%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET062-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n016.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 05:23:21 EDT 2022

% Result   : Unsatisfiable 0.20s 0.43s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   13 (   6 unt;   4 nHn;  13 RR)
%            Number of literals    :   21 (   0 equ;   7 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ subclass(null_class,x__dfg),
    file('SET062-6.p',unknown),
    [] ).

cnf(3,axiom,
    ( subclass(u,v)
    | member(not_subclass_element(u,v),u) ),
    file('SET062-6.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ member(not_subclass_element(u,v),v)
    | subclass(u,v) ),
    file('SET062-6.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ equal(u,v)
    | subclass(v,u) ),
    file('SET062-6.p',unknown),
    [] ).

cnf(22,axiom,
    ( ~ member(u,intersection(v,w))
    | member(u,v) ),
    file('SET062-6.p',unknown),
    [] ).

cnf(68,axiom,
    ( equal(u,null_class)
    | equal(intersection(u,regular(u)),null_class) ),
    file('SET062-6.p',unknown),
    [] ).

cnf(95,plain,
    ~ member(not_subclass_element(null_class,x__dfg),x__dfg),
    inference(res,[status(thm),theory(equality)],[4,1]),
    [iquote('0:Res:4.1,1.0')] ).

cnf(96,plain,
    member(not_subclass_element(null_class,x__dfg),null_class),
    inference(res,[status(thm),theory(equality)],[3,1]),
    [iquote('0:Res:3.1,1.0')] ).

cnf(97,plain,
    ~ equal(x__dfg,null_class),
    inference(res,[status(thm),theory(equality)],[7,1]),
    [iquote('0:Res:7.1,1.0')] ).

cnf(140,plain,
    ( ~ member(u,null_class)
    | equal(v,null_class)
    | member(u,v) ),
    inference(spl,[status(thm),theory(equality)],[68,22]),
    [iquote('0:SpL:68.1,22.0')] ).

cnf(165,plain,
    ( equal(u,null_class)
    | member(not_subclass_element(null_class,x__dfg),u) ),
    inference(res,[status(thm),theory(equality)],[96,140]),
    [iquote('0:Res:96.0,140.0')] ).

cnf(169,plain,
    equal(x__dfg,null_class),
    inference(res,[status(thm),theory(equality)],[165,95]),
    [iquote('0:Res:165.1,95.0')] ).

cnf(175,plain,
    $false,
    inference(mrr,[status(thm)],[169,97]),
    [iquote('0:MRR:169.0,97.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET062-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n016.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sun Jul 10 01:31:55 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.20/0.43  
% 0.20/0.43  SPASS V 3.9 
% 0.20/0.43  SPASS beiseite: Proof found.
% 0.20/0.43  % SZS status Theorem
% 0.20/0.43  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.43  SPASS derived 74 clauses, backtracked 0 clauses, performed 0 splits and kept 147 clauses.
% 0.20/0.43  SPASS allocated 75850 KBytes.
% 0.20/0.43  SPASS spent	0:00:00.08 on the problem.
% 0.20/0.43  		0:00:00.04 for the input.
% 0.20/0.43  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.43  		0:00:00.00 for inferences.
% 0.20/0.43  		0:00:00.00 for the backtracking.
% 0.20/0.43  		0:00:00.02 for the reduction.
% 0.20/0.43  
% 0.20/0.43  
% 0.20/0.43  Here is a proof with depth 3, length 13 :
% 0.20/0.43  % SZS output start Refutation
% See solution above
% 0.20/0.43  Formulae used in the proof : prove_null_class_is_subclass_1 not_subclass_members1 not_subclass_members2 equal_implies_subclass2 intersection1 regularity2
% 0.20/0.43  
%------------------------------------------------------------------------------