%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LAT032-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n009.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 : Sun Jul 17 06:48:41 EDT 2022

% Result   : Unsatisfiable 0.18s 0.42s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    6
% Syntax   : Number of clauses     :    9 (   9 unt;   0 nHn;   9 RR)
%            Number of literals    :    9 (   0 equ;   2 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    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(join(u,meet(v,w)),meet(join(u,v),join(u,w))),
    file('LAT032-1.p',unknown),
    [] ).

cnf(2,axiom,
    ~ equal(join(meet(xx,yy),meet(xx,zz)),meet(xx,join(yy,zz))),
    file('LAT032-1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(join(u,u),u),
    file('LAT032-1.p',unknown),
    [] ).

cnf(5,axiom,
    equal(meet(u,join(u,v)),u),
    file('LAT032-1.p',unknown),
    [] ).

cnf(8,axiom,
    equal(join(u,v),join(v,u)),
    file('LAT032-1.p',unknown),
    [] ).

cnf(9,axiom,
    equal(meet(meet(u,v),w),meet(u,meet(v,w))),
    file('LAT032-1.p',unknown),
    [] ).

cnf(13,plain,
    ~ equal(meet(xx,meet(join(xx,zz),join(yy,zz))),meet(xx,join(yy,zz))),
    inference(rew,[status(thm),theory(equality)],[5,2,4,1,8]),
    [iquote('0:Rew:5.0,2.0,4.0,2.0,1.0,2.0,8.0,2.0,8.0,2.0,8.0,2.0,1.0,2.0,8.0,2.0,1.0,2.0')] ).

cnf(87,plain,
    equal(meet(u,meet(join(u,v),w)),meet(u,w)),
    inference(spr,[status(thm),theory(equality)],[5,9]),
    [iquote('0:SpR:5.0,9.0')] ).

cnf(92,plain,
    $false,
    inference(unc,[status(thm)],[87,13]),
    [iquote('0:UnC:87.0,13.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : LAT032-1 : TPTP v8.1.0. Released v2.4.0.
% 0.04/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n009.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 : Wed Jun 29 23:33:37 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.18/0.42  
% 0.18/0.42  SPASS V 3.9 
% 0.18/0.42  SPASS beiseite: Proof found.
% 0.18/0.42  % SZS status Theorem
% 0.18/0.42  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.18/0.42  SPASS derived 71 clauses, backtracked 0 clauses, performed 0 splits and kept 31 clauses.
% 0.18/0.42  SPASS allocated 63192 KBytes.
% 0.18/0.42  SPASS spent	0:00:00.07 on the problem.
% 0.18/0.42  		0:00:00.04 for the input.
% 0.18/0.42  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.42  		0:00:00.00 for inferences.
% 0.18/0.42  		0:00:00.00 for the backtracking.
% 0.18/0.42  		0:00:00.00 for the reduction.
% 0.18/0.42  
% 0.18/0.42  
% 0.18/0.42  Here is a proof with depth 1, length 9 :
% 0.18/0.42  % SZS output start Refutation
% See solution above
% 0.18/0.42  Formulae used in the proof : dist_join dist_meet idempotence_of_join absorption1 commutativity_of_join associativity_of_meet
% 0.18/0.42  
%------------------------------------------------------------------------------