%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LAT035-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n003.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 06:48:42 EDT 2022

% Result   : Unsatisfiable 0.11s 0.39s
% Output   : Refutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    7 (   5 unt;   0 nHn;   7 RR)
%            Number of literals    :    9 (   0 equ;   4 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(6,axiom,
    equal(meet(k(u),k(v)),k(join(u,v))),
    file('LAT035-1.p',unknown),
    [] ).

cnf(8,axiom,
    equal(k(n0),n1),
    file('LAT035-1.p',unknown),
    [] ).

cnf(10,axiom,
    equal(join(f(u),f(v)),f(meet(u,v))),
    file('LAT035-1.p',unknown),
    [] ).

cnf(11,axiom,
    equal(f(n1),n0),
    file('LAT035-1.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ equal(join(f(k(aa)),f(k(bb))),f(k(join(aa,bb))))
    | ~ equal(f(k(n0)),n0) ),
    file('LAT035-1.p',unknown),
    [] ).

cnf(21,plain,
    ( ~ equal(f(k(join(aa,bb))),f(k(join(aa,bb))))
    | ~ equal(n0,n0) ),
    inference(rew,[status(thm),theory(equality)],[11,12,8,6,10]),
    [iquote('0:Rew:11.0,12.1,8.0,12.1,6.0,12.0,10.0,12.0')] ).

cnf(22,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[21]),
    [iquote('0:Obv:21.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : LAT035-1 : TPTP v8.1.0. Released v2.4.0.
% 0.10/0.12  % Command  : run_spass %d %s
% 0.11/0.33  % Computer : n003.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 600
% 0.11/0.33  % DateTime : Wed Jun 29 20:01:21 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 0.11/0.39  
% 0.11/0.39  SPASS V 3.9 
% 0.11/0.39  SPASS beiseite: Proof found.
% 0.11/0.39  % SZS status Theorem
% 0.11/0.39  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.11/0.39  SPASS derived 0 clauses, backtracked 0 clauses, performed 0 splits and kept 20 clauses.
% 0.11/0.39  SPASS allocated 63106 KBytes.
% 0.11/0.39  SPASS spent	0:00:00.04 on the problem.
% 0.11/0.39  		0:00:00.03 for the input.
% 0.11/0.39  		0:00:00.00 for the FLOTTER CNF translation.
% 0.11/0.39  		0:00:00.00 for inferences.
% 0.11/0.39  		0:00:00.00 for the backtracking.
% 0.11/0.39  		0:00:00.00 for the reduction.
% 0.11/0.39  
% 0.11/0.39  
% 0.11/0.39  Here is a proof with depth 0, length 7 :
% 0.11/0.39  % SZS output start Refutation
% See solution above
% 0.11/0.39  Formulae used in the proof : k_on_join k_on_bottom f_on_meet f_on_top comp_join_hemimorphism
% 0.11/0.39  
%------------------------------------------------------------------------------