%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : GRP188-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 11:46:14 EDT 2022

% Result   : Unsatisfiable 0.18s 0.41s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   10 (  10 unt;   0 nHn;  10 RR)
%            Number of literals    :   10 (   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(4,axiom,
    ~ equal(least_upper_bound(b,least_upper_bound(a,b)),least_upper_bound(a,b)),
    file('GRP188-2.p',unknown),
    [] ).

cnf(8,axiom,
    equal(greatest_lower_bound(u,v),greatest_lower_bound(v,u)),
    file('GRP188-2.p',unknown),
    [] ).

cnf(9,axiom,
    equal(least_upper_bound(u,v),least_upper_bound(v,u)),
    file('GRP188-2.p',unknown),
    [] ).

cnf(14,axiom,
    equal(least_upper_bound(u,greatest_lower_bound(u,v)),u),
    file('GRP188-2.p',unknown),
    [] ).

cnf(15,axiom,
    equal(greatest_lower_bound(u,least_upper_bound(u,v)),u),
    file('GRP188-2.p',unknown),
    [] ).

cnf(20,plain,
    ~ equal(least_upper_bound(b,least_upper_bound(b,a)),least_upper_bound(b,a)),
    inference(rew,[status(thm),theory(equality)],[9,4]),
    [iquote('0:Rew:9.0,4.0')] ).

cnf(50,plain,
    equal(least_upper_bound(u,greatest_lower_bound(v,u)),u),
    inference(spr,[status(thm),theory(equality)],[8,14]),
    [iquote('0:SpR:8.0,14.0')] ).

cnf(70,plain,
    equal(least_upper_bound(least_upper_bound(u,v),u),least_upper_bound(u,v)),
    inference(spr,[status(thm),theory(equality)],[15,50]),
    [iquote('0:SpR:15.0,50.0')] ).

cnf(75,plain,
    equal(least_upper_bound(u,least_upper_bound(u,v)),least_upper_bound(u,v)),
    inference(rew,[status(thm),theory(equality)],[9,70]),
    [iquote('0:Rew:9.0,70.0')] ).

cnf(76,plain,
    $false,
    inference(unc,[status(thm)],[75,20]),
    [iquote('0:UnC:75.0,20.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP188-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n007.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 : Mon Jun 13 04:26:23 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.18/0.41  
% 0.18/0.41  SPASS V 3.9 
% 0.18/0.41  SPASS beiseite: Proof found.
% 0.18/0.41  % SZS status Theorem
% 0.18/0.41  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.18/0.41  SPASS derived 52 clauses, backtracked 0 clauses, performed 0 splits and kept 26 clauses.
% 0.18/0.41  SPASS allocated 63142 KBytes.
% 0.18/0.41  SPASS spent	0:00:00.06 on the problem.
% 0.18/0.41  		0:00:00.04 for the input.
% 0.18/0.41  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.41  		0:00:00.00 for inferences.
% 0.18/0.41  		0:00:00.00 for the backtracking.
% 0.18/0.41  		0:00:00.00 for the reduction.
% 0.18/0.41  
% 0.18/0.41  
% 0.18/0.41  Here is a proof with depth 2, length 10 :
% 0.18/0.41  % SZS output start Refutation
% See solution above
% 0.18/0.41  Formulae used in the proof : prove_p38a symmetry_of_glb symmetry_of_lub lub_absorbtion glb_absorbtion
% 0.18/0.41  
%------------------------------------------------------------------------------