%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET064-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 08:35:35 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 8 unt; 0 def)
% Number of atoms : 16 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 11 ( 6 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 6 ( 1 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_null_class_is_unique_2,axiom,
~ member(not_subclass_element(z,null_class),z),
file('theBenchmark.p',prove_null_class_is_unique_2) ).
cnf(c_33,plain,
~ member(not_subclass_element(z,null_class),z),
inference(clausify,[status(thm)],[prove_null_class_is_unique_2]) ).
fof(prove_null_class_is_unique_1,axiom,
z != null_class,
file('theBenchmark.p',prove_null_class_is_unique_1) ).
cnf(c_34,plain,
z != null_class,
inference(clausify,[status(thm)],[prove_null_class_is_unique_1]) ).
fof(existence_of_null_class,axiom,
! [VAR_0] : ~ member(VAR_0,null_class),
file('theBenchmark.p',existence_of_null_class) ).
cnf(c_38,plain,
~ member(A,null_class),
inference(clausify,[status(thm)],[existence_of_null_class]) ).
fof(equality1,axiom,
! [VAR_0,VAR_1] :
( member(not_subclass_element(VAR_1,VAR_0),VAR_1)
| member(not_subclass_element(VAR_0,VAR_1),VAR_0)
| VAR_0 = VAR_1 ),
file('theBenchmark.p',equality1) ).
cnf(c_43,plain,
( member(not_subclass_element(B,A),B)
| member(not_subclass_element(A,B),A)
| A = B ),
inference(clausify,[status(thm)],[equality1]) ).
cnf(c_218,plain,
( member(not_subclass_element(null_class,z),null_class)
| z = null_class ),
inference(resolve,[status(thm)],[c_43,c_33]) ).
cnf(c_219,plain,
member(not_subclass_element(null_class,z),null_class),
inference(resolve,[status(thm)],[c_34,c_218]) ).
cnf(c_217,plain,
$false,
inference(resolve,[status(thm)],[c_38,c_219]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET064-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 07:02:28 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3027779 was started by sandbox2 on n008,
% 0.09/0.37 % Sat Sep 26 07:02:28 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.14/0.40
% 0.14/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.40
% 0.14/0.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/0.40 % Length of proof is 5.
% 0.14/0.40 % Level of proof is 1.
% 0.14/0.40 % Maximum clause weight is 13.000.
% 0.14/0.40 % Given clauses 11.
% 0.14/0.40
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------