%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP006-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n028.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 11:44:43 EDT 2022

% Result   : Unsatisfiable 0.18s 0.41s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   12 (   7 unt;   0 nHn;  12 RR)
%            Number of literals    :   21 (   0 equ;  14 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,
    product(identity,u,u),
    file('GRP006-1.p',unknown),
    [] ).

cnf(3,axiom,
    product(u,inverse(u),identity),
    file('GRP006-1.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ an_element(u)
    | ~ an_element(v)
    | ~ product(v,inverse(u),w)
    | an_element(w) ),
    file('GRP006-1.p',unknown),
    [] ).

cnf(8,axiom,
    an_element(the_element),
    file('GRP006-1.p',unknown),
    [] ).

cnf(9,axiom,
    ~ an_element(inverse(the_element)),
    file('GRP006-1.p',unknown),
    [] ).

cnf(10,plain,
    ( ~ an_element(u)
    | ~ an_element(v)
    | ~ product(v,inverse(u),inverse(the_element)) ),
    inference(res,[status(thm),theory(equality)],[5,9]),
    [iquote('0:Res:5.3,9.0')] ).

cnf(13,plain,
    ( ~ an_element(the_element)
    | ~ an_element(identity) ),
    inference(res,[status(thm),theory(equality)],[1,10]),
    [iquote('0:Res:1.0,10.2')] ).

cnf(14,plain,
    ~ an_element(identity),
    inference(ssi,[status(thm)],[13,8]),
    [iquote('0:SSi:13.0,8.0')] ).

cnf(17,plain,
    ( ~ an_element(u)
    | ~ an_element(u)
    | an_element(identity) ),
    inference(res,[status(thm),theory(equality)],[3,5]),
    [iquote('0:Res:3.0,5.2')] ).

cnf(18,plain,
    ( ~ an_element(u)
    | an_element(identity) ),
    inference(obv,[status(thm),theory(equality)],[17]),
    [iquote('0:Obv:17.0')] ).

cnf(19,plain,
    ~ an_element(u),
    inference(mrr,[status(thm)],[18,14]),
    [iquote('0:MRR:18.1,14.0')] ).

cnf(20,plain,
    $false,
    inference(unc,[status(thm)],[19,8]),
    [iquote('0:UnC:19.0,8.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP006-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n028.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 03:17:38 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.41  
% 0.18/0.41  SPASS V 3.9 
% 0.18/0.41  SPASS beiseite: Proof found.
% 0.18/0.41  % SZS status Theorem
% 0.18/0.41  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.18/0.41  SPASS derived 5 clauses, backtracked 0 clauses, performed 0 splits and kept 13 clauses.
% 0.18/0.41  SPASS allocated 75591 KBytes.
% 0.18/0.41  SPASS spent	0:00:00.06 on the problem.
% 0.18/0.41  		0:00:00.04 for the input.
% 0.18/0.41  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.41  		0:00:00.00 for inferences.
% 0.18/0.41  		0:00:00.00 for the backtracking.
% 0.18/0.41  		0:00:00.00 for the reduction.
% 0.18/0.41  
% 0.18/0.41  
% 0.18/0.41  Here is a proof with depth 2, length 12 :
% 0.18/0.41  % SZS output start Refutation
% See solution above
% 0.18/0.41  Formulae used in the proof : left_identity right_inverse condition element_of_set prove_b_inverse_is_in_set
% 0.18/0.41  
%------------------------------------------------------------------------------