%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET064-6 : 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 : n014.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 0.23s 0.52s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 12 unt; 0 def)
% Number of atoms : 42 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 35 ( 19 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 22 ( 1 sgn 10 !; 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_34,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_35,plain,
z != null_class,
inference(clausify,[status(thm)],[prove_null_class_is_unique_1]) ).
fof(regularity2,axiom,
! [VAR_0] :
( intersection(VAR_0,regular(VAR_0)) = null_class
| VAR_0 = null_class ),
file('theBenchmark.p',regularity2) ).
cnf(c_50,plain,
( intersection(A,regular(A)) = null_class
| A = null_class ),
inference(clausify,[status(thm)],[regularity2]) ).
cnf(c_51,plain,
( intersection(A,regular(A)) = null_class
| null_class = A ),
inference(copy,[status(thm)],[c_50]) ).
fof(intersection1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,VAR_1)
| ~ member(VAR_0,intersection(VAR_1,VAR_2)) ),
file('theBenchmark.p',intersection1) ).
cnf(c_99,plain,
( member(A,B)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection1]) ).
fof(subclass_implies_equal,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| ~ subclass(VAR_1,VAR_0)
| ~ subclass(VAR_0,VAR_1) ),
file('theBenchmark.p',subclass_implies_equal) ).
cnf(c_115,plain,
( A = B
| ~ subclass(B,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_implies_equal]) ).
fof(not_subclass_members2,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_0,VAR_1)
| ~ member(not_subclass_element(VAR_0,VAR_1),VAR_1) ),
file('theBenchmark.p',not_subclass_members2) ).
cnf(c_119,plain,
( subclass(A,B)
| ~ member(not_subclass_element(A,B),B) ),
inference(clausify,[status(thm)],[not_subclass_members2]) ).
fof(not_subclass_members1,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_0,VAR_1)
| member(not_subclass_element(VAR_0,VAR_1),VAR_0) ),
file('theBenchmark.p',not_subclass_members1) ).
cnf(c_120,plain,
( subclass(A,B)
| member(not_subclass_element(A,B),A) ),
inference(clausify,[status(thm)],[not_subclass_members1]) ).
cnf(c_650,plain,
null_class != z,
inference(copy,[status(thm)],[c_35]) ).
cnf(c_147,plain,
intersection(z,regular(z)) = null_class,
inference(resolve,[status(thm)],[c_51,c_650]) ).
cnf(c_334,plain,
subclass(z,null_class),
inference(resolve,[status(thm)],[c_120,c_34]) ).
cnf(c_394,plain,
( member(A,z)
| ~ member(A,null_class) ),
inference(paramod,[status(thm)],[c_147,c_99]) ).
cnf(c_651,plain,
( null_class = z
| ~ subclass(null_class,z) ),
inference(resolve,[status(thm)],[c_334,c_115]) ).
cnf(c_652,plain,
( z = null_class
| ~ subclass(null_class,z) ),
inference(copy,[status(thm)],[c_651]) ).
cnf(c_414,plain,
~ subclass(null_class,z),
inference(resolve,[status(thm)],[c_35,c_652]) ).
cnf(c_418,plain,
member(not_subclass_element(null_class,z),null_class),
inference(resolve,[status(thm)],[c_414,c_120]) ).
cnf(c_419,plain,
~ member(not_subclass_element(null_class,z),z),
inference(resolve,[status(thm)],[c_119,c_414]) ).
cnf(c_653,plain,
~ member(not_subclass_element(null_class,z),null_class),
inference(resolve,[status(thm)],[c_394,c_419]) ).
cnf(c_649,plain,
$false,
inference(resolve,[status(thm)],[c_418,c_653]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET064-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n014.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 07:01:32 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 2446920 was started by sandbox2 on n014,
% 0.19/0.45 % Sat Sep 26 07:01:32 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 0.23/0.52
% 0.23/0.52 % SZS status Unsatisfiable for theBenchmark
% 0.23/0.52
% 0.23/0.52 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.23/0.52 % Length of proof is 15.
% 0.23/0.52 % Level of proof is 4.
% 0.23/0.52 % Maximum clause weight is 24.000.
% 0.23/0.52 % Given clauses 137.
% 0.23/0.52
% 0.23/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------