%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP165-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n018.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 11:46:00 EDT 2022

% Result   : Unsatisfiable 0.19s 0.44s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    8 (   8 unt;   0 nHn;   8 RR)
%            Number of literals    :    8 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    3 (   1 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(greatest_lower_bound(a,identity),identity),
    file('GRP165-2.p',unknown),
    [] ).

cnf(2,axiom,
    ~ equal(greatest_lower_bound(a,multiply(a,a)),a),
    file('GRP165-2.p',unknown),
    [] ).

cnf(3,axiom,
    equal(multiply(identity,u),u),
    file('GRP165-2.p',unknown),
    [] ).

cnf(6,axiom,
    equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
    file('GRP165-2.p',unknown),
    [] ).

cnf(17,axiom,
    equal(multiply(greatest_lower_bound(u,v),w),greatest_lower_bound(multiply(u,w),multiply(v,w))),
    file('GRP165-2.p',unknown),
    [] ).

cnf(288,plain,
    equal(greatest_lower_bound(multiply(a,u),multiply(identity,u)),multiply(identity,u)),
    inference(spr,[status(thm),theory(equality)],[1,17]),
    [iquote('0:SpR:1.0,17.0')] ).

cnf(299,plain,
    equal(greatest_lower_bound(u,multiply(a,u)),u),
    inference(rew,[status(thm),theory(equality)],[6,288,3]),
    [iquote('0:Rew:6.0,288.0,3.0,288.0')] ).

cnf(300,plain,
    $false,
    inference(unc,[status(thm)],[299,2]),
    [iquote('0:UnC:299.0,2.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP165-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n018.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Tue Jun 14 05:05:58 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.44  
% 0.19/0.44  SPASS V 3.9 
% 0.19/0.44  SPASS beiseite: Proof found.
% 0.19/0.44  % SZS status Theorem
% 0.19/0.44  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.44  SPASS derived 236 clauses, backtracked 0 clauses, performed 0 splits and kept 74 clauses.
% 0.19/0.44  SPASS allocated 63393 KBytes.
% 0.19/0.44  SPASS spent	0:00:00.08 on the problem.
% 0.19/0.44  		0:00:00.04 for the input.
% 0.19/0.44  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.44  		0:00:00.00 for inferences.
% 0.19/0.44  		0:00:00.00 for the backtracking.
% 0.19/0.44  		0:00:00.01 for the reduction.
% 0.19/0.44  
% 0.19/0.44  
% 0.19/0.44  Here is a proof with depth 1, length 8 :
% 0.19/0.44  % SZS output start Refutation
% See solution above
% 0.19/0.44  Formulae used in the proof : lat1b_1 prove_lat1b left_identity symmetry_of_glb monotony_glb2
% 0.19/0.44  
%------------------------------------------------------------------------------