%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET027-7 : 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 05:22:51 EDT 2022

% Result   : Unsatisfiable 0.12s 0.35s
% Output   : Refutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   13 (   8 unt;   1 nHn;  13 RR)
%            Number of literals    :   19 (   0 equ;   9 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    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(6,axiom,
    subclass(x__dfg,y__dfg),
    file('SET027-7.p',unknown),
    [] ).

cnf(7,axiom,
    subclass(y__dfg,z__dfg),
    file('SET027-7.p',unknown),
    [] ).

cnf(8,axiom,
    ~ subclass(x__dfg,z__dfg),
    file('SET027-7.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ member(u,v)
    | ~ subclass(v,w)
    | member(u,w) ),
    file('SET027-7.p',unknown),
    [] ).

cnf(10,axiom,
    ( subclass(u,v)
    | member(not_subclass_element(u,v),u) ),
    file('SET027-7.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ member(not_subclass_element(u,v),v)
    | subclass(u,v) ),
    file('SET027-7.p',unknown),
    [] ).

cnf(102,plain,
    ( ~ member(u,y__dfg)
    | member(u,z__dfg) ),
    inference(res,[status(thm),theory(equality)],[7,9]),
    [iquote('0:Res:7.0,9.0')] ).

cnf(105,plain,
    ( ~ member(u,x__dfg)
    | member(u,y__dfg) ),
    inference(res,[status(thm),theory(equality)],[6,9]),
    [iquote('0:Res:6.0,9.0')] ).

cnf(108,plain,
    ~ member(not_subclass_element(x__dfg,z__dfg),z__dfg),
    inference(res,[status(thm),theory(equality)],[11,8]),
    [iquote('0:Res:11.1,8.0')] ).

cnf(109,plain,
    member(not_subclass_element(x__dfg,z__dfg),x__dfg),
    inference(res,[status(thm),theory(equality)],[10,8]),
    [iquote('0:Res:10.1,8.0')] ).

cnf(115,plain,
    ~ member(not_subclass_element(x__dfg,z__dfg),y__dfg),
    inference(res,[status(thm),theory(equality)],[102,108]),
    [iquote('0:Res:102.1,108.0')] ).

cnf(116,plain,
    ~ member(not_subclass_element(x__dfg,z__dfg),x__dfg),
    inference(res,[status(thm),theory(equality)],[105,115]),
    [iquote('0:Res:105.1,115.0')] ).

cnf(117,plain,
    $false,
    inference(mrr,[status(thm)],[116,109]),
    [iquote('0:MRR:116.0,109.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem  : SET027-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.08/0.09  % Command  : run_spass %d %s
% 0.08/0.28  % Computer : n013.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 : Sun Jul 10 14:39:59 EDT 2022
% 0.08/0.28  % CPUTime  : 
% 0.12/0.35  
% 0.12/0.35  SPASS V 3.9 
% 0.12/0.35  SPASS beiseite: Proof found.
% 0.12/0.35  % SZS status Theorem
% 0.12/0.35  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.12/0.35  SPASS derived 15 clauses, backtracked 0 clauses, performed 0 splits and kept 108 clauses.
% 0.12/0.35  SPASS allocated 75752 KBytes.
% 0.12/0.35  SPASS spent	0:00:00.06 on the problem.
% 0.12/0.35  		0:00:00.03 for the input.
% 0.12/0.35  		0:00:00.00 for the FLOTTER CNF translation.
% 0.12/0.35  		0:00:00.00 for inferences.
% 0.12/0.35  		0:00:00.00 for the backtracking.
% 0.12/0.35  		0:00:00.01 for the reduction.
% 0.12/0.35  
% 0.12/0.35  
% 0.12/0.35  Here is a proof with depth 3, length 13 :
% 0.12/0.35  % SZS output start Refutation
% See solution above
% 0.12/0.35  Formulae used in the proof : prove_transitivity_of_subclass_1 prove_transitivity_of_subclass_2 prove_transitivity_of_subclass_3 subclass_members not_subclass_members1 not_subclass_members2
% 0.12/0.35  
%------------------------------------------------------------------------------