%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP033-3 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n018.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 : Sat Jul 16 11:44:53 EDT 2022

% Result   : Unsatisfiable 0.21s 0.43s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   12 (   7 unt;   0 nHn;  12 RR)
%            Number of literals    :   21 (   0 equ;  13 neg)
%            Maximal clause size   :    4 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(11,axiom,
    product(identity,u,u),
    file('GRP033-3.p',unknown),
    [] ).

cnf(12,axiom,
    product(u,identity,u),
    file('GRP033-3.p',unknown),
    [] ).

cnf(14,axiom,
    product(u,inverse(u),identity),
    file('GRP033-3.p',unknown),
    [] ).

cnf(19,axiom,
    ( ~ subgroup_member(u)
    | ~ subgroup_member(v)
    | ~ product(v,inverse(u),w)
    | subgroup_member(w) ),
    file('GRP033-3.p',unknown),
    [] ).

cnf(20,axiom,
    subgroup_member(a),
    file('GRP033-3.p',unknown),
    [] ).

cnf(22,axiom,
    ( ~ subgroup_member(u)
    | ~ product(u,j(u),j(u))
    | ~ product(j(u),u,j(u)) ),
    file('GRP033-3.p',unknown),
    [] ).

cnf(24,plain,
    ( ~ subgroup_member(identity)
    | ~ product(j(identity),identity,j(identity)) ),
    inference(res,[status(thm),theory(equality)],[11,22]),
    [iquote('0:Res:11.0,22.1')] ).

cnf(26,plain,
    ~ subgroup_member(identity),
    inference(mrr,[status(thm)],[24,12]),
    [iquote('0:MRR:24.1,12.0')] ).

cnf(36,plain,
    ( ~ subgroup_member(u)
    | ~ subgroup_member(u)
    | subgroup_member(identity) ),
    inference(res,[status(thm),theory(equality)],[14,19]),
    [iquote('0:Res:14.0,19.2')] ).

cnf(38,plain,
    ( ~ subgroup_member(u)
    | subgroup_member(identity) ),
    inference(obv,[status(thm),theory(equality)],[36]),
    [iquote('0:Obv:36.0')] ).

cnf(39,plain,
    ~ subgroup_member(u),
    inference(mrr,[status(thm)],[38,26]),
    [iquote('0:MRR:38.1,26.0')] ).

cnf(40,plain,
    $false,
    inference(unc,[status(thm)],[39,20]),
    [iquote('0:UnC:39.0,20.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : GRP033-3 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.08/0.14  % Command  : run_spass %d %s
% 0.14/0.35  % Computer : n018.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Mon Jun 13 06:35:57 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.21/0.43  
% 0.21/0.43  SPASS V 3.9 
% 0.21/0.43  SPASS beiseite: Proof found.
% 0.21/0.43  % SZS status Theorem
% 0.21/0.43  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.21/0.43  SPASS derived 10 clauses, backtracked 0 clauses, performed 0 splits and kept 27 clauses.
% 0.21/0.43  SPASS allocated 75613 KBytes.
% 0.21/0.43  SPASS spent	0:00:00.06 on the problem.
% 0.21/0.43  		0:00:00.04 for the input.
% 0.21/0.43  		0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.43  		0:00:00.00 for inferences.
% 0.21/0.43  		0:00:00.00 for the backtracking.
% 0.21/0.43  		0:00:00.00 for the reduction.
% 0.21/0.43  
% 0.21/0.43  
% 0.21/0.43  Here is a proof with depth 1, length 12 :
% 0.21/0.43  % SZS output start Refutation
% See solution above
% 0.21/0.43  Formulae used in the proof : left_identity right_identity right_inverse closure_of_product_and_inverse a_is_in_subgroup prove_subgr2
% 0.21/0.43  
%------------------------------------------------------------------------------