LEO-II---2.3.1.THM-CRf.s

%------------------------------------------------------------------------------
% File     : LEO-II---2.3.1
% Problem  : NUM925+4 : TPTP v9.3.1. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n002.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Oct  7 10:35:40 AM UTC 2026

% Result   : Theorem 178.56s 36.30s
% Output   : CNFRefutation 178.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      :  463
% Syntax   : Number of formulae    : 3757 (2709 unt;   0 typ;   0 def)
%            Number of atoms       : 21272 (12397 equ;   0 cnn)
%            Maximal formula atoms :    9 (   5 avg)
%            Number of connectives : 62689 (5986   ~;6457   |; 318   &;49528   @)
%                                         (  98 <=>; 302  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     : 1106 (1103 usr; 440 con; 0-8 aty)
%            Number of variables   : 7994 (   0   ^;7980   !;  14   ?;7994   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_abs_abs_int,type,
    abs_abs_int: $i ).

thf(tp_abs_abs_rat,type,
    abs_abs_rat: $i ).

thf(tp_abs_abs_real,type,
    abs_abs_real: $i ).

thf(tp_accp_P2006205492nt_int,type,
    accp_P2006205492nt_int: $i > $i ).

thf(tp_accp_P490777396at_nat,type,
    accp_P490777396at_nat: $i > $i ).

thf(tp_accp_int,type,
    accp_int: $i > $i ).

thf(tp_adjust,type,
    adjust: $i > $i ).

thf(tp_arccos,type,
    arccos: $i ).

thf(tp_archim1246769320r_real,type,
    archim1246769320r_real: $i > $i ).

thf(tp_archim791455193or_rat,type,
    archim791455193or_rat: $i > $i ).

thf(tp_archim856651990g_real,type,
    archim856651990g_real: $i > $i ).

thf(tp_arcsin,type,
    arcsin: $i ).

thf(tp_arctan,type,
    arctan: $i ).

thf(tp_arg,type,
    arg: $i > $i ).

thf(tp_at_complex,type,
    at_complex: $i > $i ).

thf(tp_at_real,type,
    at_real: $i > $i ).

thf(tp_bezw,type,
    bezw: $i > $i > $i ).

thf(tp_big_co1024481617at_int,type,
    big_co1024481617at_int: $i ).

thf(tp_big_co1548731110nt_int,type,
    big_co1548731110nt_int: $i > $i > $i ).

thf(tp_big_co1705425894at_nat,type,
    big_co1705425894at_nat: $i > $i > $i ).

thf(tp_big_co1758102091ol_nat,type,
    big_co1758102091ol_nat: $i ).

thf(tp_big_co230513141nt_int,type,
    big_co230513141nt_int: $i ).

thf(tp_big_co387207925at_nat,type,
    big_co387207925at_nat: $i ).

thf(tp_big_co604158596t_real,type,
    big_co604158596t_real: $i ).

thf(tp_bijR_int_int,type,
    bijR_int_int: $i > $i ).

thf(tp_bit0,type,
    bit0: $i ).

thf(tp_bit1,type,
    bit1: $i ).

thf(tp_bnorRset,type,
    bnorRset: $i > $i ).

thf(tp_bolzano_bisect,type,
    bolzano_bisect: $i > $i > $i > $i ).

thf(tp_bseq_real,type,
    bseq_real: $i > $i ).

thf(tp_cOMBB_1015721476ol_nat,type,
    cOMBB_1015721476ol_nat: $i ).

thf(tp_cOMBB_1102189010nt_int,type,
    cOMBB_1102189010nt_int: $i ).

thf(tp_cOMBB_1121934354l_real,type,
    cOMBB_1121934354l_real: $i ).

thf(tp_cOMBB_1146692694ol_nat,type,
    cOMBB_1146692694ol_nat: $i ).

thf(tp_cOMBB_1159313332l_real,type,
    cOMBB_1159313332l_real: $i ).

thf(tp_cOMBB_117013006ex_nat,type,
    cOMBB_117013006ex_nat: $i ).

thf(tp_cOMBB_118231410ol_int,type,
    cOMBB_118231410ol_int: $i ).

thf(tp_cOMBB_1211207212ol_int,type,
    cOMBB_1211207212ol_int: $i ).

thf(tp_cOMBB_1247074793l_real,type,
    cOMBB_1247074793l_real: $i ).

thf(tp_cOMBB_1290694363ol_int,type,
    cOMBB_1290694363ol_int: $i ).

thf(tp_cOMBB_1308947378al_nat,type,
    cOMBB_1308947378al_nat: $i ).

thf(tp_cOMBB_1317819104ol_int,type,
    cOMBB_1317819104ol_int: $i ).

thf(tp_cOMBB_1344650379nt_int,type,
    cOMBB_1344650379nt_int: $i ).

thf(tp_cOMBB_1389251822nt_int,type,
    cOMBB_1389251822nt_int: $i ).

thf(tp_cOMBB_1418110531ol_int,type,
    cOMBB_1418110531ol_int: $i ).

thf(tp_cOMBB_1419615765al_nat,type,
    cOMBB_1419615765al_nat: $i ).

thf(tp_cOMBB_1453147152l_real,type,
    cOMBB_1453147152l_real: $i ).

thf(tp_cOMBB_1459832681l_real,type,
    cOMBB_1459832681l_real: $i ).

thf(tp_cOMBB_1480366270al_nat,type,
    cOMBB_1480366270al_nat: $i ).

thf(tp_cOMBB_1484610687nt_int,type,
    cOMBB_1484610687nt_int: $i ).

thf(tp_cOMBB_1496585939nt_int,type,
    cOMBB_1496585939nt_int: $i ).

thf(tp_cOMBB_1506897658nt_int,type,
    cOMBB_1506897658nt_int: $i ).

thf(tp_cOMBB_1533963633al_nat,type,
    cOMBB_1533963633al_nat: $i ).

thf(tp_cOMBB_1550063917nt_int,type,
    cOMBB_1550063917nt_int: $i ).

thf(tp_cOMBB_1593174431ol_int,type,
    cOMBB_1593174431ol_int: $i ).

thf(tp_cOMBB_1647910634ol_int,type,
    cOMBB_1647910634ol_int: $i ).

thf(tp_cOMBB_1652995168ol_int,type,
    cOMBB_1652995168ol_int: $i ).

thf(tp_cOMBB_1657320178nt_int,type,
    cOMBB_1657320178nt_int: $i ).

thf(tp_cOMBB_170828966nt_int,type,
    cOMBB_170828966nt_int: $i ).

thf(tp_cOMBB_1714920583ex_nat,type,
    cOMBB_1714920583ex_nat: $i ).

thf(tp_cOMBB_172850899l_real,type,
    cOMBB_172850899l_real: $i ).

thf(tp_cOMBB_1768400739l_real,type,
    cOMBB_1768400739l_real: $i ).

thf(tp_cOMBB_1795223523l_real,type,
    cOMBB_1795223523l_real: $i ).

thf(tp_cOMBB_182850971nt_int,type,
    cOMBB_182850971nt_int: $i ).

thf(tp_cOMBB_1846624359nt_int,type,
    cOMBB_1846624359nt_int: $i ).

thf(tp_cOMBB_1875755114nt_int,type,
    cOMBB_1875755114nt_int: $i ).

thf(tp_cOMBB_188663909l_real,type,
    cOMBB_188663909l_real: $i ).

thf(tp_cOMBB_1896127834l_real,type,
    cOMBB_1896127834l_real: $i ).

thf(tp_cOMBB_1926947at_nat,type,
    cOMBB_1926947at_nat: $i ).

thf(tp_cOMBB_1934313333l_real,type,
    cOMBB_1934313333l_real: $i ).

thf(tp_cOMBB_1946221070al_int,type,
    cOMBB_1946221070al_int: $i ).

thf(tp_cOMBB_1948233853l_real,type,
    cOMBB_1948233853l_real: $i ).

thf(tp_cOMBB_2027861294ol_int,type,
    cOMBB_2027861294ol_int: $i ).

thf(tp_cOMBB_2046938128ol_int,type,
    cOMBB_2046938128ol_int: $i ).

thf(tp_cOMBB_2050079537l_real,type,
    cOMBB_2050079537l_real: $i ).

thf(tp_cOMBB_2086486755nt_int,type,
    cOMBB_2086486755nt_int: $i ).

thf(tp_cOMBB_2087181719ol_int,type,
    cOMBB_2087181719ol_int: $i ).

thf(tp_cOMBB_2092576745l_real,type,
    cOMBB_2092576745l_real: $i ).

thf(tp_cOMBB_2107848501l_real,type,
    cOMBB_2107848501l_real: $i ).

thf(tp_cOMBB_2125215742l_real,type,
    cOMBB_2125215742l_real: $i ).

thf(tp_cOMBB_2129825580al_int,type,
    cOMBB_2129825580al_int: $i ).

thf(tp_cOMBB_2138578194l_real,type,
    cOMBB_2138578194l_real: $i ).

thf(tp_cOMBB_214503962ol_int,type,
    cOMBB_214503962ol_int: $i ).

thf(tp_cOMBB_222539774nt_int,type,
    cOMBB_222539774nt_int: $i ).

thf(tp_cOMBB_237479429l_real,type,
    cOMBB_237479429l_real: $i ).

thf(tp_cOMBB_270132509l_real,type,
    cOMBB_270132509l_real: $i ).

thf(tp_cOMBB_320287386nt_int,type,
    cOMBB_320287386nt_int: $i ).

thf(tp_cOMBB_348438404at_nat,type,
    cOMBB_348438404at_nat: $i ).

thf(tp_cOMBB_3698607l_real,type,
    cOMBB_3698607l_real: $i ).

thf(tp_cOMBB_389152643ol_int,type,
    cOMBB_389152643ol_int: $i ).

thf(tp_cOMBB_415306361l_real,type,
    cOMBB_415306361l_real: $i ).

thf(tp_cOMBB_421464275l_real,type,
    cOMBB_421464275l_real: $i ).

thf(tp_cOMBB_421479067l_real,type,
    cOMBB_421479067l_real: $i ).

thf(tp_cOMBB_422423973l_real,type,
    cOMBB_422423973l_real: $i ).

thf(tp_cOMBB_430461877l_real,type,
    cOMBB_430461877l_real: $i ).

thf(tp_cOMBB_44084907l_real,type,
    cOMBB_44084907l_real: $i ).

thf(tp_cOMBB_47643171nt_int,type,
    cOMBB_47643171nt_int: $i ).

thf(tp_cOMBB_520243667l_real,type,
    cOMBB_520243667l_real: $i ).

thf(tp_cOMBB_550562460ol_int,type,
    cOMBB_550562460ol_int: $i ).

thf(tp_cOMBB_557258983l_real,type,
    cOMBB_557258983l_real: $i ).

thf(tp_cOMBB_562416518ol_int,type,
    cOMBB_562416518ol_int: $i ).

thf(tp_cOMBB_563965291nt_int,type,
    cOMBB_563965291nt_int: $i ).

thf(tp_cOMBB_569260360nt_int,type,
    cOMBB_569260360nt_int: $i ).

thf(tp_cOMBB_591320580ol_int,type,
    cOMBB_591320580ol_int: $i ).

thf(tp_cOMBB_595786433nt_int,type,
    cOMBB_595786433nt_int: $i ).

thf(tp_cOMBB_599996122l_real,type,
    cOMBB_599996122l_real: $i ).

thf(tp_cOMBB_624415285l_real,type,
    cOMBB_624415285l_real: $i ).

thf(tp_cOMBB_638531587nt_int,type,
    cOMBB_638531587nt_int: $i ).

thf(tp_cOMBB_64450052al_nat,type,
    cOMBB_64450052al_nat: $i ).

thf(tp_cOMBB_650041899nt_int,type,
    cOMBB_650041899nt_int: $i ).

thf(tp_cOMBB_662120866nt_int,type,
    cOMBB_662120866nt_int: $i ).

thf(tp_cOMBB_690122963l_real,type,
    cOMBB_690122963l_real: $i ).

thf(tp_cOMBB_722610049al_nat,type,
    cOMBB_722610049al_nat: $i ).

thf(tp_cOMBB_731595089l_real,type,
    cOMBB_731595089l_real: $i ).

thf(tp_cOMBB_735549356nt_int,type,
    cOMBB_735549356nt_int: $i ).

thf(tp_cOMBB_773384995nt_int,type,
    cOMBB_773384995nt_int: $i ).

thf(tp_cOMBB_782625832nt_int,type,
    cOMBB_782625832nt_int: $i ).

thf(tp_cOMBB_793166024ol_int,type,
    cOMBB_793166024ol_int: $i ).

thf(tp_cOMBB_798864284nt_int,type,
    cOMBB_798864284nt_int: $i ).

thf(tp_cOMBB_800536526ol_nat,type,
    cOMBB_800536526ol_nat: $i ).

thf(tp_cOMBB_859312247nt_nat,type,
    cOMBB_859312247nt_nat: $i ).

thf(tp_cOMBB_866192175nt_int,type,
    cOMBB_866192175nt_int: $i ).

thf(tp_cOMBB_882763271l_real,type,
    cOMBB_882763271l_real: $i ).

thf(tp_cOMBB_929094628al_int,type,
    cOMBB_929094628al_int: $i ).

thf(tp_cOMBB_95956018ol_int,type,
    cOMBB_95956018ol_int: $i ).

thf(tp_cOMBB_963856155at_nat,type,
    cOMBB_963856155at_nat: $i ).

thf(tp_cOMBB_984071017l_real,type,
    cOMBB_984071017l_real: $i ).

thf(tp_cOMBB_bool_bool_int,type,
    cOMBB_bool_bool_int: $i ).

thf(tp_cOMBB_bool_bool_nat,type,
    cOMBB_bool_bool_nat: $i ).

thf(tp_cOMBB_int_bool_int,type,
    cOMBB_int_bool_int: $i ).

thf(tp_cOMBB_int_bool_nat,type,
    cOMBB_int_bool_nat: $i ).

thf(tp_cOMBB_int_int_int,type,
    cOMBB_int_int_int: $i ).

thf(tp_cOMBB_int_int_nat,type,
    cOMBB_int_int_nat: $i ).

thf(tp_cOMBB_int_rat_int,type,
    cOMBB_int_rat_int: $i ).

thf(tp_cOMBB_int_real_int,type,
    cOMBB_int_real_int: $i ).

thf(tp_cOMBB_nat_bool_int,type,
    cOMBB_nat_bool_int: $i ).

thf(tp_cOMBB_nat_nat_nat,type,
    cOMBB_nat_nat_nat: $i ).

thf(tp_cOMBB_nat_real_nat,type,
    cOMBB_nat_real_nat: $i ).

thf(tp_cOMBB_rat_bool_int,type,
    cOMBB_rat_bool_int: $i ).

thf(tp_cOMBB_rat_rat_nat,type,
    cOMBB_rat_rat_nat: $i ).

thf(tp_cOMBB_real_bool_int,type,
    cOMBB_real_bool_int: $i ).

thf(tp_cOMBB_real_bool_nat,type,
    cOMBB_real_bool_nat: $i ).

thf(tp_cOMBB_real_bool_real,type,
    cOMBB_real_bool_real: $i ).

thf(tp_cOMBB_real_real_int,type,
    cOMBB_real_real_int: $i ).

thf(tp_cOMBB_real_real_nat,type,
    cOMBB_real_real_nat: $i ).

thf(tp_cOMBB_real_real_real,type,
    cOMBB_real_real_real: $i ).

thf(tp_cOMBC_1113900202t_bool,type,
    cOMBC_1113900202t_bool: $i ).

thf(tp_cOMBC_1329014627t_real,type,
    cOMBC_1329014627t_real: $i ).

thf(tp_cOMBC_1417754532nt_int,type,
    cOMBC_1417754532nt_int: $i ).

thf(tp_cOMBC_1508019322l_real,type,
    cOMBC_1508019322l_real: $i ).

thf(tp_cOMBC_1683390479t_bool,type,
    cOMBC_1683390479t_bool: $i ).

thf(tp_cOMBC_1801450329t_bool,type,
    cOMBC_1801450329t_bool: $i ).

thf(tp_cOMBC_1805044090nt_int,type,
    cOMBC_1805044090nt_int: $i ).

thf(tp_cOMBC_1964283556nt_int,type,
    cOMBC_1964283556nt_int: $i ).

thf(tp_cOMBC_2010481033l_real,type,
    cOMBC_2010481033l_real: $i ).

thf(tp_cOMBC_2037038898nt_int,type,
    cOMBC_2037038898nt_int: $i ).

thf(tp_cOMBC_226598744l_bool,type,
    cOMBC_226598744l_bool: $i ).

thf(tp_cOMBC_241247961t_bool,type,
    cOMBC_241247961t_bool: $i ).

thf(tp_cOMBC_243356514t_bool,type,
    cOMBC_243356514t_bool: $i ).

thf(tp_cOMBC_295337211t_real,type,
    cOMBC_295337211t_real: $i ).

thf(tp_cOMBC_33652895t_bool,type,
    cOMBC_33652895t_bool: $i ).

thf(tp_cOMBC_412863505t_bool,type,
    cOMBC_412863505t_bool: $i ).

thf(tp_cOMBC_467724138l_real,type,
    cOMBC_467724138l_real: $i ).

thf(tp_cOMBC_678732631t_bool,type,
    cOMBC_678732631t_bool: $i ).

thf(tp_cOMBC_707974837nt_int,type,
    cOMBC_707974837nt_int: $i ).

thf(tp_cOMBC_736024425nt_int,type,
    cOMBC_736024425nt_int: $i ).

thf(tp_cOMBC_746811033l_real,type,
    cOMBC_746811033l_real: $i ).

thf(tp_cOMBC_824100275t_real,type,
    cOMBC_824100275t_real: $i ).

thf(tp_cOMBC_94739984l_bool,type,
    cOMBC_94739984l_bool: $i ).

thf(tp_cOMBC_983868720t_bool,type,
    cOMBC_983868720t_bool: $i ).

thf(tp_cOMBC_int_int_bool,type,
    cOMBC_int_int_bool: $i ).

thf(tp_cOMBC_int_int_int,type,
    cOMBC_int_int_int: $i ).

thf(tp_cOMBC_int_nat_int,type,
    cOMBC_int_nat_int: $i ).

thf(tp_cOMBC_int_rat_bool,type,
    cOMBC_int_rat_bool: $i ).

thf(tp_cOMBC_int_real_bool,type,
    cOMBC_int_real_bool: $i ).

thf(tp_cOMBC_nat_int_int,type,
    cOMBC_nat_int_int: $i ).

thf(tp_cOMBC_nat_nat_bool,type,
    cOMBC_nat_nat_bool: $i ).

thf(tp_cOMBC_nat_nat_nat,type,
    cOMBC_nat_nat_nat: $i ).

thf(tp_cOMBC_nat_real_real,type,
    cOMBC_nat_real_real: $i ).

thf(tp_cOMBC_real_nat_real,type,
    cOMBC_real_nat_real: $i ).

thf(tp_cOMBC_real_real_bool,type,
    cOMBC_real_real_bool: $i ).

thf(tp_cOMBC_real_real_real,type,
    cOMBC_real_real_real: $i ).

thf(tp_cOMBI_int,type,
    cOMBI_int: $i ).

thf(tp_cOMBI_nat,type,
    cOMBI_nat: $i ).

thf(tp_cOMBI_real,type,
    cOMBI_real: $i ).

thf(tp_cOMBK_1643584600t_bool,type,
    cOMBK_1643584600t_bool: $i > $i ).

thf(tp_cOMBK_bool_nat,type,
    cOMBK_bool_nat: $i > $i ).

thf(tp_cOMBK_rat_nat,type,
    cOMBK_rat_nat: $i > $i ).

thf(tp_cOMBS_107495110l_real,type,
    cOMBS_107495110l_real: $i ).

thf(tp_cOMBS_1470252563nt_int,type,
    cOMBS_1470252563nt_int: $i ).

thf(tp_cOMBS_1610675060t_bool,type,
    cOMBS_1610675060t_bool: $i ).

thf(tp_cOMBS_163651580l_real,type,
    cOMBS_163651580l_real: $i ).

thf(tp_cOMBS_1640193733nt_int,type,
    cOMBS_1640193733nt_int: $i ).

thf(tp_cOMBS_1676841879t_bool,type,
    cOMBS_1676841879t_bool: $i ).

thf(tp_cOMBS_1720984575t_bool,type,
    cOMBS_1720984575t_bool: $i ).

thf(tp_cOMBS_1891347093nt_int,type,
    cOMBS_1891347093nt_int: $i ).

thf(tp_cOMBS_193881978l_real,type,
    cOMBS_193881978l_real: $i ).

thf(tp_cOMBS_2011279539nt_int,type,
    cOMBS_2011279539nt_int: $i ).

thf(tp_cOMBS_2019229620nt_int,type,
    cOMBS_2019229620nt_int: $i ).

thf(tp_cOMBS_337378985l_real,type,
    cOMBS_337378985l_real: $i ).

thf(tp_cOMBS_400904860l_bool,type,
    cOMBS_400904860l_bool: $i ).

thf(tp_cOMBS_480885903t_bool,type,
    cOMBS_480885903t_bool: $i ).

thf(tp_cOMBS_511527878l_real,type,
    cOMBS_511527878l_real: $i ).

thf(tp_cOMBS_549334880nt_rat,type,
    cOMBS_549334880nt_rat: $i ).

thf(tp_cOMBS_696648398omplex,type,
    cOMBS_696648398omplex: $i ).

thf(tp_cOMBS_794971624l_real,type,
    cOMBS_794971624l_real: $i ).

thf(tp_cOMBS_902912708l_real,type,
    cOMBS_902912708l_real: $i ).

thf(tp_cOMBS_int_bool_bool,type,
    cOMBS_int_bool_bool: $i ).

thf(tp_cOMBS_nat_bool_bool,type,
    cOMBS_nat_bool_bool: $i ).

thf(tp_cOMBS_nat_nat_nat,type,
    cOMBS_nat_nat_nat: $i ).

thf(tp_cOMBS_nat_rat_rat,type,
    cOMBS_nat_rat_rat: $i ).

thf(tp_cOMBS_nat_real_real,type,
    cOMBS_nat_real_real: $i ).

thf(tp_cOMBS_real_bool_bool,type,
    cOMBS_real_bool_bool: $i ).

thf(tp_cOMBS_real_real_real,type,
    cOMBS_real_real_real: $i ).

thf(tp_cauchy_complex,type,
    cauchy_complex: $i > $i ).

thf(tp_cauchy_real,type,
    cauchy_real: $i > $i ).

thf(tp_cis,type,
    cis: $i > $i ).

thf(tp_cnj,type,
    cnj: $i ).

thf(tp_code_S1047413653umeral,type,
    code_S1047413653umeral: $i > $i ).

thf(tp_code_c271388182l_size,type,
    code_c271388182l_size: $i > $i ).

thf(tp_code_d418564891umeral,type,
    code_d418564891umeral: $i > $i > $i ).

thf(tp_code_int_of,type,
    code_int_of: $i > $i ).

thf(tp_code_nat_of_aux,type,
    code_nat_of_aux: $i > $i ).

thf(tp_collec1347809874nt_int,type,
    collec1347809874nt_int: $i > $i ).

thf(tp_collec1979865426at_nat,type,
    collec1979865426at_nat: $i > $i ).

thf(tp_collec50511176nt_int,type,
    collec50511176nt_int: $i > $i ).

thf(tp_collect_int,type,
    collect_int: $i > $i ).

thf(tp_collect_nat,type,
    collect_nat: $i > $i ).

thf(tp_collect_real,type,
    collect_real: $i > $i ).

thf(tp_comple124823625p_real,type,
    comple124823625p_real: $i > $i ).

thf(tp_comple219730294t_bool,type,
    comple219730294t_bool: $i > $i ).

thf(tp_complex,type,
    complex: $i ).

thf(tp_complex_size,type,
    complex_size: $i > $i ).

thf(tp_coprime,type,
    coprime: $i ).

thf(tp_cos,type,
    cos: $i ).

thf(tp_cos_coeff,type,
    cos_coeff: $i ).

thf(tp_d22set,type,
    d22set: $i ).

thf(tp_deriv_real,type,
    deriv_real: $i > $i > $i ).

thf(tp_diffs_real,type,
    diffs_real: $i > $i ).

thf(tp_dist_dist_complex,type,
    dist_dist_complex: $i > $i ).

thf(tp_dist_dist_real,type,
    dist_dist_real: $i > $i ).

thf(tp_div_di1218280263umeral,type,
    div_di1218280263umeral: $i ).

thf(tp_div_di1430059507de_int,type,
    div_di1430059507de_int: $i ).

thf(tp_div_div_int,type,
    div_div_int: $i ).

thf(tp_div_div_nat,type,
    div_div_nat: $i ).

thf(tp_div_mo1740067990umeral,type,
    div_mo1740067990umeral: $i > $i ).

thf(tp_div_mo231679042de_int,type,
    div_mo231679042de_int: $i > $i ).

thf(tp_div_mod_int,type,
    div_mod_int: $i > $i ).

thf(tp_div_mod_nat,type,
    div_mod_nat: $i > $i ).

thf(tp_divmod_int,type,
    divmod_int: $i > $i > $i ).

thf(tp_divmod_int_rel,type,
    divmod_int_rel: $i > $i > $i ).

thf(tp_divmod_nat,type,
    divmod_nat: $i > $i > $i ).

thf(tp_divmod_nat_rel,type,
    divmod_nat_rel: $i > $i > $i ).

thf(tp_dvd_dv174992974umeral,type,
    dvd_dv174992974umeral: $i ).

thf(tp_dvd_dv1760642554de_int,type,
    dvd_dv1760642554de_int: $i ).

thf(tp_dvd_dvd_complex,type,
    dvd_dvd_complex: $i ).

thf(tp_dvd_dvd_int,type,
    dvd_dvd_int: $i ).

thf(tp_dvd_dvd_nat,type,
    dvd_dvd_nat: $i ).

thf(tp_dvd_dvd_rat,type,
    dvd_dvd_rat: $i ).

thf(tp_dvd_dvd_real,type,
    dvd_dvd_real: $i ).

thf(tp_even_odd_even_int,type,
    even_odd_even_int: $i ).

thf(tp_even_odd_even_nat,type,
    even_odd_even_nat: $i ).

thf(tp_exp_real,type,
    exp_real: $i ).

thf(tp_expi,type,
    expi: $i > $i ).

thf(tp_fEx_int,type,
    fEx_int: $i ).

thf(tp_fEx_nat,type,
    fEx_nat: $i ).

thf(tp_fFalse,type,
    fFalse: $i ).

thf(tp_fNot,type,
    fNot: $i ).

thf(tp_fTrue,type,
    fTrue: $i ).

thf(tp_fact,type,
    fact: $i ).

thf(tp_fact_fact_int,type,
    fact_fact_int: $i ).

thf(tp_fact_fact_nat,type,
    fact_fact_nat: $i ).

thf(tp_fconj,type,
    fconj: $i ).

thf(tp_fdisj,type,
    fdisj: $i > $i > $i ).

thf(tp_fequal_int,type,
    fequal_int: $i ).

thf(tp_fequal_nat,type,
    fequal_nat: $i ).

thf(tp_fequal_rat,type,
    fequal_rat: $i ).

thf(tp_fequal_real,type,
    fequal_real: $i ).

thf(tp_field_1210416355s_real,type,
    field_1210416355s_real: $i ).

thf(tp_fimplies,type,
    fimplies: $i > $i ).

thf(tp_finite1395289673t_bool,type,
    finite1395289673t_bool: $i ).

thf(tp_finite1876863882t_bool,type,
    finite1876863882t_bool: $i ).

thf(tp_finite_card_int,type,
    finite_card_int: $i ).

thf(tp_finite_card_nat,type,
    finite_card_nat: $i ).

thf(tp_finite_finite_int,type,
    finite_finite_int: $i ).

thf(tp_finite_finite_nat,type,
    finite_finite_nat: $i ).

thf(tp_frac,type,
    frac: $i ).

thf(tp_fract,type,
    fract: $i ).

thf(tp_frct,type,
    frct: $i > $i ).

thf(tp_gcd_gcd_int,type,
    gcd_gcd_int: $i ).

thf(tp_gcd_gcd_nat,type,
    gcd_gcd_nat: $i ).

thf(tp_hAPP_C10902773l_bool,type,
    hAPP_C10902773l_bool: $i > $i > $i ).

thf(tp_hAPP_C1594335432umeral,type,
    hAPP_C1594335432umeral: $i > $i > $i ).

thf(tp_hAPP_C1614127039umeral,type,
    hAPP_C1614127039umeral: $i > $i > $i ).

thf(tp_hAPP_C2129356693al_nat,type,
    hAPP_C2129356693al_nat: $i > $i > $i ).

thf(tp_hAPP_C2132160860umeral,type,
    hAPP_C2132160860umeral: $i > $i > $i ).

thf(tp_hAPP_C24501650l_bool,type,
    hAPP_C24501650l_bool: $i > $i > $i ).

thf(tp_hAPP_C471253896umeral,type,
    hAPP_C471253896umeral: $i > $i > $i ).

thf(tp_hAPP_C498520661umeral,type,
    hAPP_C498520661umeral: $i > $i > $i ).

thf(tp_hAPP_P1062890741l_bool,type,
    hAPP_P1062890741l_bool: $i > $i > $i ).

thf(tp_hAPP_P1145851913nt_int,type,
    hAPP_P1145851913nt_int: $i > $i > $i ).

thf(tp_hAPP_P1175774780nt_int,type,
    hAPP_P1175774780nt_int: $i > $i > $i ).

thf(tp_hAPP_P1333854989l_bool,type,
    hAPP_P1333854989l_bool: $i > $i > $i ).

thf(tp_hAPP_P1400155668t_bool,type,
    hAPP_P1400155668t_bool: $i > $i > $i ).

thf(tp_hAPP_P1463840893t_bool,type,
    hAPP_P1463840893t_bool: $i > $i > $i ).

thf(tp_hAPP_P1555980039t_bool,type,
    hAPP_P1555980039t_bool: $i > $i > $i ).

thf(tp_hAPP_P1586233937at_nat,type,
    hAPP_P1586233937at_nat: $i > $i > $i ).

thf(tp_hAPP_P1654798560at_nat,type,
    hAPP_P1654798560at_nat: $i > $i > $i ).

thf(tp_hAPP_P1668131738nt_int,type,
    hAPP_P1668131738nt_int: $i > $i > $i ).

thf(tp_hAPP_P1681069257l_bool,type,
    hAPP_P1681069257l_bool: $i > $i > $i ).

thf(tp_hAPP_P1853363688nt_rat,type,
    hAPP_P1853363688nt_rat: $i > $i > $i ).

thf(tp_hAPP_P1860904029l_real,type,
    hAPP_P1860904029l_real: $i > $i > $i ).

thf(tp_hAPP_P1876494581l_bool,type,
    hAPP_P1876494581l_bool: $i > $i > $i ).

thf(tp_hAPP_P1975530577nt_int,type,
    hAPP_P1975530577nt_int: $i > $i > $i ).

thf(tp_hAPP_P1982799375l_real,type,
    hAPP_P1982799375l_real: $i > $i > $i ).

thf(tp_hAPP_P2053772734t_bool,type,
    hAPP_P2053772734t_bool: $i > $i > $i ).

thf(tp_hAPP_P2110489235nt_int,type,
    hAPP_P2110489235nt_int: $i > $i > $i ).

thf(tp_hAPP_P230595783nt_int,type,
    hAPP_P230595783nt_int: $i > $i > $i ).

thf(tp_hAPP_P252494982t_bool,type,
    hAPP_P252494982t_bool: $i > $i > $i ).

thf(tp_hAPP_P369611207at_nat,type,
    hAPP_P369611207at_nat: $i > $i > $i ).

thf(tp_hAPP_P402336767at_nat,type,
    hAPP_P402336767at_nat: $i > $i > $i ).

thf(tp_hAPP_P408881810nt_int,type,
    hAPP_P408881810nt_int: $i > $i > $i ).

thf(tp_hAPP_P507092031nt_rat,type,
    hAPP_P507092031nt_rat: $i > $i > $i ).

thf(tp_hAPP_P603027463t_bool,type,
    hAPP_P603027463t_bool: $i > $i > $i ).

thf(tp_hAPP_P621635040nt_int,type,
    hAPP_P621635040nt_int: $i > $i > $i ).

thf(tp_hAPP_P62333565t_bool,type,
    hAPP_P62333565t_bool: $i > $i > $i ).

thf(tp_hAPP_P731461727l_real,type,
    hAPP_P731461727l_real: $i > $i > $i ).

thf(tp_hAPP_P752050971nt_int,type,
    hAPP_P752050971nt_int: $i > $i > $i ).

thf(tp_hAPP_P877703507t_bool,type,
    hAPP_P877703507t_bool: $i > $i > $i ).

thf(tp_hAPP_P880235623l_bool,type,
    hAPP_P880235623l_bool: $i > $i > $i ).

thf(tp_hAPP_P921862901l_bool,type,
    hAPP_P921862901l_bool: $i > $i > $i ).

thf(tp_hAPP_P941956607nt_int,type,
    hAPP_P941956607nt_int: $i > $i > $i ).

thf(tp_hAPP_P989584703t_bool,type,
    hAPP_P989584703t_bool: $i > $i > $i ).

thf(tp_hAPP_Q1010094925t_bool,type,
    hAPP_Q1010094925t_bool: $i > $i > $i ).

thf(tp_hAPP_Q1256397320de_int,type,
    hAPP_Q1256397320de_int: $i > $i > $i ).

thf(tp_hAPP_Q125967240de_int,type,
    hAPP_Q125967240de_int: $i > $i > $i ).

thf(tp_hAPP_Q1729056540de_int,type,
    hAPP_Q1729056540de_int: $i > $i > $i ).

thf(tp_hAPP_Q1762011733de_int,type,
    hAPP_Q1762011733de_int: $i > $i > $i ).

thf(tp_hAPP_Q2096512830t_bool,type,
    hAPP_Q2096512830t_bool: $i > $i > $i ).

thf(tp_hAPP_Q952608535de_int,type,
    hAPP_Q952608535de_int: $i > $i > $i ).

thf(tp_hAPP_b1463609396nt_int,type,
    hAPP_b1463609396nt_int: $i > $i > $i ).

thf(tp_hAPP_b1482221219l_real,type,
    hAPP_b1482221219l_real: $i > $i > $i ).

thf(tp_hAPP_b40753821nt_int,type,
    hAPP_b40753821nt_int: $i > $i > $i ).

thf(tp_hAPP_b589554111l_bool,type,
    hAPP_b589554111l_bool: $i > $i > $i ).

thf(tp_hAPP_b646336293l_real,type,
    hAPP_b646336293l_real: $i > $i > $i ).

thf(tp_hAPP_b992065680at_nat,type,
    hAPP_b992065680at_nat: $i > $i > $i ).

thf(tp_hAPP_bool_bool,type,
    hAPP_bool_bool: $i > $i > $i ).

thf(tp_hAPP_c1088319240omplex,type,
    hAPP_c1088319240omplex: $i > $i > $i ).

thf(tp_hAPP_c1403687985x_bool,type,
    hAPP_c1403687985x_bool: $i > $i > $i ).

thf(tp_hAPP_c172932010omplex,type,
    hAPP_c172932010omplex: $i > $i > $i ).

thf(tp_hAPP_complex_bool,type,
    hAPP_complex_bool: $i > $i > $i ).

thf(tp_hAPP_complex_complex,type,
    hAPP_complex_complex: $i > $i > $i ).

thf(tp_hAPP_complex_nat,type,
    hAPP_complex_nat: $i > $i > $i ).

thf(tp_hAPP_complex_real,type,
    hAPP_complex_real: $i > $i > $i ).

thf(tp_hAPP_f1010710745l_bool,type,
    hAPP_f1010710745l_bool: $i > $i > $i ).

thf(tp_hAPP_f101635158l_bool,type,
    hAPP_f101635158l_bool: $i > $i > $i ).

thf(tp_hAPP_f103356543l_bool,type,
    hAPP_f103356543l_bool: $i > $i > $i ).

thf(tp_hAPP_f1038672605nt_int,type,
    hAPP_f1038672605nt_int: $i > $i > $i ).

thf(tp_hAPP_f1040184293l_real,type,
    hAPP_f1040184293l_real: $i > $i > $i ).

thf(tp_hAPP_f1048215610t_bool,type,
    hAPP_f1048215610t_bool: $i > $i > $i ).

thf(tp_hAPP_f1052840010omplex,type,
    hAPP_f1052840010omplex: $i > $i > $i ).

thf(tp_hAPP_f1063001928t_bool,type,
    hAPP_f1063001928t_bool: $i > $i > $i ).

thf(tp_hAPP_f1065357839nt_rat,type,
    hAPP_f1065357839nt_rat: $i > $i > $i ).

thf(tp_hAPP_f1067681227l_real,type,
    hAPP_f1067681227l_real: $i > $i > $i ).

thf(tp_hAPP_f1073644437at_rat,type,
    hAPP_f1073644437at_rat: $i > $i > $i ).

thf(tp_hAPP_f1076489843l_real,type,
    hAPP_f1076489843l_real: $i > $i > $i ).

thf(tp_hAPP_f1080886329l_bool,type,
    hAPP_f1080886329l_bool: $i > $i > $i ).

thf(tp_hAPP_f1081447804nt_int,type,
    hAPP_f1081447804nt_int: $i > $i > $i ).

thf(tp_hAPP_f1082758869at_rat,type,
    hAPP_f1082758869at_rat: $i > $i > $i ).

thf(tp_hAPP_f1083049571t_bool,type,
    hAPP_f1083049571t_bool: $i > $i > $i ).

thf(tp_hAPP_f1084724746t_bool,type,
    hAPP_f1084724746t_bool: $i > $i > $i ).

thf(tp_hAPP_f1092742621l_real,type,
    hAPP_f1092742621l_real: $i > $i > $i ).

thf(tp_hAPP_f1108539711l_real,type,
    hAPP_f1108539711l_real: $i > $i > $i ).

thf(tp_hAPP_f1109256153l_real,type,
    hAPP_f1109256153l_real: $i > $i > $i ).

thf(tp_hAPP_f11151005nt_int,type,
    hAPP_f11151005nt_int: $i > $i > $i ).

thf(tp_hAPP_f1115375056t_bool,type,
    hAPP_f1115375056t_bool: $i > $i > $i ).

thf(tp_hAPP_f1119546819l_real,type,
    hAPP_f1119546819l_real: $i > $i > $i ).

thf(tp_hAPP_f1120137083nt_rat,type,
    hAPP_f1120137083nt_rat: $i > $i > $i ).

thf(tp_hAPP_f1121609875t_bool,type,
    hAPP_f1121609875t_bool: $i > $i > $i ).

thf(tp_hAPP_f1122023986l_real,type,
    hAPP_f1122023986l_real: $i > $i > $i ).

thf(tp_hAPP_f1129044203l_real,type,
    hAPP_f1129044203l_real: $i > $i > $i ).

thf(tp_hAPP_f1131305186at_rat,type,
    hAPP_f1131305186at_rat: $i > $i > $i ).

thf(tp_hAPP_f1131424617t_bool,type,
    hAPP_f1131424617t_bool: $i > $i > $i ).

thf(tp_hAPP_f1135648319t_real,type,
    hAPP_f1135648319t_real: $i > $i > $i ).

thf(tp_hAPP_f1139079189at_int,type,
    hAPP_f1139079189at_int: $i > $i > $i ).

thf(tp_hAPP_f1146629647l_bool,type,
    hAPP_f1146629647l_bool: $i > $i > $i ).

thf(tp_hAPP_f1148171384nt_int,type,
    hAPP_f1148171384nt_int: $i > $i > $i ).

thf(tp_hAPP_f1151807883nt_int,type,
    hAPP_f1151807883nt_int: $i > $i > $i ).

thf(tp_hAPP_f1154658180t_bool,type,
    hAPP_f1154658180t_bool: $i > $i > $i ).

thf(tp_hAPP_f115998247l_bool,type,
    hAPP_f115998247l_bool: $i > $i > $i ).

thf(tp_hAPP_f1161935955l_real,type,
    hAPP_f1161935955l_real: $i > $i > $i ).

thf(tp_hAPP_f1163894827t_real,type,
    hAPP_f1163894827t_real: $i > $i > $i ).

thf(tp_hAPP_f1169087445t_real,type,
    hAPP_f1169087445t_real: $i > $i > $i ).

thf(tp_hAPP_f11709033t_bool,type,
    hAPP_f11709033t_bool: $i > $i > $i ).

thf(tp_hAPP_f1173902867t_bool,type,
    hAPP_f1173902867t_bool: $i > $i > $i ).

thf(tp_hAPP_f1177545951t_bool,type,
    hAPP_f1177545951t_bool: $i > $i > $i ).

thf(tp_hAPP_f1182713365t_bool,type,
    hAPP_f1182713365t_bool: $i > $i > $i ).

thf(tp_hAPP_f1187443546t_bool,type,
    hAPP_f1187443546t_bool: $i > $i > $i ).

thf(tp_hAPP_f1198736473t_bool,type,
    hAPP_f1198736473t_bool: $i > $i > $i ).

thf(tp_hAPP_f1222178131t_bool,type,
    hAPP_f1222178131t_bool: $i > $i > $i ).

thf(tp_hAPP_f1228585167nt_int,type,
    hAPP_f1228585167nt_int: $i > $i > $i ).

thf(tp_hAPP_f1241350704t_bool,type,
    hAPP_f1241350704t_bool: $i > $i > $i ).

thf(tp_hAPP_f1251097615t_bool,type,
    hAPP_f1251097615t_bool: $i > $i > $i ).

thf(tp_hAPP_f125788821nt_int,type,
    hAPP_f125788821nt_int: $i > $i > $i ).

thf(tp_hAPP_f125837377t_bool,type,
    hAPP_f125837377t_bool: $i > $i > $i ).

thf(tp_hAPP_f1261108921t_bool,type,
    hAPP_f1261108921t_bool: $i > $i > $i ).

thf(tp_hAPP_f1270196437nt_rat,type,
    hAPP_f1270196437nt_rat: $i > $i > $i ).

thf(tp_hAPP_f1273270095t_bool,type,
    hAPP_f1273270095t_bool: $i > $i > $i ).

thf(tp_hAPP_f1290670424t_real,type,
    hAPP_f1290670424t_real: $i > $i > $i ).

thf(tp_hAPP_f1293550189l_real,type,
    hAPP_f1293550189l_real: $i > $i > $i ).

thf(tp_hAPP_f1295083291t_real,type,
    hAPP_f1295083291t_real: $i > $i > $i ).

thf(tp_hAPP_f1310479593l_real,type,
    hAPP_f1310479593l_real: $i > $i > $i ).

thf(tp_hAPP_f1311564564nt_int,type,
    hAPP_f1311564564nt_int: $i > $i > $i ).

thf(tp_hAPP_f1315737299t_bool,type,
    hAPP_f1315737299t_bool: $i > $i > $i ).

thf(tp_hAPP_f1323932638t_real,type,
    hAPP_f1323932638t_real: $i > $i > $i ).

thf(tp_hAPP_f1325804733t_bool,type,
    hAPP_f1325804733t_bool: $i > $i > $i ).

thf(tp_hAPP_f1341793266t_bool,type,
    hAPP_f1341793266t_bool: $i > $i > $i ).

thf(tp_hAPP_f134192053t_real,type,
    hAPP_f134192053t_real: $i > $i > $i ).

thf(tp_hAPP_f1344929775l_bool,type,
    hAPP_f1344929775l_bool: $i > $i > $i ).

thf(tp_hAPP_f1352333353l_real,type,
    hAPP_f1352333353l_real: $i > $i > $i ).

thf(tp_hAPP_f1356864277nt_int,type,
    hAPP_f1356864277nt_int: $i > $i > $i ).

thf(tp_hAPP_f1361476881t_bool,type,
    hAPP_f1361476881t_bool: $i > $i > $i ).

thf(tp_hAPP_f1375227553nt_int,type,
    hAPP_f1375227553nt_int: $i > $i > $i ).

thf(tp_hAPP_f1377453843nt_int,type,
    hAPP_f1377453843nt_int: $i > $i > $i ).

thf(tp_hAPP_f1393328161l_bool,type,
    hAPP_f1393328161l_bool: $i > $i > $i ).

thf(tp_hAPP_f1399575567t_bool,type,
    hAPP_f1399575567t_bool: $i > $i > $i ).

thf(tp_hAPP_f1402056515l_bool,type,
    hAPP_f1402056515l_bool: $i > $i > $i ).

thf(tp_hAPP_f1406902706l_real,type,
    hAPP_f1406902706l_real: $i > $i > $i ).

thf(tp_hAPP_f1407095736t_real,type,
    hAPP_f1407095736t_real: $i > $i > $i ).

thf(tp_hAPP_f1408247010at_nat,type,
    hAPP_f1408247010at_nat: $i > $i > $i ).

thf(tp_hAPP_f1418982953t_bool,type,
    hAPP_f1418982953t_bool: $i > $i > $i ).

thf(tp_hAPP_f142232355nt_int,type,
    hAPP_f142232355nt_int: $i > $i > $i ).

thf(tp_hAPP_f1431025877at_int,type,
    hAPP_f1431025877at_int: $i > $i > $i ).

thf(tp_hAPP_f1448486952t_bool,type,
    hAPP_f1448486952t_bool: $i > $i > $i ).

thf(tp_hAPP_f1456711209t_bool,type,
    hAPP_f1456711209t_bool: $i > $i > $i ).

thf(tp_hAPP_f1457396693omplex,type,
    hAPP_f1457396693omplex: $i > $i > $i ).

thf(tp_hAPP_f1459420095t_bool,type,
    hAPP_f1459420095t_bool: $i > $i > $i ).

thf(tp_hAPP_f1469637905l_bool,type,
    hAPP_f1469637905l_bool: $i > $i > $i ).

thf(tp_hAPP_f1475822739t_bool,type,
    hAPP_f1475822739t_bool: $i > $i > $i ).

thf(tp_hAPP_f1480506641t_bool,type,
    hAPP_f1480506641t_bool: $i > $i > $i ).

thf(tp_hAPP_f1485493409l_bool,type,
    hAPP_f1485493409l_bool: $i > $i > $i ).

thf(tp_hAPP_f1501066425l_bool,type,
    hAPP_f1501066425l_bool: $i > $i > $i ).

thf(tp_hAPP_f1501741374t_real,type,
    hAPP_f1501741374t_real: $i > $i > $i ).

thf(tp_hAPP_f1505651103t_bool,type,
    hAPP_f1505651103t_bool: $i > $i > $i ).

thf(tp_hAPP_f1509287679l_real,type,
    hAPP_f1509287679l_real: $i > $i > $i ).

thf(tp_hAPP_f151095827nt_int,type,
    hAPP_f151095827nt_int: $i > $i > $i ).

thf(tp_hAPP_f1512942609t_bool,type,
    hAPP_f1512942609t_bool: $i > $i > $i ).

thf(tp_hAPP_f1523861863l_real,type,
    hAPP_f1523861863l_real: $i > $i > $i ).

thf(tp_hAPP_f1545556668t_bool,type,
    hAPP_f1545556668t_bool: $i > $i > $i ).

thf(tp_hAPP_f1547007718nt_rat,type,
    hAPP_f1547007718nt_rat: $i > $i > $i ).

thf(tp_hAPP_f1566856189t_real,type,
    hAPP_f1566856189t_real: $i > $i > $i ).

thf(tp_hAPP_f1574055885nt_int,type,
    hAPP_f1574055885nt_int: $i > $i > $i ).

thf(tp_hAPP_f1576199059t_bool,type,
    hAPP_f1576199059t_bool: $i > $i > $i ).

thf(tp_hAPP_f1582586579nt_int,type,
    hAPP_f1582586579nt_int: $i > $i > $i ).

thf(tp_hAPP_f1585078997at_nat,type,
    hAPP_f1585078997at_nat: $i > $i > $i ).

thf(tp_hAPP_f1591894897l_real,type,
    hAPP_f1591894897l_real: $i > $i > $i ).

thf(tp_hAPP_f1594865479ol_int,type,
    hAPP_f1594865479ol_int: $i > $i > $i ).

thf(tp_hAPP_f1599440987ol_int,type,
    hAPP_f1599440987ol_int: $i > $i > $i ).

thf(tp_hAPP_f1607377819t_real,type,
    hAPP_f1607377819t_real: $i > $i > $i ).

thf(tp_hAPP_f1607917947l_real,type,
    hAPP_f1607917947l_real: $i > $i > $i ).

thf(tp_hAPP_f1613846310t_real,type,
    hAPP_f1613846310t_real: $i > $i > $i ).

thf(tp_hAPP_f1625314454t_bool,type,
    hAPP_f1625314454t_bool: $i > $i > $i ).

thf(tp_hAPP_f1629352853nt_int,type,
    hAPP_f1629352853nt_int: $i > $i > $i ).

thf(tp_hAPP_f1639111240at_nat,type,
    hAPP_f1639111240at_nat: $i > $i > $i ).

thf(tp_hAPP_f1644353557l_real,type,
    hAPP_f1644353557l_real: $i > $i > $i ).

thf(tp_hAPP_f1646117269omplex,type,
    hAPP_f1646117269omplex: $i > $i > $i ).

thf(tp_hAPP_f1663701695l_real,type,
    hAPP_f1663701695l_real: $i > $i > $i ).

thf(tp_hAPP_f1673103573at_int,type,
    hAPP_f1673103573at_int: $i > $i > $i ).

thf(tp_hAPP_f1676298106t_real,type,
    hAPP_f1676298106t_real: $i > $i > $i ).

thf(tp_hAPP_f167782601nt_int,type,
    hAPP_f167782601nt_int: $i > $i > $i ).

thf(tp_hAPP_f1690286043t_real,type,
    hAPP_f1690286043t_real: $i > $i > $i ).

thf(tp_hAPP_f1720068861t_real,type,
    hAPP_f1720068861t_real: $i > $i > $i ).

