%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP038-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n006.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 11:44:55 EDT 2022

% Result   : Unsatisfiable 0.19s 0.41s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    8 (   5 unt;   0 nHn;   8 RR)
%            Number of literals    :   14 (   0 equ;   9 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;   6 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    subgroup_member(a),
    file('GRP038-3.p',unknown),
    [] ).

cnf(4,axiom,
    subgroup_member(b),
    file('GRP038-3.p',unknown),
    [] ).

cnf(5,axiom,
    product(a,inverse(b),c),
    file('GRP038-3.p',unknown),
    [] ).

cnf(6,axiom,
    ~ subgroup_member(c),
    file('GRP038-3.p',unknown),
    [] ).

cnf(15,axiom,
    ( ~ subgroup_member(u)
    | ~ subgroup_member(v)
    | ~ product(v,inverse(u),w)
    | subgroup_member(w) ),
    file('GRP038-3.p',unknown),
    [] ).

cnf(16,plain,
    ( ~ subgroup_member(u)
    | ~ subgroup_member(v)
    | ~ product(v,inverse(u),c) ),
    inference(res,[status(thm),theory(equality)],[15,6]),
    [iquote('0:Res:15.3,6.0')] ).

cnf(17,plain,
    ( ~ subgroup_member(b)
    | ~ subgroup_member(a) ),
    inference(res,[status(thm),theory(equality)],[5,16]),
    [iquote('0:Res:5.0,16.2')] ).

cnf(18,plain,
    $false,
    inference(ssi,[status(thm)],[17,3,4]),
    [iquote('0:SSi:17.1,17.0,3.0,4.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GRP038-3 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12  % Command  : run_spass %d %s
% 0.14/0.33  % Computer : n006.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit : 300
% 0.14/0.33  % WCLimit  : 600
% 0.14/0.33  % DateTime : Tue Jun 14 06:56:26 EDT 2022
% 0.14/0.33  % CPUTime  : 
% 0.19/0.41  
% 0.19/0.41  SPASS V 3.9 
% 0.19/0.41  SPASS beiseite: Proof found.
% 0.19/0.41  % SZS status Theorem
% 0.19/0.41  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.41  SPASS derived 2 clauses, backtracked 0 clauses, performed 0 splits and kept 17 clauses.
% 0.19/0.41  SPASS allocated 75594 KBytes.
% 0.19/0.41  SPASS spent	0:00:00.06 on the problem.
% 0.19/0.41  		0:00:00.04 for the input.
% 0.19/0.41  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.41  		0:00:00.00 for inferences.
% 0.19/0.41  		0:00:00.00 for the backtracking.
% 0.19/0.41  		0:00:00.00 for the reduction.
% 0.19/0.41  
% 0.19/0.41  
% 0.19/0.41  Here is a proof with depth 2, length 8 :
% 0.19/0.41  % SZS output start Refutation
% See solution above
% 0.19/0.41  Formulae used in the proof : a_is_in_subgroup b_is_in_subgroup a_times_inverse_b_is_c prove_c_is_in_subgroup closure_of_product_and_inverse
% 0.19/0.41  
%------------------------------------------------------------------------------