%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP144-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n011.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 11:45:55 EDT 2022

% Result   : Unsatisfiable 0.19s 0.40s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    7 (   7 unt;   0 nHn;   7 RR)
%            Number of literals    :    7 (   0 equ;   2 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    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ equal(least_upper_bound(greatest_lower_bound(a,b),b),b),
    file('GRP144-1.p',unknown),
    [] ).

cnf(5,axiom,
    equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
    file('GRP144-1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(least_upper_bound(u,v),least_upper_bound(v,u)),
    file('GRP144-1.p',unknown),
    [] ).

cnf(11,axiom,
    equal(least_upper_bound(u,greatest_lower_bound(u,v)),u),
    file('GRP144-1.p',unknown),
    [] ).

cnf(17,plain,
    ~ equal(least_upper_bound(b,greatest_lower_bound(a,b)),b),
    inference(rew,[status(thm),theory(equality)],[6,1]),
    [iquote('0:Rew:6.0,1.0')] ).

cnf(37,plain,
    equal(least_upper_bound(u,greatest_lower_bound(v,u)),u),
    inference(spr,[status(thm),theory(equality)],[5,11]),
    [iquote('0:SpR:5.0,11.0')] ).

cnf(44,plain,
    $false,
    inference(unc,[status(thm)],[37,17]),
    [iquote('0:UnC:37.0,17.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : GRP144-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n011.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Mon Jun 13 05:21:18 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.19/0.40  
% 0.19/0.40  SPASS V 3.9 
% 0.19/0.40  SPASS beiseite: Proof found.
% 0.19/0.40  % SZS status Theorem
% 0.19/0.40  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.40  SPASS derived 26 clauses, backtracked 0 clauses, performed 0 splits and kept 19 clauses.
% 0.19/0.40  SPASS allocated 63119 KBytes.
% 0.19/0.40  SPASS spent	0:00:00.06 on the problem.
% 0.19/0.40  		0:00:00.04 for the input.
% 0.19/0.40  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.40  		0:00:00.00 for inferences.
% 0.19/0.40  		0:00:00.00 for the backtracking.
% 0.19/0.40  		0:00:00.00 for the reduction.
% 0.19/0.40  
% 0.19/0.40  
% 0.19/0.40  Here is a proof with depth 1, length 7 :
% 0.19/0.40  % SZS output start Refutation
% See solution above
% 0.19/0.40  Formulae used in the proof : prove_ax_glb3a symmetry_of_glb symmetry_of_lub lub_absorbtion
% 0.19/0.40  
%------------------------------------------------------------------------------