thf(tp_hAPP_f1722879237t_bool,type,
    hAPP_f1722879237t_bool: $i > $i > $i ).

thf(tp_hAPP_f172451459l_bool,type,
    hAPP_f172451459l_bool: $i > $i > $i ).

thf(tp_hAPP_f1730463541l_real,type,
    hAPP_f1730463541l_real: $i > $i > $i ).

thf(tp_hAPP_f1731308757nt_int,type,
    hAPP_f1731308757nt_int: $i > $i > $i ).

thf(tp_hAPP_f1731313045at_nat,type,
    hAPP_f1731313045at_nat: $i > $i > $i ).

thf(tp_hAPP_f1732848529l_real,type,
    hAPP_f1732848529l_real: $i > $i > $i ).

thf(tp_hAPP_f1734373249l_bool,type,
    hAPP_f1734373249l_bool: $i > $i > $i ).

thf(tp_hAPP_f1735705551nt_int,type,
    hAPP_f1735705551nt_int: $i > $i > $i ).

thf(tp_hAPP_f1736103445l_real,type,
    hAPP_f1736103445l_real: $i > $i > $i ).

thf(tp_hAPP_f1760145644nt_int,type,
    hAPP_f1760145644nt_int: $i > $i > $i ).

thf(tp_hAPP_f1763467369l_real,type,
    hAPP_f1763467369l_real: $i > $i > $i ).

thf(tp_hAPP_f1769710159nt_int,type,
    hAPP_f1769710159nt_int: $i > $i > $i ).

thf(tp_hAPP_f1781059817t_bool,type,
    hAPP_f1781059817t_bool: $i > $i > $i ).

thf(tp_hAPP_f1786887945l_real,type,
    hAPP_f1786887945l_real: $i > $i > $i ).

thf(tp_hAPP_f1791153283t_bool,type,
    hAPP_f1791153283t_bool: $i > $i > $i ).

thf(tp_hAPP_f1796904975t_real,type,
    hAPP_f1796904975t_real: $i > $i > $i ).

thf(tp_hAPP_f1805168059t_bool,type,
    hAPP_f1805168059t_bool: $i > $i > $i ).

thf(tp_hAPP_f1815301987t_bool,type,
    hAPP_f1815301987t_bool: $i > $i > $i ).

thf(tp_hAPP_f1830214065l_bool,type,
    hAPP_f1830214065l_bool: $i > $i > $i ).

thf(tp_hAPP_f1830834240at_rat,type,
    hAPP_f1830834240at_rat: $i > $i > $i ).

thf(tp_hAPP_f1832844496t_bool,type,
    hAPP_f1832844496t_bool: $i > $i > $i ).

thf(tp_hAPP_f183342685l_real,type,
    hAPP_f183342685l_real: $i > $i > $i ).

thf(tp_hAPP_f1840085295t_bool,type,
    hAPP_f1840085295t_bool: $i > $i > $i ).

thf(tp_hAPP_f1845081853t_bool,type,
    hAPP_f1845081853t_bool: $i > $i > $i ).

thf(tp_hAPP_f1855025978nt_int,type,
    hAPP_f1855025978nt_int: $i > $i > $i ).

thf(tp_hAPP_f1861673493l_bool,type,
    hAPP_f1861673493l_bool: $i > $i > $i ).

thf(tp_hAPP_f1874145443l_real,type,
    hAPP_f1874145443l_real: $i > $i > $i ).

thf(tp_hAPP_f1878066172t_bool,type,
    hAPP_f1878066172t_bool: $i > $i > $i ).

thf(tp_hAPP_f1879982819l_real,type,
    hAPP_f1879982819l_real: $i > $i > $i ).

thf(tp_hAPP_f1884005689l_bool,type,
    hAPP_f1884005689l_bool: $i > $i > $i ).

thf(tp_hAPP_f1888375463t_real,type,
    hAPP_f1888375463t_real: $i > $i > $i ).

thf(tp_hAPP_f1900646853l_bool,type,
    hAPP_f1900646853l_bool: $i > $i > $i ).

thf(tp_hAPP_f1900950721nt_rat,type,
    hAPP_f1900950721nt_rat: $i > $i > $i ).

thf(tp_hAPP_f1902329768t_bool,type,
    hAPP_f1902329768t_bool: $i > $i > $i ).

thf(tp_hAPP_f1904307534l_real,type,
    hAPP_f1904307534l_real: $i > $i > $i ).

thf(tp_hAPP_f1908301369l_real,type,
    hAPP_f1908301369l_real: $i > $i > $i ).

thf(tp_hAPP_f1914742907nt_int,type,
    hAPP_f1914742907nt_int: $i > $i > $i ).

thf(tp_hAPP_f1914919701at_nat,type,
    hAPP_f1914919701at_nat: $i > $i > $i ).

thf(tp_hAPP_f1920544743t_bool,type,
    hAPP_f1920544743t_bool: $i > $i > $i ).

thf(tp_hAPP_f1925507189l_bool,type,
    hAPP_f1925507189l_bool: $i > $i > $i ).

thf(tp_hAPP_f1926459811ol_int,type,
    hAPP_f1926459811ol_int: $i > $i > $i ).

thf(tp_hAPP_f1927674023t_bool,type,
    hAPP_f1927674023t_bool: $i > $i > $i ).

thf(tp_hAPP_f1935805932nt_int,type,
    hAPP_f1935805932nt_int: $i > $i > $i ).

thf(tp_hAPP_f1950183573l_real,type,
    hAPP_f1950183573l_real: $i > $i > $i ).

thf(tp_hAPP_f1960414057l_real,type,
    hAPP_f1960414057l_real: $i > $i > $i ).

thf(tp_hAPP_f1961001761l_bool,type,
    hAPP_f1961001761l_bool: $i > $i > $i ).

thf(tp_hAPP_f1965248563t_bool,type,
    hAPP_f1965248563t_bool: $i > $i > $i ).

thf(tp_hAPP_f197615720t_real,type,
    hAPP_f197615720t_real: $i > $i > $i ).

thf(tp_hAPP_f197974549nt_int,type,
    hAPP_f197974549nt_int: $i > $i > $i ).

thf(tp_hAPP_f1990636069t_bool,type,
    hAPP_f1990636069t_bool: $i > $i > $i ).

thf(tp_hAPP_f1992866895l_real,type,
    hAPP_f1992866895l_real: $i > $i > $i ).

thf(tp_hAPP_f1993765077t_real,type,
    hAPP_f1993765077t_real: $i > $i > $i ).

thf(tp_hAPP_f1998755145t_real,type,
    hAPP_f1998755145t_real: $i > $i > $i ).

thf(tp_hAPP_f2002277285nt_int,type,
    hAPP_f2002277285nt_int: $i > $i > $i ).

thf(tp_hAPP_f2004554147nt_int,type,
    hAPP_f2004554147nt_int: $i > $i > $i ).

thf(tp_hAPP_f2018027565t_bool,type,
    hAPP_f2018027565t_bool: $i > $i > $i ).

thf(tp_hAPP_f202917053t_bool,type,
    hAPP_f202917053t_bool: $i > $i > $i ).

thf(tp_hAPP_f203520653l_real,type,
    hAPP_f203520653l_real: $i > $i > $i ).

thf(tp_hAPP_f2037783381l_bool,type,
    hAPP_f2037783381l_bool: $i > $i > $i ).

thf(tp_hAPP_f2042071795t_bool,type,
    hAPP_f2042071795t_bool: $i > $i > $i ).

thf(tp_hAPP_f2050994651t_bool,type,
    hAPP_f2050994651t_bool: $i > $i > $i ).

thf(tp_hAPP_f2054677283nt_int,type,
    hAPP_f2054677283nt_int: $i > $i > $i ).

thf(tp_hAPP_f2062659861at_rat,type,
    hAPP_f2062659861at_rat: $i > $i > $i ).

thf(tp_hAPP_f2069516469l_real,type,
    hAPP_f2069516469l_real: $i > $i > $i ).

thf(tp_hAPP_f2072293513l_real,type,
    hAPP_f2072293513l_real: $i > $i > $i ).

thf(tp_hAPP_f2084827628t_bool,type,
    hAPP_f2084827628t_bool: $i > $i > $i ).

thf(tp_hAPP_f2094497995nt_int,type,
    hAPP_f2094497995nt_int: $i > $i > $i ).

thf(tp_hAPP_f2105620693nt_int,type,
    hAPP_f2105620693nt_int: $i > $i > $i ).

thf(tp_hAPP_f2114902373l_real,type,
    hAPP_f2114902373l_real: $i > $i > $i ).

thf(tp_hAPP_f2119584768l_real,type,
    hAPP_f2119584768l_real: $i > $i > $i ).

thf(tp_hAPP_f2119767738t_bool,type,
    hAPP_f2119767738t_bool: $i > $i > $i ).

thf(tp_hAPP_f212164053t_real,type,
    hAPP_f212164053t_real: $i > $i > $i ).

thf(tp_hAPP_f2126667875l_real,type,
    hAPP_f2126667875l_real: $i > $i > $i ).

thf(tp_hAPP_f213450978omplex,type,
    hAPP_f213450978omplex: $i > $i > $i ).

thf(tp_hAPP_f2135977429nt_int,type,
    hAPP_f2135977429nt_int: $i > $i > $i ).

thf(tp_hAPP_f2144054103l_bool,type,
    hAPP_f2144054103l_bool: $i > $i > $i ).

thf(tp_hAPP_f214467655t_bool,type,
    hAPP_f214467655t_bool: $i > $i > $i ).

thf(tp_hAPP_f215623910l_bool,type,
    hAPP_f215623910l_bool: $i > $i > $i ).

thf(tp_hAPP_f219720582omplex,type,
    hAPP_f219720582omplex: $i > $i > $i ).

thf(tp_hAPP_f22106695ol_nat,type,
    hAPP_f22106695ol_nat: $i > $i > $i ).

thf(tp_hAPP_f223623489t_bool,type,
    hAPP_f223623489t_bool: $i > $i > $i ).

thf(tp_hAPP_f224989205l_real,type,
    hAPP_f224989205l_real: $i > $i > $i ).

thf(tp_hAPP_f229349961t_bool,type,
    hAPP_f229349961t_bool: $i > $i > $i ).

thf(tp_hAPP_f237669397t_bool,type,
    hAPP_f237669397t_bool: $i > $i > $i ).

thf(tp_hAPP_f23851874omplex,type,
    hAPP_f23851874omplex: $i > $i > $i ).

thf(tp_hAPP_f248847589l_real,type,
    hAPP_f248847589l_real: $i > $i > $i ).

thf(tp_hAPP_f251264923nt_int,type,
    hAPP_f251264923nt_int: $i > $i > $i ).

thf(tp_hAPP_f252743847l_bool,type,
    hAPP_f252743847l_bool: $i > $i > $i ).

thf(tp_hAPP_f264196187l_real,type,
    hAPP_f264196187l_real: $i > $i > $i ).

thf(tp_hAPP_f269654879t_real,type,
    hAPP_f269654879t_real: $i > $i > $i ).

thf(tp_hAPP_f271976045t_bool,type,
    hAPP_f271976045t_bool: $i > $i > $i ).

thf(tp_hAPP_f279307923nt_int,type,
    hAPP_f279307923nt_int: $i > $i > $i ).

thf(tp_hAPP_f284875647l_bool,type,
    hAPP_f284875647l_bool: $i > $i > $i ).

thf(tp_hAPP_f289318786t_bool,type,
    hAPP_f289318786t_bool: $i > $i > $i ).

thf(tp_hAPP_f291087797t_bool,type,
    hAPP_f291087797t_bool: $i > $i > $i ).

thf(tp_hAPP_f292751352t_real,type,
    hAPP_f292751352t_real: $i > $i > $i ).

thf(tp_hAPP_f301246617nt_int,type,
    hAPP_f301246617nt_int: $i > $i > $i ).

thf(tp_hAPP_f318350629l_real,type,
    hAPP_f318350629l_real: $i > $i > $i ).

thf(tp_hAPP_f320596107l_real,type,
    hAPP_f320596107l_real: $i > $i > $i ).

thf(tp_hAPP_f324002831l_real,type,
    hAPP_f324002831l_real: $i > $i > $i ).

thf(tp_hAPP_f326728547t_bool,type,
    hAPP_f326728547t_bool: $i > $i > $i ).

thf(tp_hAPP_f327026105t_real,type,
    hAPP_f327026105t_real: $i > $i > $i ).

thf(tp_hAPP_f328572565l_real,type,
    hAPP_f328572565l_real: $i > $i > $i ).

thf(tp_hAPP_f330985925l_bool,type,
    hAPP_f330985925l_bool: $i > $i > $i ).

thf(tp_hAPP_f332806115t_bool,type,
    hAPP_f332806115t_bool: $i > $i > $i ).

thf(tp_hAPP_f334321603nt_int,type,
    hAPP_f334321603nt_int: $i > $i > $i ).

thf(tp_hAPP_f335634176l_real,type,
    hAPP_f335634176l_real: $i > $i > $i ).

thf(tp_hAPP_f340152631t_bool,type,
    hAPP_f340152631t_bool: $i > $i > $i ).

thf(tp_hAPP_f351634443t_bool,type,
    hAPP_f351634443t_bool: $i > $i > $i ).

thf(tp_hAPP_f352196356l_real,type,
    hAPP_f352196356l_real: $i > $i > $i ).

thf(tp_hAPP_f352226557t_real,type,
    hAPP_f352226557t_real: $i > $i > $i ).

thf(tp_hAPP_f365317245l_bool,type,
    hAPP_f365317245l_bool: $i > $i > $i ).

thf(tp_hAPP_f374502857t_bool,type,
    hAPP_f374502857t_bool: $i > $i > $i ).

thf(tp_hAPP_f381769257l_bool,type,
    hAPP_f381769257l_bool: $i > $i > $i ).

thf(tp_hAPP_f382317021nt_rat,type,
    hAPP_f382317021nt_rat: $i > $i > $i ).

thf(tp_hAPP_f389116883t_bool,type,
    hAPP_f389116883t_bool: $i > $i > $i ).

thf(tp_hAPP_f400200275nt_int,type,
    hAPP_f400200275nt_int: $i > $i > $i ).

thf(tp_hAPP_f400538607nt_int,type,
    hAPP_f400538607nt_int: $i > $i > $i ).

thf(tp_hAPP_f403082607t_bool,type,
    hAPP_f403082607t_bool: $i > $i > $i ).

thf(tp_hAPP_f406530075omplex,type,
    hAPP_f406530075omplex: $i > $i > $i ).

thf(tp_hAPP_f41603166t_bool,type,
    hAPP_f41603166t_bool: $i > $i > $i ).

thf(tp_hAPP_f416620757at_nat,type,
    hAPP_f416620757at_nat: $i > $i > $i ).

thf(tp_hAPP_f422375781t_bool,type,
    hAPP_f422375781t_bool: $i > $i > $i ).

thf(tp_hAPP_f42270917t_real,type,
    hAPP_f42270917t_real: $i > $i > $i ).

thf(tp_hAPP_f423804115t_bool,type,
    hAPP_f423804115t_bool: $i > $i > $i ).

thf(tp_hAPP_f428220345t_bool,type,
    hAPP_f428220345t_bool: $i > $i > $i ).

thf(tp_hAPP_f429384717t_bool,type,
    hAPP_f429384717t_bool: $i > $i > $i ).

thf(tp_hAPP_f429935748t_bool,type,
    hAPP_f429935748t_bool: $i > $i > $i ).

thf(tp_hAPP_f434654626nt_int,type,
    hAPP_f434654626nt_int: $i > $i > $i ).

thf(tp_hAPP_f448129468l_bool,type,
    hAPP_f448129468l_bool: $i > $i > $i ).

thf(tp_hAPP_f451358433l_real,type,
    hAPP_f451358433l_real: $i > $i > $i ).

thf(tp_hAPP_f461489489t_bool,type,
    hAPP_f461489489t_bool: $i > $i > $i ).

thf(tp_hAPP_f465821005nt_int,type,
    hAPP_f465821005nt_int: $i > $i > $i ).

thf(tp_hAPP_f472159229t_bool,type,
    hAPP_f472159229t_bool: $i > $i > $i ).

thf(tp_hAPP_f492612297t_bool,type,
    hAPP_f492612297t_bool: $i > $i > $i ).

thf(tp_hAPP_f499530369l_bool,type,
    hAPP_f499530369l_bool: $i > $i > $i ).

thf(tp_hAPP_f512004221l_bool,type,
    hAPP_f512004221l_bool: $i > $i > $i ).

thf(tp_hAPP_f513299955t_bool,type,
    hAPP_f513299955t_bool: $i > $i > $i ).

thf(tp_hAPP_f517738447l_real,type,
    hAPP_f517738447l_real: $i > $i > $i ).

thf(tp_hAPP_f521271395nt_int,type,
    hAPP_f521271395nt_int: $i > $i > $i ).

thf(tp_hAPP_f521865025ol_nat,type,
    hAPP_f521865025ol_nat: $i > $i > $i ).

thf(tp_hAPP_f526364711l_bool,type,
    hAPP_f526364711l_bool: $i > $i > $i ).

thf(tp_hAPP_f534361363nt_int,type,
    hAPP_f534361363nt_int: $i > $i > $i ).

thf(tp_hAPP_f538565589t_bool,type,
    hAPP_f538565589t_bool: $i > $i > $i ).

thf(tp_hAPP_f538843494t_bool,type,
    hAPP_f538843494t_bool: $i > $i > $i ).

thf(tp_hAPP_f54304608l_bool,type,
    hAPP_f54304608l_bool: $i > $i > $i ).

thf(tp_hAPP_f55007289nt_int,type,
    hAPP_f55007289nt_int: $i > $i > $i ).

thf(tp_hAPP_f555557763l_real,type,
    hAPP_f555557763l_real: $i > $i > $i ).

thf(tp_hAPP_f556082547l_real,type,
    hAPP_f556082547l_real: $i > $i > $i ).

thf(tp_hAPP_f561022312t_bool,type,
    hAPP_f561022312t_bool: $i > $i > $i ).

thf(tp_hAPP_f563293398t_real,type,
    hAPP_f563293398t_real: $i > $i > $i ).

thf(tp_hAPP_f571820015t_bool,type,
    hAPP_f571820015t_bool: $i > $i > $i ).

thf(tp_hAPP_f578362681nt_int,type,
    hAPP_f578362681nt_int: $i > $i > $i ).

thf(tp_hAPP_f59594445l_real,type,
    hAPP_f59594445l_real: $i > $i > $i ).

thf(tp_hAPP_f601898971t_bool,type,
    hAPP_f601898971t_bool: $i > $i > $i ).

thf(tp_hAPP_f605995867t_bool,type,
    hAPP_f605995867t_bool: $i > $i > $i ).

thf(tp_hAPP_f60716669l_bool,type,
    hAPP_f60716669l_bool: $i > $i > $i ).

thf(tp_hAPP_f617310012nt_int,type,
    hAPP_f617310012nt_int: $i > $i > $i ).

thf(tp_hAPP_f617735571l_real,type,
    hAPP_f617735571l_real: $i > $i > $i ).

thf(tp_hAPP_f618557131t_bool,type,
    hAPP_f618557131t_bool: $i > $i > $i ).

thf(tp_hAPP_f627970963t_bool,type,
    hAPP_f627970963t_bool: $i > $i > $i ).

thf(tp_hAPP_f628503027l_bool,type,
    hAPP_f628503027l_bool: $i > $i > $i ).

thf(tp_hAPP_f643658017l_bool,type,
    hAPP_f643658017l_bool: $i > $i > $i ).

thf(tp_hAPP_f644105375l_real,type,
    hAPP_f644105375l_real: $i > $i > $i ).

thf(tp_hAPP_f654702867t_bool,type,
    hAPP_f654702867t_bool: $i > $i > $i ).

thf(tp_hAPP_f659380387ol_int,type,
    hAPP_f659380387ol_int: $i > $i > $i ).

thf(tp_hAPP_f66927821l_bool,type,
    hAPP_f66927821l_bool: $i > $i > $i ).

thf(tp_hAPP_f677014621l_real,type,
    hAPP_f677014621l_real: $i > $i > $i ).

thf(tp_hAPP_f693283245t_bool,type,
    hAPP_f693283245t_bool: $i > $i > $i ).

thf(tp_hAPP_f695504873l_bool,type,
    hAPP_f695504873l_bool: $i > $i > $i ).

thf(tp_hAPP_f696844121t_bool,type,
    hAPP_f696844121t_bool: $i > $i > $i ).

thf(tp_hAPP_f704188951t_bool,type,
    hAPP_f704188951t_bool: $i > $i > $i ).

thf(tp_hAPP_f713949180nt_int,type,
    hAPP_f713949180nt_int: $i > $i > $i ).

thf(tp_hAPP_f720654810t_bool,type,
    hAPP_f720654810t_bool: $i > $i > $i ).

thf(tp_hAPP_f725770969t_bool,type,
    hAPP_f725770969t_bool: $i > $i > $i ).

thf(tp_hAPP_f727283836t_bool,type,
    hAPP_f727283836t_bool: $i > $i > $i ).

thf(tp_hAPP_f729588221t_bool,type,
    hAPP_f729588221t_bool: $i > $i > $i ).

thf(tp_hAPP_f735247205t_bool,type,
    hAPP_f735247205t_bool: $i > $i > $i ).

thf(tp_hAPP_f73570213t_real,type,
    hAPP_f73570213t_real: $i > $i > $i ).

thf(tp_hAPP_f737665877t_bool,type,
    hAPP_f737665877t_bool: $i > $i > $i ).

thf(tp_hAPP_f74147283t_real,type,
    hAPP_f74147283t_real: $i > $i > $i ).

thf(tp_hAPP_f743790483t_bool,type,
    hAPP_f743790483t_bool: $i > $i > $i ).

thf(tp_hAPP_f747162069nt_int,type,
    hAPP_f747162069nt_int: $i > $i > $i ).

thf(tp_hAPP_f747475781nt_int,type,
    hAPP_f747475781nt_int: $i > $i > $i ).

thf(tp_hAPP_f766218899t_real,type,
    hAPP_f766218899t_real: $i > $i > $i ).

thf(tp_hAPP_f77155443t_bool,type,
    hAPP_f77155443t_bool: $i > $i > $i ).

thf(tp_hAPP_f774948957l_real,type,
    hAPP_f774948957l_real: $i > $i > $i ).

thf(tp_hAPP_f782000547ol_nat,type,
    hAPP_f782000547ol_nat: $i > $i > $i ).

thf(tp_hAPP_f791698359t_bool,type,
    hAPP_f791698359t_bool: $i > $i > $i ).

thf(tp_hAPP_f800361423l_real,type,
    hAPP_f800361423l_real: $i > $i > $i ).

thf(tp_hAPP_f800510211t_bool,type,
    hAPP_f800510211t_bool: $i > $i > $i ).

thf(tp_hAPP_f801032407l_bool,type,
    hAPP_f801032407l_bool: $i > $i > $i ).

thf(tp_hAPP_f808647893nt_int,type,
    hAPP_f808647893nt_int: $i > $i > $i ).

thf(tp_hAPP_f823702159l_real,type,
    hAPP_f823702159l_real: $i > $i > $i ).

thf(tp_hAPP_f824790735l_bool,type,
    hAPP_f824790735l_bool: $i > $i > $i ).

thf(tp_hAPP_f834119977l_bool,type,
    hAPP_f834119977l_bool: $i > $i > $i ).

thf(tp_hAPP_f836602773nt_int,type,
    hAPP_f836602773nt_int: $i > $i > $i ).

thf(tp_hAPP_f837737749at_nat,type,
    hAPP_f837737749at_nat: $i > $i > $i ).

thf(tp_hAPP_f847817363t_bool,type,
    hAPP_f847817363t_bool: $i > $i > $i ).

thf(tp_hAPP_f848516149l_bool,type,
    hAPP_f848516149l_bool: $i > $i > $i ).

thf(tp_hAPP_f850851693l_real,type,
    hAPP_f850851693l_real: $i > $i > $i ).

thf(tp_hAPP_f85237525t_bool,type,
    hAPP_f85237525t_bool: $i > $i > $i ).

thf(tp_hAPP_f857296063t_bool,type,
    hAPP_f857296063t_bool: $i > $i > $i ).

thf(tp_hAPP_f866672739t_bool,type,
    hAPP_f866672739t_bool: $i > $i > $i ).

thf(tp_hAPP_f883232462nt_int,type,
    hAPP_f883232462nt_int: $i > $i > $i ).

thf(tp_hAPP_f888249301nt_int,type,
    hAPP_f888249301nt_int: $i > $i > $i ).

thf(tp_hAPP_f892584630t_bool,type,
    hAPP_f892584630t_bool: $i > $i > $i ).

thf(tp_hAPP_f894608603t_bool,type,
    hAPP_f894608603t_bool: $i > $i > $i ).

thf(tp_hAPP_f895854793t_real,type,
    hAPP_f895854793t_real: $i > $i > $i ).

thf(tp_hAPP_f908327869t_bool,type,
    hAPP_f908327869t_bool: $i > $i > $i ).

thf(tp_hAPP_f918606171t_real,type,
    hAPP_f918606171t_real: $i > $i > $i ).

thf(tp_hAPP_f93439879ol_nat,type,
    hAPP_f93439879ol_nat: $i > $i > $i ).

thf(tp_hAPP_f940061907l_bool,type,
    hAPP_f940061907l_bool: $i > $i > $i ).

thf(tp_hAPP_f956464319t_bool,type,
    hAPP_f956464319t_bool: $i > $i > $i ).

thf(tp_hAPP_f957591787ol_nat,type,
    hAPP_f957591787ol_nat: $i > $i > $i ).

thf(tp_hAPP_f960630521nt_int,type,
    hAPP_f960630521nt_int: $i > $i > $i ).

thf(tp_hAPP_f983569339t_bool,type,
    hAPP_f983569339t_bool: $i > $i > $i ).

thf(tp_hAPP_f999082675at_nat,type,
    hAPP_f999082675at_nat: $i > $i > $i ).

thf(tp_hAPP_i1153444985nt_int,type,
    hAPP_i1153444985nt_int: $i > $i > $i ).

thf(tp_hAPP_i119638232t_bool,type,
    hAPP_i119638232t_bool: $i > $i > $i ).

thf(tp_hAPP_i1216375074nt_int,type,
    hAPP_i1216375074nt_int: $i > $i > $i ).

thf(tp_hAPP_i1524277240nt_int,type,
    hAPP_i1524277240nt_int: $i > $i > $i ).

thf(tp_hAPP_i1529485324t_bool,type,
    hAPP_i1529485324t_bool: $i > $i > $i ).

thf(tp_hAPP_i157317923t_real,type,
    hAPP_i157317923t_real: $i > $i > $i ).

thf(tp_hAPP_i1584592887nt_int,type,
    hAPP_i1584592887nt_int: $i > $i > $i ).

thf(tp_hAPP_i16292313t_bool,type,
    hAPP_i16292313t_bool: $i > $i > $i ).

thf(tp_hAPP_i1671359920t_real,type,
    hAPP_i1671359920t_real: $i > $i > $i ).

thf(tp_hAPP_i1730167831nt_int,type,
    hAPP_i1730167831nt_int: $i > $i > $i ).

thf(tp_hAPP_i1732201573de_int,type,
    hAPP_i1732201573de_int: $i > $i > $i ).

thf(tp_hAPP_i1778081398nt_int,type,
    hAPP_i1778081398nt_int: $i > $i > $i ).

thf(tp_hAPP_i1796122964t_bool,type,
    hAPP_i1796122964t_bool: $i > $i > $i ).

thf(tp_hAPP_i1823918693l_bool,type,
    hAPP_i1823918693l_bool: $i > $i > $i ).

thf(tp_hAPP_i1836591008nt_int,type,
    hAPP_i1836591008nt_int: $i > $i > $i ).

thf(tp_hAPP_i1948725293t_bool,type,
    hAPP_i1948725293t_bool: $i > $i > $i ).

thf(tp_hAPP_i2104874254nt_int,type,
    hAPP_i2104874254nt_int: $i > $i > $i ).

thf(tp_hAPP_i2112223885l_bool,type,
    hAPP_i2112223885l_bool: $i > $i > $i ).

thf(tp_hAPP_i345030060t_bool,type,
    hAPP_i345030060t_bool: $i > $i > $i ).

thf(tp_hAPP_i371647666l_real,type,
    hAPP_i371647666l_real: $i > $i > $i ).

thf(tp_hAPP_i418383825t_bool,type,
    hAPP_i418383825t_bool: $i > $i > $i ).

thf(tp_hAPP_i447943416t_real,type,
    hAPP_i447943416t_real: $i > $i > $i ).

thf(tp_hAPP_i61245889nt_int,type,
    hAPP_i61245889nt_int: $i > $i > $i ).

thf(tp_hAPP_i614188481l_bool,type,
    hAPP_i614188481l_bool: $i > $i > $i ).

thf(tp_hAPP_i627165055t_real,type,
    hAPP_i627165055t_real: $i > $i > $i ).

thf(tp_hAPP_i68813070l_bool,type,
    hAPP_i68813070l_bool: $i > $i > $i ).

thf(tp_hAPP_i688218208l_bool,type,
    hAPP_i688218208l_bool: $i > $i > $i ).

thf(tp_hAPP_i744251628nt_int,type,
    hAPP_i744251628nt_int: $i > $i > $i ).

thf(tp_hAPP_i769753017umeral,type,
    hAPP_i769753017umeral: $i > $i > $i ).

thf(tp_hAPP_i872162435t_bool,type,
    hAPP_i872162435t_bool: $i > $i > $i ).

thf(tp_hAPP_i998473677nt_int,type,
    hAPP_i998473677nt_int: $i > $i > $i ).

thf(tp_hAPP_int_bool,type,
    hAPP_int_bool: $i > $i > $i ).

thf(tp_hAPP_int_complex,type,
    hAPP_int_complex: $i > $i > $i ).

thf(tp_hAPP_int_fun_int_int,type,
    hAPP_int_fun_int_int: $i > $i > $i ).

thf(tp_hAPP_int_fun_int_rat,type,
    hAPP_int_fun_int_rat: $i > $i > $i ).

thf(tp_hAPP_int_fun_nat_int,type,
    hAPP_int_fun_nat_int: $i > $i > $i ).

thf(tp_hAPP_int_int,type,
    hAPP_int_int: $i > $i > $i ).

thf(tp_hAPP_int_nat,type,
    hAPP_int_nat: $i > $i > $i ).

thf(tp_hAPP_int_rat,type,
    hAPP_int_rat: $i > $i > $i ).

thf(tp_hAPP_int_real,type,
    hAPP_int_real: $i > $i > $i ).

thf(tp_hAPP_list_int_nat,type,
    hAPP_list_int_nat: $i > $i > $i ).

thf(tp_hAPP_n1006566506l_bool,type,
    hAPP_n1006566506l_bool: $i > $i > $i ).

thf(tp_hAPP_n1108039445umeral,type,
    hAPP_n1108039445umeral: $i > $i > $i ).

thf(tp_hAPP_n1289843868at_nat,type,
    hAPP_n1289843868at_nat: $i > $i > $i ).

thf(tp_hAPP_n1699378549t_bool,type,
    hAPP_n1699378549t_bool: $i > $i > $i ).

thf(tp_hAPP_n1865633855at_nat,type,
    hAPP_n1865633855at_nat: $i > $i > $i ).

thf(tp_hAPP_n1983812447omplex,type,
    hAPP_n1983812447omplex: $i > $i > $i ).

thf(tp_hAPP_n215258509l_bool,type,
    hAPP_n215258509l_bool: $i > $i > $i ).

thf(tp_hAPP_n332733730l_real,type,
    hAPP_n332733730l_real: $i > $i > $i ).

thf(tp_hAPP_n522471361de_int,type,
    hAPP_n522471361de_int: $i > $i > $i ).

thf(tp_hAPP_n546711566l_real,type,
    hAPP_n546711566l_real: $i > $i > $i ).

thf(tp_hAPP_n682674106l_real,type,
    hAPP_n682674106l_real: $i > $i > $i ).

thf(tp_hAPP_nat_bool,type,
    hAPP_nat_bool: $i > $i > $i ).

thf(tp_hAPP_nat_complex,type,
    hAPP_nat_complex: $i > $i > $i ).

thf(tp_hAPP_nat_fun_int_int,type,
    hAPP_nat_fun_int_int: $i > $i > $i ).

thf(tp_hAPP_nat_fun_nat_nat,type,
    hAPP_nat_fun_nat_nat: $i > $i > $i ).

thf(tp_hAPP_nat_fun_rat_rat,type,
    hAPP_nat_fun_rat_rat: $i > $i > $i ).

thf(tp_hAPP_nat_int,type,
    hAPP_nat_int: $i > $i > $i ).

thf(tp_hAPP_nat_nat,type,
    hAPP_nat_nat: $i > $i > $i ).

thf(tp_hAPP_nat_rat,type,
    hAPP_nat_rat: $i > $i > $i ).

thf(tp_hAPP_nat_real,type,
    hAPP_nat_real: $i > $i > $i ).

thf(tp_hAPP_r1043989325l_real,type,
    hAPP_r1043989325l_real: $i > $i > $i ).

thf(tp_hAPP_r1130899993l_bool,type,
    hAPP_r1130899993l_bool: $i > $i > $i ).

thf(tp_hAPP_r1134773055l_bool,type,
    hAPP_r1134773055l_bool: $i > $i > $i ).

thf(tp_hAPP_r1150855451l_bool,type,
    hAPP_r1150855451l_bool: $i > $i > $i ).

thf(tp_hAPP_r1195171167l_real,type,
    hAPP_r1195171167l_real: $i > $i > $i ).

thf(tp_hAPP_r1230691443l_real,type,
    hAPP_r1230691443l_real: $i > $i > $i ).

thf(tp_hAPP_r1250527377l_real,type,
    hAPP_r1250527377l_real: $i > $i > $i ).

thf(tp_hAPP_r1392521531t_bool,type,
    hAPP_r1392521531t_bool: $i > $i > $i ).

thf(tp_hAPP_r1409264866l_real,type,
    hAPP_r1409264866l_real: $i > $i > $i ).

thf(tp_hAPP_r1562208522t_bool,type,
    hAPP_r1562208522t_bool: $i > $i > $i ).

thf(tp_hAPP_r1623423338t_bool,type,
    hAPP_r1623423338t_bool: $i > $i > $i ).

thf(tp_hAPP_r1900510169t_bool,type,
    hAPP_r1900510169t_bool: $i > $i > $i ).

thf(tp_hAPP_r1938957037l_bool,type,
    hAPP_r1938957037l_bool: $i > $i > $i ).

thf(tp_hAPP_r195310020l_real,type,
    hAPP_r195310020l_real: $i > $i > $i ).

thf(tp_hAPP_r1962736578t_bool,type,
    hAPP_r1962736578t_bool: $i > $i > $i ).

thf(tp_hAPP_r2019696015l_real,type,
    hAPP_r2019696015l_real: $i > $i > $i ).

thf(tp_hAPP_r2052264067t_bool,type,
    hAPP_r2052264067t_bool: $i > $i > $i ).

thf(tp_hAPP_r2115560837t_bool,type,
    hAPP_r2115560837t_bool: $i > $i > $i ).

thf(tp_hAPP_r224952523l_real,type,
    hAPP_r224952523l_real: $i > $i > $i ).

thf(tp_hAPP_r265291036omplex,type,
    hAPP_r265291036omplex: $i > $i > $i ).

thf(tp_hAPP_r279757445t_bool,type,
    hAPP_r279757445t_bool: $i > $i > $i ).

thf(tp_hAPP_r285062775l_bool,type,
    hAPP_r285062775l_bool: $i > $i > $i ).

thf(tp_hAPP_r337325687l_real,type,
    hAPP_r337325687l_real: $i > $i > $i ).

thf(tp_hAPP_r373117745t_bool,type,
    hAPP_r373117745t_bool: $i > $i > $i ).

thf(tp_hAPP_r474017924t_real,type,
    hAPP_r474017924t_real: $i > $i > $i ).

thf(tp_hAPP_r481142414t_bool,type,
    hAPP_r481142414t_bool: $i > $i > $i ).

thf(tp_hAPP_r50993370t_real,type,
    hAPP_r50993370t_real: $i > $i > $i ).

thf(tp_hAPP_r579619957l_real,type,
    hAPP_r579619957l_real: $i > $i > $i ).

thf(tp_hAPP_r632163725t_bool,type,
    hAPP_r632163725t_bool: $i > $i > $i ).

thf(tp_hAPP_r653725362t_bool,type,
    hAPP_r653725362t_bool: $i > $i > $i ).

thf(tp_hAPP_r712953929l_real,type,
    hAPP_r712953929l_real: $i > $i > $i ).

thf(tp_hAPP_r794344869l_real,type,
    hAPP_r794344869l_real: $i > $i > $i ).

thf(tp_hAPP_r847664445t_bool,type,
    hAPP_r847664445t_bool: $i > $i > $i ).

thf(tp_hAPP_r931665397l_real,type,
    hAPP_r931665397l_real: $i > $i > $i ).

thf(tp_hAPP_r938550413l_real,type,
    hAPP_r938550413l_real: $i > $i > $i ).

thf(tp_hAPP_rat_bool,type,
    hAPP_rat_bool: $i > $i > $i ).

thf(tp_hAPP_rat_fun_nat_rat,type,
    hAPP_rat_fun_nat_rat: $i > $i > $i ).

thf(tp_hAPP_rat_fun_rat_rat,type,
    hAPP_rat_fun_rat_rat: $i > $i > $i ).

thf(tp_hAPP_rat_rat,type,
    hAPP_rat_rat: $i > $i > $i ).

thf(tp_hAPP_real_bool,type,
    hAPP_real_bool: $i > $i > $i ).

thf(tp_hAPP_real_complex,type,
    hAPP_real_complex: $i > $i > $i ).

thf(tp_hAPP_real_real,type,
    hAPP_real_real: $i > $i > $i ).

thf(tp_hBOOL,type,
    hBOOL: $i > $o ).

thf(tp_hilbert_Eps_int,type,
    hilbert_Eps_int: $i > $i ).

thf(tp_hilbert_Eps_real,type,
    hilbert_Eps_real: $i > $i ).

thf(tp_if_Pro1731782967nt_int,type,
    if_Pro1731782967nt_int: $i ).

thf(tp_if_Pro313124157l_real,type,
    if_Pro313124157l_real: $i ).

thf(tp_if_int,type,
    if_int: $i ).

thf(tp_if_nat,type,
    if_nat: $i ).

thf(tp_if_real,type,
    if_real: $i ).

thf(tp_ii,type,
    ii: $i ).

thf(tp_im,type,
    im: $i ).

thf(tp_image_275383677t_bool,type,
    image_275383677t_bool: $i > $i > $i ).

thf(tp_image_int_int,type,
    image_int_int: $i > $i > $i ).

thf(tp_image_int_nat,type,
    image_int_nat: $i > $i > $i ).

thf(tp_image_nat_int,type,
    image_nat_int: $i > $i > $i ).

thf(tp_image_nat_nat,type,
    image_nat_nat: $i > $i > $i ).

thf(tp_int,type,
    int: $i ).

thf(tp_int_gcd,type,
    int_gcd: $i ).

thf(tp_int_ge_less_than,type,
    int_ge_less_than: $i > $i ).

thf(tp_int_ge_less_than2,type,
    int_ge_less_than2: $i > $i ).

thf(tp_int_lcm,type,
    int_lcm: $i > $i ).

thf(tp_inv,type,
    inv: $i > $i ).

thf(tp_invers1025623611omplex,type,
    invers1025623611omplex: $i ).

thf(tp_invers1449016382omplex,type,
    invers1449016382omplex: $i ).

thf(tp_inverse_divide_rat,type,
    inverse_divide_rat: $i ).

thf(tp_inverse_divide_real,type,
    inverse_divide_real: $i ).

thf(tp_inverse_inverse_rat,type,
    inverse_inverse_rat: $i ).

thf(tp_inverse_inverse_real,type,
    inverse_inverse_real: $i ).

thf(tp_isCont156215680omplex,type,
    isCont156215680omplex: $i > $i ).

thf(tp_isCont_complex_real,type,
    isCont_complex_real: $i > $i ).

thf(tp_isCont_real_real,type,
    isCont_real_real: $i > $i ).

thf(tp_is_RRset,type,
    is_RRset: $i > $i ).

thf(tp_is_bool,type,
    is_bool: $i > $o ).

thf(tp_is_int,type,
    is_int: $i > $o ).

thf(tp_iszero_int,type,
    iszero_int: $i ).

thf(tp_iszero_rat,type,
    iszero_rat: $i ).

thf(tp_lazy_small_lazy_rel,type,
    lazy_small_lazy_rel: $i ).

thf(tp_legacy_zgcd,type,
    legacy_zgcd: $i > $i ).

thf(tp_legendre,type,
    legendre: $i > $i ).

thf(tp_ln,type,
    ln: $i ).

thf(tp_log,type,
    log: $i > $i ).

thf(tp_m,type,
    m: $i ).

thf(tp_m1,type,
    m1: $i ).

thf(tp_member180897546at_nat,type,
    member180897546at_nat: $i ).

thf(tp_member2143287562nt_int,type,
    member2143287562nt_int: $i ).

thf(tp_member308914164t_bool,type,
    member308914164t_bool: $i ).

thf(tp_member_fun_int_bool,type,
    member_fun_int_bool: $i ).

thf(tp_member_int,type,
    member_int: $i ).

thf(tp_member_nat,type,
    member_nat: $i ).

thf(tp_member_real,type,
    member_real: $i ).

thf(tp_min,type,
    min: $i ).

thf(tp_minus_1690775515umeral,type,
    minus_1690775515umeral: $i ).

thf(tp_minus_534354567de_int,type,
    minus_534354567de_int: $i ).

thf(tp_minus_minus_complex,type,
    minus_minus_complex: $i ).

thf(tp_minus_minus_int,type,
    minus_minus_int: $i ).

thf(tp_minus_minus_nat,type,
    minus_minus_nat: $i ).

thf(tp_minus_minus_rat,type,
    minus_minus_rat: $i ).

thf(tp_minus_minus_real,type,
    minus_minus_real: $i ).

thf(tp_monoseq_real,type,
    monoseq_real: $i > $i ).

thf(tp_multInv,type,
    multInv: $i > $i ).

thf(tp_multInvPair,type,
    multInvPair: $i > $i > $i ).

thf(tp_n,type,
    n: $i ).

thf(tp_nat,type,
    nat: $i ).

thf(tp_nat_aux,type,
    nat_aux: $i > $i ).

thf(tp_nat_case_bool,type,
    nat_case_bool: $i > $i > $i ).

thf(tp_nat_case_nat,type,
    nat_case_nat: $i > $i > $i ).

thf(tp_nat_gcd,type,
    nat_gcd: $i > $i ).

thf(tp_nat_gcd_rel,type,
    nat_gcd_rel: $i ).

thf(tp_nat_is_nat,type,
    nat_is_nat: $i ).

thf(tp_nat_lcm,type,
    nat_lcm: $i > $i ).

thf(tp_nat_nat_set,type,
    nat_nat_set: $i ).

thf(tp_nat_neg,type,
    nat_neg: $i ).

thf(tp_nat_size,type,
    nat_size: $i ).

thf(tp_nat_tr160667106at_int,type,
    nat_tr160667106at_int: $i > $i ).

thf(tp_nat_tr876908586nt_nat,type,
    nat_tr876908586nt_nat: $i > $i ).

thf(tp_nat_tsub,type,
    nat_tsub: $i > $i ).

thf(tp_natceiling,type,
    natceiling: $i > $i ).

thf(tp_natfloor,type,
    natfloor: $i > $i ).

thf(tp_negDivAlg,type,
    negDivAlg: $i > $i > $i ).

thf(tp_negDivAlg_rel,type,
    negDivAlg_rel: $i ).

thf(tp_negateSnd,type,
    negateSnd: $i ).

thf(tp_noXRRset,type,
    noXRRset: $i > $i ).

thf(tp_norRRset,type,
    norRRset: $i ).

thf(tp_norm_frac,type,
    norm_frac: $i > $i > $i ).

thf(tp_norm_frac_rel,type,
    norm_frac_rel: $i ).

thf(tp_norm_norm_complex,type,
    norm_norm_complex: $i ).

thf(tp_norm_norm_real,type,
    norm_norm_real: $i ).

thf(tp_normalize,type,
    normalize: $i > $i ).

thf(tp_number1226105091de_int,type,
    number1226105091de_int: $i ).

thf(tp_number1443263063umeral,type,
    number1443263063umeral: $i ).

thf(tp_number267125858f_real,type,
    number267125858f_real: $i ).

thf(tp_number528085621omplex,type,
    number528085621omplex: $i ).

thf(tp_number_number_of_int,type,
    number_number_of_int: $i ).

thf(tp_number_number_of_nat,type,
    number_number_of_nat: $i ).

thf(tp_number_number_of_rat,type,
    number_number_of_rat: $i ).

thf(tp_of_real_complex,type,
    of_real_complex: $i > $i ).

thf(tp_one_on1645066479umeral,type,
    one_on1645066479umeral: $i ).

thf(tp_one_on1684967323de_int,type,
    one_on1684967323de_int: $i ).

thf(tp_one_one_complex,type,
    one_one_complex: $i ).

thf(tp_one_one_int,type,
    one_one_int: $i ).

thf(tp_one_one_nat,type,
    one_one_nat: $i ).

thf(tp_one_one_rat,type,
    one_one_rat: $i ).

thf(tp_one_one_real,type,
    one_one_real: $i ).

thf(tp_ord_at1496968948n_real,type,
    ord_at1496968948n_real: $i > $i ).

thf(tp_ord_at1589558736t_real,type,
    ord_at1589558736t_real: $i > $i ).

thf(tp_ord_at238088361st_nat,type,
    ord_at238088361st_nat: $i > $i ).

thf(tp_ord_at4362885an_nat,type,
    ord_at4362885an_nat: $i > $i ).

thf(tp_ord_at641636577an_int,type,
    ord_at641636577an_int: $i > $i ).

thf(tp_ord_at875362053st_int,type,
    ord_at875362053st_int: $i > $i ).

thf(tp_ord_atMost_nat,type,
    ord_atMost_nat: $i ).

thf(tp_ord_atMost_real,type,
    ord_atMost_real: $i ).

thf(tp_ord_gr1297742076an_int,type,
    ord_gr1297742076an_int: $i > $i ).

thf(tp_ord_gr660468384an_nat,type,
    ord_gr660468384an_nat: $i > $i ).

thf(tp_ord_gr788844697n_real,type,
    ord_gr788844697n_real: $i > $i ).

thf(tp_ord_le1304079648umeral,type,
    ord_le1304079648umeral: $i ).

thf(tp_ord_le1568362934t_bool,type,
    ord_le1568362934t_bool: $i ).

thf(tp_ord_le1860547276de_int,type,
    ord_le1860547276de_int: $i ).

thf(tp_ord_le1912455174t_bool,type,
    ord_le1912455174t_bool: $i ).

thf(tp_ord_le258702272de_int,type,
    ord_le258702272de_int: $i ).

thf(tp_ord_le382113706t_bool,type,
    ord_le382113706t_bool: $i ).

thf(tp_ord_le565307924umeral,type,
    ord_le565307924umeral: $i ).

thf(tp_ord_le951220754t_bool,type,
    ord_le951220754t_bool: $i ).

thf(tp_ord_lessThan_nat,type,
    ord_lessThan_nat: $i ).

thf(tp_ord_lessThan_real,type,
    ord_lessThan_real: $i ).

thf(tp_ord_less_eq_bool,type,
    ord_less_eq_bool: $i ).

thf(tp_ord_less_eq_int,type,
    ord_less_eq_int: $i ).

thf(tp_ord_less_eq_nat,type,
    ord_less_eq_nat: $i ).

thf(tp_ord_less_eq_rat,type,
    ord_less_eq_rat: $i ).

thf(tp_ord_less_eq_real,type,
    ord_less_eq_real: $i ).

thf(tp_ord_less_int,type,
    ord_less_int: $i ).

thf(tp_ord_less_nat,type,
    ord_less_nat: $i ).

thf(tp_ord_less_rat,type,
    ord_less_rat: $i ).

thf(tp_ord_less_real,type,
    ord_less_real: $i ).

thf(tp_ord_max_nat,type,
    ord_max_nat: $i ).

thf(tp_ord_min_nat,type,
    ord_min_nat: $i ).

thf(tp_pair_leq,type,
    pair_leq: $i ).

thf(tp_pair_less,type,
    pair_less: $i ).

thf(tp_pdivmod,type,
    pdivmod: $i > $i > $i ).

thf(tp_phi,type,
    phi: $i > $i ).

thf(tp_pi,type,
    pi: $i ).

thf(tp_pls,type,
    pls: $i ).

thf(tp_plus_p1446045655de_int,type,
    plus_p1446045655de_int: $i ).

thf(tp_plus_p1627245867umeral,type,
    plus_p1627245867umeral: $i ).

thf(tp_plus_plus_complex,type,
    plus_plus_complex: $i ).

thf(tp_plus_plus_int,type,
    plus_plus_int: $i ).

thf(tp_plus_plus_nat,type,
    plus_plus_nat: $i ).

thf(tp_plus_plus_rat,type,
    plus_plus_rat: $i ).

thf(tp_plus_plus_real,type,
    plus_plus_real: $i ).

thf(tp_posDivAlg,type,
    posDivAlg: $i > $i > $i ).

thf(tp_posDivAlg_rel,type,
    posDivAlg_rel: $i ).

thf(tp_power_2100829034umeral,type,
    power_2100829034umeral: $i ).

thf(tp_power_881366806de_int,type,
    power_881366806de_int: $i ).

thf(tp_power_power_complex,type,
    power_power_complex: $i ).

thf(tp_power_power_int,type,
    power_power_int: $i ).

thf(tp_power_power_nat,type,
    power_power_nat: $i ).

thf(tp_power_power_rat,type,
    power_power_rat: $i ).

