%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUM009-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n020.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Mon Jul 18 14:23:38 EDT 2022

% Result   : Unsatisfiable 0.22s 0.51s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   10 (   6 unt;   1 nHn;  10 RR)
%            Number of literals    :   15 (   0 equ;   7 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ member(empty_set,natural_numbers),
    file('NUM009-1.p',unknown),
    [] ).

cnf(2,axiom,
    ( ~ member(u,v)
    | little_set(u) ),
    file('NUM009-1.p',unknown),
    [] ).

cnf(62,axiom,
    member(empty_set,infinity),
    file('NUM009-1.p',unknown),
    [] ).

cnf(170,axiom,
    ( ~ little_set(u)
    | member(u,natural_numbers)
    | member(empty_set,f44(u)) ),
    file('NUM009-1.p',unknown),
    [] ).

cnf(172,axiom,
    ( ~ member(u,f44(u))
    | member(u,natural_numbers) ),
    file('NUM009-1.p',unknown),
    [] ).

cnf(224,plain,
    ( ~ little_set(empty_set)
    | member(empty_set,f44(empty_set)) ),
    inference(res,[status(thm),theory(equality)],[170,1]),
    [iquote('0:Res:170.1,1.0')] ).

cnf(226,plain,
    ~ member(empty_set,f44(empty_set)),
    inference(res,[status(thm),theory(equality)],[172,1]),
    [iquote('0:Res:172.1,1.0')] ).

cnf(254,plain,
    ~ little_set(empty_set),
    inference(mrr,[status(thm)],[224,226]),
    [iquote('0:MRR:224.1,226.0')] ).

cnf(264,plain,
    little_set(empty_set),
    inference(res,[status(thm),theory(equality)],[62,2]),
    [iquote('0:Res:62.0,2.0')] ).

cnf(267,plain,
    $false,
    inference(mrr,[status(thm)],[264,254]),
    [iquote('0:MRR:264.0,254.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : NUM009-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.08/0.15  % Command  : run_spass %d %s
% 0.15/0.36  % Computer : n020.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 600
% 0.15/0.37  % DateTime : Thu Jul  7 12:10:59 EDT 2022
% 0.15/0.37  % CPUTime  : 
% 0.22/0.51  
% 0.22/0.51  SPASS V 3.9 
% 0.22/0.51  SPASS beiseite: Proof found.
% 0.22/0.51  % SZS status Theorem
% 0.22/0.51  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.22/0.51  SPASS derived 41 clauses, backtracked 0 clauses, performed 0 splits and kept 256 clauses.
% 0.22/0.51  SPASS allocated 75971 KBytes.
% 0.22/0.51  SPASS spent	0:00:00.12 on the problem.
% 0.22/0.51  		0:00:00.04 for the input.
% 0.22/0.51  		0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.51  		0:00:00.00 for inferences.
% 0.22/0.51  		0:00:00.00 for the backtracking.
% 0.22/0.51  		0:00:00.04 for the reduction.
% 0.22/0.51  
% 0.22/0.51  
% 0.22/0.51  Here is a proof with depth 1, length 10 :
% 0.22/0.51  % SZS output start Refutation
% See solution above
% 0.22/0.51  Formulae used in the proof : prove_zero_is_a_natural a2 infinity2 natural_numbers4 natural_numbers6
% 0.22/0.51  
%------------------------------------------------------------------------------