%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP166-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n027.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 11:46:01 EDT 2022

% Result   : Unsatisfiable 0.18s 0.43s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    9 (   9 unt;   0 nHn;   9 RR)
%            Number of literals    :    9 (   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    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    equal(greatest_lower_bound(b,identity),identity),
    file('GRP166-4.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equal(greatest_lower_bound(a,multiply(b,a)),a),
    file('GRP166-4.p',unknown),
    [] ).

cnf(4,axiom,
    equal(multiply(identity,u),u),
    file('GRP166-4.p',unknown),
    [] ).

cnf(7,axiom,
    equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
    file('GRP166-4.p',unknown),
    [] ).

cnf(18,axiom,
    equal(multiply(greatest_lower_bound(u,v),w),greatest_lower_bound(multiply(u,w),multiply(v,w))),
    file('GRP166-4.p',unknown),
    [] ).

cnf(19,plain,
    equal(greatest_lower_bound(identity,b),identity),
    inference(rew,[status(thm),theory(equality)],[7,2]),
    [iquote('0:Rew:7.0,2.0')] ).

cnf(389,plain,
    equal(greatest_lower_bound(multiply(identity,u),multiply(b,u)),multiply(identity,u)),
    inference(spr,[status(thm),theory(equality)],[19,18]),
    [iquote('0:SpR:19.0,18.0')] ).

cnf(402,plain,
    equal(greatest_lower_bound(u,multiply(b,u)),u),
    inference(rew,[status(thm),theory(equality)],[4,389]),
    [iquote('0:Rew:4.0,389.0')] ).

cnf(403,plain,
    $false,
    inference(unc,[status(thm)],[402,3]),
    [iquote('0:UnC:402.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GRP166-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.06/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n027.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 04:18:16 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.43  
% 0.18/0.43  SPASS V 3.9 
% 0.18/0.43  SPASS beiseite: Proof found.
% 0.18/0.43  % SZS status Theorem
% 0.18/0.43  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.18/0.43  SPASS derived 318 clauses, backtracked 0 clauses, performed 0 splits and kept 83 clauses.
% 0.18/0.43  SPASS allocated 63468 KBytes.
% 0.18/0.43  SPASS spent	0:00:00.08 on the problem.
% 0.18/0.43  		0:00:00.03 for the input.
% 0.18/0.43  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.43  		0:00:00.00 for inferences.
% 0.18/0.43  		0:00:00.00 for the backtracking.
% 0.18/0.43  		0:00:00.02 for the reduction.
% 0.18/0.43  
% 0.18/0.43  
% 0.18/0.43  Here is a proof with depth 1, length 9 :
% 0.18/0.43  % SZS output start Refutation
% See solution above
% 0.18/0.43  Formulae used in the proof : lat3b_2 prove_lat3b left_identity symmetry_of_glb monotony_glb2
% 0.18/0.43  
%------------------------------------------------------------------------------