thf(tp_power_power_real,type,
    power_power_real: $i ).

thf(tp_powr,type,
    powr: $i ).

thf(tp_pred,type,
    pred: $i ).

thf(tp_pred_nat,type,
    pred_nat: $i ).

thf(tp_prime,type,
    prime: $i ).

thf(tp_produc1298267108nt_int,type,
    produc1298267108nt_int: $i > $i ).

thf(tp_produc1318306967de_int,type,
    produc1318306967de_int: $i ).

thf(tp_produc1391996073at_nat,type,
    produc1391996073at_nat: $i > $i ).

thf(tp_produc1518849193nt_int,type,
    produc1518849193nt_int: $i > $i ).

thf(tp_produc1922581855t_bool,type,
    produc1922581855t_bool: $i > $i ).

thf(tp_produc1935615926l_real,type,
    produc1935615926l_real: $i ).

thf(tp_produc2136830103umeral,type,
    produc2136830103umeral: $i ).

thf(tp_produc282740534nt_int,type,
    produc282740534nt_int: $i ).

thf(tp_produc494345619at_nat,type,
    produc494345619at_nat: $i ).

thf(tp_produc556554744l_real,type,
    produc556554744l_real: $i ).

thf(tp_produc595218619l_real,type,
    produc595218619l_real: $i > $i ).

thf(tp_produc713050258nt_int,type,
    produc713050258nt_int: $i > $i ).

thf(tp_produc713279741t_bool,type,
    produc713279741t_bool: $i ).

thf(tp_produc865579683l_real,type,
    produc865579683l_real: $i ).

thf(tp_produc883642259nt_int,type,
    produc883642259nt_int: $i ).

thf(tp_produc93441119t_bool,type,
    produc93441119t_bool: $i > $i ).

thf(tp_produc973645403t_bool,type,
    produc973645403t_bool: $i > $i ).

thf(tp_product_Pair_int_int,type,
    product_Pair_int_int: $i ).

thf(tp_product_Pair_nat_nat,type,
    product_Pair_nat_nat: $i ).

thf(tp_product_fst_int_int,type,
    product_fst_int_int: $i ).

thf(tp_product_fst_nat_nat,type,
    product_fst_nat_nat: $i ).

thf(tp_product_snd_int_int,type,
    product_snd_int_int: $i ).

thf(tp_product_snd_nat_nat,type,
    product_snd_nat_nat: $i ).

thf(tp_quadRes,type,
    quadRes: $i ).

thf(tp_quickc1265749348ro_rel,type,
    quickc1265749348ro_rel: $i ).

thf(tp_quickc495462417de_int,type,
    quickc495462417de_int: $i > $i > $i ).

thf(tp_quickc666637781d_zero,type,
    quickc666637781d_zero: $i > $i ).

thf(tp_quickcheck_int_of,type,
    quickcheck_int_of: $i > $i ).

thf(tp_quickcheck_nat_of,type,
    quickcheck_nat_of: $i > $i ).

thf(tp_quickcheck_of_int,type,
    quickcheck_of_int: $i ).

thf(tp_quotient_of,type,
    quotient_of: $i > $i ).

thf(tp_r,type,
    r: $i ).

thf(tp_rRset2norRR,type,
    rRset2norRR: $i > $i > $i ).

thf(tp_ratreal,type,
    ratreal: $i > $i ).

thf(tp_ratrel,type,
    ratrel: $i ).

thf(tp_rcis,type,
    rcis: $i > $i > $i ).

thf(tp_re,type,
    re: $i ).

thf(tp_real_int,type,
    real_int: $i ).

thf(tp_real_nat,type,
    real_nat: $i ).

thf(tp_resSet,type,
    resSet: $i > $i ).

thf(tp_ring_11397209091omplex,type,
    ring_11397209091omplex: $i ).

thf(tp_ring_1_Ints_real,type,
    ring_1_Ints_real: $i ).

thf(tp_ring_1_of_int_int,type,
    ring_1_of_int_int: $i ).

thf(tp_ring_1_of_int_rat,type,
    ring_1_of_int_rat: $i ).

thf(tp_ring_1_of_int_real,type,
    ring_1_of_int_real: $i ).

thf(tp_root,type,
    root: $i ).

thf(tp_rsetR,type,
    rsetR: $i > $i ).

thf(tp_s,type,
    s: $i ).

thf(tp_s1,type,
    s1: $i ).

thf(tp_sK10_M_1,type,
    sK10_M_1: $i > $i ).

thf(tp_sK11_Q_4,type,
    sK11_Q_4: $i > $i > $i ).

thf(tp_sK12_Q_4,type,
    sK12_Q_4: $i > $i > $i ).

thf(tp_sK13_X_1,type,
    sK13_X_1: $i ).

thf(tp_sK14_SY716,type,
    sK14_SY716: $i ).

thf(tp_sK15_M_1,type,
    sK15_M_1: $i > $i ).

thf(tp_sK16_SY717,type,
    sK16_SY717: $i > $i ).

thf(tp_sK1_A_4,type,
    sK1_A_4: $i > $i > $i ).

thf(tp_sK2_SY713,type,
    sK2_SY713: $i > $i > $i ).

thf(tp_sK3_N_1,type,
    sK3_N_1: $i > $i ).

thf(tp_sK4_N_1,type,
    sK4_N_1: $i > $i ).

thf(tp_sK5_C_3,type,
    sK5_C_3: $i > $i > $i ).

thf(tp_sK6_SY714,type,
    sK6_SY714: $i > $i > $i ).

thf(tp_sK7_C_3,type,
    sK7_C_3: $i > $i > $i ).

thf(tp_sK8_SY715,type,
    sK8_SY715: $i > $i > $i ).

thf(tp_sK9_Nat_1,type,
    sK9_Nat_1: $i > $i ).

thf(tp_sRStar,type,
    sRStar: $i ).

thf(tp_sa,type,
    sa: $i ).

thf(tp_scaleR1652505878omplex,type,
    scaleR1652505878omplex: $i > $i ).

thf(tp_scaleR_scaleR_real,type,
    scaleR_scaleR_real: $i > $i ).

thf(tp_semiri132038758t_real,type,
    semiri132038758t_real: $i ).

thf(tp_semiri1424489471de_int,type,
    semiri1424489471de_int: $i ).

thf(tp_semiri151668891at_rat,type,
    semiri151668891at_rat: $i ).

thf(tp_semiri1619134803umeral,type,
    semiri1619134803umeral: $i ).

thf(tp_semiri1621563631at_int,type,
    semiri1621563631at_int: $i ).

thf(tp_semiri2020571505omplex,type,
    semiri2020571505omplex: $i ).

thf(tp_semiri984289939at_nat,type,
    semiri984289939at_nat: $i ).

thf(tp_sequentially,type,
    sequentially: $i ).

thf(tp_setS,type,
    setS: $i > $i > $i ).

thf(tp_sgn_sgn_complex,type,
    sgn_sgn_complex: $i ).

thf(tp_sgn_sgn_int,type,
    sgn_sgn_int: $i ).

thf(tp_sgn_sgn_rat,type,
    sgn_sgn_rat: $i ).

thf(tp_sgn_sgn_real,type,
    sgn_sgn_real: $i ).

thf(tp_sin,type,
    sin: $i ).

thf(tp_sin_coeff,type,
    sin_coeff: $i ).

thf(tp_size_s945831648umeral,type,
    size_s945831648umeral: $i ).

thf(tp_size_size_complex,type,
    size_size_complex: $i ).

thf(tp_size_size_list_int,type,
    size_size_list_int: $i ).

thf(tp_size_size_nat,type,
    size_size_nat: $i ).

thf(tp_sqrt,type,
    sqrt: $i ).

thf(tp_sr,type,
    sr: $i ).

thf(tp_standardRes,type,
    standardRes: $i > $i ).

thf(tp_suc,type,
    suc: $i ).

thf(tp_succ,type,
    succ: $i ).

thf(tp_suminf_complex,type,
    suminf_complex: $i ).

thf(tp_suminf_real,type,
    suminf_real: $i ).

thf(tp_summable_complex,type,
    summable_complex: $i > $i ).

thf(tp_summable_real,type,
    summable_real: $i > $i ).

thf(tp_sums_complex,type,
    sums_complex: $i > $i ).

thf(tp_sums_real,type,
    sums_real: $i > $i ).

thf(tp_t,type,
    t: $i ).

thf(tp_tan,type,
    tan: $i ).

thf(tp_tendst1507391555omplex,type,
    tendst1507391555omplex: $i > $i > $i > $i ).

thf(tp_tendsto_complex_real,type,
    tendsto_complex_real: $i > $i > $i > $i ).

thf(tp_tendsto_nat_complex,type,
    tendsto_nat_complex: $i > $i > $i > $i ).

thf(tp_tendsto_nat_real,type,
    tendsto_nat_real: $i > $i > $i > $i ).

thf(tp_tendsto_real_real,type,
    tendsto_real_real: $i > $i > $i > $i ).

thf(tp_the_Pr2103884470nt_int,type,
    the_Pr2103884470nt_int: $i > $i ).

thf(tp_the_Pr588456374at_nat,type,
    the_Pr588456374at_nat: $i > $i ).

thf(tp_the_int,type,
    the_int: $i > $i ).

thf(tp_the_real,type,
    the_real: $i > $i ).

thf(tp_times_123202395de_int,type,
    times_123202395de_int: $i ).

thf(tp_times_1655362735umeral,type,
    times_1655362735umeral: $i ).

thf(tp_times_times_complex,type,
    times_times_complex: $i ).

thf(tp_times_times_int,type,
    times_times_int: $i ).

thf(tp_times_times_nat,type,
    times_times_nat: $i ).

thf(tp_times_times_rat,type,
    times_times_rat: $i ).

thf(tp_times_times_real,type,
    times_times_real: $i ).

thf(tp_tn,type,
    tn: $i ).

thf(tp_trivial_limit_nat,type,
    trivial_limit_nat: $i > $i ).

thf(tp_twoSqu1770640450sum2sq,type,
    twoSqu1770640450sum2sq: $i ).

thf(tp_twoSqu1907779896sum2sq,type,
    twoSqu1907779896sum2sq: $i ).

thf(tp_uminus473333897omplex,type,
    uminus473333897omplex: $i ).

thf(tp_uminus_uminus_int,type,
    uminus_uminus_int: $i ).

thf(tp_uminus_uminus_rat,type,
    uminus_uminus_rat: $i ).

thf(tp_uminus_uminus_real,type,
    uminus_uminus_real: $i ).

thf(tp_undefined_int,type,
    undefined_int: $i > $i ).

thf(tp_upto_rel,type,
    upto_rel: $i ).

thf(tp_v,type,
    v: $i ).

thf(tp_vanishes,type,
    vanishes: $i > $i ).

thf(tp_w,type,
    w: $i ).

thf(tp_wset,type,
    wset: $i > $i ).

thf(tp_x,type,
    x: $i ).

thf(tp_xzgcd,type,
    xzgcd: $i > $i > $i ).

thf(tp_xzgcda,type,
    xzgcda: $i > $i > $i > $i > $i > $i > $i > $i > $i ).

thf(tp_y,type,
    y: $i ).

thf(tp_z3div,type,
    z3div: $i > $i ).

thf(tp_z3mod,type,
    z3mod: $i > $i ).

thf(tp_zEven,type,
    zEven: $i ).

thf(tp_zOdd,type,
    zOdd: $i ).

thf(tp_zcong,type,
    zcong: $i > $i ).

thf(tp_zcongm,type,
    zcongm: $i > $i ).

thf(tp_zero_z126310315umeral,type,
    zero_z126310315umeral: $i ).

thf(tp_zero_z891286103de_int,type,
    zero_z891286103de_int: $i ).

thf(tp_zero_zero_complex,type,
    zero_zero_complex: $i ).

thf(tp_zero_zero_int,type,
    zero_zero_int: $i ).

thf(tp_zero_zero_nat,type,
    zero_zero_nat: $i ).

thf(tp_zero_zero_rat,type,
    zero_zero_rat: $i ).

thf(tp_zero_zero_real,type,
    zero_zero_real: $i ).

thf(tp_zfact,type,
    zfact: $i ).

thf(tp_zprime,type,
    zprime: $i ).

thf(177,axiom,
    ! [P: $i,Q: $i,R: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ ( hAPP_f2135977429nt_int @ cOMBC_int_int_int @ P ) @ Q ) @ R )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ P @ R ) @ Q ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__Int__Oint_000tc__Int__Oint_U) ).

thf(200,axiom,
    ! [P: $i] :
      ( ( hAPP_nat_nat @ cOMBI_nat @ P )
      = P ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_COMBI_000tc__Nat__Onat_U) ).

thf(201,axiom,
    ! [P: $i] :
      ( ( is_int @ P )
     => ( ( hAPP_int_int @ cOMBI_int @ P )
        = P ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_COMBI_000tc__Int__Oint_U) ).

thf(303,axiom,
    ! [A_3: $i,B_2: $i] :
      ( ( ( is_int @ A_3 )
        & ( is_int @ B_2 ) )
     => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 )
         != zero_zero_int )
       => ? [A_4: $i,B_3: $i] :
            ( ( is_int @ A_4 )
            & ( is_int @ B_3 )
            & ( A_3
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_4 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) )
            & ( B_2
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) )
            & ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_4 ) @ B_3 )
              = one_one_int ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5117_gcd__coprime__exists__int) ).

thf(413,axiom,
    ! [B_1: $i,C: $i,A_1: $i,D_1: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_1 ) @ D_1 )
        = one_one_int )
     => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ B_1 ) @ C )
          = one_one_int )
       => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ A_1 ) ) @ ( hAPP_int_int @ abs_abs_int @ C ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ B_1 ) ) @ ( hAPP_int_int @ abs_abs_int @ D_1 ) ) )
        <=> ( ( ( hAPP_int_int @ abs_abs_int @ A_1 )
              = ( hAPP_int_int @ abs_abs_int @ B_1 ) )
            & ( ( hAPP_int_int @ abs_abs_int @ C )
              = ( hAPP_int_int @ abs_abs_int @ D_1 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5007_coprime__crossproduct__int) ).

thf(414,axiom,
    ! [X: $i,Y: $i,M: $i] :
      ( ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ X ) @ Y ) ) @ M )
        = one_one_int )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ M )
        = one_one_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5006_invertible__coprime__int) ).

thf(416,axiom,
    ! [B_5: $i,A_5: $i,A_3: $i,B_2: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 )
       != zero_zero_int )
     => ( ( A_3
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_5 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) )
       => ( ( B_2
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_5 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_5 ) @ B_5 )
            = one_one_int ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5004_gcd__coprime__int) ).

thf(418,axiom,
    ! [D_3: $i,A_3: $i,B_2: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ B_2 ) )
        = one_one_int )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ B_2 )
        = one_one_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5002_coprime__rmult__int) ).

thf(419,axiom,
    ! [D_3: $i,A_3: $i,B_2: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ B_2 ) )
        = one_one_int )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ A_3 )
        = one_one_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5001_coprime__lmult__int) ).

thf(420,axiom,
    ! [B_2: $i,D_3: $i,A_3: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ A_3 )
        = one_one_int )
     => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ B_2 )
          = one_one_int )
       => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ B_2 ) )
          = one_one_int ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5000_coprime__mult__int) ).

thf(421,axiom,
    ! [M: $i,K_2: $i,N: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ K_2 ) @ N )
        = one_one_int )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ M ) ) @ N )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ M ) @ N ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4999_gcd__mult__cancel__int) ).

thf(422,axiom,
    ! [D_1: $i,A_1: $i,B_1: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_1 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ B_1 ) )
        = one_one_int )
    <=> ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_1 ) @ A_1 )
          = one_one_int )
        & ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_1 ) @ B_1 )
          = one_one_int ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4998_coprime__mul__eq__int) ).

thf(424,axiom,
    ! [Ma: $i,Na: $i] :
      ( ( ( is_int @ Ma )
        & ( is_int @ Na ) )
     => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ Ma ) @ Na )
          = zero_zero_int )
      <=> ( ( Ma = zero_zero_int )
          & ( Na = zero_zero_int ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4996_gcd__zero__int) ).

thf(425,axiom,
    ! [X: $i,Y: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ uminus_uminus_int @ X ) ) @ Y )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4995_gcd__neg1__int) ).

thf(426,axiom,
    ! [X: $i,Y: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ ( hAPP_int_int @ uminus_uminus_int @ Y ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4994_gcd__neg2__int) ).

thf(427,axiom,
    ! [A_3: $i,B_2: $i,C_1: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) @ C_1 )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ B_2 ) @ C_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4993_gcd__assoc__int) ).

thf(428,axiom,
    ! [B_2: $i,A_3: $i,C_1: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ B_2 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ C_1 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ B_2 ) @ C_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4992_gcd__int_Oleft__commute) ).

thf(429,axiom,
    ! [A_3: $i,B_2: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ B_2 ) @ A_3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4991_gcd__commute__int) ).

thf(434,axiom,
    ! [A_3: $i,N: $i,B_2: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ N ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ N ) )
      = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) @ N ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4986_gcd__exp__int) ).

thf(435,axiom,
    ! [X: $i,Y: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ Y )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ Y ) @ ( hAPP_int_int @ ( div_mod_int @ X ) @ Y ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4985_gcd__red__int) ).

thf(436,axiom,
    ! [N: $i,D_3: $i,A_3: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ A_3 )
        = one_one_int )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ N ) )
        = one_one_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4984_coprime__exp__int) ).

thf(438,axiom,
    ! [M: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ M ) @ one_one_int )
      = one_one_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4982_gcd__1__int) ).

thf(439,axiom,
    ! [N: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ N ) @ one_one_int ) ) @ N )
      = one_one_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4981_coprime__minus__one__int) ).

thf(440,axiom,
    ! [N: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ N ) @ one_one_int ) ) @ N )
      = one_one_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4980_coprime__plus__one__int) ).

thf(441,axiom,
    ! [X: $i,Y: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ abs_abs_int @ X ) ) @ Y )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4979_gcd__abs1__int) ).

thf(442,axiom,
    ! [X: $i,Y: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ ( hAPP_int_int @ abs_abs_int @ Y ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4978_gcd__abs2__int) ).

thf(443,axiom,
    ! [X: $i,Y: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ Y )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ abs_abs_int @ X ) ) @ ( hAPP_int_int @ abs_abs_int @ Y ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4977_gcd__abs__int) ).

thf(444,axiom,
    ! [X: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ X )
      = ( hAPP_int_int @ abs_abs_int @ X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4976_gcd__idem__int) ).

thf(445,axiom,
    ! [X: $i,Y: $i] :
      ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ Y ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4975_abs__gcd__int) ).

thf(448,axiom,
    ! [M: $i,N: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ M ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ M ) @ N ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ M ) @ N ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4972_gcd__add2__int) ).

thf(449,axiom,
    ! [M: $i,N: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ M ) @ N ) ) @ N )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ M ) @ N ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4971_gcd__add1__int) ).

thf(450,axiom,
    ! [K_2: $i,M: $i,N: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ K_2 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ M ) @ N ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ M ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ N ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4970_gcd__mult__distrib__int) ).

thf(451,axiom,
    ! [M: $i,K_2: $i,N: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ M ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ M ) ) @ N ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ M ) @ N ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4969_gcd__add__mult__int) ).

thf(452,axiom,
    ! [X: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ zero_zero_int ) @ X )
      = ( hAPP_int_int @ abs_abs_int @ X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4968_gcd__0__left__int) ).

thf(453,axiom,
    ! [X: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ zero_zero_int )
      = ( hAPP_int_int @ abs_abs_int @ X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4967_gcd__0__int) ).

thf(455,axiom,
    ! [B_2: $i,A_3: $i] :
      ( ( ( is_int @ B_2 )
        & ( is_int @ A_3 ) )
     => ( ( ( A_3 != zero_zero_int )
          | ( B_2 != zero_zero_int ) )
       => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ B_2 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) )
          = one_one_int ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4965_div__gcd__coprime__int) ).

thf(459,axiom,
    ! [N: $i,M: $i,A_3: $i,B_2: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 )
        = one_one_int )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ N ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ M ) )
        = one_one_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4961_coprime__exp2__int) ).

thf(664,axiom,
    ! [Z_1: $i,W: $i] :
      ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Z_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ W ) ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Z_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ W ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Z_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ W ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4756_zpower__number__of__even) ).

thf(818,axiom,
    ! [A: $i] :
      ( ( image_int_nat @ nat @ ( image_nat_int @ semiri1621563631at_int @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4602_transfer__int__nat__set__return__embed) ).

thf(820,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
    <=> ( ( image_nat_int @ semiri1621563631at_int @ A )
        = ( image_nat_int @ semiri1621563631at_int @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4600_transfer__nat__int__set__relations_I3_J) ).

thf(842,axiom,
    ! [N: $i] :
      ( ( hAPP_int_int @ ring_1_of_int_int @ ( hAPP_nat_int @ semiri1621563631at_int @ N ) )
      = ( hAPP_nat_int @ semiri1621563631at_int @ N ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4578_of__int__int__eq) ).

thf(844,axiom,
    ! [W: $i] :
      ( ( hAPP_int_int @ number_number_of_int @ W )
      = ( hAPP_int_int @ ring_1_of_int_int @ W ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4576_int__number__of__def) ).

thf(856,axiom,
    ( ( hAPP_nat_nat @ fact @ zero_zero_nat )
    = one_one_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4564_fact_Osimps_I1_J) ).

thf(872,axiom,
    ! [Z_1: $i] :
      ( ( is_int @ Z_1 )
     => ( ! [N_1: $i] :
            ( Z_1
           != ( hAPP_nat_int @ semiri1621563631at_int @ N_1 ) )
       => ~ ! [N_1: $i] :
              ( Z_1
             != ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ suc @ N_1 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4548_int__cases) ).

thf(882,axiom,
    ! [B_2: $i,A_3: $i] :
      ( ( ( is_int @ B_2 )
        & ( is_int @ A_3 ) )
     => ( ( ( A_3 != zero_zero_int )
          | ( B_2 != zero_zero_int ) )
       => ? [C_3: $i,D_2: $i] :
            ( ( is_int @ C_3 )
            & ( is_int @ D_2 )
            & ( A_3
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 ) ) @ C_3 ) )
            & ( B_2
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 ) ) @ D_2 ) )
            & ( ( hAPP_int_int @ ( legacy_zgcd @ C_3 ) @ D_2 )
              = one_one_int ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4538_make__zrelprime) ).

thf(902,axiom,
    ! [Ma: $i] :
      ( ( ( hAPP_int_int @ ( legacy_zgcd @ zero_zero_int ) @ Ma )
        = one_one_int )
    <=> ( ( hAPP_int_int @ abs_abs_int @ Ma )
        = one_one_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4518_zgcd__0__1__iff) ).

thf(908,axiom,
    ! [B_2: $i,A_3: $i] :
      ( ( ( is_int @ B_2 )
        & ( is_int @ A_3 ) )
     => ( ( ( A_3 != zero_zero_int )
          | ( B_2 != zero_zero_int ) )
       => ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ B_2 ) @ ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 ) ) )
          = one_one_int ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4512_div__zgcd__relprime) ).

thf(913,axiom,
    ! [M: $i] :
      ( ( hAPP_int_int @ ( legacy_zgcd @ M ) @ zero_zero_int )
      = ( hAPP_int_int @ abs_abs_int @ M ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4507_zgcd__0) ).

thf(914,axiom,
    ! [M: $i] :
      ( ( hAPP_int_int @ ( legacy_zgcd @ zero_zero_int ) @ M )
      = ( hAPP_int_int @ abs_abs_int @ M ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4506_zgcd__0__left) ).

thf(915,axiom,
    ! [K_2: $i,M: $i,N: $i] :
      ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ M ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ N ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ K_2 ) ) @ ( hAPP_int_int @ ( legacy_zgcd @ M ) @ N ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4505_zgcd__zmult__distrib2__abs) ).

thf(916,axiom,
    ! [N: $i,A_3: $i,B_2: $i] :
      ( ( ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 )
        = one_one_int )
     => ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ N ) ) @ B_2 )
        = one_one_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4504_zgcd__1__power__left__distrib) ).

thf(917,axiom,
    ! [N: $i,A_3: $i,B_2: $i] :
      ( ( ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 )
        = one_one_int )
     => ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ N ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ N ) )
        = one_one_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4503_zgcd__1__power__distrib) ).

thf(921,axiom,
    ! [M: $i,N: $i,K_2: $i] :
      ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ M ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ N ) @ K_2 ) ) ) @ N )
      = ( hAPP_int_int @ ( legacy_zgcd @ M ) @ N ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4499_zgcd__zadd__zmult) ).

thf(922,axiom,
    ! [I: $i,J_2: $i] :
      ( ( hAPP_int_int @ ( legacy_zgcd @ I ) @ ( hAPP_int_int @ uminus_uminus_int @ J_2 ) )
      = ( hAPP_int_int @ ( legacy_zgcd @ I ) @ J_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4498_zgcd__zminus2) ).

thf(923,axiom,
    ! [I: $i,J_2: $i] :
      ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ uminus_uminus_int @ I ) ) @ J_2 )
      = ( hAPP_int_int @ ( legacy_zgcd @ I ) @ J_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4497_zgcd__zminus) ).

thf(924,axiom,
    ! [K_2: $i,M: $i,N: $i] :
      ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( legacy_zgcd @ K_2 ) @ M ) ) @ N )
      = ( hAPP_int_int @ ( legacy_zgcd @ K_2 ) @ ( hAPP_int_int @ ( legacy_zgcd @ M ) @ N ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4496_zgcd__assoc) ).

thf(925,axiom,
    ! [K_2: $i,M: $i,N: $i] :
      ( ( hAPP_int_int @ ( legacy_zgcd @ K_2 ) @ ( hAPP_int_int @ ( legacy_zgcd @ M ) @ N ) )
      = ( hAPP_int_int @ ( legacy_zgcd @ M ) @ ( hAPP_int_int @ ( legacy_zgcd @ K_2 ) @ N ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4495_zgcd__left__commute) ).

thf(926,axiom,
    ! [I: $i,J_2: $i] :
      ( ( hAPP_int_int @ ( legacy_zgcd @ I ) @ J_2 )
      = ( hAPP_int_int @ ( legacy_zgcd @ J_2 ) @ I ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4494_zgcd__commute) ).

thf(929,axiom,
    ! [A_3: $i,B_2: $i,N: $i] :
      ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 ) ) @ N )
      = ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ N ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ N ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4491_zgcd__power__distrib) ).

thf(930,axiom,
    ! [M: $i,N: $i] :
      ( ( hAPP_int_int @ ( legacy_zgcd @ M ) @ N )
      = ( hAPP_int_int @ ( legacy_zgcd @ N ) @ ( hAPP_int_int @ ( div_mod_int @ M ) @ N ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4490_zgcd__eq) ).

thf(931,axiom,
    ! [I_1: $i,J: $i] :
      ( ( ( is_int @ I_1 )
        & ( is_int @ J ) )
     => ( ( ( hAPP_int_int @ ( legacy_zgcd @ I_1 ) @ J )
          = zero_zero_int )
      <=> ( ( I_1 = zero_zero_int )
          & ( J = zero_zero_int ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4489_zgcd0) ).

thf(932,axiom,
    ! [M: $i] :
      ( ( hAPP_int_int @ ( legacy_zgcd @ one_one_int ) @ M )
      = one_one_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4488_zgcd__1__left) ).

thf(933,axiom,
    ! [M: $i] :
      ( ( hAPP_int_int @ ( legacy_zgcd @ M ) @ one_one_int )
      = one_one_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4487_zgcd__1) ).

thf(934,axiom,
    ! [N: $i,K_2: $i,M: $i] :
      ( ( ( hAPP_int_int @ ( legacy_zgcd @ K_2 ) @ M )
        = one_one_int )
     => ( ( ( hAPP_int_int @ ( legacy_zgcd @ N ) @ M )
          = one_one_int )
       => ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ N ) ) @ M )
          = one_one_int ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4486_zgcd__zgcd__zmult) ).

thf(935,axiom,
    ! [M: $i,K_2: $i,N: $i] :
      ( ( ( hAPP_int_int @ ( legacy_zgcd @ K_2 ) @ N )
        = one_one_int )
     => ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ M ) ) @ N )
        = ( hAPP_int_int @ ( legacy_zgcd @ M ) @ N ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4485_zgcd__zmult__cancel) ).

thf(1141,axiom,
    ! [X: $i] :
      ( ( hAPP_int_int @ fact_fact_int @ ( hAPP_nat_int @ semiri1621563631at_int @ X ) )
      = ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ fact_fact_nat @ X ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4279_transfer__int__nat__factorial) ).

thf(1147,axiom,
    ( ( hAPP_int_int @ fact_fact_int @ zero_zero_int )
    = one_one_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4273_fact__0__int) ).

thf(1148,axiom,
    ( ( hAPP_int_int @ fact_fact_int @ one_one_int )
    = one_one_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4272_fact__1__int) ).

thf(1220,axiom,
    ! [M: $i,N: $i] :
      ( ( xzgcd @ M @ N )
      = ( xzgcda @ M @ N @ M @ N @ one_one_int @ zero_zero_int @ zero_zero_int @ one_one_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4200_xzgcd__def) ).

thf(1360,axiom,
    ( ( hAPP_nat_nat @ nat_size @ zero_zero_nat )
    = zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4060_nat_Osize_I1_J) ).

thf(1361,axiom,
    ( ( hAPP_nat_nat @ size_size_nat @ zero_zero_nat )
    = zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4059_nat_Osize_I3_J) ).

thf(1362,axiom,
    ! [N: $i] :
      ( ( hAPP_nat_nat @ size_size_nat @ N )
      = N ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4058_nat__size) ).

thf(1372,axiom,
    ! [K_2: $i,L_2: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ bit0 @ K_2 ) ) @ ( hAPP_int_int @ bit1 @ L_2 ) )
      = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ pred @ K_2 ) ) @ L_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4048_diff__bin__simps_I8_J) ).

thf(1373,axiom,
    ! [K_2: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ min ) @ K_2 )
      = ( hAPP_int_int @ pred @ K_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4047_add__Min) ).

thf(1374,axiom,
    ! [K_2: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ K_2 ) @ min )
      = ( hAPP_int_int @ pred @ K_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4046_add__Min__right) ).

thf(1375,axiom,
    ! [K_2: $i] :
      ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ bit1 @ K_2 ) )
      = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ pred @ ( hAPP_int_int @ uminus_uminus_int @ K_2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4045_minus__Bit1) ).

thf(1376,axiom,
    ! [K_2: $i] :
      ( ( hAPP_int_int @ pred @ K_2 )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ K_2 ) @ one_one_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4044_pred__def) ).

thf(1377,axiom,
    ( ( hAPP_int_int @ pred @ min )
    = ( hAPP_int_int @ bit0 @ min ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4043_pred__Min) ).

thf(1378,axiom,
    ( ( hAPP_int_int @ pred @ pls )
    = min ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4042_pred__Pls) ).

thf(1380,axiom,
    ! [K_2: $i] :
      ( ( hAPP_int_int @ pred @ ( hAPP_int_int @ bit1 @ K_2 ) )
      = ( hAPP_int_int @ bit0 @ K_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4040_pred__Bit1) ).

thf(1381,axiom,
    ! [K_2: $i] :
      ( ( hAPP_int_int @ pred @ ( hAPP_int_int @ bit0 @ K_2 ) )
      = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ pred @ K_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4039_pred__Bit0) ).

thf(1382,axiom,
    ! [X: $i] :
      ( ( is_int @ X )
     => ( ( hAPP_int_int @ succ @ ( hAPP_int_int @ pred @ X ) )
        = X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4038_succ__pred) ).

thf(1420,axiom,
    ! [Y: $i] :
      ( ( Y != zero_zero_nat )
     => ~ ! [Nat_1: $i] :
            ( Y
           != ( hAPP_nat_nat @ suc @ Nat_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4000_nat_Oexhaust) ).

thf(1438,axiom,
    ! [N: $i] :
      ( ( N != zero_zero_nat )
     => ? [M_1: $i] :
          ( N
          = ( hAPP_nat_nat @ suc @ M_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3982_not0__implies__Suc) ).

thf(1585,axiom,
    ( ( hAPP_nat_nat @ fact_fact_nat @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
    = ( hAPP_nat_nat @ suc @ zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3835_fact__Suc__0__nat) ).

thf(1586,axiom,
    ( ( hAPP_nat_nat @ fact_fact_nat @ zero_zero_nat )
    = ( hAPP_nat_nat @ suc @ zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3834_Fact_Ofact__0__nat) ).

thf(1587,axiom,
    ( ( hAPP_nat_nat @ fact_fact_nat @ one_one_nat )
    = one_one_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3833_fact__1__nat) ).

thf(1589,axiom,
    ! [N: $i] :
      ( ( hAPP_nat_nat @ fact_fact_nat @ N )
     != zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3831_fact__nonzero__nat) ).

thf(1921,axiom,
    ! [A_3: $i,B_2: $i] :
      ( ( is_int @ B_2 )
     => ( ( B_2 != zero_zero_int )
       => ( ( ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
              = zero_zero_int )
           => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) @ B_2 )
              = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ B_2 ) ) ) )
          & ( ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
             != zero_zero_int )
           => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) @ B_2 )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ B_2 ) ) ) @ one_one_int ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3499_zdiv__zminus1__eq__if) ).

thf(1922,axiom,
    ! [A_3: $i,B_2: $i] :
      ( ( is_int @ B_2 )
     => ( ( B_2 != zero_zero_int )
       => ( ( ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
              = zero_zero_int )
           => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ ( hAPP_int_int @ uminus_uminus_int @ B_2 ) )
              = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ B_2 ) ) ) )
          & ( ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
             != zero_zero_int )
           => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ ( hAPP_int_int @ uminus_uminus_int @ B_2 ) )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ B_2 ) ) ) @ one_one_int ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3498_zdiv__zminus2__eq__if) ).

thf(1926,axiom,
    ! [A_3: $i] :
      ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
      = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3494_power3__minus) ).

thf(1928,axiom,
    ! [A_3: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ ( hAPP_int_int @ number_number_of_int @ min ) )
      = ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3492_zdiv__minus1__right) ).

thf(1929,axiom,
    ! [A_3: $i,B_2: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
          = zero_zero_int )
       => ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ ( hAPP_int_int @ uminus_uminus_int @ B_2 ) )
          = zero_zero_int ) )
      & ( ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
         != zero_zero_int )
       => ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ ( hAPP_int_int @ uminus_uminus_int @ B_2 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 ) ) @ B_2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3491_zmod__zminus2__eq__if) ).

thf(1930,axiom,
    ! [A_3: $i,B_2: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
          = zero_zero_int )
       => ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) @ B_2 )
          = zero_zero_int ) )
      & ( ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
         != zero_zero_int )
       => ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) @ B_2 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ B_2 ) @ ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3490_zmod__zminus1__eq__if) ).

thf(1932,axiom,
    ! [V_1: $i,W: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ number_number_of_int @ V_1 ) ) @ ( hAPP_int_int @ number_number_of_int @ W ) )
      = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ V_1 ) @ ( hAPP_int_int @ uminus_uminus_int @ W ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3488_minus__numeral__code_I6_J) ).

thf(1933,axiom,
    ! [N: $i] :
      ( ( hAPP_int_nat @ nat @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ N ) ) )
      = zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3487_nat__zminus__int) ).

thf(1936,axiom,
    ( ( hAPP_int_int @ uminus_uminus_int @ min )
    = ( hAPP_int_int @ bit1 @ pls ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3484_minus__Min) ).

thf(1937,axiom,
    ! [K_2: $i,L_2: $i] :
      ( ( ( hAPP_int_int @ ( div_mod_int @ K_2 ) @ ( hAPP_int_int @ uminus_uminus_int @ L_2 ) )
       != zero_zero_int )
     => ( ( hAPP_int_int @ ( div_mod_int @ K_2 ) @ L_2 )
       != zero_zero_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3483_zmod__zminus2__not__zero) ).

thf(1938,axiom,
    ! [K_2: $i,L_2: $i] :
      ( ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ K_2 ) ) @ L_2 )
       != zero_zero_int )
     => ( ( hAPP_int_int @ ( div_mod_int @ K_2 ) @ L_2 )
       != zero_zero_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3482_zmod__zminus1__not__zero) ).

thf(1939,axiom,
    ! [K_2: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ min ) @ K_2 )
      = ( hAPP_int_int @ uminus_uminus_int @ K_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3481_mult__Min) ).

thf(1940,axiom,
    ( min
    = ( hAPP_int_int @ uminus_uminus_int @ one_one_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3480_Int_OMin__def) ).

thf(1941,axiom,
    ! [Z_1: $i,W: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ Z_1 ) @ W )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z_1 ) @ ( hAPP_int_int @ uminus_uminus_int @ W ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3479_diff__int__def) ).

thf(1942,axiom,
    ! [Z_1: $i,W: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z_1 ) @ ( hAPP_int_int @ uminus_uminus_int @ W ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ Z_1 ) @ W ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3478_diff__int__def__symmetric) ).

thf(1944,axiom,
    ! [Na: $i,Ma: $i] :
      ( ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ Na ) )
        = ( hAPP_nat_int @ semiri1621563631at_int @ Ma ) )
    <=> ( ( Na = zero_zero_nat )
        & ( Ma = zero_zero_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3476_negative__eq__positive) ).

thf(1945,axiom,
    ! [Z_1: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ uminus_uminus_int @ Z_1 ) ) @ Z_1 )
      = zero_zero_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3475_zadd__zminus__inverse2) ).

thf(1947,axiom,
    ! [A_3: $i,B_2: $i] :
      ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ ( hAPP_int_int @ uminus_uminus_int @ B_2 ) )
      = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) @ B_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3473_zmod__zminus2) ).

thf(1948,axiom,
    ! [A_3: $i,B_2: $i] :
      ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) @ ( hAPP_int_int @ uminus_uminus_int @ B_2 ) )
      = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3472_zmod__zminus__zminus) ).

thf(1949,axiom,
    ! [X: $i,M: $i] :
      ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( div_mod_int @ X ) @ M ) ) ) @ M )
      = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ X ) ) @ M ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3471_zminus__zmod) ).

thf(1950,axiom,
    ! [A_3: $i,B_2: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ ( hAPP_int_int @ uminus_uminus_int @ B_2 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) @ B_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3470_zdiv__zminus2) ).

thf(1951,axiom,
    ! [A_3: $i,B_2: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) @ ( hAPP_int_int @ uminus_uminus_int @ B_2 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ B_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3469_zdiv__zminus__zminus) ).

thf(1955,axiom,
    ! [W: $i] :
      ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ number_number_of_int @ W ) )
      = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ uminus_uminus_int @ W ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3465_minus__numeral__code_I5_J) ).

thf(1956,axiom,
    ! [Z_1: $i,W: $i] :
      ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z_1 ) @ W ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ uminus_uminus_int @ Z_1 ) ) @ ( hAPP_int_int @ uminus_uminus_int @ W ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3464_zminus__zadd__distrib) ).

thf(1957,axiom,
    ! [Z_1: $i,W: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ uminus_uminus_int @ Z_1 ) ) @ W )
      = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z_1 ) @ W ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3463_zmult__zminus) ).

thf(1958,axiom,
    ( ( hAPP_int_int @ uminus_uminus_int @ zero_zero_int )
    = zero_zero_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3462_zminus__0) ).

thf(1959,axiom,
    ! [K_2: $i] :
      ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ bit0 @ K_2 ) )
      = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ uminus_uminus_int @ K_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3461_minus__Bit0) ).

thf(1960,axiom,
    ( ( hAPP_int_int @ uminus_uminus_int @ pls )
    = pls ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3460_minus__Pls) ).

thf(1961,axiom,
    ! [Z_1: $i] :
      ( ( is_int @ Z_1 )
     => ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ uminus_uminus_int @ Z_1 ) )
        = Z_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3459_zminus__zminus) ).

thf(2094,axiom,
    ! [Z_1: $i] :
      ( ( is_int @ Z_1 )
     => ~ ! [M_1: $i,N_1: $i] :
            ( Z_1
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ M_1 ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ N_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3326_int__diff__cases) ).

thf(2213,axiom,
    ! [M: $i] :
      ( ( ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
        = zero_zero_nat )
      | ( ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
        = one_one_nat )
      | ( ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
        = ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
      | ( ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
        = ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3207_mod__exhaust__less__4) ).

thf(2217,axiom,
    ! [M: $i] :
      ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ suc @ M ) ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
      = ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3203_mod2__Suc__Suc) ).

thf(2234,axiom,
    ! [A_3: $i,B_2: $i] :
      ( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( div_mod_nat @ A_3 ) @ B_2 ) )
      = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A_3 ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3186_zmod__int) ).

thf(2235,axiom,
    ! [X: $i,Y: $i] :
      ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_nat_int @ semiri1621563631at_int @ X ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ Y ) )
      = ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( div_mod_nat @ X ) @ Y ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3185_Divides_Otransfer__int__nat__functions_I2_J) ).

thf(2243,axiom,
    ! [M: $i,N: $i] :
      ( ( ( ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ N ) )
          = N )
       => ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ M ) ) @ N )
          = zero_zero_nat ) )
      & ( ( ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ N ) )
         != N )
       => ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ M ) ) @ N )
          = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ N ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3177_mod__Suc) ).

thf(2244,axiom,
    ! [M: $i] :
      ( ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
      = zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3176_mod__1) ).

thf(2250,axiom,
    ! [M: $i,N: $i] :
      ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ M ) ) @ N )
      = ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ N ) ) ) @ N ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3170_mod__Suc__eq__Suc__mod) ).

thf(2254,axiom,
    ! [M_5: $i,D_4: $i] :
      ( ( is_int @ M_5 )
     => ( ( ( hAPP_int_int @ ( div_mod_int @ M_5 ) @ D_4 )
          = zero_zero_int )
       => ? [Q_4: $i] :
            ( ( is_int @ Q_4 )
            & ( M_5
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ D_4 ) @ Q_4 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3166_zmod__eq__0D) ).

thf(2259,axiom,
    ! [P_3: $i,A_3: $i] :
      ( ( hAPP_int_int @ ( inv @ P_3 ) @ A_3 )
      = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ nat @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ P_3 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) ) @ P_3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3161_WilsonRuss_Oinv__def) ).

thf(2266,axiom,
    ( ( hAPP_int_nat @ nat @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
    = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3154_nat__2) ).

thf(2271,axiom,
    ! [Xa: $i] :
      ( ( ( hAPP_int_int @ ( div_mod_int @ Xa ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
       != zero_zero_int )
    <=> ( ( hAPP_int_int @ ( div_mod_int @ Xa ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
        = one_one_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3149_neq__one__mod__two) ).

thf(2285,axiom,
    ( ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
    = ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3135_semiring__norm_I115_J) ).

thf(2286,axiom,
    ( ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) )
    = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3134_numeral__2__eq__2) ).

thf(2297,axiom,
    ! [V_1: $i,W: $i] :
      ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ V_1 ) ) ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ W ) ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ number_number_of_int @ V_1 ) ) @ ( hAPP_int_int @ number_number_of_int @ W ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3123_zmod__number__of__Bit0) ).

thf(2306,axiom,
    ( ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ pls ) )
    = ( hAPP_nat_nat @ suc @ zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3114_numeral__1__eq__Suc__0) ).

thf(2307,axiom,
    ( ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) )
    = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3113_numeral__3__eq__3) ).

thf(2308,axiom,
    ! [A_3: $i,B_2: $i,M: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_3 ) @ B_2 )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ M ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ M ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ B_2 ) @ M ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ M ) ) @ ( hAPP_int_int @ ( div_mod_int @ B_2 ) @ M ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3112_zcong__zmod__aux) ).

thf(2309,axiom,
    ! [R_2: $i,S_1: $i,T_1: $i,R_4: $i,S_3: $i,M: $i,T_2: $i,N: $i] :
      ( ( R_4
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ S_3 ) @ M ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ T_2 ) @ N ) ) )
     => ( ( R_2
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ S_1 ) @ M ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ T_1 ) @ N ) ) )
       => ( ( hAPP_int_int @ ( div_mod_int @ R_4 ) @ R_2 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ S_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ R_4 ) @ R_2 ) ) @ S_1 ) ) ) @ M ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ T_2 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ R_4 ) @ R_2 ) ) @ T_1 ) ) ) @ N ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3111_xzgcda__linear__aux2) ).

thf(2315,axiom,
    ! [M: $i] :
      ( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ suc @ M ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ M ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3105_int__Suc) ).

thf(2316,axiom,
    ( ( hAPP_int_nat @ nat @ one_one_int )
    = ( hAPP_nat_nat @ suc @ zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3104_nat__1) ).

thf(2317,axiom,
    ( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
    = one_one_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3103_int__Suc0__eq__1) ).

thf(2328,axiom,
    ! [M: $i,N: $i] :
      ( ( hAPP_int_int @ ( div_mod_int @ M ) @ N )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ M ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ M ) @ N ) ) @ N ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3092_zmod__zdiv__equality_H) ).

thf(2329,axiom,
    ! [N: $i,M: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ N ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ M ) @ N ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ M ) @ ( hAPP_int_int @ ( div_mod_int @ M ) @ N ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3091_zmult__div__cancel) ).

thf(2330,axiom,
    ! [A_3: $i,B_2: $i,K_2: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ B_2 ) ) @ B_2 ) ) @ ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 ) ) ) @ K_2 )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_3 ) @ K_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3090_zdiv__zmod__equality2) ).

thf(2331,axiom,
    ! [B_2: $i,A_3: $i,K_2: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_2 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ B_2 ) ) ) @ ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 ) ) ) @ K_2 )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_3 ) @ K_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3089_zdiv__zmod__equality) ).

thf(2332,axiom,
    ! [A_3: $i,B_2: $i,C_1: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ B_2 ) ) @ C_1 )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ B_2 ) @ C_1 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ ( hAPP_int_int @ ( div_mod_int @ B_2 ) @ C_1 ) ) ) @ C_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3088_zdiv__zmult1__eq) ).

thf(2333,axiom,
    ! [A_3: $i,B_2: $i] :
      ( ( is_int @ A_3 )
     => ( A_3
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_2 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ B_2 ) ) ) @ ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3087_zmod__zdiv__equality) ).

thf(2335,axiom,
    ! [A_3: $i] :
      ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ ( hAPP_int_int @ number_number_of_int @ min ) )
      = zero_zero_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3085_zmod__minus1__right) ).

thf(2373,axiom,
    ( one_one_nat
    = ( hAPP_nat_nat @ suc @ zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3047_One__nat__def) ).

thf(2383,axiom,
    ! [A_3: $i,B_2: $i,C_1: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_3 ) @ B_2 ) ) @ C_1 )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ C_1 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ B_2 ) @ C_1 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ C_1 ) ) @ ( hAPP_int_int @ ( div_mod_int @ B_2 ) @ C_1 ) ) ) @ C_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3037_zdiv__zadd1__eq) ).

thf(2384,axiom,
    ! [A_3: $i] :
      ( ( is_int @ A_3 )
     => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ zero_zero_int )
          = zero_zero_int )
        & ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ zero_zero_int )
          = A_3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3036_DIVISION__BY__ZERO) ).

thf(2385,axiom,
    ! [A_3: $i,B_2: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 ) ) @ B_2 )
      = zero_zero_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3035_zmod__zdiv__trivial) ).

thf(2388,axiom,
    ! [Ma: $i,D_1: $i] :
      ( ( is_int @ Ma )
     => ( ( ( hAPP_int_int @ ( div_mod_int @ Ma ) @ D_1 )
          = zero_zero_int )
      <=> ? [Q_4: $i] :
            ( ( is_int @ Q_4 )
            & ( Ma
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ D_1 ) @ Q_4 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3032_zmod__eq__0__iff) ).

thf(2422,axiom,
    ! [X: $i,M: $i,Y: $i] :
      ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( div_mod_int @ X ) @ M ) ) @ Y ) ) @ M )
      = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X ) @ Y ) ) @ M ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2998_zpower__zmod) ).

thf(2423,axiom,
    ! [M: $i] :
      ( ( hAPP_nat_nat @ suc @ M )
     != zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2997_Suc__neq__Zero) ).

thf(2424,axiom,
    ! [M: $i] :
      ( zero_zero_nat
     != ( hAPP_nat_nat @ suc @ M ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2996_Zero__neq__Suc) ).

thf(2425,axiom,
    ! [Nat_2: $i] :
      ( ( hAPP_nat_nat @ suc @ Nat_2 )
     != zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2995_nat_Osimps_I3_J) ).

thf(2426,axiom,
    ! [M: $i] :
      ( ( hAPP_nat_nat @ suc @ M )
     != zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2994_Suc__not__Zero) ).

thf(2427,axiom,
    ! [Nat_3: $i] :
      ( zero_zero_nat
     != ( hAPP_nat_nat @ suc @ Nat_3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2993_nat_Osimps_I2_J) ).

thf(2428,axiom,
    ! [M: $i] :
      ( zero_zero_nat
     != ( hAPP_nat_nat @ suc @ M ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2992_Zero__not__Suc) ).

thf(2429,axiom,
    ! [X: $i,Y: $i,M: $i] :
      ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ X ) @ ( hAPP_int_int @ ( div_mod_int @ Y ) @ M ) ) ) @ M )
      = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ X ) @ Y ) ) @ M ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2991_zdiff__zmod__right) ).

thf(2430,axiom,
    ! [X: $i,M: $i,Y: $i] :
      ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( div_mod_int @ X ) @ M ) ) @ Y ) ) @ M )
      = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ X ) @ Y ) ) @ M ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2990_zdiff__zmod__left) ).

thf(2431,axiom,
    ! [A_3: $i,B_2: $i,C_1: $i] :
      ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ ( hAPP_int_int @ ( div_mod_int @ B_2 ) @ C_1 ) ) ) @ C_1 )
      = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ B_2 ) ) @ C_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2989_zmod__simps_I3_J) ).

