%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET065-7 : 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 : n001.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 0.12s 0.44s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 9 unt; 0 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 9 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 12 ( 2 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(inductive1,axiom,
! [VAR_0] :
( member(null_class,VAR_0)
| ~ inductive(VAR_0) ),
file('theBenchmark.p',inductive1) ).
cnf(c_3,plain,
( member(null_class,A)
| ~ inductive(A) ),
inference(clausify,[status(thm)],[inductive1]) ).
fof(omega_is_inductive1,axiom,
inductive(omega),
file('theBenchmark.p',omega_is_inductive1) ).
cnf(c_4,plain,
inductive(omega),
inference(clausify,[status(thm)],[omega_is_inductive1]) ).
cnf(c_31,plain,
member(null_class,omega),
inference(resolve,[status(thm)],[c_4,c_3]) ).
fof(prove_null_class_is_a_set_1,axiom,
~ member(null_class,universal_class),
file('theBenchmark.p',prove_null_class_is_a_set_1) ).
cnf(c_33,plain,
~ member(null_class,universal_class),
inference(clausify,[status(thm)],[prove_null_class_is_a_set_1]) ).
fof(class_elements_are_sets,axiom,
! [VAR_0] : subclass(VAR_0,universal_class),
file('theBenchmark.p',class_elements_are_sets) ).
cnf(c_133,plain,
subclass(A,universal_class),
inference(clausify,[status(thm)],[class_elements_are_sets]) ).
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_136,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_367,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_136,c_133]) ).
cnf(c_457,plain,
member(null_class,universal_class),
inference(resolve,[status(thm)],[c_367,c_31]) ).
cnf(c_456,plain,
$false,
inference(resolve,[status(thm)],[c_33,c_457]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET065-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n001.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 26 07:07:28 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 1186018 was started by sandbox2 on n001,
% 0.08/0.35 % Sat Sep 26 07:07:28 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).
% 0.12/0.44
% 0.12/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.44
% 0.12/0.44 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.12/0.44 % Length of proof is 8.
% 0.12/0.44 % Level of proof is 2.
% 0.12/0.44 % Maximum clause weight is 14.000.
% 0.12/0.44 % Given clauses 118.
% 0.12/0.44
% 0.12/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------