%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP032-3 : TPTP v8.1.0. Released v1.0.0.
% 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 : Sat Jul 16 11:44:53 EDT 2022

% Result   : Unsatisfiable 0.18s 0.39s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    8 (   5 unt;   0 nHn;   8 RR)
%            Number of literals    :   14 (   0 equ;  10 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    :    6 (   6 usr;   5 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    subgroup_member(a),
    file('GRP032-3.p',unknown),
    [] ).

cnf(2,axiom,
    ~ subgroup_member(identity),
    file('GRP032-3.p',unknown),
    [] ).

cnf(6,axiom,
    product(u,inverse(u),identity),
    file('GRP032-3.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ subgroup_member(u)
    | ~ subgroup_member(v)
    | ~ product(v,inverse(u),w)
    | subgroup_member(w) ),
    file('GRP032-3.p',unknown),
    [] ).

cnf(12,plain,
    ( ~ subgroup_member(u)
    | ~ subgroup_member(v)
    | ~ product(v,inverse(u),identity) ),
    inference(res,[status(thm),theory(equality)],[11,2]),
    [iquote('0:Res:11.3,2.0')] ).

cnf(14,plain,
    ( ~ subgroup_member(u)
    | ~ subgroup_member(u) ),
    inference(res,[status(thm),theory(equality)],[6,12]),
    [iquote('0:Res:6.0,12.2')] ).

cnf(15,plain,
    ~ subgroup_member(u),
    inference(obv,[status(thm),theory(equality)],[14]),
    [iquote('0:Obv:14.0')] ).

cnf(16,plain,
    $false,
    inference(unc,[status(thm)],[15,1]),
    [iquote('0:UnC:15.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : GRP032-3 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n009.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 : Tue Jun 14 01:04:23 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.39  
% 0.18/0.39  SPASS V 3.9 
% 0.18/0.39  SPASS beiseite: Proof found.
% 0.18/0.39  % SZS status Theorem
% 0.18/0.39  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.18/0.39  SPASS derived 3 clauses, backtracked 0 clauses, performed 0 splits and kept 14 clauses.
% 0.18/0.39  SPASS allocated 75589 KBytes.
% 0.18/0.39  SPASS spent	0:00:00.06 on the problem.
% 0.18/0.39  		0:00:00.03 for the input.
% 0.18/0.39  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.39  		0:00:00.00 for inferences.
% 0.18/0.39  		0:00:00.00 for the backtracking.
% 0.18/0.39  		0:00:00.00 for the reduction.
% 0.18/0.39  
% 0.18/0.39  
% 0.18/0.39  Here is a proof with depth 2, length 8 :
% 0.18/0.39  % SZS output start Refutation
% See solution above
% 0.18/0.39  Formulae used in the proof : a_is_in_subgroup prove_identity_is_in_subgroup right_inverse closure_of_product_and_inverse
% 0.18/0.40  
%------------------------------------------------------------------------------