thf(2432,axiom,
    ! [A_3: $i,B_2: $i,C_1: $i] :
      ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ B_2 ) ) @ C_1 )
      = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ ( hAPP_int_int @ ( div_mod_int @ B_2 ) @ C_1 ) ) ) @ C_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2988_zmod__zmult1__eq) ).

thf(2433,axiom,
    ! [B_2: $i] :
      ( ( hAPP_int_int @ ( div_mod_int @ zero_zero_int ) @ B_2 )
      = zero_zero_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2987_zmod__zero) ).

thf(2434,axiom,
    ! [A_3: $i] :
      ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ A_3 )
      = zero_zero_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2986_zmod__self) ).

thf(2435,axiom,
    ! [N: $i] :
      ( N
     != ( hAPP_nat_nat @ suc @ N ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2985_n__not__Suc__n) ).

thf(2436,axiom,
    ! [N: $i] :
      ( ( hAPP_nat_nat @ suc @ N )
     != N ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2984_Suc__n__not__n) ).

thf(2437,axiom,
    ! [Nat_5: $i,Nat_4: $i] :
      ( ( ( hAPP_nat_nat @ suc @ Nat_5 )
        = ( hAPP_nat_nat @ suc @ Nat_4 ) )
    <=> ( Nat_5 = Nat_4 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2983_nat_Oinject) ).

thf(2438,axiom,
    ! [X: $i,Y: $i] :
      ( ( ( hAPP_nat_nat @ suc @ X )
        = ( hAPP_nat_nat @ suc @ Y ) )
     => ( X = Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2982_Suc__inject) ).

thf(2439,axiom,
    ! [M: $i,X: $i] :
      ( ( hAPP_int_int @ ( standardRes @ M ) @ X )
      = ( hAPP_int_int @ ( div_mod_int @ X ) @ M ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2981_StandardRes__def) ).

thf(2481,axiom,
    ! [X: $i] :
      ( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_int_nat @ nat @ ( hAPP_int_int @ abs_abs_int @ X ) ) )
      = ( hAPP_int_int @ abs_abs_int @ X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2939_int__nat__abs) ).

thf(2511,axiom,
    ! [P_3: $i,X: $i] :
      ( ( hAPP_int_int @ ( multInv @ P_3 ) @ X )
      = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X ) @ ( hAPP_int_nat @ nat @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ P_3 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2909_MultInv__def) ).

thf(2593,axiom,
    ! [V_1: $i,W: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ V_1 ) ) ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ W ) ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ number_number_of_int @ V_1 ) ) @ ( hAPP_int_int @ number_number_of_int @ W ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2827_zdiv__number__of__Bit0) ).

thf(2598,axiom,
    ! [A_3: $i] :
      ( ( is_int @ A_3 )
     => ( ( A_3 != zero_zero_int )
       => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ A_3 )
          = one_one_int ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2822_zdiv__self) ).

thf(2599,axiom,
    ! [B_2: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ zero_zero_int ) @ B_2 )
      = zero_zero_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2821_zdiv__zero) ).

thf(2613,axiom,
    ! [A_3: $i] :
      ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
        = one_one_int )
     => ( ( hAPP_int_int @ abs_abs_int @ A_3 )
        = one_one_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2807_power2__eq1__iff) ).

thf(2616,axiom,
    ! [A_3: $i] :
      ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
      = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ abs_abs_int @ A_3 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2804_abs__power2__distrib) ).

thf(2617,axiom,
    ! [A_1: $i,B_1: $i] :
      ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
        = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
    <=> ( ( hAPP_int_int @ abs_abs_int @ A_1 )
        = ( hAPP_int_int @ abs_abs_int @ B_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2803_power2__eq__iff__abs__eq) ).

thf(2618,axiom,
    ( ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) )
    = ( hAPP_int_nat @ nat @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2802_transfer__nat__int__numerals_I3_J) ).

thf(2634,axiom,
    ! [X: $i] :
      ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
      = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ abs_abs_int @ X ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2786_abs__power3__distrib) ).

thf(2637,axiom,
    ( ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) )
    = ( hAPP_int_nat @ nat @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2783_transfer__nat__int__numerals_I4_J) ).

thf(2652,axiom,
    ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ number_number_of_int @ min ) )
    = one_one_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2768_abs__minus__one) ).

thf(2672,axiom,
    ! [Z_2: $i] :
      ( ( is_int @ Z_2 )
     => ( ( ( hAPP_int_int @ abs_abs_int @ Z_2 )
          = one_one_int )
      <=> ( ( Z_2 = one_one_int )
          | ( Z_2
            = ( hAPP_int_int @ number_number_of_int @ min ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2748_abs__eq__1__iff) ).

thf(2673,axiom,
    ( one_one_nat
    = ( hAPP_int_nat @ nat @ one_one_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2747_transfer__nat__int__numerals_I2_J) ).

thf(2674,axiom,
    ! [W: $i] :
      ( ( hAPP_int_nat @ nat @ ( hAPP_int_int @ number_number_of_int @ W ) )
      = ( hAPP_int_nat @ number_number_of_nat @ W ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2746_nat__number__of) ).

thf(2675,axiom,
    ! [V_1: $i] :
      ( ( hAPP_int_nat @ number_number_of_nat @ V_1 )
      = ( hAPP_int_nat @ nat @ ( hAPP_int_int @ number_number_of_int @ V_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2745_nat__number__of__def) ).

thf(2680,axiom,
    ! [M: $i,N: $i] :
      ( ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ M ) @ N ) )
        = one_one_int )
     => ( ( hAPP_int_int @ abs_abs_int @ M )
        = one_one_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2740_abs__zmult__eq__1) ).

thf(2681,axiom,
    ( zero_zero_nat
    = ( hAPP_int_nat @ nat @ zero_zero_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2739_transfer__nat__int__numerals_I1_J) ).

thf(2682,axiom,
    ( ( hAPP_int_nat @ nat @ zero_zero_int )
    = zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2738_nat__0) ).

thf(2717,axiom,
    ! [N: $i] :
      ( ( hAPP_int_nat @ nat @ ( hAPP_nat_int @ semiri1621563631at_int @ N ) )
      = N ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2703_nat__int) ).

thf(2718,axiom,
    ! [M: $i] :
      ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_nat_int @ semiri1621563631at_int @ M ) )
      = ( hAPP_nat_int @ semiri1621563631at_int @ M ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2702_abs__int__eq) ).

thf(2719,axiom,
    ! [N_8: $i] :
      ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_nat_int @ semiri1621563631at_int @ N_8 ) )
      = ( hAPP_nat_int @ semiri1621563631at_int @ N_8 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2701_abs__of__nat) ).

thf(2731,axiom,
    ! [A_20: $i,N_9: $i] :
      ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_20 ) @ N_9 ) )
      = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ abs_abs_int @ A_20 ) ) @ N_9 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2689_power__abs) ).

thf(2734,axiom,
    ! [A_21: $i,B_16: $i] :
      ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_21 ) @ B_16 ) )
      = ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ B_16 ) @ A_21 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2686_abs__minus__commute) ).

thf(2737,axiom,
    ( ( hAPP_int_int @ abs_abs_int @ one_one_int )
    = one_one_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2683_abs__one) ).

thf(2740,axiom,
    ! [A_22: $i,B_17: $i] :
      ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ abs_abs_int @ A_22 ) ) @ ( hAPP_int_int @ abs_abs_int @ B_17 ) ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ abs_abs_int @ A_22 ) ) @ ( hAPP_int_int @ abs_abs_int @ B_17 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2680_abs__add__abs) ).

thf(2743,axiom,
    ! [A_23: $i,B_18: $i] :
      ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_23 ) @ B_18 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ A_23 ) ) @ ( hAPP_int_int @ abs_abs_int @ B_18 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2677_abs__mult) ).

thf(2746,axiom,
    ! [A_24: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ A_24 ) ) @ ( hAPP_int_int @ abs_abs_int @ A_24 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_24 ) @ A_24 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2674_abs__mult__self) ).

thf(2755,axiom,
    ( ( hAPP_int_int @ abs_abs_int @ zero_zero_int )
    = zero_zero_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2665_abs__zero) ).

thf(2758,axiom,
    ! [A_1: $i] :
      ( ( is_int @ A_1 )
     => ( ( ( hAPP_int_int @ abs_abs_int @ A_1 )
          = zero_zero_int )
      <=> ( A_1 = zero_zero_int ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2662_abs__eq__0) ).

thf(2764,axiom,
    ! [A_27: $i] :
      ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ abs_abs_int @ A_27 ) )
      = ( hAPP_int_int @ abs_abs_int @ A_27 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2656_abs__idempotent) ).

thf(2819,axiom,
    ! [N: $i] :
      ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ number_number_of_int @ min ) ) @ N )
        = one_one_int )
      | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ number_number_of_int @ min ) ) @ N )
        = ( hAPP_int_int @ number_number_of_int @ min ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2601_neg__one__power) ).

thf(2831,axiom,
    ! [A_3: $i,R_2: $i,B_2: $i,M: $i,C_1: $i,D_3: $i,N: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ R_2 ) @ B_2 ) ) ) @ M ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ C_1 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ R_2 ) @ D_3 ) ) ) @ N ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ M ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ C_1 ) @ N ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ R_2 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_2 ) @ M ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ D_3 ) @ N ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2589_xzgcda__linear__aux1) ).

thf(2846,axiom,
    ! [A_3: $i,B_2: $i,C_1: $i] :
      ( ( is_int @ A_3 )
     => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_3 ) @ B_2 )
          = C_1 )
       => ( A_3
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ C_1 ) @ B_2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2574_Int2_Oaux1) ).

thf(2959,axiom,
    ! [A_3: $i,B_2: $i] :
      ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_3 ) @ B_2 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ A_3 ) ) @ B_2 ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2461_zdiff__power2) ).

thf(2960,axiom,
    ! [A_3: $i,B_2: $i] :
      ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_3 ) @ B_2 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) @ B_2 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ A_3 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2460_zdiff__power3) ).

thf(2961,axiom,
    ! [X_7: $i,Y_6: $i] :
      ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ X_7 ) @ Y_6 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X_7 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Y_6 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ X_7 ) ) @ Y_6 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2459_power2__diff) ).

thf(2965,axiom,
    ! [A_3: $i,B_2: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_3 ) @ B_2 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_3 ) @ B_2 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2455_zspecial__product) ).

thf(2975,axiom,
    ! [L_2: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ min ) @ ( hAPP_int_int @ bit0 @ L_2 ) )
      = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ min ) @ L_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2445_diff__bin__simps_I5_J) ).

thf(2976,axiom,
    ! [L_2: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ min ) @ ( hAPP_int_int @ bit1 @ L_2 ) )
      = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ min ) @ L_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2444_diff__bin__simps_I6_J) ).

thf(2977,axiom,
    ! [L_2: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ pls ) @ ( hAPP_int_int @ bit1 @ L_2 ) )
      = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ min ) @ L_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2443_diff__bin__simps_I4_J) ).

thf(2980,axiom,
    ! [V_4: $i,W_2: $i,C_6: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ V_4 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ number_number_of_int @ W_2 ) ) @ C_6 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ V_4 ) @ W_2 ) ) ) @ C_6 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2440_add__number__of__diff1) ).

thf(2984,axiom,
    ! [X_9: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ X_9 ) @ X_9 ) ) @ one_one_int )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ X_9 ) @ one_one_int ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ X_9 ) @ one_one_int ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2436_real__squared__diff__one__factored) ).

thf(3007,axiom,
    ! [K_2: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ K_2 ) @ min )
      = ( hAPP_int_int @ succ @ K_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2413_diff__bin__simps_I2_J) ).

thf(3010,axiom,
    ! [L_2: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ pls ) @ ( hAPP_int_int @ bit0 @ L_2 ) )
      = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ pls ) @ L_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2410_diff__bin__simps_I3_J) ).

thf(3011,axiom,
    ! [K_2: $i,L_2: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ bit1 @ K_2 ) ) @ ( hAPP_int_int @ bit0 @ L_2 ) )
      = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ K_2 ) @ L_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2409_diff__bin__simps_I9_J) ).

thf(3012,axiom,
    ! [K_2: $i,L_2: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ bit1 @ K_2 ) ) @ ( hAPP_int_int @ bit1 @ L_2 ) )
      = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ K_2 ) @ L_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2408_diff__bin__simps_I10_J) ).

thf(3020,axiom,
    ! [A_28: $i,B_20: $i,V_5: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_28 ) @ B_20 ) ) @ ( hAPP_int_int @ number_number_of_int @ V_5 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_28 ) @ ( hAPP_int_int @ number_number_of_int @ V_5 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_20 ) @ ( hAPP_int_int @ number_number_of_int @ V_5 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2400_left__diff__distrib__number__of) ).

thf(3024,axiom,
    ! [V_6: $i,B_21: $i,C_7: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ V_6 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ B_21 ) @ C_7 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ V_6 ) ) @ B_21 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ V_6 ) ) @ C_7 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2396_right__diff__distrib__number__of) ).

thf(3028,axiom,
    ! [X_10: $i,Y_7: $i,A_29: $i,B_22: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ X_10 ) @ Y_7 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_29 ) @ B_22 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ X_10 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ Y_7 ) @ B_22 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ X_10 ) @ A_29 ) ) @ B_22 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2392_mult__diff__mult) ).

thf(3032,axiom,
    ! [A_1: $i,E_2: $i,C: $i,B_1: $i,D_1: $i] :
      ( ( is_int @ C )
     => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ E_2 ) ) @ C )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_1 ) @ E_2 ) ) @ D_1 ) )
      <=> ( C
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ B_1 ) @ A_1 ) ) @ E_2 ) ) @ D_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2388_eq__add__iff2) ).

thf(3036,axiom,
    ! [A_1: $i,E_2: $i,C: $i,B_1: $i,D_1: $i] :
      ( ( is_int @ D_1 )
     => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ E_2 ) ) @ C )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_1 ) @ E_2 ) ) @ D_1 ) )
      <=> ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_1 ) @ B_1 ) ) @ E_2 ) ) @ C )
          = D_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2384_eq__add__iff1) ).

thf(3066,axiom,
    ! [W: $i,Z1: $i,Z2: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ W ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ Z1 ) @ Z2 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ W ) @ Z1 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ W ) @ Z2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2354_zdiff__zmult__distrib2) ).

thf(3067,axiom,
    ! [Z1: $i,Z2: $i,W: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ Z1 ) @ Z2 ) ) @ W )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z1 ) @ W ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z2 ) @ W ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2353_zdiff__zmult__distrib) ).

thf(3068,axiom,
    ! [K_2: $i,L_2: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ bit0 @ K_2 ) ) @ ( hAPP_int_int @ bit0 @ L_2 ) )
      = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ K_2 ) @ L_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2352_diff__bin__simps_I7_J) ).

thf(3069,axiom,
    ! [K_2: $i] :
      ( ( is_int @ K_2 )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ K_2 ) @ pls )
        = K_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2351_diff__bin__simps_I1_J) ).

thf(3070,axiom,
    ! [A_32: $i,C_8: $i,B_24: $i,D_7: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_32 ) @ C_8 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_24 ) @ D_7 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_32 ) @ B_24 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ C_8 ) @ D_7 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2350_add__diff__add) ).

thf(3074,axiom,
    ! [A_33: $i,B_25: $i] :
      ( ( is_int @ A_33 )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_33 ) @ B_25 ) ) @ B_25 )
        = A_33 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2346_diff__add__cancel) ).

thf(3078,axiom,
    ! [A_34: $i,B_26: $i] :
      ( ( is_int @ A_34 )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_34 ) @ B_26 ) ) @ B_26 )
        = A_34 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2342_add__diff__cancel) ).

thf(3088,axiom,
    ! [A_35: $i] :
      ( ( is_int @ A_35 )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_35 ) @ zero_zero_int )
        = A_35 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2332_diff__0__right) ).

thf(3092,axiom,
    ! [A_36: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_36 ) @ A_36 )
      = zero_zero_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2328_diff__self) ).

thf(3096,axiom,
    ! [A_1: $i,B_1: $i] :
      ( ( ( is_int @ A_1 )
        & ( is_int @ B_1 ) )
     => ( ( A_1 = B_1 )
      <=> ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_1 ) @ B_1 )
          = zero_zero_int ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2324_eq__iff__diff__eq__0) ).

thf(3100,axiom,
    ! [A_1: $i,B_1: $i] :
      ( ( ( is_int @ A_1 )
        & ( is_int @ B_1 ) )
     => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_1 ) @ B_1 )
          = zero_zero_int )
      <=> ( A_1 = B_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2320_right__minus__eq) ).

thf(3189,axiom,
    ! [V_7: $i,W_3: $i] :
      ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ V_7 ) @ W_3 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ number_number_of_int @ V_7 ) ) @ ( hAPP_int_int @ number_number_of_int @ W_3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2231_number__of__diff) ).

thf(3193,axiom,
    ! [A_1: $i,B_1: $i,C: $i,D_1: $i] :
      ( ( ( is_int @ A_1 )
        & ( is_int @ B_1 )
        & ( is_int @ C )
        & ( is_int @ D_1 ) )
     => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_1 ) @ B_1 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ C ) @ D_1 ) )
       => ( ( A_1 = B_1 )
        <=> ( C = D_1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2227_diff__eq__diff__eq) ).

thf(3221,axiom,
    ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ s ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_int_int @ number_number_of_int @ min ) )
    = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ s ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ one_one_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2199__096s_____A_094_A2_A_N_A_N1_A_061_As_____A_094_A2_A_L_A1_096) ).

thf(3234,axiom,
    ! [Ma: $i,Na: $i] :
      ( ( ( is_int @ Ma )
        & ( is_int @ Na ) )
     => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Ma ) @ Na )
          = one_one_int )
      <=> ( ( ( Ma = one_one_int )
            & ( Na = one_one_int ) )
          | ( ( Ma
              = ( hAPP_int_int @ number_number_of_int @ min ) )
            & ( Na
              = ( hAPP_int_int @ number_number_of_int @ min ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2186_zmult__eq__1__iff) ).

thf(3235,axiom,
    ! [M: $i,N: $i] :
      ( ( is_int @ M )
     => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ M ) @ N )
          = one_one_int )
       => ( ( M = one_one_int )
          | ( M
            = ( hAPP_int_int @ number_number_of_int @ min ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2185_pos__zmult__eq__1__iff__lemma) ).

thf(3239,axiom,
    ( ( hAPP_int_int @ succ @ min )
    = pls ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2181_succ__Min) ).

thf(3240,axiom,
    ( ( hAPP_int_int @ number_number_of_int @ pls )
   != ( hAPP_int_int @ number_number_of_int @ min ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2180_eq__number__of__Pls__Min) ).

thf(3254,axiom,
    ! [K_2: $i] :
      ( ( hAPP_int_int @ bit0 @ K_2 )
     != min ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2166_rel__simps_I45_J) ).

thf(3255,axiom,
    ! [L_2: $i] :
      ( min
     != ( hAPP_int_int @ bit0 @ L_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2165_rel__simps_I42_J) ).

thf(3256,axiom,
    pls != min,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2164_rel__simps_I37_J) ).

thf(3257,axiom,
    min != pls,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2163_rel__simps_I40_J) ).

thf(3258,axiom,
    ! [K: $i] :
      ( ( is_int @ K )
     => ( ( ( hAPP_int_int @ bit1 @ K )
          = min )
      <=> ( K = min ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2162_rel__simps_I47_J) ).

thf(3259,axiom,
    ! [L: $i] :
      ( ( is_int @ L )
     => ( ( min
          = ( hAPP_int_int @ bit1 @ L ) )
      <=> ( min = L ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2161_rel__simps_I43_J) ).

thf(3260,axiom,
    ( ( hAPP_int_int @ bit1 @ min )
    = min ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2160_Bit1__Min) ).

thf(3348,axiom,
    ~ ! [X_1: $i,Y_1: $i] :
        ( ( ( is_int @ X_1 )
          & ( is_int @ Y_1 ) )
       => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Y_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2072__096_B_Bthesis_O_A_I_B_Bx_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_061_A_I4_) ).

thf(3364,axiom,
    ! [X_15: $i,Y_11: $i] :
      ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ X_15 ) @ Y_11 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X_15 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Y_11 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ X_15 ) ) @ Y_11 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2056_power2__sum) ).

thf(3505,axiom,
    ! [W_4: $i] :
      ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ number_number_of_int @ W_4 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ W_4 ) ) @ ( hAPP_int_int @ number_number_of_int @ W_4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1915_power2__eq__square__number__of) ).

thf(3510,axiom,
    ! [A_3: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
      = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1910_cube__square) ).

thf(3513,axiom,
    ! [X_26: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ X_26 ) @ X_26 )
      = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X_26 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1907_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).

thf(3519,axiom,
    ! [A_59: $i] :
      ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_59 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_59 ) @ A_59 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1901_power2__eq__square) ).

thf(3523,axiom,
    ! [Z_11: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ Z_11 )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z_11 ) @ Z_11 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1897_semiring__mult__2) ).

thf(3528,axiom,
    ! [Z_12: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ Z_12 )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z_12 ) @ Z_12 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1892_mult__2) ).

thf(3532,axiom,
    ! [Z_13: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z_13 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z_13 ) @ Z_13 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1888_semiring__mult__2__right) ).

thf(3537,axiom,
    ! [Z_14: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z_14 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z_14 ) @ Z_14 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1883_mult__2__right) ).

thf(3547,axiom,
    ! [A_61: $i] :
      ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_61 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_61 ) @ A_61 ) ) @ A_61 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1873_power3__eq__cube) ).

thf(3551,axiom,
    ! [W_5: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ one_one_int ) ) @ ( hAPP_int_int @ number_number_of_int @ W_5 ) )
      = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ W_5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1869_double__number__of__Bit0) ).

thf(3801,axiom,
    ! [K_2: $i,L_2: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ bit1 @ K_2 ) ) @ L_2 )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ L_2 ) ) ) @ L_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1619_mult__Bit1) ).

thf(3802,axiom,
    ! [A_74: $i] :
      ( ( is_int @ A_74 )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ pls ) ) ) @ A_74 )
        = A_74 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1618_mult__numeral__1) ).

thf(3806,axiom,
    ! [A_75: $i] :
      ( ( is_int @ A_75 )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_75 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ pls ) ) )
        = A_75 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1614_mult__numeral__1__right) ).

thf(3930,axiom,
    ! [A_89: $i,M_13: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_89 ) @ M_13 ) ) @ M_13 )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_89 ) @ one_one_int ) ) @ M_13 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1490_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).

thf(3937,axiom,
    ! [M_14: $i,A_90: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ M_14 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_90 ) @ M_14 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_90 ) @ one_one_int ) ) @ M_14 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1483_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).

thf(3944,axiom,
    ! [M_15: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ M_15 ) @ M_15 )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ one_one_int ) ) @ M_15 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1476_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).

thf(3952,axiom,
    ! [A_91: $i,B_61: $i,V_10: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_91 ) @ B_61 ) ) @ ( hAPP_int_int @ number_number_of_int @ V_10 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_91 ) @ ( hAPP_int_int @ number_number_of_int @ V_10 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_61 ) @ ( hAPP_int_int @ number_number_of_int @ V_10 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1468_left__distrib__number__of) ).

thf(3959,axiom,
    ! [V_11: $i,B_62: $i,C_34: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ V_11 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_62 ) @ C_34 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ V_11 ) ) @ B_62 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ V_11 ) ) @ C_34 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1461_right__distrib__number__of) ).

thf(3971,axiom,
    ! [C_35: $i,D_13: $i,A_92: $i,B_63: $i,R_6: $i] :
      ( ( ( is_int @ C_35 )
        & ( is_int @ D_13 )
        & ( is_int @ R_6 ) )
     => ( ( R_6 != zero_zero_int )
       => ( ( ( A_92 = B_63 )
            & ( C_35 != D_13 ) )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_92 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ R_6 ) @ C_35 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_63 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ R_6 ) @ D_13 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1449_add__scale__eq__noteq) ).

thf(3976,axiom,
    ! [Xa: $i,Ya: $i] :
      ( ( ( is_int @ Xa )
        & ( is_int @ Ya ) )
     => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Xa ) @ Xa ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Ya ) @ Ya ) )
          = zero_zero_int )
      <=> ( ( Xa = zero_zero_int )
          & ( Ya = zero_zero_int ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1444_sum__squares__eq__zero__iff) ).

thf(4144,axiom,
    ! [V_1: $i,W: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ V_1 ) ) @ ( hAPP_int_int @ number_number_of_int @ W ) )
      = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ V_1 ) @ W ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1276_times__numeral__code_I5_J) ).

thf(4156,axiom,
    ! [Z1: $i,Z2: $i,W: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z1 ) @ Z2 ) ) @ W )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z1 ) @ W ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z2 ) @ W ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1264_zadd__zmult__distrib) ).

thf(4157,axiom,
    ! [W: $i,Z1: $i,Z2: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ W ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z1 ) @ Z2 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ W ) @ Z1 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ W ) @ Z2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1263_zadd__zmult__distrib2) ).

thf(4158,axiom,
    ! [Z_1: $i] :
      ( ( is_int @ Z_1 )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z_1 ) @ one_one_int )
        = Z_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1262_zmult__1__right) ).

thf(4159,axiom,
    ! [Z_1: $i] :
      ( ( is_int @ Z_1 )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ one_one_int ) @ Z_1 )
        = Z_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1261_zmult__1) ).

thf(4165,axiom,
    ! [K_2: $i,L_2: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ bit0 @ K_2 ) ) @ L_2 )
      = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ L_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1255_mult__Bit0) ).

thf(4166,axiom,
    ! [W: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ pls ) @ W )
      = pls ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1254_mult__Pls) ).

thf(4171,axiom,
    ! [X_54: $i,Y_46: $i,Q_9: $i] :
      ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ X_54 ) @ Y_46 ) ) @ Q_9 )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X_54 ) @ Q_9 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Y_46 ) @ Q_9 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1249_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).

thf(4177,axiom,
    ! [A_121: $i,B_90: $i,N_28: $i] :
      ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_121 ) @ B_90 ) ) @ N_28 )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_121 ) @ N_28 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_90 ) @ N_28 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1243_power__mult__distrib) ).

thf(4183,axiom,
    ! [A_122: $i,N_29: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_122 ) @ N_29 ) ) @ A_122 )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_122 ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_122 ) @ N_29 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1237_power__commutes) ).

thf(4187,axiom,
    ! [A_123: $i] :
      ( ( is_int @ A_123 )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_123 ) @ one_one_int )
        = A_123 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1233_mult_Ocomm__neutral) ).

thf(4194,axiom,
    ! [A_124: $i] :
      ( ( is_int @ A_124 )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_124 ) @ one_one_int )
        = A_124 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1226_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).

thf(4201,axiom,
    ! [A_125: $i] :
      ( ( is_int @ A_125 )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_125 ) @ one_one_int )
        = A_125 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1219_mult__1__right) ).

thf(4208,axiom,
    ! [A_126: $i] :
      ( ( is_int @ A_126 )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ one_one_int ) @ A_126 )
        = A_126 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1212_mult__1) ).

thf(4215,axiom,
    ! [A_127: $i] :
      ( ( is_int @ A_127 )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ one_one_int ) @ A_127 )
        = A_127 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1205_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).

thf(4222,axiom,
    ! [A_128: $i] :
      ( ( is_int @ A_128 )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ one_one_int ) @ A_128 )
        = A_128 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1198_mult__1__left) ).

thf(4229,axiom,
    ! [Wa: $i,Ya: $i,Xa: $i,Z_2: $i] :
      ( ( ( is_int @ Wa )
        & ( is_int @ Ya )
        & ( is_int @ Xa )
        & ( is_int @ Z_2 ) )
     => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Wa ) @ Ya ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Xa ) @ Z_2 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Wa ) @ Z_2 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Xa ) @ Ya ) ) )
      <=> ( ( Wa = Xa )
          | ( Ya = Z_2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1191_crossproduct__eq) ).

thf(4234,axiom,
    ! [A_129: $i,M_17: $i,B_91: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_129 ) @ M_17 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_91 ) @ M_17 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_129 ) @ B_91 ) ) @ M_17 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1186_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).

thf(4240,axiom,
    ! [A_130: $i,B_92: $i,C_48: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_130 ) @ B_92 ) ) @ C_48 )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_130 ) @ C_48 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_92 ) @ C_48 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1180_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).

thf(4246,axiom,
    ! [C: $i,D_1: $i,A_1: $i,B_1: $i] :
      ( ( ( is_int @ C )
        & ( is_int @ D_1 )
        & ( is_int @ A_1 )
        & ( is_int @ B_1 ) )
     => ( ( ( A_1 != B_1 )
          & ( C != D_1 ) )
      <=> ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ C ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_1 ) @ D_1 ) )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ D_1 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_1 ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1174_crossproduct__noteq) ).

thf(4251,axiom,
    ! [X_55: $i,Y_47: $i,Z_19: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ X_55 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Y_47 ) @ Z_19 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ X_55 ) @ Y_47 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ X_55 ) @ Z_19 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1169_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).

thf(4257,axiom,
    ! [A_131: $i,E_3: $i,B_93: $i,C_49: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_131 ) @ E_3 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_93 ) @ E_3 ) ) @ C_49 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_131 ) @ B_93 ) ) @ E_3 ) ) @ C_49 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1163_combine__common__factor) ).

thf(4263,axiom,
    ! [A_132: $i,B_94: $i,C_50: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_132 ) @ B_94 ) ) @ C_50 )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_132 ) @ C_50 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_94 ) @ C_50 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1157_comm__semiring__class_Odistrib) ).

thf(4269,axiom,
    ! [A_133: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_133 ) @ zero_zero_int )
      = zero_zero_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1151_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).

thf(4276,axiom,
    ! [A_134: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ zero_zero_int ) @ A_134 )
      = zero_zero_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1144_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).

thf(4283,axiom,
    ! [A_135: $i,B_95: $i] :
      ( ( ( is_int @ A_135 )
        & ( is_int @ B_95 ) )
     => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_135 ) @ B_95 )
          = zero_zero_int )
       => ( ( A_135 = zero_zero_int )
          | ( B_95 = zero_zero_int ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1137_divisors__zero) ).

thf(4290,axiom,
    ! [B_96: $i,A_136: $i] :
      ( ( ( is_int @ B_96 )
        & ( is_int @ A_136 ) )
     => ( ( A_136 != zero_zero_int )
       => ( ( B_96 != zero_zero_int )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_136 ) @ B_96 )
           != zero_zero_int ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1130_no__zero__divisors) ).

thf(4297,axiom,
    ! [A_1: $i,B_1: $i] :
      ( ( ( is_int @ A_1 )
        & ( is_int @ B_1 ) )
     => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ B_1 )
          = zero_zero_int )
      <=> ( ( A_1 = zero_zero_int )
          | ( B_1 = zero_zero_int ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1123_mult__eq__0__iff) ).

thf(4301,axiom,
    ! [A_137: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_137 ) @ zero_zero_int )
      = zero_zero_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1119_mult__zero__right) ).

thf(4308,axiom,
    ! [A_138: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ zero_zero_int ) @ A_138 )
      = zero_zero_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1112_mult__zero__left) ).

thf(4321,axiom,
    ! [V_14: $i,W_6: $i] :
      ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ V_14 ) @ W_6 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ V_14 ) ) @ ( hAPP_int_int @ number_number_of_int @ W_6 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1099_number__of__mult) ).

thf(4325,axiom,
    ! [V_15: $i,W_7: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ V_15 ) ) @ ( hAPP_int_int @ number_number_of_int @ W_7 ) )
      = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ V_15 ) @ W_7 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1095_arith__simps_I32_J) ).

thf(4329,axiom,
    ! [V_16: $i,W_8: $i,Z_20: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ V_16 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ W_8 ) ) @ Z_20 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ V_16 ) @ W_8 ) ) ) @ Z_20 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1091_mult__number__of__left) ).

thf(4333,axiom,
    ! [Z1: $i,Z2: $i,Z3: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z1 ) @ Z2 ) ) @ Z3 )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z1 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z2 ) @ Z3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1087_zmult__assoc) ).

thf(4334,axiom,
    ! [Z_1: $i,W: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z_1 ) @ W )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ W ) @ Z_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1086_zmult__commute) ).

thf(4335,axiom,
    ! [Lx: $i,Ly: $i,Rx: $i,Ry: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx ) @ Ly ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Rx ) @ Ry ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx ) @ Rx ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Ly ) @ Ry ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1085_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).

thf(4341,axiom,
    ! [Lx_1: $i,Ly_1: $i,Rx_1: $i,Ry_1: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_1 ) @ Ly_1 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Rx_1 ) @ Ry_1 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Rx_1 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_1 ) @ Ly_1 ) ) @ Ry_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1079_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).

thf(4347,axiom,
    ! [Lx_2: $i,Ly_2: $i,Rx_2: $i,Ry_2: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_2 ) @ Ly_2 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Rx_2 ) @ Ry_2 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_2 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Ly_2 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Rx_2 ) @ Ry_2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1073_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).

thf(4353,axiom,
    ! [Lx_3: $i,Ly_3: $i,Rx_3: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_3 ) @ Ly_3 ) ) @ Rx_3 )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_3 ) @ Rx_3 ) ) @ Ly_3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1067_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).

thf(4359,axiom,
    ! [Lx_4: $i,Ly_4: $i,Rx_4: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_4 ) @ Ly_4 ) ) @ Rx_4 )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_4 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Ly_4 ) @ Rx_4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1061_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).

thf(4365,axiom,
    ! [A_139: $i,B_97: $i,C_51: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_139 ) @ B_97 ) ) @ C_51 )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_139 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_97 ) @ C_51 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1055_ab__semigroup__mult__class_Omult__ac_I1_J) ).

thf(4371,axiom,
    ! [Lx_5: $i,Rx_5: $i,Ry_3: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_5 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Rx_5 ) @ Ry_3 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_5 ) @ Rx_5 ) ) @ Ry_3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1049_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).

thf(4377,axiom,
    ! [Lx_6: $i,Rx_6: $i,Ry_4: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_6 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Rx_6 ) @ Ry_4 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Rx_6 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_6 ) @ Ry_4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1043_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).

thf(4383,axiom,
    ! [A_140: $i,B_98: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_140 ) @ B_98 )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_98 ) @ A_140 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1037_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).

thf(4397,axiom,
    ! [A_3: $i,B_2: $i] :
      ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_3 ) @ B_2 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ A_3 ) ) @ B_2 ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1023_zadd__power2) ).

thf(4398,axiom,
    ! [A_3: $i,B_2: $i] :
      ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_3 ) @ B_2 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) @ B_2 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ A_3 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1022_zadd__power3) ).

thf(4417,axiom,
    ! [X_57: $i] :
      ( ( is_int @ X_57 )
     => ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X_57 ) @ one_one_nat )
        = X_57 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1003_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).

thf(4469,axiom,
    ! [A_146: $i] :
      ( ( is_int @ A_146 )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ A_146 )
        = A_146 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_951_add__0__left) ).

thf(4476,axiom,
    ! [A_147: $i] :
      ( ( is_int @ A_147 )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ A_147 )
        = A_147 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_944_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).

thf(4483,axiom,
    ! [A_148: $i] :
      ( ( is_int @ A_148 )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ A_148 )
        = A_148 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_937_add__0) ).

thf(4489,axiom,
    ! [A_1: $i] :
      ( ( is_int @ A_1 )
     => ( ( zero_zero_int
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_1 ) @ A_1 ) )
      <=> ( A_1 = zero_zero_int ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_931_double__zero__sym) ).

thf(4493,axiom,
    ! [A_149: $i] :
      ( ( is_int @ A_149 )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_149 ) @ zero_zero_int )
        = A_149 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_927_add__0__right) ).

thf(4500,axiom,
    ! [A_150: $i] :
      ( ( is_int @ A_150 )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_150 ) @ zero_zero_int )
        = A_150 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_920_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).

thf(4507,axiom,
    ! [A_151: $i] :
      ( ( is_int @ A_151 )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_151 ) @ zero_zero_int )
        = A_151 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_913_add_Ocomm__neutral) ).

thf(4513,axiom,
    ! [B_1: $i,A_1: $i] :
      ( ( ( is_int @ B_1 )
        & ( is_int @ A_1 ) )
     => ( ( B_1
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_1 ) @ A_1 ) )
      <=> ( A_1 = zero_zero_int ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_907_add__0__iff) ).

thf(4545,axiom,
    ! [K_2: $i,L_2: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ bit1 @ K_2 ) ) @ ( hAPP_int_int @ bit1 @ L_2 ) )
      = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ K_2 ) @ ( hAPP_int_int @ succ @ L_2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_875_add__Bit1__Bit1) ).

thf(4546,axiom,
    ! [K_8: $i] :
      ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ succ @ K_8 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ ( hAPP_int_int @ number_number_of_int @ K_8 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_874_number__of__succ) ).

thf(4563,axiom,
    ! [K_2: $i] :
      ( ( hAPP_int_int @ succ @ K_2 )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ K_2 ) @ one_one_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_857_succ__def) ).

thf(4564,axiom,
    ! [Xa: $i] :
      ( ( is_int @ Xa )
     => ( ( one_one_int = Xa )
      <=> ( Xa = one_one_int ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_856_one__reorient) ).

thf(4565,axiom,
    ! [Xa: $i] :
      ( ( one_one_nat = Xa )
    <=> ( Xa = one_one_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_855_one__reorient) ).

thf(4571,axiom,
    ! [A_155: $i,C_57: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_155 ) @ C_57 )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ C_57 ) @ A_155 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_849_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

thf(4577,axiom,
    ! [A_156: $i,C_58: $i,D_17: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_156 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ C_58 ) @ D_17 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ C_58 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_156 ) @ D_17 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_843_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).

thf(4583,axiom,
    ! [A_157: $i,C_59: $i,D_18: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_157 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ C_59 ) @ D_18 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_157 ) @ C_59 ) ) @ D_18 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_837_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).

thf(4589,axiom,
    ! [A_158: $i,B_106: $i,C_60: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_158 ) @ B_106 ) ) @ C_60 )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_158 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_106 ) @ C_60 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_831_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).

thf(4595,axiom,
    ! [A_159: $i,B_107: $i,C_61: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_159 ) @ B_107 ) ) @ C_61 )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_159 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_107 ) @ C_61 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_825_ab__semigroup__add__class_Oadd__ac_I1_J) ).

thf(4601,axiom,
    ! [A_160: $i,B_108: $i,C_62: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_160 ) @ B_108 ) ) @ C_62 )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_160 ) @ C_62 ) ) @ B_108 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_819_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).

thf(4607,axiom,
    ! [A_1: $i,B_1: $i,C: $i] :
      ( ( ( is_int @ B_1 )
        & ( is_int @ C ) )
     => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_1 ) @ B_1 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_1 ) @ C ) )
      <=> ( B_1 = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_813_add__left__cancel) ).

thf(4613,axiom,
    ! [B_1: $i,A_1: $i,C: $i] :
      ( ( ( is_int @ B_1 )
        & ( is_int @ C ) )
     => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_1 ) @ A_1 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ C ) @ A_1 ) )
      <=> ( B_1 = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_807_add__right__cancel) ).

thf(4619,axiom,
    ! [A_161: $i,B_109: $i,C_63: $i,D_19: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_161 ) @ B_109 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ C_63 ) @ D_19 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_161 ) @ C_63 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_109 ) @ D_19 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_801_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).

thf(4625,axiom,
    ! [A_162: $i,B_110: $i,C_64: $i] :
      ( ( ( is_int @ B_110 )
        & ( is_int @ C_64 ) )
     => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_162 ) @ B_110 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_162 ) @ C_64 ) )
       => ( B_110 = C_64 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_795_add__left__imp__eq) ).

thf(4631,axiom,
    ! [A_163: $i,B_111: $i,C_65: $i] :
      ( ( ( is_int @ B_111 )
        & ( is_int @ C_65 ) )
     => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_163 ) @ B_111 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_163 ) @ C_65 ) )
       => ( B_111 = C_65 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_789_add__imp__eq) ).

thf(4637,axiom,
    ! [B_112: $i,A_164: $i,C_66: $i] :
      ( ( ( is_int @ B_112 )
        & ( is_int @ C_66 ) )
     => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_112 ) @ A_164 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ C_66 ) @ A_164 ) )
       => ( B_112 = C_66 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_783_add__right__imp__eq) ).

thf(4646,axiom,
    ! [K_2: $i] :
      ( ( hAPP_int_int @ succ @ ( hAPP_int_int @ bit0 @ K_2 ) )
      = ( hAPP_int_int @ bit1 @ K_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_774_succ__Bit0) ).

thf(4647,axiom,
    ! [K_2: $i] :
      ( ( hAPP_int_int @ succ @ ( hAPP_int_int @ bit1 @ K_2 ) )
      = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ succ @ K_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_773_succ__Bit1) ).

thf(4648,axiom,
    ( ( hAPP_int_int @ succ @ pls )
    = ( hAPP_int_int @ bit1 @ pls ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_772_succ__Pls) ).

thf(4651,axiom,
    ! [Xa: $i] :
      ( ( is_int @ Xa )
     => ( ( zero_zero_int = Xa )
      <=> ( Xa = zero_zero_int ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_769_zero__reorient) ).

thf(4652,axiom,
    ! [Xa: $i] :
      ( ( zero_zero_nat = Xa )
    <=> ( Xa = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_768_zero__reorient) ).

thf(4938,axiom,
    ! [X_62: $i] :
      ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X_62 ) @ zero_zero_nat )
      = one_one_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_482_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).

thf(4949,axiom,
    ( ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat )
    = zero_zero_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_471_of__nat__0) ).

thf(4950,axiom,
    ( ( hAPP_nat_nat @ semiri984289939at_nat @ zero_zero_nat )
    = zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_470_of__nat__0) ).

thf(4956,axiom,
    ! [A_191: $i] :
      ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_191 ) @ zero_zero_nat )
      = one_one_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_464_power__0) ).

thf(4969,axiom,
    ! [A_1: $i,Na: $i] :
      ( ( is_int @ A_1 )
     => ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_1 ) @ Na )
          = zero_zero_int )
      <=> ( ( A_1 = zero_zero_int )
          & ( Na != zero_zero_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_451_power__eq__0__iff) ).

thf(5032,axiom,
    ( one_one_int
    = ( hAPP_nat_int @ semiri1621563631at_int @ one_one_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_388_transfer__int__nat__numerals_I2_J) ).

thf(5038,axiom,
    ( ( hAPP_nat_int @ semiri1621563631at_int @ one_one_nat )
    = one_one_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_382_of__nat__1) ).

thf(5039,axiom,
    ( ( hAPP_nat_nat @ semiri984289939at_nat @ one_one_nat )
    = one_one_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_381_of__nat__1) ).

thf(5066,axiom,
    ! [N_51: $i] :
      ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ one_one_int ) @ N_51 )
      = one_one_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_354_power__one) ).

thf(5073,axiom,
    ! [N_52: $i,A_197: $i] :
      ( ( is_int @ A_197 )
     => ( ( A_197 != zero_zero_int )
       => ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_197 ) @ N_52 )
         != zero_zero_int ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_field__power__not__zero) ).

thf(5077,axiom,
    zero_zero_int != one_one_int,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_zero__neq__one) ).

thf(5078,axiom,
    zero_zero_nat != one_one_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_zero__neq__one) ).

thf(5084,axiom,
    one_one_int != zero_zero_int,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_one__neq__zero) ).

thf(5085,axiom,
    one_one_nat != zero_zero_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_one__neq__zero) ).

thf(5094,axiom,
    ! [Xa: $i,Ya: $i] :
      ( ( ( hAPP_nat_int @ semiri1621563631at_int @ Xa )
        = ( hAPP_nat_int @ semiri1621563631at_int @ Ya ) )
    <=> ( Xa = Ya ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_Nat__Transfer_Otransfer__int__nat__relations_I1_J) ).

thf(5095,axiom,
    ! [Ma: $i,Na: $i] :
      ( ( ( hAPP_nat_int @ semiri1621563631at_int @ Ma )
        = ( hAPP_nat_int @ semiri1621563631at_int @ Na ) )
    <=> ( Ma = Na ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_of__nat__eq__iff) ).

thf(5099,axiom,
    ! [A_198: $i] :
      ( ( is_int @ A_198 )
     => ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_198 ) @ one_one_nat )
        = A_198 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_power__one__right) ).

thf(5141,axiom,
    ! [K_2: $i] :
      ( ( is_int @ K_2 )
     => ( ( hAPP_int_int @ number_number_of_int @ K_2 )
        = K_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_number__of__is__id) ).

thf(5148,axiom,
    ( zero_zero_int
    = ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_transfer__int__nat__numerals_I1_J) ).

thf(5162,axiom,
    ! [N_55: $i] :
      ( ( ( N_55 = zero_zero_nat )
       => ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ N_55 )
          = one_one_int ) )
      & ( ( N_55 != zero_zero_nat )
       => ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ N_55 )
          = zero_zero_int ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_power__0__left) ).

thf(5182,axiom,
    ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) )
    = ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_transfer__int__nat__numerals_I4_J) ).

thf(5183,axiom,
    ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) )
    = ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_transfer__int__nat__numerals_I3_J) ).

thf(5188,axiom,
    ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ pls ) )
    = one_one_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_semiring__numeral__1__eq__1) ).

thf(5189,axiom,
    ( ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ pls ) )
    = one_one_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_semiring__numeral__1__eq__1) ).

thf(5193,axiom,
    ! [W_10: $i] :
      ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ W_10 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ ( hAPP_int_int @ number_number_of_int @ W_10 ) ) ) @ ( hAPP_int_int @ number_number_of_int @ W_10 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_number__of__Bit1) ).

thf(5197,axiom,
    ! [W_11: $i] :
      ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ W_11 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ ( hAPP_int_int @ number_number_of_int @ W_11 ) ) ) @ ( hAPP_int_int @ number_number_of_int @ W_11 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_number__of__Bit0) ).

thf(5213,axiom,
    ! [N_58: $i] :
      ( ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_nat_int @ semiri1621563631at_int @ N_58 ) )
      = ( hAPP_nat_nat @ semiri984289939at_nat @ N_58 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_number__of__int) ).

thf(5214,axiom,
    ! [N_58: $i] :
      ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_nat_int @ semiri1621563631at_int @ N_58 ) )
      = ( hAPP_nat_int @ semiri1621563631at_int @ N_58 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_number__of__int) ).

thf(5218,axiom,
    ! [Z_1: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ Z_1 ) ) @ Z_1 )
     != zero_zero_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_odd__nonzero) ).

thf(5219,axiom,
    ! [K_2: $i] :
      ( ( hAPP_int_int @ bit1 @ K_2 )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ K_2 ) ) @ K_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_Bit1__def) ).

thf(5220,axiom,
    ! [K_2: $i,L_2: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ bit0 @ K_2 ) ) @ ( hAPP_int_int @ bit1 @ L_2 ) )
      = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ K_2 ) @ L_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_add__Bit0__Bit1) ).

thf(5221,axiom,
    ! [K_2: $i,L_2: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ bit1 @ K_2 ) ) @ ( hAPP_int_int @ bit0 @ L_2 ) )
      = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ K_2 ) @ L_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_add__Bit1__Bit0) ).

thf(5222,axiom,
    ! [V_22: $i,W_12: $i] :
      ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ V_22 ) @ W_12 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ V_22 ) ) @ ( hAPP_int_int @ number_number_of_int @ W_12 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_number__of__add) ).

thf(5226,axiom,
    ! [V_23: $i,W_13: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ V_23 ) ) @ ( hAPP_int_int @ number_number_of_int @ W_13 ) )
      = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ V_23 ) @ W_13 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_add__number__of__eq) ).

thf(5230,axiom,
    ! [V_24: $i,W_14: $i,Z_21: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ V_24 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ W_14 ) ) @ Z_21 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ V_24 ) @ W_14 ) ) ) @ Z_21 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_add__number__of__left) ).

thf(5234,axiom,
    ! [A_1: $i,Wa: $i] :
      ( ( is_int @ A_1 )
     => ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ Wa ) )
          = zero_zero_int )
      <=> ( ( A_1 = zero_zero_int )
          & ( ( hAPP_int_nat @ number_number_of_nat @ Wa )
           != zero_zero_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_power__eq__0__iff__number__of) ).

thf(5241,axiom,
    ! [A_202: $i] :
      ( ( is_int @ A_202 )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_202 ) @ ( hAPP_int_int @ number_number_of_int @ pls ) )
        = A_202 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_add__numeral__0__right) ).

thf(5245,axiom,
    ! [A_203: $i] :
      ( ( is_int @ A_203 )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ pls ) ) @ A_203 )
        = A_203 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_add__numeral__0) ).

thf(5249,axiom,
    ( zero_zero_int
    = ( hAPP_int_int @ number_number_of_int @ pls ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_semiring__norm_I112_J) ).

thf(5253,axiom,
    ( ( hAPP_int_int @ number_number_of_int @ pls )
    = zero_zero_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_number__of__Pls) ).

thf(5257,axiom,
    ( ( hAPP_int_int @ number_number_of_int @ pls )
    = zero_zero_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_semiring__numeral__0__eq__0) ).

thf(5258,axiom,
    ( ( hAPP_int_nat @ number_number_of_nat @ pls )
    = zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_semiring__numeral__0__eq__0) ).

thf(5262,axiom,
    ! [Z_1: $i] :
      ( ( is_int @ Z_1 )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ Z_1 )
        = Z_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_zadd__0) ).

thf(5263,axiom,
    ! [Z_1: $i] :
      ( ( is_int @ Z_1 )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z_1 ) @ zero_zero_int )
        = Z_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_zadd__0__right) ).

thf(5264,axiom,
    ! [K_2: $i] :
      ( ( hAPP_int_int @ bit0 @ K_2 )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ K_2 ) @ K_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_Bit0__def) ).

thf(5265,axiom,
    ! [K_2: $i,L_2: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ bit0 @ K_2 ) ) @ ( hAPP_int_int @ bit0 @ L_2 ) )
      = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ K_2 ) @ L_2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_add__Bit0__Bit0) ).

thf(5266,axiom,
    ! [K_2: $i] :
      ( ( is_int @ K_2 )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ pls ) @ K_2 )
        = K_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_add__Pls) ).

