%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET153-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n009.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 05:24:34 EDT 2022

% Result   : Unsatisfiable 14.26s 14.44s
% Output   : Refutation 14.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   11 (   3 unt;   4 nHn;  11 RR)
%            Number of literals    :   19 (   0 equ;   6 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    3 (   2 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,
    ~ equal(intersection(complement(x__dfg),x__dfg),null_class),
    file('SET153-6.p',unknown),
    [] ).

cnf(22,axiom,
    ( ~ member(u,intersection(v,w))
    | member(u,v) ),
    file('SET153-6.p',unknown),
    [] ).

cnf(23,axiom,
    ( ~ member(u,intersection(v,w))
    | member(u,w) ),
    file('SET153-6.p',unknown),
    [] ).

cnf(25,axiom,
    ( ~ member(u,v)
    | ~ member(u,complement(v)) ),
    file('SET153-6.p',unknown),
    [] ).

cnf(67,axiom,
    ( equal(u,null_class)
    | member(regular(u),u) ),
    file('SET153-6.p',unknown),
    [] ).

cnf(169,plain,
    ( equal(intersection(u,v),null_class)
    | member(regular(intersection(u,v)),v) ),
    inference(res,[status(thm),theory(equality)],[67,23]),
    [iquote('0:Res:67.1,23.0')] ).

cnf(191,plain,
    ( equal(intersection(u,v),null_class)
    | member(regular(intersection(u,v)),u) ),
    inference(res,[status(thm),theory(equality)],[67,22]),
    [iquote('0:Res:67.1,22.0')] ).

cnf(1979,plain,
    ( ~ member(regular(intersection(complement(u),v)),u)
    | equal(intersection(complement(u),v),null_class) ),
    inference(res,[status(thm),theory(equality)],[191,25]),
    [iquote('0:Res:191.1,25.1')] ).

cnf(27890,plain,
    ( equal(intersection(complement(u),u),null_class)
    | equal(intersection(complement(u),u),null_class) ),
    inference(res,[status(thm),theory(equality)],[169,1979]),
    [iquote('0:Res:169.1,1979.0')] ).

cnf(27896,plain,
    equal(intersection(complement(u),u),null_class),
    inference(obv,[status(thm),theory(equality)],[27890]),
    [iquote('0:Obv:27890.0')] ).

cnf(27897,plain,
    $false,
    inference(unc,[status(thm)],[27896,1]),
    [iquote('0:UnC:27896.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.08  % Problem  : SET153-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.09  % Command  : run_spass %d %s
% 0.08/0.28  % Computer : n009.cluster.edu
% 0.08/0.28  % Model    : x86_64 x86_64
% 0.08/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28  % Memory   : 8042.1875MB
% 0.08/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28  % CPULimit : 300
% 0.08/0.28  % WCLimit  : 600
% 0.08/0.28  % DateTime : Sat Jul  9 18:57:22 EDT 2022
% 0.08/0.28  % CPUTime  : 
% 14.26/14.44  
% 14.26/14.44  SPASS V 3.9 
% 14.26/14.44  SPASS beiseite: Proof found.
% 14.26/14.44  % SZS status Theorem
% 14.26/14.44  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 14.26/14.44  SPASS derived 21648 clauses, backtracked 235 clauses, performed 6 splits and kept 9583 clauses.
% 14.26/14.44  SPASS allocated 100150 KBytes.
% 14.26/14.44  SPASS spent	0:0:13.94 on the problem.
% 14.26/14.44  		0:00:00.03 for the input.
% 14.26/14.44  		0:00:00.00 for the FLOTTER CNF translation.
% 14.26/14.44  		0:00:00.33 for inferences.
% 14.26/14.44  		0:00:00.87 for the backtracking.
% 14.26/14.44  		0:0:12.49 for the reduction.
% 14.26/14.44  
% 14.26/14.44  
% 14.26/14.44  Here is a proof with depth 3, length 11 :
% 14.26/14.44  % SZS output start Refutation
% See solution above
% 14.26/14.44  Formulae used in the proof : prove_intersection_with_complement_1 intersection1 intersection2 complement1 regularity1
% 14.26/14.44  
%------------------------------------------------------------------------------