%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : NUM416^1 : TPTP v8.1.2. Released v3.6.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.s7Dj1yoqZW true

% Computer : n020.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  : 300s
% DateTime : Thu Aug 31 12:41:18 EDT 2023

% Result   : Theorem 0.20s 0.82s
% Output   : Refutation 1.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   20 (  16 unt;   4 typ;   0 def)
%            Number of atoms       :   16 (  15 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives : 4077 (   1   ~;   0   |;   0   &;4076   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   78 (  78   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    6 (   4 usr;   1 con; 0-4 aty)
%            Number of variables   :   40 (  36   ^;   4   !;   0   ?;  40   :)

% Comments : 
%------------------------------------------------------------------------------
thf(mult_type,type,
    mult: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).

thf(five_type,type,
    five: ( $i > $i ) > $i > $i ).

thf(ten_type,type,
    ten: ( $i > $i ) > $i > $i ).

thf(plus_type,type,
    plus: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).

thf(mult_ax,axiom,
    ( mult
    = ( ^ [M: ( $i > $i ) > $i > $i,N: ( $i > $i ) > $i > $i,X: $i > $i,Y: $i] : ( M @ ( N @ X ) @ Y ) ) ) ).

thf('0',plain,
    ( mult
    = ( ^ [M: ( $i > $i ) > $i > $i,N: ( $i > $i ) > $i > $i,X: $i > $i,Y: $i] : ( M @ ( N @ X ) @ Y ) ) ),
    inference(simplify_rw_rule,[status(thm)],[mult_ax]) ).

thf('1',plain,
    ( mult
    = ( ^ [V_1: ( $i > $i ) > $i > $i,V_2: ( $i > $i ) > $i > $i,V_3: $i > $i,V_4: $i] : ( V_1 @ ( V_2 @ V_3 ) @ V_4 ) ) ),
    define([status(thm)]) ).

thf(plus_ax,axiom,
    ( plus
    = ( ^ [M: ( $i > $i ) > $i > $i,N: ( $i > $i ) > $i > $i,X: $i > $i,Y: $i] : ( M @ X @ ( N @ X @ Y ) ) ) ) ).

thf('2',plain,
    ( plus
    = ( ^ [M: ( $i > $i ) > $i > $i,N: ( $i > $i ) > $i > $i,X: $i > $i,Y: $i] : ( M @ X @ ( N @ X @ Y ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[plus_ax]) ).

thf('3',plain,
    ( plus
    = ( ^ [V_1: ( $i > $i ) > $i > $i,V_2: ( $i > $i ) > $i > $i,V_3: $i > $i,V_4: $i] : ( V_1 @ V_3 @ ( V_2 @ V_3 @ V_4 ) ) ) ),
    define([status(thm)]) ).

thf(ten_ax,axiom,
    ( ten
    = ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ).

thf('4',plain,
    ( ten
    = ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ) ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[ten_ax]) ).

thf('5',plain,
    ( ten
    = ( ^ [V_1: $i > $i,V_2: $i] : ( V_1 @ ( V_1 @ ( V_1 @ ( V_1 @ ( V_1 @ ( V_1 @ ( V_1 @ ( V_1 @ ( V_1 @ ( V_1 @ V_2 ) ) ) ) ) ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(five_ax,axiom,
    ( five
    = ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ) ).

thf('6',plain,
    ( five
    = ( ^ [X: $i > $i,Y: $i] : ( X @ ( X @ ( X @ ( X @ ( X @ Y ) ) ) ) ) ) ),
    inference(simplify_rw_rule,[status(thm)],[five_ax]) ).

thf('7',plain,
    ( five
    = ( ^ [V_1: $i > $i,V_2: $i] : ( V_1 @ ( V_1 @ ( V_1 @ ( V_1 @ ( V_1 @ V_2 ) ) ) ) ) ) ),
    define([status(thm)]) ).

thf(thm,conjecture,
    ( ( mult @ ten @ ( mult @ ten @ ten ) )
    = ( mult @ ( plus @ ten @ ten ) @ ( mult @ five @ ten ) ) ) ).

thf(zf_stmt_0,conjecture,
    ! [V_3: $i > $i,V_4: $i] :
      ( ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ V_4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
      = ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ V_4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(zf_stmt_1,negated_conjecture,
    ~ ! [V_3: $i > $i,V_4: $i] :
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@ ( V_3 @ V_4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
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@ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 @ ( V_3 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@ ( V_3 @ V_4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl0,plain,
    $false,
    inference(cnf,[status(esa)],[zf_stmt_1]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : NUM416^1 : TPTP v8.1.2. Released v3.6.0.
% 0.11/0.13  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.s7Dj1yoqZW true
% 0.14/0.34  % Computer : n020.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Fri Aug 25 15:06:15 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  % Running portfolio for 300 s
% 0.14/0.35  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.35  % Number of cores: 8
% 0.14/0.35  % Python version: Python 3.6.8
% 0.14/0.35  % Running in HO mode
% 0.20/0.66  % Total configuration time : 828
% 0.20/0.66  % Estimated wc time : 1656
% 0.20/0.66  % Estimated cpu time (8 cpus) : 207.0
% 0.20/0.70  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.20/0.75  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.20/0.76  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.20/0.76  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.20/0.76  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.20/0.76  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.20/0.76  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.20/0.80  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.20/0.82  % Solved by lams/40_c.s.sh.
% 0.20/0.82  % done 0 iterations in 0.027s
% 0.20/0.82  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 0.20/0.82  % SZS output start Refutation
% See solution above
% 1.48/0.84  
% 1.48/0.84  
% 1.48/0.84  % Terminating...
% 1.48/0.84  % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 2.28/0.95  % Runner terminated.
% 2.28/0.96  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------