%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP020-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n003.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 11:44:47 EDT 2022

% Result   : Unsatisfiable 0.23s 0.43s
% Output   : Refutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    7 (   5 unt;   0 nHn;   7 RR)
%            Number of literals    :   10 (   0 equ;   6 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ equal(multiply(inverse(a),a),identity),
    file('GRP020-1.p',unknown),
    [] ).

cnf(4,axiom,
    product(inverse(u),u,identity),
    file('GRP020-1.p',unknown),
    [] ).

cnf(6,axiom,
    product(u,v,multiply(u,v)),
    file('GRP020-1.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ product(u,v,w)
    | ~ product(u,v,x)
    | equal(x,w) ),
    file('GRP020-1.p',unknown),
    [] ).

cnf(10,plain,
    ( ~ product(u,v,identity)
    | ~ product(u,v,multiply(inverse(a),a)) ),
    inference(res,[status(thm),theory(equality)],[7,1]),
    [iquote('0:Res:7.2,1.0')] ).

cnf(14,plain,
    ~ product(inverse(a),a,identity),
    inference(res,[status(thm),theory(equality)],[6,10]),
    [iquote('0:Res:6.0,10.1')] ).

cnf(15,plain,
    $false,
    inference(mrr,[status(thm)],[14,4]),
    [iquote('0:MRR:14.0,4.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : GRP020-1 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.15  % Command  : run_spass %d %s
% 0.16/0.36  % Computer : n003.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 600
% 0.16/0.36  % DateTime : Mon Jun 13 21:59:54 EDT 2022
% 0.16/0.37  % CPUTime  : 
% 0.23/0.43  
% 0.23/0.43  SPASS V 3.9 
% 0.23/0.43  SPASS beiseite: Proof found.
% 0.23/0.43  % SZS status Theorem
% 0.23/0.43  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.23/0.43  SPASS derived 5 clauses, backtracked 0 clauses, performed 0 splits and kept 13 clauses.
% 0.23/0.43  SPASS allocated 63091 KBytes.
% 0.23/0.43  SPASS spent	0:00:00.06 on the problem.
% 0.23/0.43  		0:00:00.03 for the input.
% 0.23/0.43  		0:00:00.00 for the FLOTTER CNF translation.
% 0.23/0.43  		0:00:00.00 for inferences.
% 0.23/0.43  		0:00:00.00 for the backtracking.
% 0.23/0.43  		0:00:00.00 for the reduction.
% 0.23/0.43  
% 0.23/0.43  
% 0.23/0.43  Here is a proof with depth 2, length 7 :
% 0.23/0.43  % SZS output start Refutation
% See solution above
% 0.23/0.43  Formulae used in the proof : prove_inverse_X_times_X_is_id left_inverse total_function1 total_function2
% 0.23/0.43  
%------------------------------------------------------------------------------