thf(5267,axiom,
    ! [K_2: $i] :
      ( ( is_int @ K_2 )
     => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ K_2 ) @ pls )
        = K_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_add__Pls__right) ).

thf(5268,axiom,
    zero_zero_int != one_one_int,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_int__0__neq__1) ).

thf(5269,axiom,
    pls = zero_zero_int,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_Pls__def) ).

thf(5283,axiom,
    ( ( hAPP_int_int @ bit0 @ pls )
    = pls ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_Bit0__Pls) ).

thf(5284,axiom,
    ! [L: $i] :
      ( ( is_int @ L )
     => ( ( pls
          = ( hAPP_int_int @ bit0 @ L ) )
      <=> ( pls = L ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_rel__simps_I38_J) ).

thf(5285,axiom,
    ! [K: $i] :
      ( ( is_int @ K )
     => ( ( ( hAPP_int_int @ bit0 @ K )
          = pls )
      <=> ( K = pls ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_rel__simps_I44_J) ).

thf(5286,axiom,
    ! [K_2: $i,L_2: $i] :
      ( ( hAPP_int_int @ bit0 @ K_2 )
     != ( hAPP_int_int @ bit1 @ L_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_rel__simps_I49_J) ).

thf(5287,axiom,
    ! [K_2: $i,L_2: $i] :
      ( ( hAPP_int_int @ bit1 @ K_2 )
     != ( hAPP_int_int @ bit0 @ L_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_rel__simps_I50_J) ).

thf(5288,axiom,
    ! [L_2: $i] :
      ( pls
     != ( hAPP_int_int @ bit1 @ L_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_rel__simps_I39_J) ).

thf(5289,axiom,
    ! [K_2: $i] :
      ( ( hAPP_int_int @ bit1 @ K_2 )
     != pls ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_rel__simps_I46_J) ).

thf(5290,axiom,
    ! [A_1: $i] :
      ( ( is_int @ A_1 )
     => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_1 ) @ A_1 )
          = zero_zero_int )
      <=> ( A_1 = zero_zero_int ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_double__eq__0__iff) ).

thf(5317,axiom,
    ! [Ma: $i,Na: $i] :
      ( ( ( hAPP_nat_int @ semiri1621563631at_int @ Ma )
        = ( hAPP_nat_int @ semiri1621563631at_int @ Na ) )
    <=> ( Ma = Na ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_int__int__eq) ).

thf(5318,axiom,
    ! [Z_1: $i,W: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z_1 ) @ W )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ W ) @ Z_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_zadd__commute) ).

thf(5319,axiom,
    ! [X: $i,Y: $i,Z_1: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ X ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Y ) @ Z_1 ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Y ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ X ) @ Z_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_zadd__left__commute) ).

thf(5320,axiom,
    ! [Z1: $i,Z2: $i,Z3: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z1 ) @ Z2 ) ) @ Z3 )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z1 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z2 ) @ Z3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_zadd__assoc) ).

thf(5324,axiom,
    ! [K: $i,L: $i] :
      ( ( ( is_int @ K )
        & ( is_int @ L ) )
     => ( ( ( hAPP_int_int @ bit0 @ K )
          = ( hAPP_int_int @ bit0 @ L ) )
      <=> ( K = L ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_rel__simps_I48_J) ).

thf(5325,axiom,
    ! [K: $i,L: $i] :
      ( ( ( is_int @ K )
        & ( is_int @ L ) )
     => ( ( ( hAPP_int_int @ bit1 @ K )
          = ( hAPP_int_int @ bit1 @ L ) )
      <=> ( K = L ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_rel__simps_I51_J) ).

thf(5326,axiom,
    ! [Wa: $i,Xa: $i] :
      ( ( ( hAPP_int_nat @ number_number_of_nat @ Wa )
        = Xa )
    <=> ( Xa
        = ( hAPP_int_nat @ number_number_of_nat @ Wa ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_number__of__reorient) ).

thf(5327,axiom,
    ! [Wa: $i,Xa: $i] :
      ( ( is_int @ Xa )
     => ( ( ( hAPP_int_int @ number_number_of_int @ Wa )
          = Xa )
      <=> ( Xa
          = ( hAPP_int_int @ number_number_of_int @ Wa ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_number__of__reorient) ).

thf(5333,axiom,
    ! [Xa: $i,Ya: $i] :
      ( ( ( is_int @ Xa )
        & ( is_int @ Ya ) )
     => ( ( ( hAPP_int_int @ number_number_of_int @ Xa )
          = ( hAPP_int_int @ number_number_of_int @ Ya ) )
      <=> ( Xa = Ya ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_eq__number__of) ).

thf(5337,axiom,
    ( one_one_nat
    = ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ pls ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_Numeral1__eq1__nat) ).

thf(5338,axiom,
    ( ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ pls ) )
    = one_one_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_nat__numeral__1__eq__1) ).

thf(5339,axiom,
    ( one_one_int
    = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ pls ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_one__is__num__one) ).

thf(5348,axiom,
    ( ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat )
    = zero_zero_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_int__0) ).

thf(5349,axiom,
    ! [Na: $i] :
      ( ( ( hAPP_nat_int @ semiri1621563631at_int @ Na )
        = zero_zero_int )
    <=> ( Na = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_int__eq__0__conv) ).

thf(5350,axiom,
    ( zero_zero_nat
    = ( hAPP_int_nat @ number_number_of_nat @ pls ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_semiring__norm_I113_J) ).

thf(5351,axiom,
    ( ( hAPP_int_nat @ number_number_of_nat @ pls )
    = zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_nat__number__of__Pls) ).

thf(5352,axiom,
    ( ( hAPP_nat_int @ semiri1621563631at_int @ one_one_nat )
    = one_one_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_int__1) ).

thf(5357,axiom,
    ( zero_zero_int
    = ( hAPP_int_int @ number_number_of_int @ pls ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_zero__is__num__zero) ).

thf(5361,axiom,
    ! [V_1: $i,W: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ V_1 ) ) @ ( hAPP_int_int @ number_number_of_int @ W ) )
      = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ V_1 ) @ W ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_plus__numeral__code_I9_J) ).

thf(5365,axiom,
    ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ pls ) )
    = one_one_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_numeral__1__eq__1) ).

thf(5369,axiom,
    ( one_one_int
    = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ pls ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_semiring__norm_I110_J) ).

thf(5373,axiom,
    ! [W_15: $i] :
      ( ( ( ( hAPP_int_nat @ number_number_of_nat @ W_15 )
          = zero_zero_nat )
       => ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ ( hAPP_int_nat @ number_number_of_nat @ W_15 ) )
          = one_one_int ) )
      & ( ( ( hAPP_int_nat @ number_number_of_nat @ W_15 )
         != zero_zero_nat )
       => ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ ( hAPP_int_nat @ number_number_of_nat @ W_15 ) )
          = zero_zero_int ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_power__0__left__number__of) ).

thf(5380,axiom,
    ! [X: $i] :
      ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
      = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_quartic__square__square) ).

thf(5381,axiom,
    ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ one_one_int )
    = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_semiring__one__add__one__is__two) ).

thf(5386,axiom,
    ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ one_one_int )
    = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_one__add__one__is__two) ).

thf(5390,axiom,
    ! [V_25: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ V_25 ) ) @ one_one_int )
      = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ V_25 ) @ ( hAPP_int_int @ bit1 @ pls ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_add__special_I3_J) ).

thf(5394,axiom,
    ! [W_16: $i] :
      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ ( hAPP_int_int @ number_number_of_int @ W_16 ) )
      = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ bit1 @ pls ) ) @ W_16 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_add__special_I2_J) ).

thf(5398,axiom,
    ! [A_1: $i] :
      ( ( is_int @ A_1 )
     => ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = zero_zero_int )
      <=> ( A_1 = zero_zero_int ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_zero__eq__power2) ).

thf(5402,axiom,
    ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
    = zero_zero_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_zero__power2) ).

thf(5409,axiom,
    ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ one_one_int ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
    = one_one_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_one__power2) ).

thf(5416,axiom,
    ! [Xa: $i,Ya: $i] :
      ( ( ( is_int @ Xa )
        & ( is_int @ Ya ) )
     => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Xa ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Ya ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
          = zero_zero_int )
      <=> ( ( Xa = zero_zero_int )
          & ( Ya = zero_zero_int ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_sum__power2__eq__zero__iff) ).

thf(5421,axiom,
    is_int @ y,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_y____) ).

thf(5422,axiom,
    is_int @ x,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_x____) ).

thf(5423,axiom,
    is_int @ w,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_w____) ).

thf(5424,axiom,
    is_int @ v,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_v____) ).

thf(5425,axiom,
    is_int @ t,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_t____) ).

thf(5426,axiom,
    is_int @ sa,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_sa____) ).

thf(5427,axiom,
    is_int @ s,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_s____) ).

thf(5428,axiom,
    is_int @ s1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_s1____) ).

thf(5429,axiom,
    is_int @ r,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_r____) ).

thf(5430,axiom,
    is_int @ m1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_m1____) ).

thf(5431,axiom,
    is_int @ m,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_m) ).

thf(5437,axiom,
    ! [B_1_1: $i,B_2_1: $i] : ( is_int @ ( hAPP_P1175774780nt_int @ B_1_1 @ B_2_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Int__Oint_Mtc__Int__Oint_J_000tc__Int__Oint) ).

thf(5444,axiom,
    ! [B_1_1: $i,B_2_1: $i] : ( is_int @ ( hAPP_f659380387ol_int @ B_1_1 @ B_2_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Int__Oint) ).

thf(5446,axiom,
    ! [B_1_1: $i,B_2_1: $i] : ( is_int @ ( hAPP_f1594865479ol_int @ B_1_1 @ B_2_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__Int__Oint) ).

thf(5466,axiom,
    ! [B_1_1: $i] : ( is_int @ ( quickcheck_int_of @ B_1_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Quickcheck__Narrowing_Oint__of) ).

thf(5473,axiom,
    is_int @ min,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Int_OMin) ).

thf(5474,axiom,
    ! [B_1_1: $i] : ( is_int @ ( hilbert_Eps_int @ B_1_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Hilbert__Choice_OEps_000tc__Int__Oint) ).

thf(5476,axiom,
    ! [B_1_1: $i] : ( is_int @ ( the_int @ B_1_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_HOL_OThe_000tc__Int__Oint) ).

thf(5477,axiom,
    ! [B_1_1: $i] : ( is_int @ ( code_int_of @ B_1_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Code__Numeral_Oint__of) ).

thf(5478,axiom,
    ! [B_1_1: $i,B_2_1: $i] : ( is_int @ ( big_co1548731110nt_int @ B_1_1 @ B_2_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Big__Operators_Ocomm__monoid__mult__class_Osetprod_000tc__Int__Oint_000tc_) ).

thf(5479,axiom,
    ! [B_1_1: $i] : ( is_int @ ( archim1246769320r_real @ B_1_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_000tc__RealDef__Oreal) ).

thf(5480,axiom,
    ! [B_1_1: $i] : ( is_int @ ( archim791455193or_rat @ B_1_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_000tc__Rat__Orat) ).

thf(5481,axiom,
    ! [B_1_1: $i] : ( is_int @ ( archim856651990g_real @ B_1_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Archimedean__Field_Oceiling_000tc__RealDef__Oreal) ).

thf(5482,axiom,
    ! [B_1_1: $i,B_2_1: $i] : ( is_int @ ( hAPP_nat_int @ B_1_1 @ B_2_1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint) ).

thf(5483,axiom,
    ! [B_1_1: $i,B_2_1: $i] :
      ( ( is_int @ B_2_1 )
     => ( is_int @ ( hAPP_int_int @ B_1_1 @ B_2_1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Int__Oint_000tc__Int__Oint) ).

thf(5484,axiom,
    is_int @ pls,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Int_OPls) ).

thf(5485,axiom,
    is_int @ zero_zero_int,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint) ).

thf(5486,axiom,
    is_int @ one_one_int,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint) ).

thf(5487,conjecture,
    ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
   != zero_zero_int ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(5488,negated_conjecture,
    ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
     != zero_zero_int )
    = $false ),
    inference(negate_conjecture,[status(cth)],[5487]) ).

thf(5489,plain,
    ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
     != zero_zero_int )
    = $false ),
    inference(unfold_def,[status(thm)],[5488]) ).

thf(5490,plain,
    ( ( ! [P: $i] :
          ( ( hAPP_nat_nat @ cOMBI_nat @ P )
          = P ) )
    = $true ),
    inference(unfold_def,[status(thm)],[200]) ).

thf(5491,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( ( is_int @ A_3 )
            & ( is_int @ B_2 ) )
         => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 )
             != zero_zero_int )
           => ? [A_4: $i,B_3: $i] :
                ( ( is_int @ A_4 )
                & ( is_int @ B_3 )
                & ( A_3
                  = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_4 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) )
                & ( B_2
                  = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) )
                & ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_4 ) @ B_3 )
                  = one_one_int ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[303]) ).

thf(5492,plain,
    ( ( ! [B_1: $i,C: $i,A_1: $i,D_1: $i] :
          ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_1 ) @ D_1 )
            = one_one_int )
         => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ B_1 ) @ C )
              = one_one_int )
           => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ A_1 ) ) @ ( hAPP_int_int @ abs_abs_int @ C ) )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ B_1 ) ) @ ( hAPP_int_int @ abs_abs_int @ D_1 ) ) )
            <=> ( ( ( hAPP_int_int @ abs_abs_int @ A_1 )
                  = ( hAPP_int_int @ abs_abs_int @ B_1 ) )
                & ( ( hAPP_int_int @ abs_abs_int @ C )
                  = ( hAPP_int_int @ abs_abs_int @ D_1 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[413]) ).

thf(5493,plain,
    ( ( ! [X: $i,Y: $i,M: $i] :
          ( ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ X ) @ Y ) ) @ M )
            = one_one_int )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ M )
            = one_one_int ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[414]) ).

thf(5494,plain,
    ( ( ! [K_2: $i,M: $i,N: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ K_2 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ M ) @ N ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ M ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ N ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[450]) ).

thf(5495,plain,
    ( ( ! [B_2: $i,A_3: $i] :
          ( ( ( is_int @ B_2 )
            & ( is_int @ A_3 ) )
         => ( ( ( A_3 != zero_zero_int )
              | ( B_2 != zero_zero_int ) )
           => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ B_2 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) )
              = one_one_int ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[455]) ).

thf(5496,plain,
    ( ( ! [A: $i] :
          ( ( image_int_nat @ nat @ ( image_nat_int @ semiri1621563631at_int @ A ) )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[818]) ).

thf(5497,plain,
    ( ( ( hAPP_nat_nat @ fact @ zero_zero_nat )
      = one_one_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[856]) ).

thf(5498,plain,
    ( ( ! [Z_1: $i] :
          ( ( is_int @ Z_1 )
         => ( ! [N_1: $i] :
                ( Z_1
               != ( hAPP_nat_int @ semiri1621563631at_int @ N_1 ) )
           => ~ ! [N_1: $i] :
                  ( Z_1
                 != ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ suc @ N_1 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[872]) ).

thf(5499,plain,
    ( ( ! [B_2: $i,A_3: $i] :
          ( ( ( is_int @ B_2 )
            & ( is_int @ A_3 ) )
         => ( ( ( A_3 != zero_zero_int )
              | ( B_2 != zero_zero_int ) )
           => ? [C_3: $i,D_2: $i] :
                ( ( is_int @ C_3 )
                & ( is_int @ D_2 )
                & ( A_3
                  = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 ) ) @ C_3 ) )
                & ( B_2
                  = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 ) ) @ D_2 ) )
                & ( ( hAPP_int_int @ ( legacy_zgcd @ C_3 ) @ D_2 )
                  = one_one_int ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[882]) ).

thf(5500,plain,
    ( ( ! [B_2: $i,A_3: $i] :
          ( ( ( is_int @ B_2 )
            & ( is_int @ A_3 ) )
         => ( ( ( A_3 != zero_zero_int )
              | ( B_2 != zero_zero_int ) )
           => ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ B_2 ) @ ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 ) ) )
              = one_one_int ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[908]) ).

thf(5501,plain,
    ( ( ! [K_2: $i,M: $i,N: $i] :
          ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ M ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ N ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ K_2 ) ) @ ( hAPP_int_int @ ( legacy_zgcd @ M ) @ N ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[915]) ).

thf(5502,plain,
    ( ( ! [X: $i] :
          ( ( hAPP_int_int @ fact_fact_int @ ( hAPP_nat_int @ semiri1621563631at_int @ X ) )
          = ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ fact_fact_nat @ X ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1141]) ).

thf(5503,plain,
    ( ( ( hAPP_nat_nat @ nat_size @ zero_zero_nat )
      = zero_zero_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1360]) ).

thf(5504,plain,
    ( ( ( hAPP_nat_nat @ size_size_nat @ zero_zero_nat )
      = zero_zero_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1361]) ).

thf(5505,plain,
    ( ( ! [N: $i] :
          ( ( hAPP_nat_nat @ size_size_nat @ N )
          = N ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1362]) ).

thf(5506,plain,
    ( ( ! [X: $i] :
          ( ( is_int @ X )
         => ( ( hAPP_int_int @ succ @ ( hAPP_int_int @ pred @ X ) )
            = X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1382]) ).

thf(5507,plain,
    ( ( ! [Y: $i] :
          ( ( Y != zero_zero_nat )
         => ~ ! [Nat_1: $i] :
                ( Y
               != ( hAPP_nat_nat @ suc @ Nat_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1420]) ).

thf(5508,plain,
    ( ( ! [N: $i] :
          ( ( N != zero_zero_nat )
         => ? [M_1: $i] :
              ( N
              = ( hAPP_nat_nat @ suc @ M_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1438]) ).

thf(5509,plain,
    ( ( ( hAPP_nat_nat @ fact_fact_nat @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
      = ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1585]) ).

thf(5510,plain,
    ( ( ( hAPP_nat_nat @ fact_fact_nat @ zero_zero_nat )
      = ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1586]) ).

thf(5511,plain,
    ( ( ( hAPP_nat_nat @ fact_fact_nat @ one_one_nat )
      = one_one_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[1587]) ).

thf(5512,plain,
    ( ( ! [N: $i] :
          ( ( hAPP_nat_nat @ fact_fact_nat @ N )
         != zero_zero_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1589]) ).

thf(5513,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( is_int @ B_2 )
         => ( ( B_2 != zero_zero_int )
           => ( ( ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
                  = zero_zero_int )
               => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) @ B_2 )
                  = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ B_2 ) ) ) )
              & ( ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
                 != zero_zero_int )
               => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) @ B_2 )
                  = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ B_2 ) ) ) @ one_one_int ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1921]) ).

thf(5514,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( is_int @ B_2 )
         => ( ( B_2 != zero_zero_int )
           => ( ( ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
                  = zero_zero_int )
               => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ ( hAPP_int_int @ uminus_uminus_int @ B_2 ) )
                  = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ B_2 ) ) ) )
              & ( ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
                 != zero_zero_int )
               => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ ( hAPP_int_int @ uminus_uminus_int @ B_2 ) )
                  = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ B_2 ) ) ) @ one_one_int ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1922]) ).

thf(5515,plain,
    ( ( ! [A_3: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ ( hAPP_int_int @ number_number_of_int @ min ) )
          = ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1928]) ).

thf(5516,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
              = zero_zero_int )
           => ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ ( hAPP_int_int @ uminus_uminus_int @ B_2 ) )
              = zero_zero_int ) )
          & ( ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
             != zero_zero_int )
           => ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ ( hAPP_int_int @ uminus_uminus_int @ B_2 ) )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 ) ) @ B_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1929]) ).

thf(5517,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
              = zero_zero_int )
           => ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) @ B_2 )
              = zero_zero_int ) )
          & ( ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
             != zero_zero_int )
           => ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) @ B_2 )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ B_2 ) @ ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1930]) ).

thf(5518,plain,
    ( ( ! [V_1: $i,W: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ number_number_of_int @ V_1 ) ) @ ( hAPP_int_int @ number_number_of_int @ W ) )
          = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ V_1 ) @ ( hAPP_int_int @ uminus_uminus_int @ W ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1932]) ).

thf(5519,plain,
    ( ( ! [N: $i] :
          ( ( hAPP_int_nat @ nat @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ N ) ) )
          = zero_zero_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1933]) ).

thf(5520,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ min ) @ K_2 )
          = ( hAPP_int_int @ uminus_uminus_int @ K_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1939]) ).

thf(5521,plain,
    ( ( ! [M: $i] :
          ( ( ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
            = zero_zero_nat )
          | ( ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
            = one_one_nat )
          | ( ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
            = ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          | ( ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
            = ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2213]) ).

thf(5522,plain,
    ( ( ! [M: $i] :
          ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ suc @ M ) ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2217]) ).

thf(5523,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( div_mod_nat @ A_3 ) @ B_2 ) )
          = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A_3 ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2234]) ).

thf(5524,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_nat_int @ semiri1621563631at_int @ X ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ Y ) )
          = ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( div_mod_nat @ X ) @ Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2235]) ).

thf(5525,plain,
    ( ( ! [M: $i,N: $i] :
          ( ( ( ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ N ) )
              = N )
           => ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ M ) ) @ N )
              = zero_zero_nat ) )
          & ( ( ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ N ) )
             != N )
           => ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ M ) ) @ N )
              = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ N ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2243]) ).

thf(5526,plain,
    ( ( ! [M: $i] :
          ( ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
          = zero_zero_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2244]) ).

thf(5527,plain,
    ( ( ! [M: $i,N: $i] :
          ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ M ) ) @ N )
          = ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ N ) ) ) @ N ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2250]) ).

thf(5528,plain,
    ( ( ! [M_5: $i,D_4: $i] :
          ( ( is_int @ M_5 )
         => ( ( ( hAPP_int_int @ ( div_mod_int @ M_5 ) @ D_4 )
              = zero_zero_int )
           => ? [Q_4: $i] :
                ( ( is_int @ Q_4 )
                & ( M_5
                  = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ D_4 ) @ Q_4 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2254]) ).

thf(5529,plain,
    ( ( ! [P_3: $i,A_3: $i] :
          ( ( hAPP_int_int @ ( inv @ P_3 ) @ A_3 )
          = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ nat @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ P_3 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) ) @ P_3 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2259]) ).

thf(5530,plain,
    ( ( ( hAPP_int_nat @ nat @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
      = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2266]) ).

thf(5531,plain,
    ( ( ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
      = ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2285]) ).

thf(5532,plain,
    ( ( ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) )
      = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2286]) ).

thf(5533,plain,
    ( ( ! [V_1: $i,W: $i] :
          ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ V_1 ) ) ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ W ) ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ number_number_of_int @ V_1 ) ) @ ( hAPP_int_int @ number_number_of_int @ W ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2297]) ).

thf(5534,plain,
    ( ( ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ pls ) )
      = ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2306]) ).

thf(5535,plain,
    ( ( ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) )
      = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2307]) ).

thf(5536,plain,
    ( ( ! [A_3: $i,B_2: $i,M: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_3 ) @ B_2 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ M ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ M ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ B_2 ) @ M ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ M ) ) @ ( hAPP_int_int @ ( div_mod_int @ B_2 ) @ M ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2308]) ).

thf(5537,plain,
    ( ( ! [R_2: $i,S_1: $i,T_1: $i,R_4: $i,S_3: $i,M: $i,T_2: $i,N: $i] :
          ( ( R_4
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ S_3 ) @ M ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ T_2 ) @ N ) ) )
         => ( ( R_2
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ S_1 ) @ M ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ T_1 ) @ N ) ) )
           => ( ( hAPP_int_int @ ( div_mod_int @ R_4 ) @ R_2 )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ S_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ R_4 ) @ R_2 ) ) @ S_1 ) ) ) @ M ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ T_2 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ R_4 ) @ R_2 ) ) @ T_1 ) ) ) @ N ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2309]) ).

thf(5538,plain,
    ( ( ( hAPP_int_nat @ nat @ one_one_int )
      = ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2316]) ).

thf(5539,plain,
    ( ( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
      = one_one_int )
    = $true ),
    inference(unfold_def,[status(thm)],[2317]) ).

thf(5540,plain,
    ( ( ! [M: $i,N: $i] :
          ( ( hAPP_int_int @ ( div_mod_int @ M ) @ N )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ M ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ M ) @ N ) ) @ N ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2328]) ).

thf(5541,plain,
    ( ( ! [N: $i,M: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ N ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ M ) @ N ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ M ) @ ( hAPP_int_int @ ( div_mod_int @ M ) @ N ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2329]) ).

thf(5542,plain,
    ( ( ! [A_3: $i,B_2: $i,K_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ B_2 ) ) @ B_2 ) ) @ ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 ) ) ) @ K_2 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_3 ) @ K_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2330]) ).

thf(5543,plain,
    ( ( ! [B_2: $i,A_3: $i,K_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_2 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ B_2 ) ) ) @ ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 ) ) ) @ K_2 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_3 ) @ K_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2331]) ).

thf(5544,plain,
    ( ( ! [A_3: $i,B_2: $i,C_1: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ B_2 ) ) @ C_1 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ B_2 ) @ C_1 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ ( hAPP_int_int @ ( div_mod_int @ B_2 ) @ C_1 ) ) ) @ C_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2332]) ).

thf(5545,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( is_int @ A_3 )
         => ( A_3
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_2 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ B_2 ) ) ) @ ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2333]) ).

thf(5546,plain,
    ( ( ! [A_3: $i] :
          ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ ( hAPP_int_int @ number_number_of_int @ min ) )
          = zero_zero_int ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2335]) ).

thf(5547,plain,
    ( ( one_one_nat
      = ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2373]) ).

thf(5548,plain,
    ( ( ! [A_3: $i] :
          ( ( is_int @ A_3 )
         => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ zero_zero_int )
              = zero_zero_int )
            & ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ zero_zero_int )
              = A_3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2384]) ).

thf(5549,plain,
    ( ( ! [Ma: $i,D_1: $i] :
          ( ( is_int @ Ma )
         => ( ( ( hAPP_int_int @ ( div_mod_int @ Ma ) @ D_1 )
              = zero_zero_int )
          <=> ? [Q_4: $i] :
                ( ( is_int @ Q_4 )
                & ( Ma
                  = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ D_1 ) @ Q_4 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2388]) ).

thf(5550,plain,
    ( ( ! [M: $i] :
          ( ( hAPP_nat_nat @ suc @ M )
         != zero_zero_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2423]) ).

thf(5551,plain,
    ( ( ! [M: $i] :
          ( zero_zero_nat
         != ( hAPP_nat_nat @ suc @ M ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2424]) ).

thf(5552,plain,
    ( ( ! [Nat_2: $i] :
          ( ( hAPP_nat_nat @ suc @ Nat_2 )
         != zero_zero_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2425]) ).

thf(5553,plain,
    ( ( ! [M: $i] :
          ( ( hAPP_nat_nat @ suc @ M )
         != zero_zero_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2426]) ).

thf(5554,plain,
    ( ( ! [Nat_3: $i] :
          ( zero_zero_nat
         != ( hAPP_nat_nat @ suc @ Nat_3 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2427]) ).

thf(5555,plain,
    ( ( ! [M: $i] :
          ( zero_zero_nat
         != ( hAPP_nat_nat @ suc @ M ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2428]) ).

thf(5556,plain,
    ( ( ! [N: $i] :
          ( N
         != ( hAPP_nat_nat @ suc @ N ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2435]) ).

thf(5557,plain,
    ( ( ! [N: $i] :
          ( ( hAPP_nat_nat @ suc @ N )
         != N ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2436]) ).

thf(5558,plain,
    ( ( ! [Nat_5: $i,Nat_4: $i] :
          ( ( ( hAPP_nat_nat @ suc @ Nat_5 )
            = ( hAPP_nat_nat @ suc @ Nat_4 ) )
        <=> ( Nat_5 = Nat_4 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2437]) ).

thf(5559,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( ( hAPP_nat_nat @ suc @ X )
            = ( hAPP_nat_nat @ suc @ Y ) )
         => ( X = Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2438]) ).

thf(5560,plain,
    ( ( ! [P_3: $i,X: $i] :
          ( ( hAPP_int_int @ ( multInv @ P_3 ) @ X )
          = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X ) @ ( hAPP_int_nat @ nat @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ P_3 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2511]) ).

thf(5561,plain,
    ( ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ number_number_of_int @ min ) )
      = one_one_int )
    = $true ),
    inference(unfold_def,[status(thm)],[2652]) ).

thf(5562,plain,
    ( ( ! [Z_2: $i] :
          ( ( is_int @ Z_2 )
         => ( ( ( hAPP_int_int @ abs_abs_int @ Z_2 )
              = one_one_int )
          <=> ( ( Z_2 = one_one_int )
              | ( Z_2
                = ( hAPP_int_int @ number_number_of_int @ min ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2672]) ).

thf(5563,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_3 ) @ B_2 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ A_3 ) ) @ B_2 ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2959]) ).

thf(5564,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_3 ) @ B_2 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) @ B_2 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ A_3 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2960]) ).

thf(5565,plain,
    ( ( ! [X_7: $i,Y_6: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ X_7 ) @ Y_6 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X_7 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Y_6 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ X_7 ) ) @ Y_6 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2961]) ).

thf(5566,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ K_2 ) @ min )
          = ( hAPP_int_int @ succ @ K_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3007]) ).

thf(5567,plain,
    ( ( ! [A_28: $i,B_20: $i,V_5: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_28 ) @ B_20 ) ) @ ( hAPP_int_int @ number_number_of_int @ V_5 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_28 ) @ ( hAPP_int_int @ number_number_of_int @ V_5 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_20 ) @ ( hAPP_int_int @ number_number_of_int @ V_5 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3020]) ).

thf(5568,plain,
    ( ( ! [V_6: $i,B_21: $i,C_7: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ V_6 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ B_21 ) @ C_7 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ V_6 ) ) @ B_21 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ V_6 ) ) @ C_7 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3024]) ).

thf(5569,plain,
    ( ( ! [A_1: $i,E_2: $i,C: $i,B_1: $i,D_1: $i] :
          ( ( is_int @ C )
         => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ E_2 ) ) @ C )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_1 ) @ E_2 ) ) @ D_1 ) )
          <=> ( C
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ B_1 ) @ A_1 ) ) @ E_2 ) ) @ D_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3032]) ).

thf(5570,plain,
    ( ( ! [A_1: $i,E_2: $i,C: $i,B_1: $i,D_1: $i] :
          ( ( is_int @ D_1 )
         => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ E_2 ) ) @ C )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_1 ) @ E_2 ) ) @ D_1 ) )
          <=> ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_1 ) @ B_1 ) ) @ E_2 ) ) @ C )
              = D_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3036]) ).

thf(5571,plain,
    ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ s ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_int_int @ number_number_of_int @ min ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ s ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ one_one_int ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3221]) ).

thf(5572,plain,
    ( ( ! [Ma: $i,Na: $i] :
          ( ( ( is_int @ Ma )
            & ( is_int @ Na ) )
         => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Ma ) @ Na )
              = one_one_int )
          <=> ( ( ( Ma = one_one_int )
                & ( Na = one_one_int ) )
              | ( ( Ma
                  = ( hAPP_int_int @ number_number_of_int @ min ) )
                & ( Na
                  = ( hAPP_int_int @ number_number_of_int @ min ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3234]) ).

thf(5573,plain,
    ( ( ! [M: $i,N: $i] :
          ( ( is_int @ M )
         => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ M ) @ N )
              = one_one_int )
           => ( ( M = one_one_int )
              | ( M
                = ( hAPP_int_int @ number_number_of_int @ min ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3235]) ).

thf(5574,plain,
    ( ( ~ ! [X_1: $i,Y_1: $i] :
            ( ( ( is_int @ X_1 )
              & ( is_int @ Y_1 ) )
           => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Y_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3348]) ).

thf(5575,plain,
    ( ( ! [A_74: $i] :
          ( ( is_int @ A_74 )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ pls ) ) ) @ A_74 )
            = A_74 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3802]) ).

thf(5576,plain,
    ( ( ! [A_75: $i] :
          ( ( is_int @ A_75 )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_75 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ pls ) ) )
            = A_75 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3806]) ).

thf(5577,plain,
    ( ( ! [Xa: $i] :
          ( ( one_one_nat = Xa )
        <=> ( Xa = one_one_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4565]) ).

thf(5578,plain,
    ( ( ! [Xa: $i] :
          ( ( zero_zero_nat = Xa )
        <=> ( Xa = zero_zero_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4652]) ).

thf(5579,plain,
    ( ( ( hAPP_nat_nat @ semiri984289939at_nat @ zero_zero_nat )
      = zero_zero_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[4950]) ).

thf(5580,plain,
    ( ( ( hAPP_nat_nat @ semiri984289939at_nat @ one_one_nat )
      = one_one_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[5039]) ).

thf(5581,plain,
    ( ( zero_zero_nat != one_one_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[5078]) ).

thf(5582,plain,
    ( ( one_one_nat != zero_zero_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[5085]) ).

thf(5583,plain,
    ( ( is_int @ y )
    = $true ),
    inference(unfold_def,[status(thm)],[5421]) ).

thf(5584,plain,
    ( ( is_int @ x )
    = $true ),
    inference(unfold_def,[status(thm)],[5422]) ).

thf(5585,plain,
    ( ( is_int @ w )
    = $true ),
    inference(unfold_def,[status(thm)],[5423]) ).

thf(5586,plain,
    ( ( is_int @ v )
    = $true ),
    inference(unfold_def,[status(thm)],[5424]) ).

thf(5587,plain,
    ( ( is_int @ t )
    = $true ),
    inference(unfold_def,[status(thm)],[5425]) ).

thf(5588,plain,
    ( ( is_int @ sa )
    = $true ),
    inference(unfold_def,[status(thm)],[5426]) ).

thf(5589,plain,
    ( ( is_int @ s )
    = $true ),
    inference(unfold_def,[status(thm)],[5427]) ).

thf(5590,plain,
    ( ( is_int @ s1 )
    = $true ),
    inference(unfold_def,[status(thm)],[5428]) ).

thf(5591,plain,
    ( ( is_int @ r )
    = $true ),
    inference(unfold_def,[status(thm)],[5429]) ).

thf(5592,plain,
    ( ( is_int @ m1 )
    = $true ),
    inference(unfold_def,[status(thm)],[5430]) ).

thf(5593,plain,
    ( ( is_int @ m )
    = $true ),
    inference(unfold_def,[status(thm)],[5431]) ).

thf(5594,plain,
    ( ( ! [B_1_1: $i,B_2_1: $i] : ( is_int @ ( hAPP_P1175774780nt_int @ B_1_1 @ B_2_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5437]) ).

thf(5595,plain,
    ( ( ! [B_1_1: $i,B_2_1: $i] : ( is_int @ ( hAPP_f659380387ol_int @ B_1_1 @ B_2_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5444]) ).

thf(5596,plain,
    ( ( ! [B_1_1: $i,B_2_1: $i] : ( is_int @ ( hAPP_f1594865479ol_int @ B_1_1 @ B_2_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5446]) ).

thf(5597,plain,
    ( ( ! [B_1_1: $i] : ( is_int @ ( quickcheck_int_of @ B_1_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5466]) ).

thf(5598,plain,
    ( ( is_int @ min )
    = $true ),
    inference(unfold_def,[status(thm)],[5473]) ).

thf(5599,plain,
    ( ( ! [B_1_1: $i] : ( is_int @ ( hilbert_Eps_int @ B_1_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5474]) ).

thf(5600,plain,
    ( ( ! [B_1_1: $i] : ( is_int @ ( the_int @ B_1_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5476]) ).

thf(5601,plain,
    ( ( ! [B_1_1: $i] : ( is_int @ ( code_int_of @ B_1_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5477]) ).

thf(5602,plain,
    ( ( ! [B_1_1: $i,B_2_1: $i] : ( is_int @ ( big_co1548731110nt_int @ B_1_1 @ B_2_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5478]) ).

thf(5603,plain,
    ( ( ! [B_1_1: $i] : ( is_int @ ( archim1246769320r_real @ B_1_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5479]) ).

thf(5604,plain,
    ( ( ! [B_1_1: $i] : ( is_int @ ( archim791455193or_rat @ B_1_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5480]) ).

thf(5605,plain,
    ( ( ! [B_1_1: $i] : ( is_int @ ( archim856651990g_real @ B_1_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5481]) ).

thf(5606,plain,
    ( ( ! [P: $i,Q: $i,R: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ ( hAPP_f2135977429nt_int @ cOMBC_int_int_int @ P ) @ Q ) @ R )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ P @ R ) @ Q ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[177]) ).

thf(5607,plain,
    ( ( ! [P: $i] :
          ( ( is_int @ P )
         => ( ( hAPP_int_int @ cOMBI_int @ P )
            = P ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[201]) ).

thf(5608,plain,
    ( ( ! [B_5: $i,A_5: $i,A_3: $i,B_2: $i] :
          ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 )
           != zero_zero_int )
         => ( ( A_3
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_5 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) )
           => ( ( B_2
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_5 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) )
             => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_5 ) @ B_5 )
                = one_one_int ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[416]) ).

thf(5609,plain,
    ( ( ! [D_3: $i,A_3: $i,B_2: $i] :
          ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ B_2 ) )
            = one_one_int )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ B_2 )
            = one_one_int ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[418]) ).

thf(5610,plain,
    ( ( ! [D_3: $i,A_3: $i,B_2: $i] :
          ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ B_2 ) )
            = one_one_int )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ A_3 )
            = one_one_int ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[419]) ).

thf(5611,plain,
    ( ( ! [B_2: $i,D_3: $i,A_3: $i] :
          ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ A_3 )
            = one_one_int )
         => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ B_2 )
              = one_one_int )
           => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ B_2 ) )
              = one_one_int ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[420]) ).

thf(5612,plain,
    ( ( ! [M: $i,K_2: $i,N: $i] :
          ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ K_2 ) @ N )
            = one_one_int )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ M ) ) @ N )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ M ) @ N ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[421]) ).

thf(5613,plain,
    ( ( ! [D_1: $i,A_1: $i,B_1: $i] :
          ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_1 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ B_1 ) )
            = one_one_int )
        <=> ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_1 ) @ A_1 )
              = one_one_int )
            & ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_1 ) @ B_1 )
              = one_one_int ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[422]) ).

thf(5614,plain,
    ( ( ! [Ma: $i,Na: $i] :
          ( ( ( is_int @ Ma )
            & ( is_int @ Na ) )
         => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ Ma ) @ Na )
              = zero_zero_int )
          <=> ( ( Ma = zero_zero_int )
              & ( Na = zero_zero_int ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[424]) ).

thf(5615,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ uminus_uminus_int @ X ) ) @ Y )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[425]) ).

thf(5616,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ ( hAPP_int_int @ uminus_uminus_int @ Y ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[426]) ).

thf(5617,plain,
    ( ( ! [A_3: $i,B_2: $i,C_1: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) @ C_1 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ B_2 ) @ C_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[427]) ).

thf(5618,plain,
    ( ( ! [B_2: $i,A_3: $i,C_1: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ B_2 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ C_1 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ B_2 ) @ C_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[428]) ).

thf(5619,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ B_2 ) @ A_3 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[429]) ).

thf(5620,plain,
    ( ( ! [A_3: $i,N: $i,B_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ N ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ N ) )
          = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) @ N ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[434]) ).

thf(5621,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ Y )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ Y ) @ ( hAPP_int_int @ ( div_mod_int @ X ) @ Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[435]) ).

thf(5622,plain,
    ( ( ! [N: $i,D_3: $i,A_3: $i] :
          ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ A_3 )
            = one_one_int )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ N ) )
            = one_one_int ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[436]) ).

thf(5623,plain,
    ( ( ! [M: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ M ) @ one_one_int )
          = one_one_int ) )
    = $true ),
    inference(unfold_def,[status(thm)],[438]) ).

thf(5624,plain,
    ( ( ! [N: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ N ) @ one_one_int ) ) @ N )
          = one_one_int ) )
    = $true ),
    inference(unfold_def,[status(thm)],[439]) ).

thf(5625,plain,
    ( ( ! [N: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ N ) @ one_one_int ) ) @ N )
          = one_one_int ) )
    = $true ),
    inference(unfold_def,[status(thm)],[440]) ).

thf(5626,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ abs_abs_int @ X ) ) @ Y )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[441]) ).

thf(5627,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ ( hAPP_int_int @ abs_abs_int @ Y ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[442]) ).

thf(5628,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ Y )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ abs_abs_int @ X ) ) @ ( hAPP_int_int @ abs_abs_int @ Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[443]) ).

thf(5629,plain,
    ( ( ! [X: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ X )
          = ( hAPP_int_int @ abs_abs_int @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[444]) ).

thf(5630,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ Y ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[445]) ).

thf(5631,plain,
    ( ( ! [M: $i,N: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ M ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ M ) @ N ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ M ) @ N ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[448]) ).

thf(5632,plain,
    ( ( ! [M: $i,N: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ M ) @ N ) ) @ N )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ M ) @ N ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[449]) ).

thf(5633,plain,
    ( ( ! [M: $i,K_2: $i,N: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ M ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ M ) ) @ N ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ M ) @ N ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[451]) ).

thf(5634,plain,
    ( ( ! [X: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ zero_zero_int ) @ X )
          = ( hAPP_int_int @ abs_abs_int @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[452]) ).

thf(5635,plain,
    ( ( ! [X: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ zero_zero_int )
          = ( hAPP_int_int @ abs_abs_int @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[453]) ).

thf(5636,plain,
    ( ( ! [N: $i,M: $i,A_3: $i,B_2: $i] :
          ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 )
            = one_one_int )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ N ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ M ) )
            = one_one_int ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[459]) ).

thf(5637,plain,
    ( ( ! [Z_1: $i,W: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Z_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ W ) ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Z_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ W ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Z_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ W ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[664]) ).

thf(5638,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A = B )
        <=> ( ( image_nat_int @ semiri1621563631at_int @ A )
            = ( image_nat_int @ semiri1621563631at_int @ B ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[820]) ).

thf(5639,plain,
    ( ( ! [N: $i] :
          ( ( hAPP_int_int @ ring_1_of_int_int @ ( hAPP_nat_int @ semiri1621563631at_int @ N ) )
          = ( hAPP_nat_int @ semiri1621563631at_int @ N ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[842]) ).

thf(5640,plain,
    ( ( ! [W: $i] :
          ( ( hAPP_int_int @ number_number_of_int @ W )
          = ( hAPP_int_int @ ring_1_of_int_int @ W ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[844]) ).

thf(5641,plain,
    ( ( ! [Ma: $i] :
          ( ( ( hAPP_int_int @ ( legacy_zgcd @ zero_zero_int ) @ Ma )
            = one_one_int )
        <=> ( ( hAPP_int_int @ abs_abs_int @ Ma )
            = one_one_int ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[902]) ).

thf(5642,plain,
    ( ( ! [M: $i] :
          ( ( hAPP_int_int @ ( legacy_zgcd @ M ) @ zero_zero_int )
          = ( hAPP_int_int @ abs_abs_int @ M ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[913]) ).

thf(5643,plain,
    ( ( ! [M: $i] :
          ( ( hAPP_int_int @ ( legacy_zgcd @ zero_zero_int ) @ M )
          = ( hAPP_int_int @ abs_abs_int @ M ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[914]) ).

thf(5644,plain,
    ( ( ! [N: $i,A_3: $i,B_2: $i] :
          ( ( ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 )
            = one_one_int )
         => ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ N ) ) @ B_2 )
            = one_one_int ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[916]) ).

thf(5645,plain,
    ( ( ! [N: $i,A_3: $i,B_2: $i] :
          ( ( ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 )
            = one_one_int )
         => ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ N ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ N ) )
            = one_one_int ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[917]) ).

thf(5646,plain,
    ( ( ! [M: $i,N: $i,K_2: $i] :
          ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ M ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ N ) @ K_2 ) ) ) @ N )
          = ( hAPP_int_int @ ( legacy_zgcd @ M ) @ N ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[921]) ).

thf(5647,plain,
    ( ( ! [I: $i,J_2: $i] :
          ( ( hAPP_int_int @ ( legacy_zgcd @ I ) @ ( hAPP_int_int @ uminus_uminus_int @ J_2 ) )
          = ( hAPP_int_int @ ( legacy_zgcd @ I ) @ J_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[922]) ).

thf(5648,plain,
    ( ( ! [I: $i,J_2: $i] :
          ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ uminus_uminus_int @ I ) ) @ J_2 )
          = ( hAPP_int_int @ ( legacy_zgcd @ I ) @ J_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[923]) ).

thf(5649,plain,
    ( ( ! [K_2: $i,M: $i,N: $i] :
          ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( legacy_zgcd @ K_2 ) @ M ) ) @ N )
          = ( hAPP_int_int @ ( legacy_zgcd @ K_2 ) @ ( hAPP_int_int @ ( legacy_zgcd @ M ) @ N ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[924]) ).

thf(5650,plain,
    ( ( ! [K_2: $i,M: $i,N: $i] :
          ( ( hAPP_int_int @ ( legacy_zgcd @ K_2 ) @ ( hAPP_int_int @ ( legacy_zgcd @ M ) @ N ) )
          = ( hAPP_int_int @ ( legacy_zgcd @ M ) @ ( hAPP_int_int @ ( legacy_zgcd @ K_2 ) @ N ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[925]) ).

thf(5651,plain,
    ( ( ! [I: $i,J_2: $i] :
          ( ( hAPP_int_int @ ( legacy_zgcd @ I ) @ J_2 )
          = ( hAPP_int_int @ ( legacy_zgcd @ J_2 ) @ I ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[926]) ).

thf(5652,plain,
    ( ( ! [A_3: $i,B_2: $i,N: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 ) ) @ N )
          = ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ N ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ N ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[929]) ).

thf(5653,plain,
    ( ( ! [M: $i,N: $i] :
          ( ( hAPP_int_int @ ( legacy_zgcd @ M ) @ N )
          = ( hAPP_int_int @ ( legacy_zgcd @ N ) @ ( hAPP_int_int @ ( div_mod_int @ M ) @ N ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[930]) ).

thf(5654,plain,
    ( ( ! [I_1: $i,J: $i] :
          ( ( ( is_int @ I_1 )
            & ( is_int @ J ) )
         => ( ( ( hAPP_int_int @ ( legacy_zgcd @ I_1 ) @ J )
              = zero_zero_int )
          <=> ( ( I_1 = zero_zero_int )
              & ( J = zero_zero_int ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[931]) ).

thf(5655,plain,
    ( ( ! [M: $i] :
          ( ( hAPP_int_int @ ( legacy_zgcd @ one_one_int ) @ M )
          = one_one_int ) )
    = $true ),
    inference(unfold_def,[status(thm)],[932]) ).

thf(5656,plain,
    ( ( ! [M: $i] :
          ( ( hAPP_int_int @ ( legacy_zgcd @ M ) @ one_one_int )
          = one_one_int ) )
    = $true ),
    inference(unfold_def,[status(thm)],[933]) ).

thf(5657,plain,
    ( ( ! [N: $i,K_2: $i,M: $i] :
          ( ( ( hAPP_int_int @ ( legacy_zgcd @ K_2 ) @ M )
            = one_one_int )
         => ( ( ( hAPP_int_int @ ( legacy_zgcd @ N ) @ M )
              = one_one_int )
           => ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ N ) ) @ M )
              = one_one_int ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[934]) ).

thf(5658,plain,
    ( ( ! [M: $i,K_2: $i,N: $i] :
          ( ( ( hAPP_int_int @ ( legacy_zgcd @ K_2 ) @ N )
            = one_one_int )
         => ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ M ) ) @ N )
            = ( hAPP_int_int @ ( legacy_zgcd @ M ) @ N ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[935]) ).

thf(5659,plain,
    ( ( ( hAPP_int_int @ fact_fact_int @ zero_zero_int )
      = one_one_int )
    = $true ),
    inference(unfold_def,[status(thm)],[1147]) ).

thf(5660,plain,
    ( ( ( hAPP_int_int @ fact_fact_int @ one_one_int )
      = one_one_int )
    = $true ),
    inference(unfold_def,[status(thm)],[1148]) ).

thf(5661,plain,
    ( ( ! [M: $i,N: $i] :
          ( ( xzgcd @ M @ N )
          = ( xzgcda @ M @ N @ M @ N @ one_one_int @ zero_zero_int @ zero_zero_int @ one_one_int ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1220]) ).

thf(5662,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ bit0 @ K_2 ) ) @ ( hAPP_int_int @ bit1 @ L_2 ) )
          = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ pred @ K_2 ) ) @ L_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1372]) ).

thf(5663,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ min ) @ K_2 )
          = ( hAPP_int_int @ pred @ K_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1373]) ).

thf(5664,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ K_2 ) @ min )
          = ( hAPP_int_int @ pred @ K_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1374]) ).

thf(5665,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ bit1 @ K_2 ) )
          = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ pred @ ( hAPP_int_int @ uminus_uminus_int @ K_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1375]) ).

thf(5666,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ pred @ K_2 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ K_2 ) @ one_one_int ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1376]) ).

thf(5667,plain,
    ( ( ( hAPP_int_int @ pred @ min )
      = ( hAPP_int_int @ bit0 @ min ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1377]) ).

thf(5668,plain,
    ( ( ( hAPP_int_int @ pred @ pls )
      = min )
    = $true ),
    inference(unfold_def,[status(thm)],[1378]) ).

thf(5669,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ pred @ ( hAPP_int_int @ bit1 @ K_2 ) )
          = ( hAPP_int_int @ bit0 @ K_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1380]) ).

thf(5670,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ pred @ ( hAPP_int_int @ bit0 @ K_2 ) )
          = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ pred @ K_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1381]) ).

thf(5671,plain,
    ( ( ! [A_3: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1926]) ).

thf(5672,plain,
    ( ( ( hAPP_int_int @ uminus_uminus_int @ min )
      = ( hAPP_int_int @ bit1 @ pls ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1936]) ).

