%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET506-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n013.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 05:26:39 EDT 2022

% Result   : Unsatisfiable 0.18s 0.44s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   13 (   5 unt;   4 nHn;  13 RR)
%            Number of literals    :   22 (   0 equ;   8 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(null_class,universal_class),
    file('SET506-6.p',unknown),
    [] ).

cnf(22,axiom,
    ( ~ member(u,intersection(v,w))
    | member(u,v) ),
    file('SET506-6.p',unknown),
    [] ).

cnf(25,axiom,
    ( ~ member(u,v)
    | ~ member(u,complement(v)) ),
    file('SET506-6.p',unknown),
    [] ).

cnf(53,axiom,
    member(omega,universal_class),
    file('SET506-6.p',unknown),
    [] ).

cnf(68,axiom,
    ( equal(u,null_class)
    | equal(intersection(u,regular(u)),null_class) ),
    file('SET506-6.p',unknown),
    [] ).

cnf(116,plain,
    ( equal(u,universal_class)
    | equal(intersection(u,regular(u)),universal_class) ),
    inference(rew,[status(thm),theory(equality)],[1,68]),
    [iquote('0:Rew:1.0,68.1,1.0,68.0')] ).

cnf(194,plain,
    ( ~ member(u,universal_class)
    | equal(v,universal_class)
    | member(u,v) ),
    inference(spl,[status(thm),theory(equality)],[116,22]),
    [iquote('0:SpL:116.1,22.0')] ).

cnf(296,plain,
    ( equal(u,universal_class)
    | member(omega,u) ),
    inference(res,[status(thm),theory(equality)],[53,194]),
    [iquote('0:Res:53.0,194.0')] ).

cnf(299,plain,
    ( ~ member(omega,u)
    | equal(complement(u),universal_class) ),
    inference(res,[status(thm),theory(equality)],[296,25]),
    [iquote('0:Res:296.1,25.1')] ).

cnf(315,plain,
    equal(complement(universal_class),universal_class),
    inference(res,[status(thm),theory(equality)],[53,299]),
    [iquote('0:Res:53.0,299.0')] ).

cnf(338,plain,
    ( ~ member(u,universal_class)
    | ~ member(u,universal_class) ),
    inference(spl,[status(thm),theory(equality)],[315,25]),
    [iquote('0:SpL:315.0,25.1')] ).

cnf(339,plain,
    ~ member(u,universal_class),
    inference(obv,[status(thm),theory(equality)],[338]),
    [iquote('0:Obv:338.0')] ).

cnf(340,plain,
    $false,
    inference(unc,[status(thm)],[339,53]),
    [iquote('0:UnC:339.0,53.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SET506-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.00/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n013.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sun Jul 10 09:42:59 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.44  
% 0.18/0.44  SPASS V 3.9 
% 0.18/0.44  SPASS beiseite: Proof found.
% 0.18/0.44  % SZS status Theorem
% 0.18/0.44  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.18/0.44  SPASS derived 180 clauses, backtracked 17 clauses, performed 3 splits and kept 261 clauses.
% 0.18/0.44  SPASS allocated 76005 KBytes.
% 0.18/0.44  SPASS spent	0:00:00.10 on the problem.
% 0.18/0.44  		0:00:00.04 for the input.
% 0.18/0.44  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.44  		0:00:00.00 for inferences.
% 0.18/0.44  		0:00:00.00 for the backtracking.
% 0.18/0.44  		0:00:00.03 for the reduction.
% 0.18/0.44  
% 0.18/0.44  
% 0.18/0.44  Here is a proof with depth 5, length 13 :
% 0.18/0.44  % SZS output start Refutation
% See solution above
% 0.18/0.44  Formulae used in the proof : prove_universal_class_not_null_class_1 intersection1 complement1 omega_in_universal regularity2
% 0.18/0.44  
%------------------------------------------------------------------------------