conjecture,
uri_ex_w != uri_ex_u,
inference(copy,[status(thm)],[c_72]) ).
cnf(c_73,plain,
( A = C
| ~ icext(B,C)
| ~ iext(uri_owl_oneOf,B,sK1)
| ~ iext(uri_rdf_first,sK1,A) ),
inference(resolve,[status(thm)],[c_16,c_27]) ).
cnf(c_74,plain,
( A = B
| ~ icext(sK0,B)
| ~ iext(uri_rdf_first,sK1,A) ),
inference(resolve,[status(thm)],[c_73,c_24]) ).
cnf(c_75,plain,
( A = uri_ex_w
| ~ iext(uri_rdf_first,sK1,A) ),
inference(resolve,[status(thm)],[c_74,c_37]) ).
cnf(c_76,plain,
uri_ex_u != uri_ex_w,
inference(copy,[status(thm)],[c_65]) ).
cnf(c_77,plain,
~ iext(uri_rdf_first,sK1,uri_ex_u),
inference(resolve,[status(thm)],[c_75,c_76]) ).
cnf(c_68,plain,
$false,
inference(resolve,[status(thm)],[c_25,c_77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWB023+2 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.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 11:49:31 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 30326 was started by sandbox2 on n009,
% 0.08/0.35 % Sat Sep 26 11:49:31 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.37
% 0.13/0.37 % SZS status Theorem for theBenchmark
% 0.13/0.37
% 0.13/0.37 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.13/0.37 % Length of proof is 24.
% 0.13/0.37 % Level of proof is 7.
% 0.13/0.37 % Maximum clause weight is 18.000.
% 0.13/0.37 % Given clauses 25.
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------