thf(5673,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( ( hAPP_int_int @ ( div_mod_int @ K_2 ) @ ( hAPP_int_int @ uminus_uminus_int @ L_2 ) )
           != zero_zero_int )
         => ( ( hAPP_int_int @ ( div_mod_int @ K_2 ) @ L_2 )
           != zero_zero_int ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1937]) ).

thf(5674,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ K_2 ) ) @ L_2 )
           != zero_zero_int )
         => ( ( hAPP_int_int @ ( div_mod_int @ K_2 ) @ L_2 )
           != zero_zero_int ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1938]) ).

thf(5675,plain,
    ( ( min
      = ( hAPP_int_int @ uminus_uminus_int @ one_one_int ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1940]) ).

thf(5676,plain,
    ( ( ! [Z_1: $i,W: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ Z_1 ) @ W )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z_1 ) @ ( hAPP_int_int @ uminus_uminus_int @ W ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1941]) ).

thf(5677,plain,
    ( ( ! [Z_1: $i,W: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z_1 ) @ ( hAPP_int_int @ uminus_uminus_int @ W ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ Z_1 ) @ W ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1942]) ).

thf(5678,plain,
    ( ( ! [Na: $i,Ma: $i] :
          ( ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ Na ) )
            = ( hAPP_nat_int @ semiri1621563631at_int @ Ma ) )
        <=> ( ( Na = zero_zero_nat )
            & ( Ma = zero_zero_nat ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1944]) ).

thf(5679,plain,
    ( ( ! [Z_1: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ uminus_uminus_int @ Z_1 ) ) @ Z_1 )
          = zero_zero_int ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1945]) ).

thf(5680,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ ( hAPP_int_int @ uminus_uminus_int @ B_2 ) )
          = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) @ B_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1947]) ).

thf(5681,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) @ ( hAPP_int_int @ uminus_uminus_int @ B_2 ) )
          = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1948]) ).

thf(5682,plain,
    ( ( ! [X: $i,M: $i] :
          ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( div_mod_int @ X ) @ M ) ) ) @ M )
          = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ X ) ) @ M ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1949]) ).

thf(5683,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ ( hAPP_int_int @ uminus_uminus_int @ B_2 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) @ B_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1950]) ).

thf(5684,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) @ ( hAPP_int_int @ uminus_uminus_int @ B_2 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ B_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1951]) ).

thf(5685,plain,
    ( ( ! [W: $i] :
          ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ number_number_of_int @ W ) )
          = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ uminus_uminus_int @ W ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1955]) ).

thf(5686,plain,
    ( ( ! [Z_1: $i,W: $i] :
          ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z_1 ) @ W ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ uminus_uminus_int @ Z_1 ) ) @ ( hAPP_int_int @ uminus_uminus_int @ W ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1956]) ).

thf(5687,plain,
    ( ( ! [Z_1: $i,W: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ uminus_uminus_int @ Z_1 ) ) @ W )
          = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z_1 ) @ W ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1957]) ).

thf(5688,plain,
    ( ( ( hAPP_int_int @ uminus_uminus_int @ zero_zero_int )
      = zero_zero_int )
    = $true ),
    inference(unfold_def,[status(thm)],[1958]) ).

thf(5689,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ bit0 @ K_2 ) )
          = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ uminus_uminus_int @ K_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1959]) ).

thf(5690,plain,
    ( ( ( hAPP_int_int @ uminus_uminus_int @ pls )
      = pls )
    = $true ),
    inference(unfold_def,[status(thm)],[1960]) ).

thf(5691,plain,
    ( ( ! [Z_1: $i] :
          ( ( is_int @ Z_1 )
         => ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ uminus_uminus_int @ Z_1 ) )
            = Z_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1961]) ).

thf(5692,plain,
    ( ( ! [Z_1: $i] :
          ( ( is_int @ Z_1 )
         => ~ ! [M_1: $i,N_1: $i] :
                ( Z_1
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ M_1 ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ N_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2094]) ).

thf(5693,plain,
    ( ( ! [Xa: $i] :
          ( ( ( hAPP_int_int @ ( div_mod_int @ Xa ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
           != zero_zero_int )
        <=> ( ( hAPP_int_int @ ( div_mod_int @ Xa ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
            = one_one_int ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2271]) ).

thf(5694,plain,
    ( ( ! [M: $i] :
          ( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ suc @ M ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ M ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2315]) ).

thf(5695,plain,
    ( ( ! [A_3: $i,B_2: $i,C_1: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_3 ) @ B_2 ) ) @ C_1 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ C_1 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ B_2 ) @ C_1 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ C_1 ) ) @ ( hAPP_int_int @ ( div_mod_int @ B_2 ) @ C_1 ) ) ) @ C_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2383]) ).

thf(5696,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 ) ) @ B_2 )
          = zero_zero_int ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2385]) ).

thf(5697,plain,
    ( ( ! [X: $i,M: $i,Y: $i] :
          ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( div_mod_int @ X ) @ M ) ) @ Y ) ) @ M )
          = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X ) @ Y ) ) @ M ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2422]) ).

thf(5698,plain,
    ( ( ! [X: $i,Y: $i,M: $i] :
          ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ X ) @ ( hAPP_int_int @ ( div_mod_int @ Y ) @ M ) ) ) @ M )
          = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ X ) @ Y ) ) @ M ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2429]) ).

thf(5699,plain,
    ( ( ! [X: $i,M: $i,Y: $i] :
          ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( div_mod_int @ X ) @ M ) ) @ Y ) ) @ M )
          = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ X ) @ Y ) ) @ M ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2430]) ).

thf(5700,plain,
    ( ( ! [A_3: $i,B_2: $i,C_1: $i] :
          ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ ( hAPP_int_int @ ( div_mod_int @ B_2 ) @ C_1 ) ) ) @ C_1 )
          = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ B_2 ) ) @ C_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2431]) ).

thf(5701,plain,
    ( ( ! [A_3: $i,B_2: $i,C_1: $i] :
          ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ B_2 ) ) @ C_1 )
          = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ ( hAPP_int_int @ ( div_mod_int @ B_2 ) @ C_1 ) ) ) @ C_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2432]) ).

thf(5702,plain,
    ( ( ! [B_2: $i] :
          ( ( hAPP_int_int @ ( div_mod_int @ zero_zero_int ) @ B_2 )
          = zero_zero_int ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2433]) ).

thf(5703,plain,
    ( ( ! [A_3: $i] :
          ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ A_3 )
          = zero_zero_int ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2434]) ).

thf(5704,plain,
    ( ( ! [M: $i,X: $i] :
          ( ( hAPP_int_int @ ( standardRes @ M ) @ X )
          = ( hAPP_int_int @ ( div_mod_int @ X ) @ M ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2439]) ).

thf(5705,plain,
    ( ( ! [X: $i] :
          ( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_int_nat @ nat @ ( hAPP_int_int @ abs_abs_int @ X ) ) )
          = ( hAPP_int_int @ abs_abs_int @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2481]) ).

thf(5706,plain,
    ( ( ! [V_1: $i,W: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ V_1 ) ) ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ W ) ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ number_number_of_int @ V_1 ) ) @ ( hAPP_int_int @ number_number_of_int @ W ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2593]) ).

thf(5707,plain,
    ( ( ! [A_3: $i] :
          ( ( is_int @ A_3 )
         => ( ( A_3 != zero_zero_int )
           => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ A_3 )
              = one_one_int ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2598]) ).

thf(5708,plain,
    ( ( ! [B_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ zero_zero_int ) @ B_2 )
          = zero_zero_int ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2599]) ).

thf(5709,plain,
    ( ( ! [A_3: $i] :
          ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
            = one_one_int )
         => ( ( hAPP_int_int @ abs_abs_int @ A_3 )
            = one_one_int ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2613]) ).

thf(5710,plain,
    ( ( ! [A_3: $i] :
          ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
          = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ abs_abs_int @ A_3 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2616]) ).

thf(5711,plain,
    ( ( ! [A_1: $i,B_1: $i] :
          ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
            = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
        <=> ( ( hAPP_int_int @ abs_abs_int @ A_1 )
            = ( hAPP_int_int @ abs_abs_int @ B_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2617]) ).

thf(5712,plain,
    ( ( ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) )
      = ( hAPP_int_nat @ nat @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2618]) ).

thf(5713,plain,
    ( ( ! [X: $i] :
          ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
          = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ abs_abs_int @ X ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2634]) ).

thf(5714,plain,
    ( ( ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) )
      = ( hAPP_int_nat @ nat @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2637]) ).

thf(5715,plain,
    ( ( one_one_nat
      = ( hAPP_int_nat @ nat @ one_one_int ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2673]) ).

thf(5716,plain,
    ( ( ! [W: $i] :
          ( ( hAPP_int_nat @ nat @ ( hAPP_int_int @ number_number_of_int @ W ) )
          = ( hAPP_int_nat @ number_number_of_nat @ W ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2674]) ).

thf(5717,plain,
    ( ( ! [V_1: $i] :
          ( ( hAPP_int_nat @ number_number_of_nat @ V_1 )
          = ( hAPP_int_nat @ nat @ ( hAPP_int_int @ number_number_of_int @ V_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2675]) ).

thf(5718,plain,
    ( ( ! [M: $i,N: $i] :
          ( ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ M ) @ N ) )
            = one_one_int )
         => ( ( hAPP_int_int @ abs_abs_int @ M )
            = one_one_int ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2680]) ).

thf(5719,plain,
    ( ( zero_zero_nat
      = ( hAPP_int_nat @ nat @ zero_zero_int ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2681]) ).

thf(5720,plain,
    ( ( ( hAPP_int_nat @ nat @ zero_zero_int )
      = zero_zero_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[2682]) ).

thf(5721,plain,
    ( ( ! [N: $i] :
          ( ( hAPP_int_nat @ nat @ ( hAPP_nat_int @ semiri1621563631at_int @ N ) )
          = N ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2717]) ).

thf(5722,plain,
    ( ( ! [M: $i] :
          ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_nat_int @ semiri1621563631at_int @ M ) )
          = ( hAPP_nat_int @ semiri1621563631at_int @ M ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2718]) ).

thf(5723,plain,
    ( ( ! [N_8: $i] :
          ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_nat_int @ semiri1621563631at_int @ N_8 ) )
          = ( hAPP_nat_int @ semiri1621563631at_int @ N_8 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2719]) ).

thf(5724,plain,
    ( ( ! [A_20: $i,N_9: $i] :
          ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_20 ) @ N_9 ) )
          = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ abs_abs_int @ A_20 ) ) @ N_9 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2731]) ).

thf(5725,plain,
    ( ( ! [A_21: $i,B_16: $i] :
          ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_21 ) @ B_16 ) )
          = ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ B_16 ) @ A_21 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2734]) ).

thf(5726,plain,
    ( ( ( hAPP_int_int @ abs_abs_int @ one_one_int )
      = one_one_int )
    = $true ),
    inference(unfold_def,[status(thm)],[2737]) ).

thf(5727,plain,
    ( ( ! [A_22: $i,B_17: $i] :
          ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ abs_abs_int @ A_22 ) ) @ ( hAPP_int_int @ abs_abs_int @ B_17 ) ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ abs_abs_int @ A_22 ) ) @ ( hAPP_int_int @ abs_abs_int @ B_17 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2740]) ).

thf(5728,plain,
    ( ( ! [A_23: $i,B_18: $i] :
          ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_23 ) @ B_18 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ A_23 ) ) @ ( hAPP_int_int @ abs_abs_int @ B_18 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2743]) ).

thf(5729,plain,
    ( ( ! [A_24: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ A_24 ) ) @ ( hAPP_int_int @ abs_abs_int @ A_24 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_24 ) @ A_24 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2746]) ).

thf(5730,plain,
    ( ( ( hAPP_int_int @ abs_abs_int @ zero_zero_int )
      = zero_zero_int )
    = $true ),
    inference(unfold_def,[status(thm)],[2755]) ).

thf(5731,plain,
    ( ( ! [A_1: $i] :
          ( ( is_int @ A_1 )
         => ( ( ( hAPP_int_int @ abs_abs_int @ A_1 )
              = zero_zero_int )
          <=> ( A_1 = zero_zero_int ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2758]) ).

thf(5732,plain,
    ( ( ! [A_27: $i] :
          ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ abs_abs_int @ A_27 ) )
          = ( hAPP_int_int @ abs_abs_int @ A_27 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2764]) ).

thf(5733,plain,
    ( ( ! [N: $i] :
          ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ number_number_of_int @ min ) ) @ N )
            = one_one_int )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ number_number_of_int @ min ) ) @ N )
            = ( hAPP_int_int @ number_number_of_int @ min ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2819]) ).

thf(5734,plain,
    ( ( ! [A_3: $i,R_2: $i,B_2: $i,M: $i,C_1: $i,D_3: $i,N: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ R_2 ) @ B_2 ) ) ) @ M ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ C_1 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ R_2 ) @ D_3 ) ) ) @ N ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ M ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ C_1 ) @ N ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ R_2 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_2 ) @ M ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ D_3 ) @ N ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2831]) ).

thf(5735,plain,
    ( ( ! [A_3: $i,B_2: $i,C_1: $i] :
          ( ( is_int @ A_3 )
         => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_3 ) @ B_2 )
              = C_1 )
           => ( A_3
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ C_1 ) @ B_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2846]) ).

thf(5736,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_3 ) @ B_2 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_3 ) @ B_2 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2965]) ).

thf(5737,plain,
    ( ( ! [L_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ min ) @ ( hAPP_int_int @ bit0 @ L_2 ) )
          = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ min ) @ L_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2975]) ).

thf(5738,plain,
    ( ( ! [L_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ min ) @ ( hAPP_int_int @ bit1 @ L_2 ) )
          = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ min ) @ L_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2976]) ).

thf(5739,plain,
    ( ( ! [L_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ pls ) @ ( hAPP_int_int @ bit1 @ L_2 ) )
          = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ min ) @ L_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2977]) ).

thf(5740,plain,
    ( ( ! [V_4: $i,W_2: $i,C_6: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ V_4 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ number_number_of_int @ W_2 ) ) @ C_6 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ V_4 ) @ W_2 ) ) ) @ C_6 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2980]) ).

thf(5741,plain,
    ( ( ! [X_9: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ X_9 ) @ X_9 ) ) @ one_one_int )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ X_9 ) @ one_one_int ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ X_9 ) @ one_one_int ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2984]) ).

thf(5742,plain,
    ( ( ! [L_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ pls ) @ ( hAPP_int_int @ bit0 @ L_2 ) )
          = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ pls ) @ L_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3010]) ).

thf(5743,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ bit1 @ K_2 ) ) @ ( hAPP_int_int @ bit0 @ L_2 ) )
          = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ K_2 ) @ L_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3011]) ).

thf(5744,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ bit1 @ K_2 ) ) @ ( hAPP_int_int @ bit1 @ L_2 ) )
          = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ K_2 ) @ L_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3012]) ).

thf(5745,plain,
    ( ( ! [X_10: $i,Y_7: $i,A_29: $i,B_22: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ X_10 ) @ Y_7 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_29 ) @ B_22 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ X_10 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ Y_7 ) @ B_22 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ X_10 ) @ A_29 ) ) @ B_22 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3028]) ).

thf(5746,plain,
    ( ( ! [W: $i,Z1: $i,Z2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ W ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ Z1 ) @ Z2 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ W ) @ Z1 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ W ) @ Z2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3066]) ).

thf(5747,plain,
    ( ( ! [Z1: $i,Z2: $i,W: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ Z1 ) @ Z2 ) ) @ W )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z1 ) @ W ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z2 ) @ W ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3067]) ).

thf(5748,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ bit0 @ K_2 ) ) @ ( hAPP_int_int @ bit0 @ L_2 ) )
          = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ K_2 ) @ L_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3068]) ).

thf(5749,plain,
    ( ( ! [K_2: $i] :
          ( ( is_int @ K_2 )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ K_2 ) @ pls )
            = K_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3069]) ).

thf(5750,plain,
    ( ( ! [A_32: $i,C_8: $i,B_24: $i,D_7: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_32 ) @ C_8 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_24 ) @ D_7 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_32 ) @ B_24 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ C_8 ) @ D_7 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3070]) ).

thf(5751,plain,
    ( ( ! [A_33: $i,B_25: $i] :
          ( ( is_int @ A_33 )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_33 ) @ B_25 ) ) @ B_25 )
            = A_33 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3074]) ).

thf(5752,plain,
    ( ( ! [A_34: $i,B_26: $i] :
          ( ( is_int @ A_34 )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_34 ) @ B_26 ) ) @ B_26 )
            = A_34 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3078]) ).

thf(5753,plain,
    ( ( ! [A_35: $i] :
          ( ( is_int @ A_35 )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_35 ) @ zero_zero_int )
            = A_35 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3088]) ).

thf(5754,plain,
    ( ( ! [A_36: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_36 ) @ A_36 )
          = zero_zero_int ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3092]) ).

thf(5755,plain,
    ( ( ! [A_1: $i,B_1: $i] :
          ( ( ( is_int @ A_1 )
            & ( is_int @ B_1 ) )
         => ( ( A_1 = B_1 )
          <=> ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_1 ) @ B_1 )
              = zero_zero_int ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3096]) ).

thf(5756,plain,
    ( ( ! [A_1: $i,B_1: $i] :
          ( ( ( is_int @ A_1 )
            & ( is_int @ B_1 ) )
         => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_1 ) @ B_1 )
              = zero_zero_int )
          <=> ( A_1 = B_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3100]) ).

thf(5757,plain,
    ( ( ! [V_7: $i,W_3: $i] :
          ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ V_7 ) @ W_3 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ number_number_of_int @ V_7 ) ) @ ( hAPP_int_int @ number_number_of_int @ W_3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3189]) ).

thf(5758,plain,
    ( ( ! [A_1: $i,B_1: $i,C: $i,D_1: $i] :
          ( ( ( is_int @ A_1 )
            & ( is_int @ B_1 )
            & ( is_int @ C )
            & ( is_int @ D_1 ) )
         => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_1 ) @ B_1 )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ C ) @ D_1 ) )
           => ( ( A_1 = B_1 )
            <=> ( C = D_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3193]) ).

thf(5759,plain,
    ( ( ( hAPP_int_int @ succ @ min )
      = pls )
    = $true ),
    inference(unfold_def,[status(thm)],[3239]) ).

thf(5760,plain,
    ( ( ( hAPP_int_int @ number_number_of_int @ pls )
     != ( hAPP_int_int @ number_number_of_int @ min ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3240]) ).

thf(5761,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ bit0 @ K_2 )
         != min ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3254]) ).

thf(5762,plain,
    ( ( ! [L_2: $i] :
          ( min
         != ( hAPP_int_int @ bit0 @ L_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3255]) ).

thf(5763,plain,
    ( ( pls != min )
    = $true ),
    inference(unfold_def,[status(thm)],[3256]) ).

thf(5764,plain,
    ( ( min != pls )
    = $true ),
    inference(unfold_def,[status(thm)],[3257]) ).

thf(5765,plain,
    ( ( ! [K: $i] :
          ( ( is_int @ K )
         => ( ( ( hAPP_int_int @ bit1 @ K )
              = min )
          <=> ( K = min ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3258]) ).

thf(5766,plain,
    ( ( ! [L: $i] :
          ( ( is_int @ L )
         => ( ( min
              = ( hAPP_int_int @ bit1 @ L ) )
          <=> ( min = L ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3259]) ).

thf(5767,plain,
    ( ( ( hAPP_int_int @ bit1 @ min )
      = min )
    = $true ),
    inference(unfold_def,[status(thm)],[3260]) ).

thf(5768,plain,
    ( ( ! [X_15: $i,Y_11: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ X_15 ) @ Y_11 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X_15 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Y_11 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ X_15 ) ) @ Y_11 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3364]) ).

thf(5769,plain,
    ( ( ! [W_4: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ number_number_of_int @ W_4 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ W_4 ) ) @ ( hAPP_int_int @ number_number_of_int @ W_4 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3505]) ).

thf(5770,plain,
    ( ( ! [A_3: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
          = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3510]) ).

thf(5771,plain,
    ( ( ! [X_26: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ X_26 ) @ X_26 )
          = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X_26 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3513]) ).

thf(5772,plain,
    ( ( ! [A_59: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_59 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_59 ) @ A_59 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3519]) ).

thf(5773,plain,
    ( ( ! [Z_11: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ Z_11 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z_11 ) @ Z_11 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3523]) ).

thf(5774,plain,
    ( ( ! [Z_12: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ Z_12 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z_12 ) @ Z_12 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3528]) ).

thf(5775,plain,
    ( ( ! [Z_13: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z_13 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z_13 ) @ Z_13 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3532]) ).

thf(5776,plain,
    ( ( ! [Z_14: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z_14 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z_14 ) @ Z_14 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3537]) ).

thf(5777,plain,
    ( ( ! [A_61: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_61 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_61 ) @ A_61 ) ) @ A_61 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3547]) ).

thf(5778,plain,
    ( ( ! [W_5: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ one_one_int ) ) @ ( hAPP_int_int @ number_number_of_int @ W_5 ) )
          = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ W_5 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3551]) ).

thf(5779,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ bit1 @ K_2 ) ) @ L_2 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ L_2 ) ) ) @ L_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3801]) ).

thf(5780,plain,
    ( ( ! [A_89: $i,M_13: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_89 ) @ M_13 ) ) @ M_13 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_89 ) @ one_one_int ) ) @ M_13 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3930]) ).

thf(5781,plain,
    ( ( ! [M_14: $i,A_90: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ M_14 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_90 ) @ M_14 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_90 ) @ one_one_int ) ) @ M_14 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3937]) ).

thf(5782,plain,
    ( ( ! [M_15: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ M_15 ) @ M_15 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ one_one_int ) ) @ M_15 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3944]) ).

thf(5783,plain,
    ( ( ! [A_91: $i,B_61: $i,V_10: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_91 ) @ B_61 ) ) @ ( hAPP_int_int @ number_number_of_int @ V_10 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_91 ) @ ( hAPP_int_int @ number_number_of_int @ V_10 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_61 ) @ ( hAPP_int_int @ number_number_of_int @ V_10 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3952]) ).

thf(5784,plain,
    ( ( ! [V_11: $i,B_62: $i,C_34: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ V_11 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_62 ) @ C_34 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ V_11 ) ) @ B_62 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ V_11 ) ) @ C_34 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3959]) ).

thf(5785,plain,
    ( ( ! [C_35: $i,D_13: $i,A_92: $i,B_63: $i,R_6: $i] :
          ( ( ( is_int @ C_35 )
            & ( is_int @ D_13 )
            & ( is_int @ R_6 ) )
         => ( ( R_6 != zero_zero_int )
           => ( ( ( A_92 = B_63 )
                & ( C_35 != D_13 ) )
             => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_92 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ R_6 ) @ C_35 ) )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_63 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ R_6 ) @ D_13 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3971]) ).

thf(5786,plain,
    ( ( ! [Xa: $i,Ya: $i] :
          ( ( ( is_int @ Xa )
            & ( is_int @ Ya ) )
         => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Xa ) @ Xa ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Ya ) @ Ya ) )
              = zero_zero_int )
          <=> ( ( Xa = zero_zero_int )
              & ( Ya = zero_zero_int ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3976]) ).

thf(5787,plain,
    ( ( ! [V_1: $i,W: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ V_1 ) ) @ ( hAPP_int_int @ number_number_of_int @ W ) )
          = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ V_1 ) @ W ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4144]) ).

thf(5788,plain,
    ( ( ! [Z1: $i,Z2: $i,W: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z1 ) @ Z2 ) ) @ W )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z1 ) @ W ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z2 ) @ W ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4156]) ).

thf(5789,plain,
    ( ( ! [W: $i,Z1: $i,Z2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ W ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z1 ) @ Z2 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ W ) @ Z1 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ W ) @ Z2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4157]) ).

thf(5790,plain,
    ( ( ! [Z_1: $i] :
          ( ( is_int @ Z_1 )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z_1 ) @ one_one_int )
            = Z_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4158]) ).

thf(5791,plain,
    ( ( ! [Z_1: $i] :
          ( ( is_int @ Z_1 )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ one_one_int ) @ Z_1 )
            = Z_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4159]) ).

thf(5792,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ bit0 @ K_2 ) ) @ L_2 )
          = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ L_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4165]) ).

thf(5793,plain,
    ( ( ! [W: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ pls ) @ W )
          = pls ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4166]) ).

thf(5794,plain,
    ( ( ! [X_54: $i,Y_46: $i,Q_9: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ X_54 ) @ Y_46 ) ) @ Q_9 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X_54 ) @ Q_9 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Y_46 ) @ Q_9 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4171]) ).

thf(5795,plain,
    ( ( ! [A_121: $i,B_90: $i,N_28: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_121 ) @ B_90 ) ) @ N_28 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_121 ) @ N_28 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_90 ) @ N_28 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4177]) ).

thf(5796,plain,
    ( ( ! [A_122: $i,N_29: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_122 ) @ N_29 ) ) @ A_122 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_122 ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_122 ) @ N_29 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4183]) ).

thf(5797,plain,
    ( ( ! [A_123: $i] :
          ( ( is_int @ A_123 )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_123 ) @ one_one_int )
            = A_123 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4187]) ).

thf(5798,plain,
    ( ( ! [A_124: $i] :
          ( ( is_int @ A_124 )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_124 ) @ one_one_int )
            = A_124 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4194]) ).

thf(5799,plain,
    ( ( ! [A_125: $i] :
          ( ( is_int @ A_125 )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_125 ) @ one_one_int )
            = A_125 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4201]) ).

thf(5800,plain,
    ( ( ! [A_126: $i] :
          ( ( is_int @ A_126 )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ one_one_int ) @ A_126 )
            = A_126 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4208]) ).

thf(5801,plain,
    ( ( ! [A_127: $i] :
          ( ( is_int @ A_127 )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ one_one_int ) @ A_127 )
            = A_127 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4215]) ).

thf(5802,plain,
    ( ( ! [A_128: $i] :
          ( ( is_int @ A_128 )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ one_one_int ) @ A_128 )
            = A_128 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4222]) ).

thf(5803,plain,
    ( ( ! [Wa: $i,Ya: $i,Xa: $i,Z_2: $i] :
          ( ( ( is_int @ Wa )
            & ( is_int @ Ya )
            & ( is_int @ Xa )
            & ( is_int @ Z_2 ) )
         => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Wa ) @ Ya ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Xa ) @ Z_2 ) )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Wa ) @ Z_2 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Xa ) @ Ya ) ) )
          <=> ( ( Wa = Xa )
              | ( Ya = Z_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4229]) ).

thf(5804,plain,
    ( ( ! [A_129: $i,M_17: $i,B_91: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_129 ) @ M_17 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_91 ) @ M_17 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_129 ) @ B_91 ) ) @ M_17 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4234]) ).

thf(5805,plain,
    ( ( ! [A_130: $i,B_92: $i,C_48: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_130 ) @ B_92 ) ) @ C_48 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_130 ) @ C_48 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_92 ) @ C_48 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4240]) ).

thf(5806,plain,
    ( ( ! [C: $i,D_1: $i,A_1: $i,B_1: $i] :
          ( ( ( is_int @ C )
            & ( is_int @ D_1 )
            & ( is_int @ A_1 )
            & ( is_int @ B_1 ) )
         => ( ( ( A_1 != B_1 )
              & ( C != D_1 ) )
          <=> ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ C ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_1 ) @ D_1 ) )
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ D_1 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_1 ) @ C ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4246]) ).

thf(5807,plain,
    ( ( ! [X_55: $i,Y_47: $i,Z_19: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ X_55 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Y_47 ) @ Z_19 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ X_55 ) @ Y_47 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ X_55 ) @ Z_19 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4251]) ).

thf(5808,plain,
    ( ( ! [A_131: $i,E_3: $i,B_93: $i,C_49: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_131 ) @ E_3 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_93 ) @ E_3 ) ) @ C_49 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_131 ) @ B_93 ) ) @ E_3 ) ) @ C_49 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4257]) ).

thf(5809,plain,
    ( ( ! [A_132: $i,B_94: $i,C_50: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_132 ) @ B_94 ) ) @ C_50 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_132 ) @ C_50 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_94 ) @ C_50 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4263]) ).

thf(5810,plain,
    ( ( ! [A_133: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_133 ) @ zero_zero_int )
          = zero_zero_int ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4269]) ).

thf(5811,plain,
    ( ( ! [A_134: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ zero_zero_int ) @ A_134 )
          = zero_zero_int ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4276]) ).

thf(5812,plain,
    ( ( ! [A_135: $i,B_95: $i] :
          ( ( ( is_int @ A_135 )
            & ( is_int @ B_95 ) )
         => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_135 ) @ B_95 )
              = zero_zero_int )
           => ( ( A_135 = zero_zero_int )
              | ( B_95 = zero_zero_int ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4283]) ).

thf(5813,plain,
    ( ( ! [B_96: $i,A_136: $i] :
          ( ( ( is_int @ B_96 )
            & ( is_int @ A_136 ) )
         => ( ( A_136 != zero_zero_int )
           => ( ( B_96 != zero_zero_int )
             => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_136 ) @ B_96 )
               != zero_zero_int ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4290]) ).

thf(5814,plain,
    ( ( ! [A_1: $i,B_1: $i] :
          ( ( ( is_int @ A_1 )
            & ( is_int @ B_1 ) )
         => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ B_1 )
              = zero_zero_int )
          <=> ( ( A_1 = zero_zero_int )
              | ( B_1 = zero_zero_int ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4297]) ).

thf(5815,plain,
    ( ( ! [A_137: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_137 ) @ zero_zero_int )
          = zero_zero_int ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4301]) ).

thf(5816,plain,
    ( ( ! [A_138: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ zero_zero_int ) @ A_138 )
          = zero_zero_int ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4308]) ).

thf(5817,plain,
    ( ( ! [V_14: $i,W_6: $i] :
          ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ V_14 ) @ W_6 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ V_14 ) ) @ ( hAPP_int_int @ number_number_of_int @ W_6 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4321]) ).

thf(5818,plain,
    ( ( ! [V_15: $i,W_7: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ V_15 ) ) @ ( hAPP_int_int @ number_number_of_int @ W_7 ) )
          = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ V_15 ) @ W_7 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4325]) ).

thf(5819,plain,
    ( ( ! [V_16: $i,W_8: $i,Z_20: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ V_16 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ W_8 ) ) @ Z_20 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ V_16 ) @ W_8 ) ) ) @ Z_20 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4329]) ).

thf(5820,plain,
    ( ( ! [Z1: $i,Z2: $i,Z3: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z1 ) @ Z2 ) ) @ Z3 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z1 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z2 ) @ Z3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4333]) ).

thf(5821,plain,
    ( ( ! [Z_1: $i,W: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z_1 ) @ W )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ W ) @ Z_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4334]) ).

thf(5822,plain,
    ( ( ! [Lx: $i,Ly: $i,Rx: $i,Ry: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx ) @ Ly ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Rx ) @ Ry ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx ) @ Rx ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Ly ) @ Ry ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4335]) ).

thf(5823,plain,
    ( ( ! [Lx_1: $i,Ly_1: $i,Rx_1: $i,Ry_1: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_1 ) @ Ly_1 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Rx_1 ) @ Ry_1 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Rx_1 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_1 ) @ Ly_1 ) ) @ Ry_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4341]) ).

thf(5824,plain,
    ( ( ! [Lx_2: $i,Ly_2: $i,Rx_2: $i,Ry_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_2 ) @ Ly_2 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Rx_2 ) @ Ry_2 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_2 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Ly_2 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Rx_2 ) @ Ry_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4347]) ).

thf(5825,plain,
    ( ( ! [Lx_3: $i,Ly_3: $i,Rx_3: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_3 ) @ Ly_3 ) ) @ Rx_3 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_3 ) @ Rx_3 ) ) @ Ly_3 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4353]) ).

thf(5826,plain,
    ( ( ! [Lx_4: $i,Ly_4: $i,Rx_4: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_4 ) @ Ly_4 ) ) @ Rx_4 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_4 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Ly_4 ) @ Rx_4 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4359]) ).

thf(5827,plain,
    ( ( ! [A_139: $i,B_97: $i,C_51: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_139 ) @ B_97 ) ) @ C_51 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_139 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_97 ) @ C_51 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4365]) ).

thf(5828,plain,
    ( ( ! [Lx_5: $i,Rx_5: $i,Ry_3: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_5 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Rx_5 ) @ Ry_3 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_5 ) @ Rx_5 ) ) @ Ry_3 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4371]) ).

thf(5829,plain,
    ( ( ! [Lx_6: $i,Rx_6: $i,Ry_4: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_6 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Rx_6 ) @ Ry_4 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Rx_6 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_6 ) @ Ry_4 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4377]) ).

thf(5830,plain,
    ( ( ! [A_140: $i,B_98: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_140 ) @ B_98 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_98 ) @ A_140 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4383]) ).

thf(5831,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_3 ) @ B_2 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ A_3 ) ) @ B_2 ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4397]) ).

thf(5832,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_3 ) @ B_2 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) @ B_2 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ A_3 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4398]) ).

thf(5833,plain,
    ( ( ! [X_57: $i] :
          ( ( is_int @ X_57 )
         => ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X_57 ) @ one_one_nat )
            = X_57 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4417]) ).

thf(5834,plain,
    ( ( ! [A_146: $i] :
          ( ( is_int @ A_146 )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ A_146 )
            = A_146 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4469]) ).

thf(5835,plain,
    ( ( ! [A_147: $i] :
          ( ( is_int @ A_147 )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ A_147 )
            = A_147 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4476]) ).

thf(5836,plain,
    ( ( ! [A_148: $i] :
          ( ( is_int @ A_148 )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ A_148 )
            = A_148 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4483]) ).

thf(5837,plain,
    ( ( ! [A_1: $i] :
          ( ( is_int @ A_1 )
         => ( ( zero_zero_int
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_1 ) @ A_1 ) )
          <=> ( A_1 = zero_zero_int ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4489]) ).

thf(5838,plain,
    ( ( ! [A_149: $i] :
          ( ( is_int @ A_149 )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_149 ) @ zero_zero_int )
            = A_149 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4493]) ).

thf(5839,plain,
    ( ( ! [A_150: $i] :
          ( ( is_int @ A_150 )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_150 ) @ zero_zero_int )
            = A_150 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4500]) ).

thf(5840,plain,
    ( ( ! [A_151: $i] :
          ( ( is_int @ A_151 )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_151 ) @ zero_zero_int )
            = A_151 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4507]) ).

thf(5841,plain,
    ( ( ! [B_1: $i,A_1: $i] :
          ( ( ( is_int @ B_1 )
            & ( is_int @ A_1 ) )
         => ( ( B_1
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_1 ) @ A_1 ) )
          <=> ( A_1 = zero_zero_int ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4513]) ).

thf(5842,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ bit1 @ K_2 ) ) @ ( hAPP_int_int @ bit1 @ L_2 ) )
          = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ K_2 ) @ ( hAPP_int_int @ succ @ L_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4545]) ).

thf(5843,plain,
    ( ( ! [K_8: $i] :
          ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ succ @ K_8 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ ( hAPP_int_int @ number_number_of_int @ K_8 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4546]) ).

thf(5844,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ succ @ K_2 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ K_2 ) @ one_one_int ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4563]) ).

thf(5845,plain,
    ( ( ! [Xa: $i] :
          ( ( is_int @ Xa )
         => ( ( one_one_int = Xa )
          <=> ( Xa = one_one_int ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4564]) ).

thf(5846,plain,
    ( ( ! [A_155: $i,C_57: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_155 ) @ C_57 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ C_57 ) @ A_155 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4571]) ).

thf(5847,plain,
    ( ( ! [A_156: $i,C_58: $i,D_17: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_156 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ C_58 ) @ D_17 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ C_58 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_156 ) @ D_17 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4577]) ).

thf(5848,plain,
    ( ( ! [A_157: $i,C_59: $i,D_18: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_157 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ C_59 ) @ D_18 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_157 ) @ C_59 ) ) @ D_18 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4583]) ).

thf(5849,plain,
    ( ( ! [A_158: $i,B_106: $i,C_60: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_158 ) @ B_106 ) ) @ C_60 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_158 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_106 ) @ C_60 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4589]) ).

thf(5850,plain,
    ( ( ! [A_159: $i,B_107: $i,C_61: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_159 ) @ B_107 ) ) @ C_61 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_159 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_107 ) @ C_61 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4595]) ).

thf(5851,plain,
    ( ( ! [A_160: $i,B_108: $i,C_62: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_160 ) @ B_108 ) ) @ C_62 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_160 ) @ C_62 ) ) @ B_108 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4601]) ).

thf(5852,plain,
    ( ( ! [A_1: $i,B_1: $i,C: $i] :
          ( ( ( is_int @ B_1 )
            & ( is_int @ C ) )
         => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_1 ) @ B_1 )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_1 ) @ C ) )
          <=> ( B_1 = C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4607]) ).

thf(5853,plain,
    ( ( ! [B_1: $i,A_1: $i,C: $i] :
          ( ( ( is_int @ B_1 )
            & ( is_int @ C ) )
         => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_1 ) @ A_1 )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ C ) @ A_1 ) )
          <=> ( B_1 = C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4613]) ).

thf(5854,plain,
    ( ( ! [A_161: $i,B_109: $i,C_63: $i,D_19: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_161 ) @ B_109 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ C_63 ) @ D_19 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_161 ) @ C_63 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_109 ) @ D_19 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4619]) ).

thf(5855,plain,
    ( ( ! [A_162: $i,B_110: $i,C_64: $i] :
          ( ( ( is_int @ B_110 )
            & ( is_int @ C_64 ) )
         => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_162 ) @ B_110 )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_162 ) @ C_64 ) )
           => ( B_110 = C_64 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4625]) ).

thf(5856,plain,
    ( ( ! [A_163: $i,B_111: $i,C_65: $i] :
          ( ( ( is_int @ B_111 )
            & ( is_int @ C_65 ) )
         => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_163 ) @ B_111 )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_163 ) @ C_65 ) )
           => ( B_111 = C_65 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4631]) ).

thf(5857,plain,
    ( ( ! [B_112: $i,A_164: $i,C_66: $i] :
          ( ( ( is_int @ B_112 )
            & ( is_int @ C_66 ) )
         => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_112 ) @ A_164 )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ C_66 ) @ A_164 ) )
           => ( B_112 = C_66 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4637]) ).

thf(5858,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ succ @ ( hAPP_int_int @ bit0 @ K_2 ) )
          = ( hAPP_int_int @ bit1 @ K_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4646]) ).

thf(5859,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ succ @ ( hAPP_int_int @ bit1 @ K_2 ) )
          = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ succ @ K_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4647]) ).

thf(5860,plain,
    ( ( ( hAPP_int_int @ succ @ pls )
      = ( hAPP_int_int @ bit1 @ pls ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4648]) ).

thf(5861,plain,
    ( ( ! [Xa: $i] :
          ( ( is_int @ Xa )
         => ( ( zero_zero_int = Xa )
          <=> ( Xa = zero_zero_int ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4651]) ).

thf(5862,plain,
    ( ( ! [X_62: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X_62 ) @ zero_zero_nat )
          = one_one_int ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4938]) ).

thf(5863,plain,
    ( ( ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat )
      = zero_zero_int )
    = $true ),
    inference(unfold_def,[status(thm)],[4949]) ).

thf(5864,plain,
    ( ( ! [A_191: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_191 ) @ zero_zero_nat )
          = one_one_int ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4956]) ).

thf(5865,plain,
    ( ( ! [A_1: $i,Na: $i] :
          ( ( is_int @ A_1 )
         => ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_1 ) @ Na )
              = zero_zero_int )
          <=> ( ( A_1 = zero_zero_int )
              & ( Na != zero_zero_nat ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4969]) ).

thf(5866,plain,
    ( ( one_one_int
      = ( hAPP_nat_int @ semiri1621563631at_int @ one_one_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5032]) ).

thf(5867,plain,
    ( ( ( hAPP_nat_int @ semiri1621563631at_int @ one_one_nat )
      = one_one_int )
    = $true ),
    inference(unfold_def,[status(thm)],[5038]) ).

thf(5868,plain,
    ( ( ! [N_51: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ one_one_int ) @ N_51 )
          = one_one_int ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5066]) ).

thf(5869,plain,
    ( ( ! [N_52: $i,A_197: $i] :
          ( ( is_int @ A_197 )
         => ( ( A_197 != zero_zero_int )
           => ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_197 ) @ N_52 )
             != zero_zero_int ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5073]) ).

thf(5870,plain,
    ( ( zero_zero_int != one_one_int )
    = $true ),
    inference(unfold_def,[status(thm)],[5077]) ).

thf(5871,plain,
    ( ( one_one_int != zero_zero_int )
    = $true ),
    inference(unfold_def,[status(thm)],[5084]) ).

thf(5872,plain,
    ( ( ! [Xa: $i,Ya: $i] :
          ( ( ( hAPP_nat_int @ semiri1621563631at_int @ Xa )
            = ( hAPP_nat_int @ semiri1621563631at_int @ Ya ) )
        <=> ( Xa = Ya ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5094]) ).

thf(5873,plain,
    ( ( ! [Ma: $i,Na: $i] :
          ( ( ( hAPP_nat_int @ semiri1621563631at_int @ Ma )
            = ( hAPP_nat_int @ semiri1621563631at_int @ Na ) )
        <=> ( Ma = Na ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5095]) ).

thf(5874,plain,
    ( ( ! [A_198: $i] :
          ( ( is_int @ A_198 )
         => ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_198 ) @ one_one_nat )
            = A_198 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5099]) ).

thf(5875,plain,
    ( ( ! [K_2: $i] :
          ( ( is_int @ K_2 )
         => ( ( hAPP_int_int @ number_number_of_int @ K_2 )
            = K_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5141]) ).

thf(5876,plain,
    ( ( zero_zero_int
      = ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5148]) ).

thf(5877,plain,
    ( ( ! [N_55: $i] :
          ( ( ( N_55 = zero_zero_nat )
           => ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ N_55 )
              = one_one_int ) )
          & ( ( N_55 != zero_zero_nat )
           => ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ N_55 )
              = zero_zero_int ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5162]) ).

thf(5878,plain,
    ( ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) )
      = ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5182]) ).

thf(5879,plain,
    ( ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) )
      = ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5183]) ).

thf(5880,plain,
    ( ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ pls ) )
      = one_one_int )
    = $true ),
    inference(unfold_def,[status(thm)],[5188]) ).

thf(5881,plain,
    ( ( ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ pls ) )
      = one_one_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[5189]) ).

thf(5882,plain,
    ( ( ! [W_10: $i] :
          ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ W_10 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ ( hAPP_int_int @ number_number_of_int @ W_10 ) ) ) @ ( hAPP_int_int @ number_number_of_int @ W_10 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5193]) ).

thf(5883,plain,
    ( ( ! [W_11: $i] :
          ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ W_11 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ ( hAPP_int_int @ number_number_of_int @ W_11 ) ) ) @ ( hAPP_int_int @ number_number_of_int @ W_11 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5197]) ).

thf(5884,plain,
    ( ( ! [N_58: $i] :
          ( ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_nat_int @ semiri1621563631at_int @ N_58 ) )
          = ( hAPP_nat_nat @ semiri984289939at_nat @ N_58 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5213]) ).

thf(5885,plain,
    ( ( ! [N_58: $i] :
          ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_nat_int @ semiri1621563631at_int @ N_58 ) )
          = ( hAPP_nat_int @ semiri1621563631at_int @ N_58 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5214]) ).

thf(5886,plain,
    ( ( ! [Z_1: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ Z_1 ) ) @ Z_1 )
         != zero_zero_int ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5218]) ).

thf(5887,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ bit1 @ K_2 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ K_2 ) ) @ K_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5219]) ).

thf(5888,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ bit0 @ K_2 ) ) @ ( hAPP_int_int @ bit1 @ L_2 ) )
          = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ K_2 ) @ L_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5220]) ).

thf(5889,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ bit1 @ K_2 ) ) @ ( hAPP_int_int @ bit0 @ L_2 ) )
          = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ K_2 ) @ L_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5221]) ).

thf(5890,plain,
    ( ( ! [V_22: $i,W_12: $i] :
          ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ V_22 ) @ W_12 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ V_22 ) ) @ ( hAPP_int_int @ number_number_of_int @ W_12 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5222]) ).

thf(5891,plain,
    ( ( ! [V_23: $i,W_13: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ V_23 ) ) @ ( hAPP_int_int @ number_number_of_int @ W_13 ) )
          = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ V_23 ) @ W_13 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5226]) ).

thf(5892,plain,
    ( ( ! [V_24: $i,W_14: $i,Z_21: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ V_24 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ W_14 ) ) @ Z_21 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ V_24 ) @ W_14 ) ) ) @ Z_21 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5230]) ).

thf(5893,plain,
    ( ( ! [A_1: $i,Wa: $i] :
          ( ( is_int @ A_1 )
         => ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ Wa ) )
              = zero_zero_int )
          <=> ( ( A_1 = zero_zero_int )
              & ( ( hAPP_int_nat @ number_number_of_nat @ Wa )
               != zero_zero_nat ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5234]) ).

thf(5894,plain,
    ( ( ! [A_202: $i] :
          ( ( is_int @ A_202 )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_202 ) @ ( hAPP_int_int @ number_number_of_int @ pls ) )
            = A_202 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5241]) ).

thf(5895,plain,
    ( ( ! [A_203: $i] :
          ( ( is_int @ A_203 )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ pls ) ) @ A_203 )
            = A_203 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5245]) ).

thf(5896,plain,
    ( ( zero_zero_int
      = ( hAPP_int_int @ number_number_of_int @ pls ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5249]) ).

thf(5897,plain,
    ( ( ( hAPP_int_int @ number_number_of_int @ pls )
      = zero_zero_int )
    = $true ),
    inference(unfold_def,[status(thm)],[5253]) ).

thf(5898,plain,
    ( ( ( hAPP_int_int @ number_number_of_int @ pls )
      = zero_zero_int )
    = $true ),
    inference(unfold_def,[status(thm)],[5257]) ).

thf(5899,plain,
    ( ( ( hAPP_int_nat @ number_number_of_nat @ pls )
      = zero_zero_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[5258]) ).

thf(5900,plain,
    ( ( ! [Z_1: $i] :
          ( ( is_int @ Z_1 )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ Z_1 )
            = Z_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5262]) ).

thf(5901,plain,
    ( ( ! [Z_1: $i] :
          ( ( is_int @ Z_1 )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z_1 ) @ zero_zero_int )
            = Z_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5263]) ).

thf(5902,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ bit0 @ K_2 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ K_2 ) @ K_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5264]) ).

thf(5903,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ bit0 @ K_2 ) ) @ ( hAPP_int_int @ bit0 @ L_2 ) )
          = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ K_2 ) @ L_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5265]) ).

thf(5904,plain,
    ( ( ! [K_2: $i] :
          ( ( is_int @ K_2 )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ pls ) @ K_2 )
            = K_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5266]) ).

thf(5905,plain,
    ( ( ! [K_2: $i] :
          ( ( is_int @ K_2 )
         => ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ K_2 ) @ pls )
            = K_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5267]) ).

thf(5906,plain,
    ( ( zero_zero_int != one_one_int )
    = $true ),
    inference(unfold_def,[status(thm)],[5268]) ).

thf(5907,plain,
    ( ( pls = zero_zero_int )
    = $true ),
    inference(unfold_def,[status(thm)],[5269]) ).

thf(5908,plain,
    ( ( ( hAPP_int_int @ bit0 @ pls )
      = pls )
    = $true ),
    inference(unfold_def,[status(thm)],[5283]) ).

thf(5909,plain,
    ( ( ! [L: $i] :
          ( ( is_int @ L )
         => ( ( pls
              = ( hAPP_int_int @ bit0 @ L ) )
          <=> ( pls = L ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5284]) ).

thf(5910,plain,
    ( ( ! [K: $i] :
          ( ( is_int @ K )
         => ( ( ( hAPP_int_int @ bit0 @ K )
              = pls )
          <=> ( K = pls ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5285]) ).

thf(5911,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( hAPP_int_int @ bit0 @ K_2 )
         != ( hAPP_int_int @ bit1 @ L_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5286]) ).

thf(5912,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( hAPP_int_int @ bit1 @ K_2 )
         != ( hAPP_int_int @ bit0 @ L_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5287]) ).

thf(5913,plain,
    ( ( ! [L_2: $i] :
          ( pls
         != ( hAPP_int_int @ bit1 @ L_2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5288]) ).

thf(5914,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ bit1 @ K_2 )
         != pls ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5289]) ).

thf(5915,plain,
    ( ( ! [A_1: $i] :
          ( ( is_int @ A_1 )
         => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_1 ) @ A_1 )
              = zero_zero_int )
          <=> ( A_1 = zero_zero_int ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5290]) ).

thf(5916,plain,
    ( ( ! [Ma: $i,Na: $i] :
          ( ( ( hAPP_nat_int @ semiri1621563631at_int @ Ma )
            = ( hAPP_nat_int @ semiri1621563631at_int @ Na ) )
        <=> ( Ma = Na ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5317]) ).

thf(5917,plain,
    ( ( ! [Z_1: $i,W: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z_1 ) @ W )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ W ) @ Z_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5318]) ).

thf(5918,plain,
    ( ( ! [X: $i,Y: $i,Z_1: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ X ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Y ) @ Z_1 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Y ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ X ) @ Z_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5319]) ).

thf(5919,plain,
    ( ( ! [Z1: $i,Z2: $i,Z3: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z1 ) @ Z2 ) ) @ Z3 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z1 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z2 ) @ Z3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5320]) ).

thf(5920,plain,
    ( ( ! [K: $i,L: $i] :
          ( ( ( is_int @ K )
            & ( is_int @ L ) )
         => ( ( ( hAPP_int_int @ bit0 @ K )
              = ( hAPP_int_int @ bit0 @ L ) )
          <=> ( K = L ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5324]) ).

thf(5921,plain,
    ( ( ! [K: $i,L: $i] :
          ( ( ( is_int @ K )
            & ( is_int @ L ) )
         => ( ( ( hAPP_int_int @ bit1 @ K )
              = ( hAPP_int_int @ bit1 @ L ) )
          <=> ( K = L ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5325]) ).

