%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET507-6 : 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 : n006.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 08:36:24 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.46s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 25 ( 8 unt; 0 def)
% Number of atoms : 46 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 17 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 4 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_universal_class_not_subclass_of_null_class_1,axiom,
subclass(universal_class,null_class),
file('theBenchmark.p',prove_universal_class_not_subclass_of_null_class_1) ).
cnf(c_36,plain,
subclass(universal_class,null_class),
inference(clausify,[status(thm)],[prove_universal_class_not_subclass_of_null_class_1]) ).
fof(regularity2,axiom,
! [VAR_0] :
( intersection(VAR_0,regular(VAR_0)) = null_class
| VAR_0 = null_class ),
file('theBenchmark.p',regularity2) ).
cnf(c_73,plain,
( intersection(A,regular(A)) = null_class
| A = null_class ),
inference(clausify,[status(thm)],[regularity2]) ).
cnf(c_74,plain,
( intersection(A,regular(A)) = null_class
| null_class = A ),
inference(copy,[status(thm)],[c_73]) ).
fof(omega_in_universal,axiom,
member(omega,universal_class),
file('theBenchmark.p',omega_in_universal) ).
cnf(c_86,plain,
member(omega,universal_class),
inference(clausify,[status(thm)],[omega_in_universal]) ).
fof(complement1,axiom,
! [VAR_0,VAR_1] :
( ~ member(VAR_0,VAR_1)
| ~ member(VAR_0,complement(VAR_1)) ),
file('theBenchmark.p',complement1) ).
cnf(c_119,plain,
( ~ member(A,B)
| ~ member(A,complement(B)) ),
inference(clausify,[status(thm)],[complement1]) ).
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_122,plain,
( member(A,B)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection1]) ).
fof(equal_implies_subclass1,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_0,VAR_1)
| VAR_0 != VAR_1 ),
file('theBenchmark.p',equal_implies_subclass1) ).
cnf(c_140,plain,
( subclass(A,B)
| A != B ),
inference(clausify,[status(thm)],[equal_implies_subclass1]) ).
fof(subclass_members,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_2,VAR_1)
| ~ member(VAR_2,VAR_0)
| ~ subclass(VAR_0,VAR_1) ),
file('theBenchmark.p',subclass_members) ).
cnf(c_144,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_245,plain,
( member(B,A)
| ~ member(B,null_class)
| null_class = A ),
inference(paramod,[status(thm)],[c_74,c_122]) ).
cnf(c_410,plain,
( member(A,null_class)
| ~ member(A,universal_class) ),
inference(resolve,[status(thm)],[c_144,c_36]) ).
cnf(c_544,plain,
member(omega,null_class),
inference(resolve,[status(thm)],[c_410,c_86]) ).
cnf(c_606,plain,
( member(omega,A)
| null_class = A ),
inference(resolve,[status(thm)],[c_245,c_544]) ).
cnf(c_611,plain,
( subclass(null_class,A)
| member(omega,A) ),
inference(resolve,[status(thm)],[c_606,c_140]) ).
cnf(c_700,plain,
( member(B,A)
| ~ member(B,null_class)
| member(omega,A) ),
inference(resolve,[status(thm)],[c_611,c_144]) ).
cnf(c_711,plain,
( ~ member(omega,null_class)
| member(omega,A) ),
inference(factor,[status(thm)],[c_700]) ).
cnf(c_702,plain,
member(omega,A),
inference(resolve,[status(thm)],[c_544,c_711]) ).
cnf(c_712,plain,
~ member(omega,A),
inference(resolve,[status(thm)],[c_702,c_119]) ).
cnf(c_710,plain,
$false,
inference(resolve,[status(thm)],[c_702,c_712]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET507-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n006.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 07:49:55 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 748031 was started by sandbox2 on n006,
% 0.11/0.37 % Sat Sep 26 07:49:55 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.11/0.46
% 0.11/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.46
% 0.11/0.46 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.11/0.46 % Length of proof is 16.
% 0.11/0.46 % Level of proof is 7.
% 0.11/0.46 % Maximum clause weight is 24.000.
% 0.11/0.46 % Given clauses 154.
% 0.11/0.46
% 0.11/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------