%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP005-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n025.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 11:44:42 EDT 2022

% Result   : Unsatisfiable 0.19s 0.40s
% Output   : Refutation 0.19s
% 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(3,axiom,
    product(u,inverse(u),identity),
    file('GRP005-1.p',unknown),
    [] ).

cnf(5,axiom,
    an_element(a),
    file('GRP005-1.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ an_element(u)
    | ~ an_element(v)
    | ~ product(v,inverse(u),w)
    | an_element(w) ),
    file('GRP005-1.p',unknown),
    [] ).

cnf(9,axiom,
    ~ an_element(identity),
    file('GRP005-1.p',unknown),
    [] ).

cnf(10,plain,
    ( ~ an_element(u)
    | ~ an_element(v)
    | ~ product(v,inverse(u),identity) ),
    inference(res,[status(thm),theory(equality)],[6,9]),
    [iquote('0:Res:6.3,9.0')] ).

cnf(14,plain,
    ( ~ an_element(u)
    | ~ an_element(u) ),
    inference(res,[status(thm),theory(equality)],[3,10]),
    [iquote('0:Res:3.0,10.2')] ).

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

cnf(16,plain,
    $false,
    inference(unc,[status(thm)],[15,5]),
    [iquote('0:UnC:15.0,5.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : GRP005-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n025.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 : Mon Jun 13 11:52:38 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.40  
% 0.19/0.40  SPASS V 3.9 
% 0.19/0.40  SPASS beiseite: Proof found.
% 0.19/0.40  % SZS status Theorem
% 0.19/0.40  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.40  SPASS derived 3 clauses, backtracked 0 clauses, performed 0 splits and kept 12 clauses.
% 0.19/0.40  SPASS allocated 75587 KBytes.
% 0.19/0.40  SPASS spent	0:00:00.05 on the problem.
% 0.19/0.40  		0:00:00.03 for the input.
% 0.19/0.40  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.40  		0:00:00.00 for inferences.
% 0.19/0.40  		0:00:00.00 for the backtracking.
% 0.19/0.40  		0:00:00.00 for the reduction.
% 0.19/0.40  
% 0.19/0.40  
% 0.19/0.40  Here is a proof with depth 2, length 8 :
% 0.19/0.40  % SZS output start Refutation
% See solution above
% 0.19/0.40  Formulae used in the proof : right_inverse element_of_set condition prove_identity_is_an_element
% 0.19/0.40  
%------------------------------------------------------------------------------