thf(5922,plain,
    ( ( ! [Wa: $i,Xa: $i] :
          ( ( ( hAPP_int_nat @ number_number_of_nat @ Wa )
            = Xa )
        <=> ( Xa
            = ( hAPP_int_nat @ number_number_of_nat @ Wa ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5326]) ).

thf(5923,plain,
    ( ( ! [Wa: $i,Xa: $i] :
          ( ( is_int @ Xa )
         => ( ( ( hAPP_int_int @ number_number_of_int @ Wa )
              = Xa )
          <=> ( Xa
              = ( hAPP_int_int @ number_number_of_int @ Wa ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5327]) ).

thf(5924,plain,
    ( ( ! [Xa: $i,Ya: $i] :
          ( ( ( is_int @ Xa )
            & ( is_int @ Ya ) )
         => ( ( ( hAPP_int_int @ number_number_of_int @ Xa )
              = ( hAPP_int_int @ number_number_of_int @ Ya ) )
          <=> ( Xa = Ya ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5333]) ).

thf(5925,plain,
    ( ( one_one_nat
      = ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ pls ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5337]) ).

thf(5926,plain,
    ( ( ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ pls ) )
      = one_one_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[5338]) ).

thf(5927,plain,
    ( ( one_one_int
      = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ pls ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5339]) ).

thf(5928,plain,
    ( ( ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat )
      = zero_zero_int )
    = $true ),
    inference(unfold_def,[status(thm)],[5348]) ).

thf(5929,plain,
    ( ( ! [Na: $i] :
          ( ( ( hAPP_nat_int @ semiri1621563631at_int @ Na )
            = zero_zero_int )
        <=> ( Na = zero_zero_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5349]) ).

thf(5930,plain,
    ( ( zero_zero_nat
      = ( hAPP_int_nat @ number_number_of_nat @ pls ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5350]) ).

thf(5931,plain,
    ( ( ( hAPP_int_nat @ number_number_of_nat @ pls )
      = zero_zero_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[5351]) ).

thf(5932,plain,
    ( ( ( hAPP_nat_int @ semiri1621563631at_int @ one_one_nat )
      = one_one_int )
    = $true ),
    inference(unfold_def,[status(thm)],[5352]) ).

thf(5933,plain,
    ( ( zero_zero_int
      = ( hAPP_int_int @ number_number_of_int @ pls ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5357]) ).

thf(5934,plain,
    ( ( ! [V_1: $i,W: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ V_1 ) ) @ ( hAPP_int_int @ number_number_of_int @ W ) )
          = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ V_1 ) @ W ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5361]) ).

thf(5935,plain,
    ( ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ pls ) )
      = one_one_int )
    = $true ),
    inference(unfold_def,[status(thm)],[5365]) ).

thf(5936,plain,
    ( ( one_one_int
      = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ pls ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5369]) ).

thf(5937,plain,
    ( ( ! [W_15: $i] :
          ( ( ( ( hAPP_int_nat @ number_number_of_nat @ W_15 )
              = zero_zero_nat )
           => ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ ( hAPP_int_nat @ number_number_of_nat @ W_15 ) )
              = one_one_int ) )
          & ( ( ( hAPP_int_nat @ number_number_of_nat @ W_15 )
             != zero_zero_nat )
           => ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ ( hAPP_int_nat @ number_number_of_nat @ W_15 ) )
              = zero_zero_int ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5373]) ).

thf(5938,plain,
    ( ( ! [X: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5380]) ).

thf(5939,plain,
    ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ one_one_int )
      = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5381]) ).

thf(5940,plain,
    ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ one_one_int )
      = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5386]) ).

thf(5941,plain,
    ( ( ! [V_25: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ V_25 ) ) @ one_one_int )
          = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ V_25 ) @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5390]) ).

thf(5942,plain,
    ( ( ! [W_16: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ ( hAPP_int_int @ number_number_of_int @ W_16 ) )
          = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ bit1 @ pls ) ) @ W_16 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5394]) ).

thf(5943,plain,
    ( ( ! [A_1: $i] :
          ( ( is_int @ A_1 )
         => ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
              = zero_zero_int )
          <=> ( A_1 = zero_zero_int ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5398]) ).

thf(5944,plain,
    ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
      = zero_zero_int )
    = $true ),
    inference(unfold_def,[status(thm)],[5402]) ).

thf(5945,plain,
    ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ one_one_int ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
      = one_one_int )
    = $true ),
    inference(unfold_def,[status(thm)],[5409]) ).

thf(5946,plain,
    ( ( ! [Xa: $i,Ya: $i] :
          ( ( ( is_int @ Xa )
            & ( is_int @ Ya ) )
         => ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Xa ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Ya ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
              = zero_zero_int )
          <=> ( ( Xa = zero_zero_int )
              & ( Ya = zero_zero_int ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5416]) ).

thf(5947,plain,
    ( ( ! [B_1_1: $i,B_2_1: $i] : ( is_int @ ( hAPP_nat_int @ B_1_1 @ B_2_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5482]) ).

thf(5948,plain,
    ( ( ! [B_1_1: $i,B_2_1: $i] :
          ( ( is_int @ B_2_1 )
         => ( is_int @ ( hAPP_int_int @ B_1_1 @ B_2_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5483]) ).

thf(5949,plain,
    ( ( is_int @ pls )
    = $true ),
    inference(unfold_def,[status(thm)],[5484]) ).

thf(5950,plain,
    ( ( is_int @ zero_zero_int )
    = $true ),
    inference(unfold_def,[status(thm)],[5485]) ).

thf(5951,plain,
    ( ( is_int @ one_one_int )
    = $true ),
    inference(unfold_def,[status(thm)],[5486]) ).

thf(5952,plain,
    ( ( ~ ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
           != zero_zero_int ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[5489]) ).

thf(5953,plain,
    ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
      = zero_zero_int )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5952]) ).

thf(5954,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ~ ( is_int @ A_3 )
          | ~ ( is_int @ B_2 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 )
            = zero_zero_int )
          | ( ( is_int @ ( sK1_A_4 @ B_2 @ A_3 ) )
            & ( is_int @ ( sK2_SY713 @ B_2 @ A_3 ) )
            & ( A_3
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK1_A_4 @ B_2 @ A_3 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) )
            & ( B_2
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK2_SY713 @ B_2 @ A_3 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) )
            & ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( sK1_A_4 @ B_2 @ A_3 ) ) @ ( sK2_SY713 @ B_2 @ A_3 ) )
              = one_one_int ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5491]) ).

thf(5955,plain,
    ( ( ! [B_1: $i,C: $i] :
          ( ! [A_1: $i,D_1: $i] :
              ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_1 ) @ D_1 )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ B_1 ) @ C )
               != one_one_int )
              | ( ( hAPP_int_int @ abs_abs_int @ A_1 )
               != ( hAPP_int_int @ abs_abs_int @ B_1 ) )
              | ( ( hAPP_int_int @ abs_abs_int @ C )
               != ( hAPP_int_int @ abs_abs_int @ D_1 ) )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ A_1 ) ) @ ( hAPP_int_int @ abs_abs_int @ C ) )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ B_1 ) ) @ ( hAPP_int_int @ abs_abs_int @ D_1 ) ) ) )
          & ! [A_1: $i,D_1: $i] :
              ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_1 ) @ D_1 )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ B_1 ) @ C )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ A_1 ) ) @ ( hAPP_int_int @ abs_abs_int @ C ) )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ B_1 ) ) @ ( hAPP_int_int @ abs_abs_int @ D_1 ) ) )
              | ( ( hAPP_int_int @ abs_abs_int @ A_1 )
                = ( hAPP_int_int @ abs_abs_int @ B_1 ) ) )
          & ! [A_1: $i,D_1: $i] :
              ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_1 ) @ D_1 )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ B_1 ) @ C )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ A_1 ) ) @ ( hAPP_int_int @ abs_abs_int @ C ) )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ B_1 ) ) @ ( hAPP_int_int @ abs_abs_int @ D_1 ) ) )
              | ( ( hAPP_int_int @ abs_abs_int @ C )
                = ( hAPP_int_int @ abs_abs_int @ D_1 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5492]) ).

thf(5956,plain,
    ( ( ! [X: $i,Y: $i,M: $i] :
          ( ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ X ) @ Y ) ) @ M )
           != one_one_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ M )
            = one_one_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5493]) ).

thf(5957,plain,
    ( ( ! [B_2: $i,A_3: $i] :
          ( ~ ( is_int @ B_2 )
          | ~ ( is_int @ A_3 )
          | ( A_3 = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ B_2 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) )
            = one_one_int ) )
      & ! [B_2: $i,A_3: $i] :
          ( ~ ( is_int @ B_2 )
          | ~ ( is_int @ A_3 )
          | ( B_2 = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ B_2 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) )
            = one_one_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5495]) ).

thf(5958,plain,
    ( ( ! [Z_1: $i] :
          ( ~ ( is_int @ Z_1 )
          | ( Z_1
            = ( hAPP_nat_int @ semiri1621563631at_int @ ( sK4_N_1 @ Z_1 ) ) )
          | ( Z_1
            = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ suc @ ( sK3_N_1 @ Z_1 ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5498]) ).

thf(5959,plain,
    ( ( ! [B_2: $i,A_3: $i] :
          ( ~ ( is_int @ B_2 )
          | ~ ( is_int @ A_3 )
          | ( A_3 = zero_zero_int )
          | ( ( is_int @ ( sK7_C_3 @ A_3 @ B_2 ) )
            & ( is_int @ ( sK8_SY715 @ A_3 @ B_2 ) )
            & ( A_3
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 ) ) @ ( sK7_C_3 @ A_3 @ B_2 ) ) )
            & ( B_2
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 ) ) @ ( sK8_SY715 @ A_3 @ B_2 ) ) )
            & ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK7_C_3 @ A_3 @ B_2 ) ) @ ( sK8_SY715 @ A_3 @ B_2 ) )
              = one_one_int ) ) )
      & ! [B_2: $i,A_3: $i] :
          ( ~ ( is_int @ B_2 )
          | ~ ( is_int @ A_3 )
          | ( B_2 = zero_zero_int )
          | ( ( is_int @ ( sK5_C_3 @ A_3 @ B_2 ) )
            & ( is_int @ ( sK6_SY714 @ A_3 @ B_2 ) )
            & ( A_3
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 ) ) @ ( sK5_C_3 @ A_3 @ B_2 ) ) )
            & ( B_2
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 ) ) @ ( sK6_SY714 @ A_3 @ B_2 ) ) )
            & ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK5_C_3 @ A_3 @ B_2 ) ) @ ( sK6_SY714 @ A_3 @ B_2 ) )
              = one_one_int ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5499]) ).

thf(5960,plain,
    ( ( ! [B_2: $i,A_3: $i] :
          ( ~ ( is_int @ B_2 )
          | ~ ( is_int @ A_3 )
          | ( A_3 = zero_zero_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ B_2 ) @ ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 ) ) )
            = one_one_int ) )
      & ! [B_2: $i,A_3: $i] :
          ( ~ ( is_int @ B_2 )
          | ~ ( is_int @ A_3 )
          | ( B_2 = zero_zero_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ B_2 ) @ ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 ) ) )
            = one_one_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5500]) ).

thf(5961,plain,
    ( ( ! [X: $i] :
          ( ~ ( is_int @ X )
          | ( ( hAPP_int_int @ succ @ ( hAPP_int_int @ pred @ X ) )
            = X ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5506]) ).

thf(5962,plain,
    ( ( ! [Y: $i] :
          ( ( Y = zero_zero_nat )
          | ( Y
            = ( hAPP_nat_nat @ suc @ ( sK9_Nat_1 @ Y ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5507]) ).

thf(5963,plain,
    ( ( ! [N: $i] :
          ( ( N = zero_zero_nat )
          | ( N
            = ( hAPP_nat_nat @ suc @ ( sK10_M_1 @ N ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5508]) ).

thf(5964,plain,
    ( ( ! [N: $i] :
          ( ( hAPP_nat_nat @ fact_fact_nat @ N )
         != zero_zero_nat ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5512]) ).

thf(5965,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ~ ( is_int @ B_2 )
          | ( B_2 = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
           != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) @ B_2 )
            = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ B_2 ) ) ) )
      & ! [A_3: $i,B_2: $i] :
          ( ~ ( is_int @ B_2 )
          | ( B_2 = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
            = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) @ B_2 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ B_2 ) ) ) @ one_one_int ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5513]) ).

thf(5966,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ~ ( is_int @ B_2 )
          | ( B_2 = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
           != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ ( hAPP_int_int @ uminus_uminus_int @ B_2 ) )
            = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ B_2 ) ) ) )
      & ! [A_3: $i,B_2: $i] :
          ( ~ ( is_int @ B_2 )
          | ( B_2 = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
            = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ ( hAPP_int_int @ uminus_uminus_int @ B_2 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ B_2 ) ) ) @ one_one_int ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5514]) ).

thf(5967,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
           != zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ ( hAPP_int_int @ uminus_uminus_int @ B_2 ) )
            = zero_zero_int ) )
      & ! [A_3: $i,B_2: $i] :
          ( ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
            = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ ( hAPP_int_int @ uminus_uminus_int @ B_2 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 ) ) @ B_2 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5516]) ).

thf(5968,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
           != zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) @ B_2 )
            = zero_zero_int ) )
      & ! [A_3: $i,B_2: $i] :
          ( ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
            = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) @ B_2 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ B_2 ) @ ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5517]) ).

thf(5969,plain,
    ( ( ! [M: $i] :
          ( ( ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
            = ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          | ( ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
            = ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          | ( ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
            = zero_zero_nat )
          | ( ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
            = one_one_nat ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5521]) ).

thf(5970,plain,
    ( ( ! [M: $i,N: $i] :
          ( ( ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ N ) )
           != N )
          | ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ M ) ) @ N )
            = zero_zero_nat ) )
      & ! [M: $i,N: $i] :
          ( ( ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ N ) )
            = N )
          | ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ M ) ) @ N )
            = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ N ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5525]) ).

thf(5971,plain,
    ( ( ! [M_5: $i] :
          ( ~ ( is_int @ M_5 )
          | ! [D_4: $i] :
              ( ( ( hAPP_int_int @ ( div_mod_int @ M_5 ) @ D_4 )
               != zero_zero_int )
              | ( ( M_5
                  = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ D_4 ) @ ( sK11_Q_4 @ D_4 @ M_5 ) ) )
                & ( is_int @ ( sK11_Q_4 @ D_4 @ M_5 ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5528]) ).

thf(5972,plain,
    ( ( ! [R_2: $i,S_1: $i,T_1: $i,R_4: $i,S_3: $i,M: $i,T_2: $i,N: $i] :
          ( ( R_4
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ S_3 ) @ M ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ T_2 ) @ N ) ) )
          | ( R_2
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ S_1 ) @ M ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ T_1 ) @ N ) ) )
          | ( ( hAPP_int_int @ ( div_mod_int @ R_4 ) @ R_2 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ S_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ R_4 ) @ R_2 ) ) @ S_1 ) ) ) @ M ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ T_2 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ R_4 ) @ R_2 ) ) @ T_1 ) ) ) @ N ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5537]) ).

thf(5973,plain,
    ( ( ! [A_3: $i] :
          ( ~ ( is_int @ A_3 )
          | ! [B_2: $i] :
              ( A_3
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_2 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ B_2 ) ) ) @ ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5545]) ).

thf(5974,plain,
    ( ( ! [A_3: $i] :
          ( ~ ( is_int @ A_3 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ zero_zero_int )
            = zero_zero_int ) )
      & ! [A_3: $i] :
          ( ~ ( is_int @ A_3 )
          | ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ zero_zero_int )
            = A_3 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5548]) ).

thf(5975,plain,
    ( ( ! [Ma: $i] :
          ( ~ ( is_int @ Ma )
          | ! [D_1: $i] :
              ( ( ( hAPP_int_int @ ( div_mod_int @ Ma ) @ D_1 )
               != zero_zero_int )
              | ( ( Ma
                  = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ D_1 ) @ ( sK12_Q_4 @ D_1 @ Ma ) ) )
                & ( is_int @ ( sK12_Q_4 @ D_1 @ Ma ) ) ) ) )
      & ! [Ma: $i] :
          ( ~ ( is_int @ Ma )
          | ! [D_1: $i] :
              ( ! [Q_4: $i] :
                  ( ( Ma
                   != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ D_1 ) @ Q_4 ) )
                  | ~ ( is_int @ Q_4 ) )
              | ( ( hAPP_int_int @ ( div_mod_int @ Ma ) @ D_1 )
                = zero_zero_int ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5549]) ).

thf(5976,plain,
    ( ( ! [M: $i] :
          ( ( hAPP_nat_nat @ suc @ M )
         != zero_zero_nat ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5550]) ).

thf(5977,plain,
    ( ( ! [M: $i] :
          ( zero_zero_nat
         != ( hAPP_nat_nat @ suc @ M ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5551]) ).

thf(5978,plain,
    ( ( ! [Nat_2: $i] :
          ( ( hAPP_nat_nat @ suc @ Nat_2 )
         != zero_zero_nat ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5552]) ).

thf(5979,plain,
    ( ( ! [M: $i] :
          ( ( hAPP_nat_nat @ suc @ M )
         != zero_zero_nat ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5553]) ).

thf(5980,plain,
    ( ( ! [Nat_3: $i] :
          ( zero_zero_nat
         != ( hAPP_nat_nat @ suc @ Nat_3 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5554]) ).

thf(5981,plain,
    ( ( ! [M: $i] :
          ( zero_zero_nat
         != ( hAPP_nat_nat @ suc @ M ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5555]) ).

thf(5982,plain,
    ( ( ! [N: $i] :
          ( N
         != ( hAPP_nat_nat @ suc @ N ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5556]) ).

thf(5983,plain,
    ( ( ! [N: $i] :
          ( ( hAPP_nat_nat @ suc @ N )
         != N ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5557]) ).

thf(5984,plain,
    ( ( ! [Nat_5: $i,Nat_4: $i] :
          ( ( ( hAPP_nat_nat @ suc @ Nat_5 )
           != ( hAPP_nat_nat @ suc @ Nat_4 ) )
          | ( Nat_5 = Nat_4 ) )
      & ! [Nat_5: $i,Nat_4: $i] :
          ( ( Nat_5 != Nat_4 )
          | ( ( hAPP_nat_nat @ suc @ Nat_5 )
            = ( hAPP_nat_nat @ suc @ Nat_4 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5558]) ).

thf(5985,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( ( hAPP_nat_nat @ suc @ X )
           != ( hAPP_nat_nat @ suc @ Y ) )
          | ( X = Y ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5559]) ).

thf(5986,plain,
    ( ( ! [Z_2: $i] :
          ( ~ ( is_int @ Z_2 )
          | ( ( hAPP_int_int @ abs_abs_int @ Z_2 )
           != one_one_int )
          | ( Z_2 = one_one_int )
          | ( Z_2
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
      & ! [Z_2: $i] :
          ( ~ ( is_int @ Z_2 )
          | ( Z_2 != one_one_int )
          | ( ( hAPP_int_int @ abs_abs_int @ Z_2 )
            = one_one_int ) )
      & ! [Z_2: $i] :
          ( ~ ( is_int @ Z_2 )
          | ( Z_2
           != ( hAPP_int_int @ number_number_of_int @ min ) )
          | ( ( hAPP_int_int @ abs_abs_int @ Z_2 )
            = one_one_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5562]) ).

thf(5987,plain,
    ( ( ! [A_1: $i,E_2: $i,C: $i] :
          ( ( ~ ( is_int @ C )
            | ! [B_1: $i,D_1: $i] :
                ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ E_2 ) ) @ C )
                 != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_1 ) @ E_2 ) ) @ D_1 ) )
                | ( C
                  = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ B_1 ) @ A_1 ) ) @ E_2 ) ) @ D_1 ) ) ) )
          & ( ~ ( is_int @ C )
            | ! [B_1: $i,D_1: $i] :
                ( ( C
                 != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ B_1 ) @ A_1 ) ) @ E_2 ) ) @ D_1 ) )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ E_2 ) ) @ C )
                  = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_1 ) @ E_2 ) ) @ D_1 ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5569]) ).

thf(5988,plain,
    ( ( ! [A_1: $i,E_2: $i,C: $i] :
          ( ! [B_1: $i,D_1: $i] :
              ( ~ ( is_int @ D_1 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ E_2 ) ) @ C )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_1 ) @ E_2 ) ) @ D_1 ) )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_1 ) @ B_1 ) ) @ E_2 ) ) @ C )
                = D_1 ) )
          & ! [B_1: $i,D_1: $i] :
              ( ~ ( is_int @ D_1 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_1 ) @ B_1 ) ) @ E_2 ) ) @ C )
               != D_1 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ E_2 ) ) @ C )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_1 ) @ E_2 ) ) @ D_1 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5570]) ).

thf(5989,plain,
    ( ( ! [Ma: $i,Na: $i] :
          ( ~ ( is_int @ Ma )
          | ~ ( is_int @ Na )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Ma ) @ Na )
           != one_one_int )
          | ( Ma = one_one_int )
          | ( Ma
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
      & ! [Ma: $i,Na: $i] :
          ( ~ ( is_int @ Ma )
          | ~ ( is_int @ Na )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Ma ) @ Na )
           != one_one_int )
          | ( Ma = one_one_int )
          | ( Na
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
      & ! [Ma: $i,Na: $i] :
          ( ~ ( is_int @ Ma )
          | ~ ( is_int @ Na )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Ma ) @ Na )
           != one_one_int )
          | ( Na = one_one_int )
          | ( Ma
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
      & ! [Ma: $i,Na: $i] :
          ( ~ ( is_int @ Ma )
          | ~ ( is_int @ Na )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Ma ) @ Na )
           != one_one_int )
          | ( Na = one_one_int )
          | ( Na
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
      & ! [Ma: $i,Na: $i] :
          ( ~ ( is_int @ Ma )
          | ~ ( is_int @ Na )
          | ( Ma != one_one_int )
          | ( Na != one_one_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Ma ) @ Na )
            = one_one_int ) )
      & ! [Ma: $i,Na: $i] :
          ( ~ ( is_int @ Ma )
          | ~ ( is_int @ Na )
          | ( Ma
           != ( hAPP_int_int @ number_number_of_int @ min ) )
          | ( Na
           != ( hAPP_int_int @ number_number_of_int @ min ) )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Ma ) @ Na )
            = one_one_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5572]) ).

thf(5990,plain,
    ( ( ! [M: $i] :
          ( ~ ( is_int @ M )
          | ! [N: $i] :
              ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ M ) @ N )
             != one_one_int )
          | ( M = one_one_int )
          | ( M
            = ( hAPP_int_int @ number_number_of_int @ min ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5573]) ).

thf(5991,plain,
    ( ( ( is_int @ sK13_X_1 )
      & ( is_int @ sK14_SY716 )
      & ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ sK13_X_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ sK14_SY716 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5574]) ).

thf(5992,plain,
    ( ( ! [A_74: $i] :
          ( ~ ( is_int @ A_74 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ pls ) ) ) @ A_74 )
            = A_74 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5575]) ).

thf(5993,plain,
    ( ( ! [A_75: $i] :
          ( ~ ( is_int @ A_75 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_75 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ pls ) ) )
            = A_75 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5576]) ).

thf(5994,plain,
    ( ( ! [Xa: $i] :
          ( ( one_one_nat != Xa )
          | ( Xa = one_one_nat ) )
      & ! [Xa: $i] :
          ( ( Xa != one_one_nat )
          | ( one_one_nat = Xa ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5577]) ).

thf(5995,plain,
    ( ( ! [Xa: $i] :
          ( ( zero_zero_nat != Xa )
          | ( Xa = zero_zero_nat ) )
      & ! [Xa: $i] :
          ( ( Xa != zero_zero_nat )
          | ( zero_zero_nat = Xa ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5578]) ).

thf(5996,plain,
    ( ( zero_zero_nat != one_one_nat )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5581]) ).

thf(5997,plain,
    ( ( one_one_nat != zero_zero_nat )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5582]) ).

thf(5998,plain,
    ( ( ! [P: $i] :
          ( ~ ( is_int @ P )
          | ( ( hAPP_int_int @ cOMBI_int @ P )
            = P ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5607]) ).

thf(5999,plain,
    ( ( ! [B_5: $i,A_5: $i,A_3: $i,B_2: $i] :
          ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 )
            = zero_zero_int )
          | ( A_3
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_5 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) )
          | ( B_2
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_5 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_5 ) @ B_5 )
            = one_one_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5608]) ).

thf(6000,plain,
    ( ( ! [D_3: $i,A_3: $i,B_2: $i] :
          ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ B_2 ) )
           != one_one_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ B_2 )
            = one_one_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5609]) ).

thf(6001,plain,
    ( ( ! [D_3: $i,A_3: $i] :
          ( ! [B_2: $i] :
              ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ B_2 ) )
             != one_one_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ A_3 )
            = one_one_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5610]) ).

thf(6002,plain,
    ( ( ! [B_2: $i,D_3: $i,A_3: $i] :
          ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ A_3 )
           != one_one_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ B_2 )
           != one_one_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ B_2 ) )
            = one_one_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5611]) ).

thf(6003,plain,
    ( ( ! [M: $i,K_2: $i,N: $i] :
          ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ K_2 ) @ N )
           != one_one_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ M ) ) @ N )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ M ) @ N ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5612]) ).

thf(6004,plain,
    ( ( ! [D_1: $i] :
          ( ! [A_1: $i,B_1: $i] :
              ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_1 ) @ A_1 )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_1 ) @ B_1 )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_1 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ B_1 ) )
                = one_one_int ) )
          & ! [A_1: $i] :
              ( ! [B_1: $i] :
                  ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_1 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ B_1 ) )
                 != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_1 ) @ A_1 )
                = one_one_int ) )
          & ! [A_1: $i,B_1: $i] :
              ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_1 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ B_1 ) )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_1 ) @ B_1 )
                = one_one_int ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5613]) ).

thf(6005,plain,
    ( ( ! [Ma: $i,Na: $i] :
          ( ~ ( is_int @ Ma )
          | ~ ( is_int @ Na )
          | ( Ma != zero_zero_int )
          | ( Na != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ Ma ) @ Na )
            = zero_zero_int ) )
      & ! [Ma: $i,Na: $i] :
          ( ~ ( is_int @ Ma )
          | ~ ( is_int @ Na )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ Ma ) @ Na )
           != zero_zero_int )
          | ( Ma = zero_zero_int ) )
      & ! [Ma: $i,Na: $i] :
          ( ~ ( is_int @ Ma )
          | ~ ( is_int @ Na )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ Ma ) @ Na )
           != zero_zero_int )
          | ( Na = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5614]) ).

thf(6006,plain,
    ( ( ! [N: $i,D_3: $i,A_3: $i] :
          ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ A_3 )
           != one_one_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ N ) )
            = one_one_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5622]) ).

thf(6007,plain,
    ( ( ! [N: $i,M: $i,A_3: $i,B_2: $i] :
          ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 )
           != one_one_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ N ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ M ) )
            = one_one_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5636]) ).

thf(6008,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A != B )
          | ( ( image_nat_int @ semiri1621563631at_int @ A )
            = ( image_nat_int @ semiri1621563631at_int @ B ) ) )
      & ! [A: $i,B: $i] :
          ( ( ( image_nat_int @ semiri1621563631at_int @ A )
           != ( image_nat_int @ semiri1621563631at_int @ B ) )
          | ( A = B ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5638]) ).

thf(6009,plain,
    ( ( ! [Ma: $i] :
          ( ( ( hAPP_int_int @ ( legacy_zgcd @ zero_zero_int ) @ Ma )
           != one_one_int )
          | ( ( hAPP_int_int @ abs_abs_int @ Ma )
            = one_one_int ) )
      & ! [Ma: $i] :
          ( ( ( hAPP_int_int @ abs_abs_int @ Ma )
           != one_one_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ zero_zero_int ) @ Ma )
            = one_one_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5641]) ).

thf(6010,plain,
    ( ( ! [N: $i,A_3: $i,B_2: $i] :
          ( ( ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 )
           != one_one_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ N ) ) @ B_2 )
            = one_one_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5644]) ).

thf(6011,plain,
    ( ( ! [N: $i,A_3: $i,B_2: $i] :
          ( ( ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 )
           != one_one_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ N ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ N ) )
            = one_one_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5645]) ).

thf(6012,plain,
    ( ( ! [I_1: $i,J: $i] :
          ( ~ ( is_int @ I_1 )
          | ~ ( is_int @ J )
          | ( I_1 != zero_zero_int )
          | ( J != zero_zero_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ I_1 ) @ J )
            = zero_zero_int ) )
      & ! [I_1: $i,J: $i] :
          ( ~ ( is_int @ I_1 )
          | ~ ( is_int @ J )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ I_1 ) @ J )
           != zero_zero_int )
          | ( I_1 = zero_zero_int ) )
      & ! [I_1: $i,J: $i] :
          ( ~ ( is_int @ I_1 )
          | ~ ( is_int @ J )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ I_1 ) @ J )
           != zero_zero_int )
          | ( J = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5654]) ).

thf(6013,plain,
    ( ( ! [N: $i,K_2: $i,M: $i] :
          ( ( ( hAPP_int_int @ ( legacy_zgcd @ K_2 ) @ M )
           != one_one_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ N ) @ M )
           != one_one_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ N ) ) @ M )
            = one_one_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5657]) ).

thf(6014,plain,
    ( ( ! [M: $i,K_2: $i,N: $i] :
          ( ( ( hAPP_int_int @ ( legacy_zgcd @ K_2 ) @ N )
           != one_one_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ M ) ) @ N )
            = ( hAPP_int_int @ ( legacy_zgcd @ M ) @ N ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5658]) ).

thf(6015,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( ( hAPP_int_int @ ( div_mod_int @ K_2 ) @ ( hAPP_int_int @ uminus_uminus_int @ L_2 ) )
            = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ K_2 ) @ L_2 )
           != zero_zero_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5673]) ).

thf(6016,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ K_2 ) ) @ L_2 )
            = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ K_2 ) @ L_2 )
           != zero_zero_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5674]) ).

thf(6017,plain,
    ( ( ! [Na: $i,Ma: $i] :
          ( ( Na != zero_zero_nat )
          | ( Ma != zero_zero_nat )
          | ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ Na ) )
            = ( hAPP_nat_int @ semiri1621563631at_int @ Ma ) ) )
      & ! [Na: $i] :
          ( ! [Ma: $i] :
              ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ Na ) )
             != ( hAPP_nat_int @ semiri1621563631at_int @ Ma ) )
          | ( Na = zero_zero_nat ) )
      & ! [Na: $i,Ma: $i] :
          ( ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ Na ) )
           != ( hAPP_nat_int @ semiri1621563631at_int @ Ma ) )
          | ( Ma = zero_zero_nat ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5678]) ).

thf(6018,plain,
    ( ( ! [Z_1: $i] :
          ( ~ ( is_int @ Z_1 )
          | ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ uminus_uminus_int @ Z_1 ) )
            = Z_1 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5691]) ).

thf(6019,plain,
    ( ( ! [Z_1: $i] :
          ( ~ ( is_int @ Z_1 )
          | ( Z_1
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ ( sK15_M_1 @ Z_1 ) ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ ( sK16_SY717 @ Z_1 ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5692]) ).

thf(6020,plain,
    ( ( ! [Xa: $i] :
          ( ( ( hAPP_int_int @ ( div_mod_int @ Xa ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
            = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ Xa ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
            = one_one_int ) )
      & ! [Xa: $i] :
          ( ( ( hAPP_int_int @ ( div_mod_int @ Xa ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
           != one_one_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ Xa ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
           != zero_zero_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5693]) ).

thf(6021,plain,
    ( ( ! [A_3: $i] :
          ( ~ ( is_int @ A_3 )
          | ( A_3 = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ A_3 )
            = one_one_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5707]) ).

thf(6022,plain,
    ( ( ! [A_3: $i] :
          ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
           != one_one_int )
          | ( ( hAPP_int_int @ abs_abs_int @ A_3 )
            = one_one_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5709]) ).

thf(6023,plain,
    ( ( ! [A_1: $i,B_1: $i] :
          ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
           != ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
          | ( ( hAPP_int_int @ abs_abs_int @ A_1 )
            = ( hAPP_int_int @ abs_abs_int @ B_1 ) ) )
      & ! [A_1: $i,B_1: $i] :
          ( ( ( hAPP_int_int @ abs_abs_int @ A_1 )
           != ( hAPP_int_int @ abs_abs_int @ B_1 ) )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
            = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5711]) ).

thf(6024,plain,
    ( ( ! [M: $i] :
          ( ! [N: $i] :
              ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ M ) @ N ) )
             != one_one_int )
          | ( ( hAPP_int_int @ abs_abs_int @ M )
            = one_one_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5718]) ).

thf(6025,plain,
    ( ( ! [A_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ( ( hAPP_int_int @ abs_abs_int @ A_1 )
           != zero_zero_int )
          | ( A_1 = zero_zero_int ) )
      & ! [A_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ( A_1 != zero_zero_int )
          | ( ( hAPP_int_int @ abs_abs_int @ A_1 )
            = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5731]) ).

thf(6026,plain,
    ( ( ! [A_3: $i] :
          ( ~ ( is_int @ A_3 )
          | ! [B_2: $i,C_1: $i] :
              ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_3 ) @ B_2 )
               != C_1 )
              | ( A_3
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ C_1 ) @ B_2 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5735]) ).

thf(6027,plain,
    ( ( ! [K_2: $i] :
          ( ~ ( is_int @ K_2 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ K_2 ) @ pls )
            = K_2 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5749]) ).

thf(6028,plain,
    ( ( ! [A_33: $i] :
          ( ~ ( is_int @ A_33 )
          | ! [B_25: $i] :
              ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_33 ) @ B_25 ) ) @ B_25 )
              = A_33 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5751]) ).

thf(6029,plain,
    ( ( ! [A_34: $i] :
          ( ~ ( is_int @ A_34 )
          | ! [B_26: $i] :
              ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_34 ) @ B_26 ) ) @ B_26 )
              = A_34 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5752]) ).

thf(6030,plain,
    ( ( ! [A_35: $i] :
          ( ~ ( is_int @ A_35 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_35 ) @ zero_zero_int )
            = A_35 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5753]) ).

thf(6031,plain,
    ( ( ! [A_1: $i,B_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ~ ( is_int @ B_1 )
          | ( A_1 != B_1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_1 ) @ B_1 )
            = zero_zero_int ) )
      & ! [A_1: $i,B_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ~ ( is_int @ B_1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_1 ) @ B_1 )
           != zero_zero_int )
          | ( A_1 = B_1 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5755]) ).

thf(6032,plain,
    ( ( ! [A_1: $i,B_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ~ ( is_int @ B_1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_1 ) @ B_1 )
           != zero_zero_int )
          | ( A_1 = B_1 ) )
      & ! [A_1: $i,B_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ~ ( is_int @ B_1 )
          | ( A_1 != B_1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_1 ) @ B_1 )
            = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5756]) ).

thf(6033,plain,
    ( ( ! [A_1: $i,B_1: $i] :
          ( ! [C: $i,D_1: $i] :
              ( ~ ( is_int @ A_1 )
              | ~ ( is_int @ B_1 )
              | ~ ( is_int @ C )
              | ~ ( is_int @ D_1 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_1 ) @ B_1 )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ C ) @ D_1 ) )
              | ( A_1 != B_1 )
              | ( C = D_1 ) )
          & ! [C: $i,D_1: $i] :
              ( ~ ( is_int @ A_1 )
              | ~ ( is_int @ B_1 )
              | ~ ( is_int @ C )
              | ~ ( is_int @ D_1 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_1 ) @ B_1 )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ C ) @ D_1 ) )
              | ( C != D_1 )
              | ( A_1 = B_1 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5758]) ).

thf(6034,plain,
    ( ( ( hAPP_int_int @ number_number_of_int @ pls )
     != ( hAPP_int_int @ number_number_of_int @ min ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5760]) ).

thf(6035,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ bit0 @ K_2 )
         != min ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5761]) ).

thf(6036,plain,
    ( ( ! [L_2: $i] :
          ( min
         != ( hAPP_int_int @ bit0 @ L_2 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5762]) ).

thf(6037,plain,
    ( ( pls != min )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5763]) ).

thf(6038,plain,
    ( ( min != pls )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5764]) ).

thf(6039,plain,
    ( ( ! [K: $i] :
          ( ~ ( is_int @ K )
          | ( ( hAPP_int_int @ bit1 @ K )
           != min )
          | ( K = min ) )
      & ! [K: $i] :
          ( ~ ( is_int @ K )
          | ( K != min )
          | ( ( hAPP_int_int @ bit1 @ K )
            = min ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5765]) ).

thf(6040,plain,
    ( ( ! [L: $i] :
          ( ~ ( is_int @ L )
          | ( min
           != ( hAPP_int_int @ bit1 @ L ) )
          | ( min = L ) )
      & ! [L: $i] :
          ( ~ ( is_int @ L )
          | ( min != L )
          | ( min
            = ( hAPP_int_int @ bit1 @ L ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5766]) ).

thf(6041,plain,
    ( ( ! [C_35: $i,D_13: $i,A_92: $i,B_63: $i,R_6: $i] :
          ( ~ ( is_int @ C_35 )
          | ~ ( is_int @ D_13 )
          | ~ ( is_int @ R_6 )
          | ( R_6 = zero_zero_int )
          | ( C_35 = D_13 )
          | ( A_92 != B_63 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_92 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ R_6 ) @ C_35 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_63 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ R_6 ) @ D_13 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5785]) ).

thf(6042,plain,
    ( ( ! [Xa: $i,Ya: $i] :
          ( ~ ( is_int @ Xa )
          | ~ ( is_int @ Ya )
          | ( Xa != zero_zero_int )
          | ( Ya != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Xa ) @ Xa ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Ya ) @ Ya ) )
            = zero_zero_int ) )
      & ! [Xa: $i,Ya: $i] :
          ( ~ ( is_int @ Xa )
          | ~ ( is_int @ Ya )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Xa ) @ Xa ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Ya ) @ Ya ) )
           != zero_zero_int )
          | ( Xa = zero_zero_int ) )
      & ! [Xa: $i,Ya: $i] :
          ( ~ ( is_int @ Xa )
          | ~ ( is_int @ Ya )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Xa ) @ Xa ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Ya ) @ Ya ) )
           != zero_zero_int )
          | ( Ya = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5786]) ).

thf(6043,plain,
    ( ( ! [Z_1: $i] :
          ( ~ ( is_int @ Z_1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z_1 ) @ one_one_int )
            = Z_1 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5790]) ).

thf(6044,plain,
    ( ( ! [Z_1: $i] :
          ( ~ ( is_int @ Z_1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ one_one_int ) @ Z_1 )
            = Z_1 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5791]) ).

thf(6045,plain,
    ( ( ! [A_123: $i] :
          ( ~ ( is_int @ A_123 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_123 ) @ one_one_int )
            = A_123 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5797]) ).

thf(6046,plain,
    ( ( ! [A_124: $i] :
          ( ~ ( is_int @ A_124 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_124 ) @ one_one_int )
            = A_124 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5798]) ).

thf(6047,plain,
    ( ( ! [A_125: $i] :
          ( ~ ( is_int @ A_125 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_125 ) @ one_one_int )
            = A_125 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5799]) ).

thf(6048,plain,
    ( ( ! [A_126: $i] :
          ( ~ ( is_int @ A_126 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ one_one_int ) @ A_126 )
            = A_126 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5800]) ).

thf(6049,plain,
    ( ( ! [A_127: $i] :
          ( ~ ( is_int @ A_127 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ one_one_int ) @ A_127 )
            = A_127 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5801]) ).

thf(6050,plain,
    ( ( ! [A_128: $i] :
          ( ~ ( is_int @ A_128 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ one_one_int ) @ A_128 )
            = A_128 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5802]) ).

thf(6051,plain,
    ( ( ! [Wa: $i,Ya: $i] :
          ( ! [Xa: $i,Z_2: $i] :
              ( ~ ( is_int @ Wa )
              | ~ ( is_int @ Ya )
              | ~ ( is_int @ Xa )
              | ~ ( is_int @ Z_2 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Wa ) @ Ya ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Xa ) @ Z_2 ) )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Wa ) @ Z_2 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Xa ) @ Ya ) ) )
              | ( Wa = Xa )
              | ( Ya = Z_2 ) )
          & ! [Xa: $i,Z_2: $i] :
              ( ~ ( is_int @ Wa )
              | ~ ( is_int @ Ya )
              | ~ ( is_int @ Xa )
              | ~ ( is_int @ Z_2 )
              | ( Wa != Xa )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Wa ) @ Ya ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Xa ) @ Z_2 ) )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Wa ) @ Z_2 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Xa ) @ Ya ) ) ) )
          & ! [Xa: $i,Z_2: $i] :
              ( ~ ( is_int @ Wa )
              | ~ ( is_int @ Ya )
              | ~ ( is_int @ Xa )
              | ~ ( is_int @ Z_2 )
              | ( Ya != Z_2 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Wa ) @ Ya ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Xa ) @ Z_2 ) )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Wa ) @ Z_2 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Xa ) @ Ya ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5803]) ).

thf(6052,plain,
    ( ( ! [C: $i,D_1: $i] :
          ( ! [A_1: $i,B_1: $i] :
              ( ~ ( is_int @ C )
              | ~ ( is_int @ D_1 )
              | ~ ( is_int @ A_1 )
              | ~ ( is_int @ B_1 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ C ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_1 ) @ D_1 ) )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ D_1 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_1 ) @ C ) ) )
              | ( A_1 != B_1 ) )
          & ! [A_1: $i,B_1: $i] :
              ( ~ ( is_int @ C )
              | ~ ( is_int @ D_1 )
              | ~ ( is_int @ A_1 )
              | ~ ( is_int @ B_1 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ C ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_1 ) @ D_1 ) )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ D_1 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_1 ) @ C ) ) )
              | ( C != D_1 ) )
          & ! [A_1: $i,B_1: $i] :
              ( ~ ( is_int @ C )
              | ~ ( is_int @ D_1 )
              | ~ ( is_int @ A_1 )
              | ~ ( is_int @ B_1 )
              | ( A_1 = B_1 )
              | ( C = D_1 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ C ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_1 ) @ D_1 ) )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ D_1 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_1 ) @ C ) ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5806]) ).

thf(6053,plain,
    ( ( ! [A_135: $i,B_95: $i] :
          ( ~ ( is_int @ A_135 )
          | ~ ( is_int @ B_95 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_135 ) @ B_95 )
           != zero_zero_int )
          | ( A_135 = zero_zero_int )
          | ( B_95 = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5812]) ).

thf(6054,plain,
    ( ( ! [B_96: $i,A_136: $i] :
          ( ~ ( is_int @ B_96 )
          | ~ ( is_int @ A_136 )
          | ( A_136 = zero_zero_int )
          | ( B_96 = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_136 ) @ B_96 )
           != zero_zero_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5813]) ).

thf(6055,plain,
    ( ( ! [A_1: $i,B_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ~ ( is_int @ B_1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ B_1 )
           != zero_zero_int )
          | ( A_1 = zero_zero_int )
          | ( B_1 = zero_zero_int ) )
      & ! [A_1: $i,B_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ~ ( is_int @ B_1 )
          | ( A_1 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ B_1 )
            = zero_zero_int ) )
      & ! [A_1: $i,B_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ~ ( is_int @ B_1 )
          | ( B_1 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ B_1 )
            = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5814]) ).

thf(6056,plain,
    ( ( ! [X_57: $i] :
          ( ~ ( is_int @ X_57 )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X_57 ) @ one_one_nat )
            = X_57 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5833]) ).

thf(6057,plain,
    ( ( ! [A_146: $i] :
          ( ~ ( is_int @ A_146 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ A_146 )
            = A_146 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5834]) ).

thf(6058,plain,
    ( ( ! [A_147: $i] :
          ( ~ ( is_int @ A_147 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ A_147 )
            = A_147 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5835]) ).

thf(6059,plain,
    ( ( ! [A_148: $i] :
          ( ~ ( is_int @ A_148 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ A_148 )
            = A_148 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5836]) ).

thf(6060,plain,
    ( ( ! [A_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ( zero_zero_int
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_1 ) @ A_1 ) )
          | ( A_1 = zero_zero_int ) )
      & ! [A_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ( A_1 != zero_zero_int )
          | ( zero_zero_int
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_1 ) @ A_1 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5837]) ).

thf(6061,plain,
    ( ( ! [A_149: $i] :
          ( ~ ( is_int @ A_149 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_149 ) @ zero_zero_int )
            = A_149 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5838]) ).

thf(6062,plain,
    ( ( ! [A_150: $i] :
          ( ~ ( is_int @ A_150 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_150 ) @ zero_zero_int )
            = A_150 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5839]) ).

thf(6063,plain,
    ( ( ! [A_151: $i] :
          ( ~ ( is_int @ A_151 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_151 ) @ zero_zero_int )
            = A_151 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5840]) ).

thf(6064,plain,
    ( ( ! [B_1: $i,A_1: $i] :
          ( ~ ( is_int @ B_1 )
          | ~ ( is_int @ A_1 )
          | ( B_1
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_1 ) @ A_1 ) )
          | ( A_1 = zero_zero_int ) )
      & ! [B_1: $i,A_1: $i] :
          ( ~ ( is_int @ B_1 )
          | ~ ( is_int @ A_1 )
          | ( A_1 != zero_zero_int )
          | ( B_1
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_1 ) @ A_1 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5841]) ).

thf(6065,plain,
    ( ( ! [Xa: $i] :
          ( ~ ( is_int @ Xa )
          | ( one_one_int != Xa )
          | ( Xa = one_one_int ) )
      & ! [Xa: $i] :
          ( ~ ( is_int @ Xa )
          | ( Xa != one_one_int )
          | ( one_one_int = Xa ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5845]) ).

thf(6066,plain,
    ( ( ! [A_1: $i] :
          ( ! [B_1: $i,C: $i] :
              ( ~ ( is_int @ B_1 )
              | ~ ( is_int @ C )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_1 ) @ B_1 )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_1 ) @ C ) )
              | ( B_1 = C ) )
          & ! [B_1: $i,C: $i] :
              ( ~ ( is_int @ B_1 )
              | ~ ( is_int @ C )
              | ( B_1 != C )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_1 ) @ B_1 )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_1 ) @ C ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5852]) ).

thf(6067,plain,
    ( ( ! [B_1: $i] :
          ( ! [A_1: $i,C: $i] :
              ( ~ ( is_int @ B_1 )
              | ~ ( is_int @ C )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_1 ) @ A_1 )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ C ) @ A_1 ) )
              | ( B_1 = C ) )
          & ! [A_1: $i,C: $i] :
              ( ~ ( is_int @ B_1 )
              | ~ ( is_int @ C )
              | ( B_1 != C )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_1 ) @ A_1 )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ C ) @ A_1 ) ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5853]) ).

thf(6068,plain,
    ( ( ! [A_162: $i,B_110: $i,C_64: $i] :
          ( ~ ( is_int @ B_110 )
          | ~ ( is_int @ C_64 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_162 ) @ B_110 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_162 ) @ C_64 ) )
          | ( B_110 = C_64 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5855]) ).

thf(6069,plain,
    ( ( ! [A_163: $i,B_111: $i,C_65: $i] :
          ( ~ ( is_int @ B_111 )
          | ~ ( is_int @ C_65 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_163 ) @ B_111 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_163 ) @ C_65 ) )
          | ( B_111 = C_65 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5856]) ).

thf(6070,plain,
    ( ( ! [B_112: $i,A_164: $i,C_66: $i] :
          ( ~ ( is_int @ B_112 )
          | ~ ( is_int @ C_66 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_112 ) @ A_164 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ C_66 ) @ A_164 ) )
          | ( B_112 = C_66 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5857]) ).

thf(6071,plain,
    ( ( ! [Xa: $i] :
          ( ~ ( is_int @ Xa )
          | ( zero_zero_int != Xa )
          | ( Xa = zero_zero_int ) )
      & ! [Xa: $i] :
          ( ~ ( is_int @ Xa )
          | ( Xa != zero_zero_int )
          | ( zero_zero_int = Xa ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5861]) ).

thf(6072,plain,
    ( ( ! [A_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ! [Na: $i] :
              ( ( Na = zero_zero_nat )
              | ( A_1 != zero_zero_int )
              | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_1 ) @ Na )
                = zero_zero_int ) ) )
      & ! [A_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ! [Na: $i] :
              ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_1 ) @ Na )
               != zero_zero_int )
              | ( Na != zero_zero_nat ) ) )
      & ! [A_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ! [Na: $i] :
              ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_1 ) @ Na )
             != zero_zero_int )
          | ( A_1 = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5865]) ).

thf(6073,plain,
    ( ( ! [N_52: $i,A_197: $i] :
          ( ~ ( is_int @ A_197 )
          | ( A_197 = zero_zero_int )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_197 ) @ N_52 )
           != zero_zero_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5869]) ).

thf(6074,plain,
    ( ( zero_zero_int != one_one_int )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5870]) ).

thf(6075,plain,
    ( ( one_one_int != zero_zero_int )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5871]) ).

thf(6076,plain,
    ( ( ! [Xa: $i,Ya: $i] :
          ( ( ( hAPP_nat_int @ semiri1621563631at_int @ Xa )
           != ( hAPP_nat_int @ semiri1621563631at_int @ Ya ) )
          | ( Xa = Ya ) )
      & ! [Xa: $i,Ya: $i] :
          ( ( Xa != Ya )
          | ( ( hAPP_nat_int @ semiri1621563631at_int @ Xa )
            = ( hAPP_nat_int @ semiri1621563631at_int @ Ya ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5872]) ).

thf(6077,plain,
    ( ( ! [Ma: $i,Na: $i] :
          ( ( ( hAPP_nat_int @ semiri1621563631at_int @ Ma )
           != ( hAPP_nat_int @ semiri1621563631at_int @ Na ) )
          | ( Ma = Na ) )
      & ! [Ma: $i,Na: $i] :
          ( ( Ma != Na )
          | ( ( hAPP_nat_int @ semiri1621563631at_int @ Ma )
            = ( hAPP_nat_int @ semiri1621563631at_int @ Na ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5873]) ).

