%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET065-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n026.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 : Tue Jul 19 05:23:26 EDT 2022

% Result   : Unsatisfiable 0.19s 0.42s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    9 (   6 unt;   0 nHn;   9 RR)
%            Number of literals    :   13 (   0 equ;   8 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   6 con; 0-0 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ member(null_class,universal_class),
    file('SET065-6.p',unknown),
    [] ).

cnf(2,axiom,
    ( ~ member(u,v)
    | ~ subclass(v,w)
    | member(u,w) ),
    file('SET065-6.p',unknown),
    [] ).

cnf(5,axiom,
    subclass(u,universal_class),
    file('SET065-6.p',unknown),
    [] ).

cnf(48,axiom,
    ( ~ inductive(u)
    | member(null_class,u) ),
    file('SET065-6.p',unknown),
    [] ).

cnf(51,axiom,
    inductive(omega),
    file('SET065-6.p',unknown),
    [] ).

cnf(101,plain,
    ( ~ subclass(u,universal_class)
    | ~ member(null_class,u) ),
    inference(res,[status(thm),theory(equality)],[2,1]),
    [iquote('0:Res:2.2,1.0')] ).

cnf(103,plain,
    ~ member(null_class,u),
    inference(mrr,[status(thm)],[101,5]),
    [iquote('0:MRR:101.0,5.0')] ).

cnf(104,plain,
    ~ inductive(u),
    inference(mrr,[status(thm)],[48,103]),
    [iquote('0:MRR:48.1,103.0')] ).

cnf(105,plain,
    $false,
    inference(unc,[status(thm)],[104,51]),
    [iquote('0:UnC:104.0,51.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET065-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n026.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sun Jul 10 22:12:41 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.42  
% 0.19/0.42  SPASS V 3.9 
% 0.19/0.42  SPASS beiseite: Proof found.
% 0.19/0.42  % SZS status Theorem
% 0.19/0.42  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.42  SPASS derived 9 clauses, backtracked 0 clauses, performed 0 splits and kept 98 clauses.
% 0.19/0.42  SPASS allocated 75739 KBytes.
% 0.19/0.42  SPASS spent	0:00:00.07 on the problem.
% 0.19/0.42  		0:00:00.04 for the input.
% 0.19/0.42  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.42  		0:00:00.00 for inferences.
% 0.19/0.42  		0:00:00.00 for the backtracking.
% 0.19/0.42  		0:00:00.01 for the reduction.
% 0.19/0.42  
% 0.19/0.42  
% 0.19/0.42  Here is a proof with depth 1, length 9 :
% 0.19/0.42  % SZS output start Refutation
% See solution above
% 0.19/0.42  Formulae used in the proof : prove_null_class_is_a_set_1 subclass_members class_elements_are_sets inductive1 omega_is_inductive1
% 0.19/0.42  
%------------------------------------------------------------------------------