%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP022-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n007.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 11:44:48 EDT 2022

% Result   : Unsatisfiable 0.20s 0.41s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   10 (  10 unt;   0 nHn;  10 RR)
%            Number of literals    :   10 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(multiply(u,identity),u),
    file('GRP022-2.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equal(inverse(inverse(a)),a),
    file('GRP022-2.p',unknown),
    [] ).

cnf(4,axiom,
    equal(multiply(identity,u),u),
    file('GRP022-2.p',unknown),
    [] ).

cnf(5,axiom,
    equal(multiply(inverse(u),u),identity),
    file('GRP022-2.p',unknown),
    [] ).

cnf(6,axiom,
    equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
    file('GRP022-2.p',unknown),
    [] ).

cnf(22,plain,
    equal(multiply(inverse(u),multiply(u,v)),multiply(identity,v)),
    inference(spr,[status(thm),theory(equality)],[5,6]),
    [iquote('0:SpR:5.0,6.0')] ).

cnf(27,plain,
    equal(multiply(inverse(u),multiply(u,v)),v),
    inference(rew,[status(thm),theory(equality)],[4,22]),
    [iquote('0:Rew:4.0,22.0')] ).

cnf(34,plain,
    equal(multiply(inverse(inverse(u)),identity),u),
    inference(spr,[status(thm),theory(equality)],[5,27]),
    [iquote('0:SpR:5.0,27.0')] ).

cnf(40,plain,
    equal(inverse(inverse(u)),u),
    inference(rew,[status(thm),theory(equality)],[1,34]),
    [iquote('0:Rew:1.0,34.0')] ).

cnf(41,plain,
    $false,
    inference(unc,[status(thm)],[40,3]),
    [iquote('0:UnC:40.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : GRP022-2 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n007.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Tue Jun 14 13:45:10 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.41  
% 0.20/0.41  SPASS V 3.9 
% 0.20/0.41  SPASS beiseite: Proof found.
% 0.20/0.41  % SZS status Theorem
% 0.20/0.41  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.41  SPASS derived 27 clauses, backtracked 0 clauses, performed 0 splits and kept 13 clauses.
% 0.20/0.41  SPASS allocated 63119 KBytes.
% 0.20/0.41  SPASS spent	0:00:00.06 on the problem.
% 0.20/0.41  		0:00:00.03 for the input.
% 0.20/0.41  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.41  		0:00:00.00 for inferences.
% 0.20/0.41  		0:00:00.00 for the backtracking.
% 0.20/0.41  		0:00:00.00 for the reduction.
% 0.20/0.41  
% 0.20/0.41  
% 0.20/0.41  Here is a proof with depth 2, length 10 :
% 0.20/0.41  % SZS output start Refutation
% See solution above
% 0.20/0.41  Formulae used in the proof : right_identity prove_inverse_of_inverse_is_original left_identity left_inverse associativity
% 0.20/0.41  
%------------------------------------------------------------------------------