%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET062-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 08:35:33 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.61s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 8 unt; 0 def)
% Number of atoms : 35 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 14 ~; 14 |; 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 : 24 ( 1 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_null_class_is_subclass_1,axiom,
~ subclass(null_class,x),
file('theBenchmark.p',prove_null_class_is_subclass_1) ).
cnf(c_34,plain,
~ subclass(null_class,x),
inference(clausify,[status(thm)],[prove_null_class_is_subclass_1]) ).
fof(regularity2,axiom,
! [VAR_0] :
( intersection(VAR_0,regular(VAR_0)) = null_class
| VAR_0 = null_class ),
file('theBenchmark.p',regularity2) ).
cnf(c_49,plain,
( intersection(A,regular(A)) = null_class
| A = null_class ),
inference(clausify,[status(thm)],[regularity2]) ).
cnf(c_50,plain,
( intersection(A,regular(A)) = null_class
| null_class = A ),
inference(copy,[status(thm)],[c_49]) ).
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_98,plain,
( member(A,B)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection1]) ).
fof(equal_implies_subclass2,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_1,VAR_0)
| VAR_0 != VAR_1 ),
file('theBenchmark.p',equal_implies_subclass2) ).
cnf(c_115,plain,
( subclass(B,A)
| A != B ),
inference(clausify,[status(thm)],[equal_implies_subclass2]) ).
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_118,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_119,plain,
( subclass(A,B)
| member(not_subclass_element(A,B),A) ),
inference(clausify,[status(thm)],[not_subclass_members1]) ).
cnf(c_201,plain,
( member(B,A)
| ~ member(B,null_class)
| null_class = A ),
inference(paramod,[status(thm)],[c_50,c_98]) ).
cnf(c_301,plain,
x != null_class,
inference(resolve,[status(thm)],[c_115,c_34]) ).
cnf(c_303,plain,
~ member(not_subclass_element(null_class,x),x),
inference(resolve,[status(thm)],[c_118,c_34]) ).
cnf(c_306,plain,
member(not_subclass_element(null_class,x),null_class),
inference(resolve,[status(thm)],[c_119,c_34]) ).
cnf(c_562,plain,
null_class != x,
inference(copy,[status(thm)],[c_301]) ).
cnf(c_563,plain,
( member(A,x)
| ~ member(A,null_class) ),
inference(resolve,[status(thm)],[c_201,c_562]) ).
cnf(c_564,plain,
~ member(not_subclass_element(null_class,x),null_class),
inference(resolve,[status(thm)],[c_563,c_303]) ).
cnf(c_561,plain,
$false,
inference(resolve,[status(thm)],[c_306,c_564]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET062-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.55 % Computer : n013.cluster.edu
% 0.08/0.55 % Model : x86_64 x86_64
% 0.08/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.55 % Memory : 8046.5625MB
% 0.08/0.55 % OS : Linux 6.8.0-71-generic
% 0.08/0.55 % CPULimit : 300
% 0.08/0.55 % WCLimit : 300
% 0.08/0.55 % DateTime : Sat Sep 26 07:00:38 UTC 2026
% 0.12/0.56 % CPUTime :
% 0.12/0.56 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.56 % Process 2169459 was started by sandbox on n013,
% 0.12/0.56 % Sat Sep 26 07:00:38 2026
% 0.12/0.56 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.56
% 0.12/0.56 % From the command line: assign(max_seconds, 300).
% 0.12/0.61
% 0.12/0.61 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.61
% 0.12/0.61 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.12/0.61 % Length of proof is 12.
% 0.12/0.61 % Level of proof is 3.
% 0.12/0.61 % Maximum clause weight is 24.000.
% 0.12/0.61 % Given clauses 129.
% 0.12/0.61
% 0.12/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------