%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM009-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 08:16:01 AM UTC 2026
% Result : Unsatisfiable 4.04s 1.01s
% Output : CNFRefutation 4.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 8 unt; 0 def)
% Number of atoms : 24 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 8 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 8 ( 1 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_zero_is_a_natural,axiom,
~ member(empty_set,natural_numbers),
file('theBenchmark.p',prove_zero_is_a_natural) ).
cnf(c_132,plain,
~ member(empty_set,natural_numbers),
inference(clausify,[status(thm)],[prove_zero_is_a_natural]) ).
fof(natural_numbers6,axiom,
! [VAR_0] :
( ~ member(VAR_0,f44(VAR_0))
| member(VAR_0,natural_numbers) ),
file('theBenchmark.p',natural_numbers6) ).
cnf(c_185,plain,
( ~ member(A,f44(A))
| member(A,natural_numbers) ),
inference(clausify,[status(thm)],[natural_numbers6]) ).
fof(natural_numbers4,axiom,
! [VAR_0] :
( member(empty_set,f44(VAR_0))
| ~ little_set(VAR_0)
| member(VAR_0,natural_numbers) ),
file('theBenchmark.p',natural_numbers4) ).
cnf(c_187,plain,
( member(empty_set,f44(A))
| ~ little_set(A)
| member(A,natural_numbers) ),
inference(clausify,[status(thm)],[natural_numbers4]) ).
fof(infinity2,axiom,
member(empty_set,infinity),
file('theBenchmark.p',infinity2) ).
cnf(c_250,plain,
member(empty_set,infinity),
inference(clausify,[status(thm)],[infinity2]) ).
fof(a2,axiom,
! [VAR_0,VAR_1] :
( little_set(VAR_0)
| ~ member(VAR_0,VAR_1) ),
file('theBenchmark.p',a2) ).
cnf(c_322,plain,
( little_set(A)
| ~ member(A,B) ),
inference(clausify,[status(thm)],[a2]) ).
cnf(c_2405,plain,
little_set(empty_set),
inference(resolve,[status(thm)],[c_322,c_250]) ).
cnf(c_3376,plain,
( member(empty_set,f44(empty_set))
| member(empty_set,natural_numbers) ),
inference(resolve,[status(thm)],[c_2405,c_187]) ).
cnf(c_2899,plain,
member(empty_set,f44(empty_set)),
inference(resolve,[status(thm)],[c_132,c_3376]) ).
cnf(c_3377,plain,
member(empty_set,natural_numbers),
inference(resolve,[status(thm)],[c_2899,c_185]) ).
cnf(c_3375,plain,
$false,
inference(resolve,[status(thm)],[c_132,c_3377]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM009-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n009.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 26 01:53:00 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.39 % Process 3108325 was started by sandbox2 on n009,
% 0.10/0.39 % Sat Sep 26 01:53:00 2026
% 0.10/0.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.40
% 0.15/0.40 % From the command line: assign(max_seconds, 300).
% 4.04/1.01
% 4.04/1.01 % SZS status Unsatisfiable for theBenchmark
% 4.04/1.01
% 4.04/1.01 % Proof 1 at 0.46 (+ 0.07) seconds.
% 4.04/1.01 % Length of proof is 8.
% 4.04/1.01 % Level of proof is 3.
% 4.04/1.01 % Maximum clause weight is 19.000.
% 4.04/1.01 % Given clauses 498.
% 4.04/1.01
% 4.04/1.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------