thf(6078,plain,
    ( ( ! [A_198: $i] :
          ( ~ ( is_int @ A_198 )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_198 ) @ one_one_nat )
            = A_198 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5874]) ).

thf(6079,plain,
    ( ( ! [K_2: $i] :
          ( ~ ( is_int @ K_2 )
          | ( ( hAPP_int_int @ number_number_of_int @ K_2 )
            = K_2 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5875]) ).

thf(6080,plain,
    ( ( ! [N_55: $i] :
          ( ( N_55 != zero_zero_nat )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ N_55 )
            = one_one_int ) )
      & ! [N_55: $i] :
          ( ( N_55 = zero_zero_nat )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ N_55 )
            = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5877]) ).

thf(6081,plain,
    ( ( ! [Z_1: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ Z_1 ) ) @ Z_1 )
         != zero_zero_int ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5886]) ).

thf(6082,plain,
    ( ( ! [A_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ! [Wa: $i] :
              ( ( ( hAPP_int_nat @ number_number_of_nat @ Wa )
                = zero_zero_nat )
              | ( A_1 != zero_zero_int )
              | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ Wa ) )
                = zero_zero_int ) ) )
      & ! [A_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ! [Wa: $i] :
              ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ Wa ) )
               != zero_zero_int )
              | ( ( hAPP_int_nat @ number_number_of_nat @ Wa )
               != zero_zero_nat ) ) )
      & ! [A_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ! [Wa: $i] :
              ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ Wa ) )
             != zero_zero_int )
          | ( A_1 = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5893]) ).

thf(6083,plain,
    ( ( ! [A_202: $i] :
          ( ~ ( is_int @ A_202 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_202 ) @ ( hAPP_int_int @ number_number_of_int @ pls ) )
            = A_202 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5894]) ).

thf(6084,plain,
    ( ( ! [A_203: $i] :
          ( ~ ( is_int @ A_203 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ pls ) ) @ A_203 )
            = A_203 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5895]) ).

thf(6085,plain,
    ( ( ! [Z_1: $i] :
          ( ~ ( is_int @ Z_1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ Z_1 )
            = Z_1 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5900]) ).

thf(6086,plain,
    ( ( ! [Z_1: $i] :
          ( ~ ( is_int @ Z_1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z_1 ) @ zero_zero_int )
            = Z_1 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5901]) ).

thf(6087,plain,
    ( ( ! [K_2: $i] :
          ( ~ ( is_int @ K_2 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ pls ) @ K_2 )
            = K_2 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5904]) ).

thf(6088,plain,
    ( ( ! [K_2: $i] :
          ( ~ ( is_int @ K_2 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ K_2 ) @ pls )
            = K_2 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5905]) ).

thf(6089,plain,
    ( ( zero_zero_int != one_one_int )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5906]) ).

thf(6090,plain,
    ( ( ! [L: $i] :
          ( ~ ( is_int @ L )
          | ( pls
           != ( hAPP_int_int @ bit0 @ L ) )
          | ( pls = L ) )
      & ! [L: $i] :
          ( ~ ( is_int @ L )
          | ( pls != L )
          | ( pls
            = ( hAPP_int_int @ bit0 @ L ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5909]) ).

thf(6091,plain,
    ( ( ! [K: $i] :
          ( ~ ( is_int @ K )
          | ( ( hAPP_int_int @ bit0 @ K )
           != pls )
          | ( K = pls ) )
      & ! [K: $i] :
          ( ~ ( is_int @ K )
          | ( K != pls )
          | ( ( hAPP_int_int @ bit0 @ K )
            = pls ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5910]) ).

thf(6092,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( hAPP_int_int @ bit0 @ K_2 )
         != ( hAPP_int_int @ bit1 @ L_2 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5911]) ).

thf(6093,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( hAPP_int_int @ bit1 @ K_2 )
         != ( hAPP_int_int @ bit0 @ L_2 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5912]) ).

thf(6094,plain,
    ( ( ! [L_2: $i] :
          ( pls
         != ( hAPP_int_int @ bit1 @ L_2 ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5913]) ).

thf(6095,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ bit1 @ K_2 )
         != pls ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5914]) ).

thf(6096,plain,
    ( ( ! [A_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_1 ) @ A_1 )
           != zero_zero_int )
          | ( A_1 = zero_zero_int ) )
      & ! [A_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ( A_1 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_1 ) @ A_1 )
            = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5915]) ).

thf(6097,plain,
    ( ( ! [Ma: $i,Na: $i] :
          ( ( ( hAPP_nat_int @ semiri1621563631at_int @ Ma )
           != ( hAPP_nat_int @ semiri1621563631at_int @ Na ) )
          | ( Ma = Na ) )
      & ! [Ma: $i,Na: $i] :
          ( ( Ma != Na )
          | ( ( hAPP_nat_int @ semiri1621563631at_int @ Ma )
            = ( hAPP_nat_int @ semiri1621563631at_int @ Na ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5916]) ).

thf(6098,plain,
    ( ( ! [K: $i,L: $i] :
          ( ~ ( is_int @ K )
          | ~ ( is_int @ L )
          | ( ( hAPP_int_int @ bit0 @ K )
           != ( hAPP_int_int @ bit0 @ L ) )
          | ( K = L ) )
      & ! [K: $i,L: $i] :
          ( ~ ( is_int @ K )
          | ~ ( is_int @ L )
          | ( K != L )
          | ( ( hAPP_int_int @ bit0 @ K )
            = ( hAPP_int_int @ bit0 @ L ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5920]) ).

thf(6099,plain,
    ( ( ! [K: $i,L: $i] :
          ( ~ ( is_int @ K )
          | ~ ( is_int @ L )
          | ( ( hAPP_int_int @ bit1 @ K )
           != ( hAPP_int_int @ bit1 @ L ) )
          | ( K = L ) )
      & ! [K: $i,L: $i] :
          ( ~ ( is_int @ K )
          | ~ ( is_int @ L )
          | ( K != L )
          | ( ( hAPP_int_int @ bit1 @ K )
            = ( hAPP_int_int @ bit1 @ L ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5921]) ).

thf(6100,plain,
    ( ( ! [Wa: $i,Xa: $i] :
          ( ( ( hAPP_int_nat @ number_number_of_nat @ Wa )
           != Xa )
          | ( Xa
            = ( hAPP_int_nat @ number_number_of_nat @ Wa ) ) )
      & ! [Wa: $i,Xa: $i] :
          ( ( Xa
           != ( hAPP_int_nat @ number_number_of_nat @ Wa ) )
          | ( ( hAPP_int_nat @ number_number_of_nat @ Wa )
            = Xa ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5922]) ).

thf(6101,plain,
    ( ( ! [Wa: $i,Xa: $i] :
          ( ~ ( is_int @ Xa )
          | ( ( hAPP_int_int @ number_number_of_int @ Wa )
           != Xa )
          | ( Xa
            = ( hAPP_int_int @ number_number_of_int @ Wa ) ) )
      & ! [Wa: $i,Xa: $i] :
          ( ~ ( is_int @ Xa )
          | ( Xa
           != ( hAPP_int_int @ number_number_of_int @ Wa ) )
          | ( ( hAPP_int_int @ number_number_of_int @ Wa )
            = Xa ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5923]) ).

thf(6102,plain,
    ( ( ! [Xa: $i,Ya: $i] :
          ( ~ ( is_int @ Xa )
          | ~ ( is_int @ Ya )
          | ( ( hAPP_int_int @ number_number_of_int @ Xa )
           != ( hAPP_int_int @ number_number_of_int @ Ya ) )
          | ( Xa = Ya ) )
      & ! [Xa: $i,Ya: $i] :
          ( ~ ( is_int @ Xa )
          | ~ ( is_int @ Ya )
          | ( Xa != Ya )
          | ( ( hAPP_int_int @ number_number_of_int @ Xa )
            = ( hAPP_int_int @ number_number_of_int @ Ya ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5924]) ).

thf(6103,plain,
    ( ( ! [Na: $i] :
          ( ( ( hAPP_nat_int @ semiri1621563631at_int @ Na )
           != zero_zero_int )
          | ( Na = zero_zero_nat ) )
      & ! [Na: $i] :
          ( ( Na != zero_zero_nat )
          | ( ( hAPP_nat_int @ semiri1621563631at_int @ Na )
            = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5929]) ).

thf(6104,plain,
    ( ( ! [W_15: $i] :
          ( ( ( hAPP_int_nat @ number_number_of_nat @ W_15 )
           != zero_zero_nat )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ ( hAPP_int_nat @ number_number_of_nat @ W_15 ) )
            = one_one_int ) )
      & ! [W_15: $i] :
          ( ( ( hAPP_int_nat @ number_number_of_nat @ W_15 )
            = zero_zero_nat )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ ( hAPP_int_nat @ number_number_of_nat @ W_15 ) )
            = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5937]) ).

thf(6105,plain,
    ( ( ! [A_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
           != zero_zero_int )
          | ( A_1 = zero_zero_int ) )
      & ! [A_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ( A_1 != zero_zero_int )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
            = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5943]) ).

thf(6106,plain,
    ( ( ! [Xa: $i,Ya: $i] :
          ( ~ ( is_int @ Xa )
          | ~ ( is_int @ Ya )
          | ( Xa != zero_zero_int )
          | ( Ya != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Xa ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Ya ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
            = zero_zero_int ) )
      & ! [Xa: $i,Ya: $i] :
          ( ~ ( is_int @ Xa )
          | ~ ( is_int @ Ya )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Xa ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Ya ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
           != zero_zero_int )
          | ( Xa = zero_zero_int ) )
      & ! [Xa: $i,Ya: $i] :
          ( ~ ( is_int @ Xa )
          | ~ ( is_int @ Ya )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Xa ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Ya ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
           != zero_zero_int )
          | ( Ya = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5946]) ).

thf(6107,plain,
    ( ( ! [B_1_1: $i,B_2_1: $i] :
          ( ~ ( is_int @ B_2_1 )
          | ( is_int @ ( hAPP_int_int @ B_1_1 @ B_2_1 ) ) ) )
    = $true ),
    inference(extcnf_combined,[status(esa)],[5948]) ).

thf(6108,plain,
    ( ( is_int @ one_one_int )
    = $true ),
    inference(copy,[status(thm)],[5951]) ).

thf(6109,plain,
    ( ( is_int @ zero_zero_int )
    = $true ),
    inference(copy,[status(thm)],[5950]) ).

thf(6110,plain,
    ( ( is_int @ pls )
    = $true ),
    inference(copy,[status(thm)],[5949]) ).

thf(6111,plain,
    ( ( ! [B_1_1: $i,B_2_1: $i] :
          ( ~ ( is_int @ B_2_1 )
          | ( is_int @ ( hAPP_int_int @ B_1_1 @ B_2_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6107]) ).

thf(6112,plain,
    ( ( ! [B_1_1: $i,B_2_1: $i] : ( is_int @ ( hAPP_nat_int @ B_1_1 @ B_2_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5947]) ).

thf(6113,plain,
    ( ( ! [Xa: $i,Ya: $i] :
          ( ~ ( is_int @ Xa )
          | ~ ( is_int @ Ya )
          | ( Xa != zero_zero_int )
          | ( Ya != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Xa ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Ya ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
            = zero_zero_int ) )
      & ! [Xa: $i,Ya: $i] :
          ( ~ ( is_int @ Xa )
          | ~ ( is_int @ Ya )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Xa ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Ya ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
           != zero_zero_int )
          | ( Xa = zero_zero_int ) )
      & ! [Xa: $i,Ya: $i] :
          ( ~ ( is_int @ Xa )
          | ~ ( is_int @ Ya )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Xa ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Ya ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
           != zero_zero_int )
          | ( Ya = zero_zero_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6106]) ).

thf(6114,plain,
    ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ one_one_int ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
      = one_one_int )
    = $true ),
    inference(copy,[status(thm)],[5945]) ).

thf(6115,plain,
    ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
      = zero_zero_int )
    = $true ),
    inference(copy,[status(thm)],[5944]) ).

thf(6116,plain,
    ( ( ! [A_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
           != zero_zero_int )
          | ( A_1 = zero_zero_int ) )
      & ! [A_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ( A_1 != zero_zero_int )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
            = zero_zero_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6105]) ).

thf(6117,plain,
    ( ( ! [W_16: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ ( hAPP_int_int @ number_number_of_int @ W_16 ) )
          = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ bit1 @ pls ) ) @ W_16 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5942]) ).

thf(6118,plain,
    ( ( ! [V_25: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ V_25 ) ) @ one_one_int )
          = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ V_25 ) @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5941]) ).

thf(6119,plain,
    ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ one_one_int )
      = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5940]) ).

thf(6120,plain,
    ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ one_one_int )
      = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5939]) ).

thf(6121,plain,
    ( ( ! [X: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5938]) ).

thf(6122,plain,
    ( ( ! [W_15: $i] :
          ( ( ( hAPP_int_nat @ number_number_of_nat @ W_15 )
           != zero_zero_nat )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ ( hAPP_int_nat @ number_number_of_nat @ W_15 ) )
            = one_one_int ) )
      & ! [W_15: $i] :
          ( ( ( hAPP_int_nat @ number_number_of_nat @ W_15 )
            = zero_zero_nat )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ ( hAPP_int_nat @ number_number_of_nat @ W_15 ) )
            = zero_zero_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6104]) ).

thf(6123,plain,
    ( ( one_one_int
      = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ pls ) ) )
    = $true ),
    inference(copy,[status(thm)],[5936]) ).

thf(6124,plain,
    ( ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ pls ) )
      = one_one_int )
    = $true ),
    inference(copy,[status(thm)],[5935]) ).

thf(6125,plain,
    ( ( ! [V_1: $i,W: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ V_1 ) ) @ ( hAPP_int_int @ number_number_of_int @ W ) )
          = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ V_1 ) @ W ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5934]) ).

thf(6126,plain,
    ( ( zero_zero_int
      = ( hAPP_int_int @ number_number_of_int @ pls ) )
    = $true ),
    inference(copy,[status(thm)],[5933]) ).

thf(6127,plain,
    ( ( ( hAPP_nat_int @ semiri1621563631at_int @ one_one_nat )
      = one_one_int )
    = $true ),
    inference(copy,[status(thm)],[5932]) ).

thf(6128,plain,
    ( ( ( hAPP_int_nat @ number_number_of_nat @ pls )
      = zero_zero_nat )
    = $true ),
    inference(copy,[status(thm)],[5931]) ).

thf(6129,plain,
    ( ( zero_zero_nat
      = ( hAPP_int_nat @ number_number_of_nat @ pls ) )
    = $true ),
    inference(copy,[status(thm)],[5930]) ).

thf(6130,plain,
    ( ( ! [Na: $i] :
          ( ( ( hAPP_nat_int @ semiri1621563631at_int @ Na )
           != zero_zero_int )
          | ( Na = zero_zero_nat ) )
      & ! [Na: $i] :
          ( ( Na != zero_zero_nat )
          | ( ( hAPP_nat_int @ semiri1621563631at_int @ Na )
            = zero_zero_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6103]) ).

thf(6131,plain,
    ( ( ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat )
      = zero_zero_int )
    = $true ),
    inference(copy,[status(thm)],[5928]) ).

thf(6132,plain,
    ( ( one_one_int
      = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ pls ) ) )
    = $true ),
    inference(copy,[status(thm)],[5927]) ).

thf(6133,plain,
    ( ( ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ pls ) )
      = one_one_nat )
    = $true ),
    inference(copy,[status(thm)],[5926]) ).

thf(6134,plain,
    ( ( one_one_nat
      = ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ pls ) ) )
    = $true ),
    inference(copy,[status(thm)],[5925]) ).

thf(6135,plain,
    ( ( ! [Xa: $i,Ya: $i] :
          ( ~ ( is_int @ Xa )
          | ~ ( is_int @ Ya )
          | ( ( hAPP_int_int @ number_number_of_int @ Xa )
           != ( hAPP_int_int @ number_number_of_int @ Ya ) )
          | ( Xa = Ya ) )
      & ! [Xa: $i,Ya: $i] :
          ( ~ ( is_int @ Xa )
          | ~ ( is_int @ Ya )
          | ( Xa != Ya )
          | ( ( hAPP_int_int @ number_number_of_int @ Xa )
            = ( hAPP_int_int @ number_number_of_int @ Ya ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6102]) ).

thf(6136,plain,
    ( ( ! [Wa: $i,Xa: $i] :
          ( ~ ( is_int @ Xa )
          | ( ( hAPP_int_int @ number_number_of_int @ Wa )
           != Xa )
          | ( Xa
            = ( hAPP_int_int @ number_number_of_int @ Wa ) ) )
      & ! [Wa: $i,Xa: $i] :
          ( ~ ( is_int @ Xa )
          | ( Xa
           != ( hAPP_int_int @ number_number_of_int @ Wa ) )
          | ( ( hAPP_int_int @ number_number_of_int @ Wa )
            = Xa ) ) )
    = $true ),
    inference(copy,[status(thm)],[6101]) ).

thf(6137,plain,
    ( ( ! [Wa: $i,Xa: $i] :
          ( ( ( hAPP_int_nat @ number_number_of_nat @ Wa )
           != Xa )
          | ( Xa
            = ( hAPP_int_nat @ number_number_of_nat @ Wa ) ) )
      & ! [Wa: $i,Xa: $i] :
          ( ( Xa
           != ( hAPP_int_nat @ number_number_of_nat @ Wa ) )
          | ( ( hAPP_int_nat @ number_number_of_nat @ Wa )
            = Xa ) ) )
    = $true ),
    inference(copy,[status(thm)],[6100]) ).

thf(6138,plain,
    ( ( ! [K: $i,L: $i] :
          ( ~ ( is_int @ K )
          | ~ ( is_int @ L )
          | ( ( hAPP_int_int @ bit1 @ K )
           != ( hAPP_int_int @ bit1 @ L ) )
          | ( K = L ) )
      & ! [K: $i,L: $i] :
          ( ~ ( is_int @ K )
          | ~ ( is_int @ L )
          | ( K != L )
          | ( ( hAPP_int_int @ bit1 @ K )
            = ( hAPP_int_int @ bit1 @ L ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6099]) ).

thf(6139,plain,
    ( ( ! [K: $i,L: $i] :
          ( ~ ( is_int @ K )
          | ~ ( is_int @ L )
          | ( ( hAPP_int_int @ bit0 @ K )
           != ( hAPP_int_int @ bit0 @ L ) )
          | ( K = L ) )
      & ! [K: $i,L: $i] :
          ( ~ ( is_int @ K )
          | ~ ( is_int @ L )
          | ( K != L )
          | ( ( hAPP_int_int @ bit0 @ K )
            = ( hAPP_int_int @ bit0 @ L ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6098]) ).

thf(6140,plain,
    ( ( ! [Z1: $i,Z2: $i,Z3: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z1 ) @ Z2 ) ) @ Z3 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z1 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z2 ) @ Z3 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5919]) ).

thf(6141,plain,
    ( ( ! [X: $i,Y: $i,Z_1: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ X ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Y ) @ Z_1 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Y ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ X ) @ Z_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5918]) ).

thf(6142,plain,
    ( ( ! [Z_1: $i,W: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z_1 ) @ W )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ W ) @ Z_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5917]) ).

thf(6143,plain,
    ( ( ! [Ma: $i,Na: $i] :
          ( ( ( hAPP_nat_int @ semiri1621563631at_int @ Ma )
           != ( hAPP_nat_int @ semiri1621563631at_int @ Na ) )
          | ( Ma = Na ) )
      & ! [Ma: $i,Na: $i] :
          ( ( Ma != Na )
          | ( ( hAPP_nat_int @ semiri1621563631at_int @ Ma )
            = ( hAPP_nat_int @ semiri1621563631at_int @ Na ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6097]) ).

thf(6144,plain,
    ( ( ! [A_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_1 ) @ A_1 )
           != zero_zero_int )
          | ( A_1 = zero_zero_int ) )
      & ! [A_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ( A_1 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_1 ) @ A_1 )
            = zero_zero_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6096]) ).

thf(6145,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ bit1 @ K_2 )
         != pls ) )
    = $true ),
    inference(copy,[status(thm)],[6095]) ).

thf(6146,plain,
    ( ( ! [L_2: $i] :
          ( pls
         != ( hAPP_int_int @ bit1 @ L_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6094]) ).

thf(6147,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( hAPP_int_int @ bit1 @ K_2 )
         != ( hAPP_int_int @ bit0 @ L_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6093]) ).

thf(6148,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( hAPP_int_int @ bit0 @ K_2 )
         != ( hAPP_int_int @ bit1 @ L_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6092]) ).

thf(6149,plain,
    ( ( ! [K: $i] :
          ( ~ ( is_int @ K )
          | ( ( hAPP_int_int @ bit0 @ K )
           != pls )
          | ( K = pls ) )
      & ! [K: $i] :
          ( ~ ( is_int @ K )
          | ( K != pls )
          | ( ( hAPP_int_int @ bit0 @ K )
            = pls ) ) )
    = $true ),
    inference(copy,[status(thm)],[6091]) ).

thf(6150,plain,
    ( ( ! [L: $i] :
          ( ~ ( is_int @ L )
          | ( pls
           != ( hAPP_int_int @ bit0 @ L ) )
          | ( pls = L ) )
      & ! [L: $i] :
          ( ~ ( is_int @ L )
          | ( pls != L )
          | ( pls
            = ( hAPP_int_int @ bit0 @ L ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6090]) ).

thf(6151,plain,
    ( ( ( hAPP_int_int @ bit0 @ pls )
      = pls )
    = $true ),
    inference(copy,[status(thm)],[5908]) ).

thf(6152,plain,
    ( ( pls = zero_zero_int )
    = $true ),
    inference(copy,[status(thm)],[5907]) ).

thf(6153,plain,
    ( ( zero_zero_int != one_one_int )
    = $true ),
    inference(copy,[status(thm)],[6089]) ).

thf(6154,plain,
    ( ( ! [K_2: $i] :
          ( ~ ( is_int @ K_2 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ K_2 ) @ pls )
            = K_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6088]) ).

thf(6155,plain,
    ( ( ! [K_2: $i] :
          ( ~ ( is_int @ K_2 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ pls ) @ K_2 )
            = K_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6087]) ).

thf(6156,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ bit0 @ K_2 ) ) @ ( hAPP_int_int @ bit0 @ L_2 ) )
          = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ K_2 ) @ L_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5903]) ).

thf(6157,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ bit0 @ K_2 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ K_2 ) @ K_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5902]) ).

thf(6158,plain,
    ( ( ! [Z_1: $i] :
          ( ~ ( is_int @ Z_1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z_1 ) @ zero_zero_int )
            = Z_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6086]) ).

thf(6159,plain,
    ( ( ! [Z_1: $i] :
          ( ~ ( is_int @ Z_1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ Z_1 )
            = Z_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6085]) ).

thf(6160,plain,
    ( ( ( hAPP_int_nat @ number_number_of_nat @ pls )
      = zero_zero_nat )
    = $true ),
    inference(copy,[status(thm)],[5899]) ).

thf(6161,plain,
    ( ( ( hAPP_int_int @ number_number_of_int @ pls )
      = zero_zero_int )
    = $true ),
    inference(copy,[status(thm)],[5898]) ).

thf(6162,plain,
    ( ( ( hAPP_int_int @ number_number_of_int @ pls )
      = zero_zero_int )
    = $true ),
    inference(copy,[status(thm)],[5897]) ).

thf(6163,plain,
    ( ( zero_zero_int
      = ( hAPP_int_int @ number_number_of_int @ pls ) )
    = $true ),
    inference(copy,[status(thm)],[5896]) ).

thf(6164,plain,
    ( ( ! [A_203: $i] :
          ( ~ ( is_int @ A_203 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ pls ) ) @ A_203 )
            = A_203 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6084]) ).

thf(6165,plain,
    ( ( ! [A_202: $i] :
          ( ~ ( is_int @ A_202 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_202 ) @ ( hAPP_int_int @ number_number_of_int @ pls ) )
            = A_202 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6083]) ).

thf(6166,plain,
    ( ( ! [A_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ! [Wa: $i] :
              ( ( ( hAPP_int_nat @ number_number_of_nat @ Wa )
                = zero_zero_nat )
              | ( A_1 != zero_zero_int )
              | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ Wa ) )
                = zero_zero_int ) ) )
      & ! [A_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ! [Wa: $i] :
              ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ Wa ) )
               != zero_zero_int )
              | ( ( hAPP_int_nat @ number_number_of_nat @ Wa )
               != zero_zero_nat ) ) )
      & ! [A_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ! [Wa: $i] :
              ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ Wa ) )
             != zero_zero_int )
          | ( A_1 = zero_zero_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6082]) ).

thf(6167,plain,
    ( ( ! [V_24: $i,W_14: $i,Z_21: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ V_24 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ W_14 ) ) @ Z_21 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ V_24 ) @ W_14 ) ) ) @ Z_21 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5892]) ).

thf(6168,plain,
    ( ( ! [V_23: $i,W_13: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ V_23 ) ) @ ( hAPP_int_int @ number_number_of_int @ W_13 ) )
          = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ V_23 ) @ W_13 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5891]) ).

thf(6169,plain,
    ( ( ! [V_22: $i,W_12: $i] :
          ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ V_22 ) @ W_12 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ V_22 ) ) @ ( hAPP_int_int @ number_number_of_int @ W_12 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5890]) ).

thf(6170,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ bit1 @ K_2 ) ) @ ( hAPP_int_int @ bit0 @ L_2 ) )
          = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ K_2 ) @ L_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5889]) ).

thf(6171,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ bit0 @ K_2 ) ) @ ( hAPP_int_int @ bit1 @ L_2 ) )
          = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ K_2 ) @ L_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5888]) ).

thf(6172,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ bit1 @ K_2 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ K_2 ) ) @ K_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5887]) ).

thf(6173,plain,
    ( ( ! [Z_1: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ Z_1 ) ) @ Z_1 )
         != zero_zero_int ) )
    = $true ),
    inference(copy,[status(thm)],[6081]) ).

thf(6174,plain,
    ( ( ! [N_58: $i] :
          ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_nat_int @ semiri1621563631at_int @ N_58 ) )
          = ( hAPP_nat_int @ semiri1621563631at_int @ N_58 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5885]) ).

thf(6175,plain,
    ( ( ! [N_58: $i] :
          ( ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_nat_int @ semiri1621563631at_int @ N_58 ) )
          = ( hAPP_nat_nat @ semiri984289939at_nat @ N_58 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5884]) ).

thf(6176,plain,
    ( ( ! [W_11: $i] :
          ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ W_11 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ ( hAPP_int_int @ number_number_of_int @ W_11 ) ) ) @ ( hAPP_int_int @ number_number_of_int @ W_11 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5883]) ).

thf(6177,plain,
    ( ( ! [W_10: $i] :
          ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ W_10 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ ( hAPP_int_int @ number_number_of_int @ W_10 ) ) ) @ ( hAPP_int_int @ number_number_of_int @ W_10 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5882]) ).

thf(6178,plain,
    ( ( ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ pls ) )
      = one_one_nat )
    = $true ),
    inference(copy,[status(thm)],[5881]) ).

thf(6179,plain,
    ( ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ pls ) )
      = one_one_int )
    = $true ),
    inference(copy,[status(thm)],[5880]) ).

thf(6180,plain,
    ( ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) )
      = ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5879]) ).

thf(6181,plain,
    ( ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) )
      = ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5878]) ).

thf(6182,plain,
    ( ( ! [N_55: $i] :
          ( ( N_55 != zero_zero_nat )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ N_55 )
            = one_one_int ) )
      & ! [N_55: $i] :
          ( ( N_55 = zero_zero_nat )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ N_55 )
            = zero_zero_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6080]) ).

thf(6183,plain,
    ( ( zero_zero_int
      = ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat ) )
    = $true ),
    inference(copy,[status(thm)],[5876]) ).

thf(6184,plain,
    ( ( ! [K_2: $i] :
          ( ~ ( is_int @ K_2 )
          | ( ( hAPP_int_int @ number_number_of_int @ K_2 )
            = K_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6079]) ).

thf(6185,plain,
    ( ( ! [A_198: $i] :
          ( ~ ( is_int @ A_198 )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_198 ) @ one_one_nat )
            = A_198 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6078]) ).

thf(6186,plain,
    ( ( ! [Ma: $i,Na: $i] :
          ( ( ( hAPP_nat_int @ semiri1621563631at_int @ Ma )
           != ( hAPP_nat_int @ semiri1621563631at_int @ Na ) )
          | ( Ma = Na ) )
      & ! [Ma: $i,Na: $i] :
          ( ( Ma != Na )
          | ( ( hAPP_nat_int @ semiri1621563631at_int @ Ma )
            = ( hAPP_nat_int @ semiri1621563631at_int @ Na ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6077]) ).

thf(6187,plain,
    ( ( ! [Xa: $i,Ya: $i] :
          ( ( ( hAPP_nat_int @ semiri1621563631at_int @ Xa )
           != ( hAPP_nat_int @ semiri1621563631at_int @ Ya ) )
          | ( Xa = Ya ) )
      & ! [Xa: $i,Ya: $i] :
          ( ( Xa != Ya )
          | ( ( hAPP_nat_int @ semiri1621563631at_int @ Xa )
            = ( hAPP_nat_int @ semiri1621563631at_int @ Ya ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6076]) ).

thf(6188,plain,
    ( ( one_one_int != zero_zero_int )
    = $true ),
    inference(copy,[status(thm)],[6075]) ).

thf(6189,plain,
    ( ( zero_zero_int != one_one_int )
    = $true ),
    inference(copy,[status(thm)],[6074]) ).

thf(6190,plain,
    ( ( ! [N_52: $i,A_197: $i] :
          ( ~ ( is_int @ A_197 )
          | ( A_197 = zero_zero_int )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_197 ) @ N_52 )
           != zero_zero_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6073]) ).

thf(6191,plain,
    ( ( ! [N_51: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ one_one_int ) @ N_51 )
          = one_one_int ) )
    = $true ),
    inference(copy,[status(thm)],[5868]) ).

thf(6192,plain,
    ( ( ( hAPP_nat_int @ semiri1621563631at_int @ one_one_nat )
      = one_one_int )
    = $true ),
    inference(copy,[status(thm)],[5867]) ).

thf(6193,plain,
    ( ( one_one_int
      = ( hAPP_nat_int @ semiri1621563631at_int @ one_one_nat ) )
    = $true ),
    inference(copy,[status(thm)],[5866]) ).

thf(6194,plain,
    ( ( ! [A_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ! [Na: $i] :
              ( ( Na = zero_zero_nat )
              | ( A_1 != zero_zero_int )
              | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_1 ) @ Na )
                = zero_zero_int ) ) )
      & ! [A_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ! [Na: $i] :
              ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_1 ) @ Na )
               != zero_zero_int )
              | ( Na != zero_zero_nat ) ) )
      & ! [A_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ! [Na: $i] :
              ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_1 ) @ Na )
             != zero_zero_int )
          | ( A_1 = zero_zero_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6072]) ).

thf(6195,plain,
    ( ( ! [A_191: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_191 ) @ zero_zero_nat )
          = one_one_int ) )
    = $true ),
    inference(copy,[status(thm)],[5864]) ).

thf(6196,plain,
    ( ( ( hAPP_nat_int @ semiri1621563631at_int @ zero_zero_nat )
      = zero_zero_int )
    = $true ),
    inference(copy,[status(thm)],[5863]) ).

thf(6197,plain,
    ( ( ! [X_62: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X_62 ) @ zero_zero_nat )
          = one_one_int ) )
    = $true ),
    inference(copy,[status(thm)],[5862]) ).

thf(6198,plain,
    ( ( ! [Xa: $i] :
          ( ~ ( is_int @ Xa )
          | ( zero_zero_int != Xa )
          | ( Xa = zero_zero_int ) )
      & ! [Xa: $i] :
          ( ~ ( is_int @ Xa )
          | ( Xa != zero_zero_int )
          | ( zero_zero_int = Xa ) ) )
    = $true ),
    inference(copy,[status(thm)],[6071]) ).

thf(6199,plain,
    ( ( ( hAPP_int_int @ succ @ pls )
      = ( hAPP_int_int @ bit1 @ pls ) )
    = $true ),
    inference(copy,[status(thm)],[5860]) ).

thf(6200,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ succ @ ( hAPP_int_int @ bit1 @ K_2 ) )
          = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ succ @ K_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5859]) ).

thf(6201,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ succ @ ( hAPP_int_int @ bit0 @ K_2 ) )
          = ( hAPP_int_int @ bit1 @ K_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5858]) ).

thf(6202,plain,
    ( ( ! [B_112: $i,A_164: $i,C_66: $i] :
          ( ~ ( is_int @ B_112 )
          | ~ ( is_int @ C_66 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_112 ) @ A_164 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ C_66 ) @ A_164 ) )
          | ( B_112 = C_66 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6070]) ).

thf(6203,plain,
    ( ( ! [A_163: $i,B_111: $i,C_65: $i] :
          ( ~ ( is_int @ B_111 )
          | ~ ( is_int @ C_65 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_163 ) @ B_111 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_163 ) @ C_65 ) )
          | ( B_111 = C_65 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6069]) ).

thf(6204,plain,
    ( ( ! [A_162: $i,B_110: $i,C_64: $i] :
          ( ~ ( is_int @ B_110 )
          | ~ ( is_int @ C_64 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_162 ) @ B_110 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_162 ) @ C_64 ) )
          | ( B_110 = C_64 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6068]) ).

thf(6205,plain,
    ( ( ! [A_161: $i,B_109: $i,C_63: $i,D_19: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_161 ) @ B_109 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ C_63 ) @ D_19 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_161 ) @ C_63 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_109 ) @ D_19 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5854]) ).

thf(6206,plain,
    ( ( ! [B_1: $i] :
          ( ! [A_1: $i,C: $i] :
              ( ~ ( is_int @ B_1 )
              | ~ ( is_int @ C )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_1 ) @ A_1 )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ C ) @ A_1 ) )
              | ( B_1 = C ) )
          & ! [A_1: $i,C: $i] :
              ( ~ ( is_int @ B_1 )
              | ~ ( is_int @ C )
              | ( B_1 != C )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_1 ) @ A_1 )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ C ) @ A_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6067]) ).

thf(6207,plain,
    ( ( ! [A_1: $i] :
          ( ! [B_1: $i,C: $i] :
              ( ~ ( is_int @ B_1 )
              | ~ ( is_int @ C )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_1 ) @ B_1 )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_1 ) @ C ) )
              | ( B_1 = C ) )
          & ! [B_1: $i,C: $i] :
              ( ~ ( is_int @ B_1 )
              | ~ ( is_int @ C )
              | ( B_1 != C )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_1 ) @ B_1 )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_1 ) @ C ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6066]) ).

thf(6208,plain,
    ( ( ! [A_160: $i,B_108: $i,C_62: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_160 ) @ B_108 ) ) @ C_62 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_160 ) @ C_62 ) ) @ B_108 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5851]) ).

thf(6209,plain,
    ( ( ! [A_159: $i,B_107: $i,C_61: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_159 ) @ B_107 ) ) @ C_61 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_159 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_107 ) @ C_61 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5850]) ).

thf(6210,plain,
    ( ( ! [A_158: $i,B_106: $i,C_60: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_158 ) @ B_106 ) ) @ C_60 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_158 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_106 ) @ C_60 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5849]) ).

thf(6211,plain,
    ( ( ! [A_157: $i,C_59: $i,D_18: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_157 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ C_59 ) @ D_18 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_157 ) @ C_59 ) ) @ D_18 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5848]) ).

thf(6212,plain,
    ( ( ! [A_156: $i,C_58: $i,D_17: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_156 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ C_58 ) @ D_17 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ C_58 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_156 ) @ D_17 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5847]) ).

thf(6213,plain,
    ( ( ! [A_155: $i,C_57: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_155 ) @ C_57 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ C_57 ) @ A_155 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5846]) ).

thf(6214,plain,
    ( ( ! [Xa: $i] :
          ( ~ ( is_int @ Xa )
          | ( one_one_int != Xa )
          | ( Xa = one_one_int ) )
      & ! [Xa: $i] :
          ( ~ ( is_int @ Xa )
          | ( Xa != one_one_int )
          | ( one_one_int = Xa ) ) )
    = $true ),
    inference(copy,[status(thm)],[6065]) ).

thf(6215,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ succ @ K_2 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ K_2 ) @ one_one_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[5844]) ).

thf(6216,plain,
    ( ( ! [K_8: $i] :
          ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ succ @ K_8 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ ( hAPP_int_int @ number_number_of_int @ K_8 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5843]) ).

thf(6217,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ bit1 @ K_2 ) ) @ ( hAPP_int_int @ bit1 @ L_2 ) )
          = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ K_2 ) @ ( hAPP_int_int @ succ @ L_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5842]) ).

thf(6218,plain,
    ( ( ! [B_1: $i,A_1: $i] :
          ( ~ ( is_int @ B_1 )
          | ~ ( is_int @ A_1 )
          | ( B_1
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_1 ) @ A_1 ) )
          | ( A_1 = zero_zero_int ) )
      & ! [B_1: $i,A_1: $i] :
          ( ~ ( is_int @ B_1 )
          | ~ ( is_int @ A_1 )
          | ( A_1 != zero_zero_int )
          | ( B_1
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_1 ) @ A_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6064]) ).

thf(6219,plain,
    ( ( ! [A_151: $i] :
          ( ~ ( is_int @ A_151 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_151 ) @ zero_zero_int )
            = A_151 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6063]) ).

thf(6220,plain,
    ( ( ! [A_150: $i] :
          ( ~ ( is_int @ A_150 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_150 ) @ zero_zero_int )
            = A_150 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6062]) ).

thf(6221,plain,
    ( ( ! [A_149: $i] :
          ( ~ ( is_int @ A_149 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_149 ) @ zero_zero_int )
            = A_149 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6061]) ).

thf(6222,plain,
    ( ( ! [A_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ( zero_zero_int
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_1 ) @ A_1 ) )
          | ( A_1 = zero_zero_int ) )
      & ! [A_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ( A_1 != zero_zero_int )
          | ( zero_zero_int
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_1 ) @ A_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6060]) ).

thf(6223,plain,
    ( ( ! [A_148: $i] :
          ( ~ ( is_int @ A_148 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ A_148 )
            = A_148 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6059]) ).

thf(6224,plain,
    ( ( ! [A_147: $i] :
          ( ~ ( is_int @ A_147 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ A_147 )
            = A_147 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6058]) ).

thf(6225,plain,
    ( ( ! [A_146: $i] :
          ( ~ ( is_int @ A_146 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ A_146 )
            = A_146 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6057]) ).

thf(6226,plain,
    ( ( ! [X_57: $i] :
          ( ~ ( is_int @ X_57 )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X_57 ) @ one_one_nat )
            = X_57 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6056]) ).

thf(6227,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_3 ) @ B_2 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) @ B_2 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ A_3 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5832]) ).

thf(6228,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_3 ) @ B_2 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ A_3 ) ) @ B_2 ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5831]) ).

thf(6229,plain,
    ( ( ! [A_140: $i,B_98: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_140 ) @ B_98 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_98 ) @ A_140 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5830]) ).

thf(6230,plain,
    ( ( ! [Lx_6: $i,Rx_6: $i,Ry_4: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_6 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Rx_6 ) @ Ry_4 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Rx_6 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_6 ) @ Ry_4 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5829]) ).

thf(6231,plain,
    ( ( ! [Lx_5: $i,Rx_5: $i,Ry_3: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_5 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Rx_5 ) @ Ry_3 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_5 ) @ Rx_5 ) ) @ Ry_3 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5828]) ).

thf(6232,plain,
    ( ( ! [A_139: $i,B_97: $i,C_51: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_139 ) @ B_97 ) ) @ C_51 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_139 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_97 ) @ C_51 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5827]) ).

thf(6233,plain,
    ( ( ! [Lx_4: $i,Ly_4: $i,Rx_4: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_4 ) @ Ly_4 ) ) @ Rx_4 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_4 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Ly_4 ) @ Rx_4 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5826]) ).

thf(6234,plain,
    ( ( ! [Lx_3: $i,Ly_3: $i,Rx_3: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_3 ) @ Ly_3 ) ) @ Rx_3 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_3 ) @ Rx_3 ) ) @ Ly_3 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5825]) ).

thf(6235,plain,
    ( ( ! [Lx_2: $i,Ly_2: $i,Rx_2: $i,Ry_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_2 ) @ Ly_2 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Rx_2 ) @ Ry_2 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_2 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Ly_2 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Rx_2 ) @ Ry_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5824]) ).

thf(6236,plain,
    ( ( ! [Lx_1: $i,Ly_1: $i,Rx_1: $i,Ry_1: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_1 ) @ Ly_1 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Rx_1 ) @ Ry_1 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Rx_1 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx_1 ) @ Ly_1 ) ) @ Ry_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5823]) ).

thf(6237,plain,
    ( ( ! [Lx: $i,Ly: $i,Rx: $i,Ry: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx ) @ Ly ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Rx ) @ Ry ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Lx ) @ Rx ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Ly ) @ Ry ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5822]) ).

thf(6238,plain,
    ( ( ! [Z_1: $i,W: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z_1 ) @ W )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ W ) @ Z_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5821]) ).

thf(6239,plain,
    ( ( ! [Z1: $i,Z2: $i,Z3: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z1 ) @ Z2 ) ) @ Z3 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z1 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z2 ) @ Z3 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5820]) ).

thf(6240,plain,
    ( ( ! [V_16: $i,W_8: $i,Z_20: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ V_16 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ W_8 ) ) @ Z_20 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ V_16 ) @ W_8 ) ) ) @ Z_20 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5819]) ).

thf(6241,plain,
    ( ( ! [V_15: $i,W_7: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ V_15 ) ) @ ( hAPP_int_int @ number_number_of_int @ W_7 ) )
          = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ V_15 ) @ W_7 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5818]) ).

thf(6242,plain,
    ( ( ! [V_14: $i,W_6: $i] :
          ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ V_14 ) @ W_6 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ V_14 ) ) @ ( hAPP_int_int @ number_number_of_int @ W_6 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5817]) ).

thf(6243,plain,
    ( ( ! [A_138: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ zero_zero_int ) @ A_138 )
          = zero_zero_int ) )
    = $true ),
    inference(copy,[status(thm)],[5816]) ).

thf(6244,plain,
    ( ( ! [A_137: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_137 ) @ zero_zero_int )
          = zero_zero_int ) )
    = $true ),
    inference(copy,[status(thm)],[5815]) ).

thf(6245,plain,
    ( ( ! [A_1: $i,B_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ~ ( is_int @ B_1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ B_1 )
           != zero_zero_int )
          | ( A_1 = zero_zero_int )
          | ( B_1 = zero_zero_int ) )
      & ! [A_1: $i,B_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ~ ( is_int @ B_1 )
          | ( A_1 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ B_1 )
            = zero_zero_int ) )
      & ! [A_1: $i,B_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ~ ( is_int @ B_1 )
          | ( B_1 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ B_1 )
            = zero_zero_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6055]) ).

thf(6246,plain,
    ( ( ! [B_96: $i,A_136: $i] :
          ( ~ ( is_int @ B_96 )
          | ~ ( is_int @ A_136 )
          | ( A_136 = zero_zero_int )
          | ( B_96 = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_136 ) @ B_96 )
           != zero_zero_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6054]) ).

thf(6247,plain,
    ( ( ! [A_135: $i,B_95: $i] :
          ( ~ ( is_int @ A_135 )
          | ~ ( is_int @ B_95 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_135 ) @ B_95 )
           != zero_zero_int )
          | ( A_135 = zero_zero_int )
          | ( B_95 = zero_zero_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6053]) ).

thf(6248,plain,
    ( ( ! [A_134: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ zero_zero_int ) @ A_134 )
          = zero_zero_int ) )
    = $true ),
    inference(copy,[status(thm)],[5811]) ).

thf(6249,plain,
    ( ( ! [A_133: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_133 ) @ zero_zero_int )
          = zero_zero_int ) )
    = $true ),
    inference(copy,[status(thm)],[5810]) ).

thf(6250,plain,
    ( ( ! [A_132: $i,B_94: $i,C_50: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_132 ) @ B_94 ) ) @ C_50 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_132 ) @ C_50 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_94 ) @ C_50 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5809]) ).

thf(6251,plain,
    ( ( ! [A_131: $i,E_3: $i,B_93: $i,C_49: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_131 ) @ E_3 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_93 ) @ E_3 ) ) @ C_49 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_131 ) @ B_93 ) ) @ E_3 ) ) @ C_49 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5808]) ).

thf(6252,plain,
    ( ( ! [X_55: $i,Y_47: $i,Z_19: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ X_55 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Y_47 ) @ Z_19 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ X_55 ) @ Y_47 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ X_55 ) @ Z_19 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5807]) ).

thf(6253,plain,
    ( ( ! [C: $i,D_1: $i] :
          ( ! [A_1: $i,B_1: $i] :
              ( ~ ( is_int @ C )
              | ~ ( is_int @ D_1 )
              | ~ ( is_int @ A_1 )
              | ~ ( is_int @ B_1 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ C ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_1 ) @ D_1 ) )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ D_1 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_1 ) @ C ) ) )
              | ( A_1 != B_1 ) )
          & ! [A_1: $i,B_1: $i] :
              ( ~ ( is_int @ C )
              | ~ ( is_int @ D_1 )
              | ~ ( is_int @ A_1 )
              | ~ ( is_int @ B_1 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ C ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_1 ) @ D_1 ) )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ D_1 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_1 ) @ C ) ) )
              | ( C != D_1 ) )
          & ! [A_1: $i,B_1: $i] :
              ( ~ ( is_int @ C )
              | ~ ( is_int @ D_1 )
              | ~ ( is_int @ A_1 )
              | ~ ( is_int @ B_1 )
              | ( A_1 = B_1 )
              | ( C = D_1 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ C ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_1 ) @ D_1 ) )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ D_1 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_1 ) @ C ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6052]) ).

thf(6254,plain,
    ( ( ! [A_130: $i,B_92: $i,C_48: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_130 ) @ B_92 ) ) @ C_48 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_130 ) @ C_48 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_92 ) @ C_48 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5805]) ).

thf(6255,plain,
    ( ( ! [A_129: $i,M_17: $i,B_91: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_129 ) @ M_17 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_91 ) @ M_17 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_129 ) @ B_91 ) ) @ M_17 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5804]) ).

thf(6256,plain,
    ( ( ! [Wa: $i,Ya: $i] :
          ( ! [Xa: $i,Z_2: $i] :
              ( ~ ( is_int @ Wa )
              | ~ ( is_int @ Ya )
              | ~ ( is_int @ Xa )
              | ~ ( is_int @ Z_2 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Wa ) @ Ya ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Xa ) @ Z_2 ) )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Wa ) @ Z_2 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Xa ) @ Ya ) ) )
              | ( Wa = Xa )
              | ( Ya = Z_2 ) )
          & ! [Xa: $i,Z_2: $i] :
              ( ~ ( is_int @ Wa )
              | ~ ( is_int @ Ya )
              | ~ ( is_int @ Xa )
              | ~ ( is_int @ Z_2 )
              | ( Wa != Xa )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Wa ) @ Ya ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Xa ) @ Z_2 ) )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Wa ) @ Z_2 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Xa ) @ Ya ) ) ) )
          & ! [Xa: $i,Z_2: $i] :
              ( ~ ( is_int @ Wa )
              | ~ ( is_int @ Ya )
              | ~ ( is_int @ Xa )
              | ~ ( is_int @ Z_2 )
              | ( Ya != Z_2 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Wa ) @ Ya ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Xa ) @ Z_2 ) )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Wa ) @ Z_2 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Xa ) @ Ya ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6051]) ).

thf(6257,plain,
    ( ( ! [A_128: $i] :
          ( ~ ( is_int @ A_128 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ one_one_int ) @ A_128 )
            = A_128 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6050]) ).

thf(6258,plain,
    ( ( ! [A_127: $i] :
          ( ~ ( is_int @ A_127 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ one_one_int ) @ A_127 )
            = A_127 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6049]) ).

thf(6259,plain,
    ( ( ! [A_126: $i] :
          ( ~ ( is_int @ A_126 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ one_one_int ) @ A_126 )
            = A_126 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6048]) ).

thf(6260,plain,
    ( ( ! [A_125: $i] :
          ( ~ ( is_int @ A_125 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_125 ) @ one_one_int )
            = A_125 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6047]) ).

thf(6261,plain,
    ( ( ! [A_124: $i] :
          ( ~ ( is_int @ A_124 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_124 ) @ one_one_int )
            = A_124 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6046]) ).

thf(6262,plain,
    ( ( ! [A_123: $i] :
          ( ~ ( is_int @ A_123 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_123 ) @ one_one_int )
            = A_123 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6045]) ).

thf(6263,plain,
    ( ( ! [A_122: $i,N_29: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_122 ) @ N_29 ) ) @ A_122 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_122 ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_122 ) @ N_29 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5796]) ).

thf(6264,plain,
    ( ( ! [A_121: $i,B_90: $i,N_28: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_121 ) @ B_90 ) ) @ N_28 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_121 ) @ N_28 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_90 ) @ N_28 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5795]) ).

thf(6265,plain,
    ( ( ! [X_54: $i,Y_46: $i,Q_9: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ X_54 ) @ Y_46 ) ) @ Q_9 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X_54 ) @ Q_9 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Y_46 ) @ Q_9 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5794]) ).

thf(6266,plain,
    ( ( ! [W: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ pls ) @ W )
          = pls ) )
    = $true ),
    inference(copy,[status(thm)],[5793]) ).

thf(6267,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ bit0 @ K_2 ) ) @ L_2 )
          = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ L_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5792]) ).

thf(6268,plain,
    ( ( ! [Z_1: $i] :
          ( ~ ( is_int @ Z_1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ one_one_int ) @ Z_1 )
            = Z_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6044]) ).

thf(6269,plain,
    ( ( ! [Z_1: $i] :
          ( ~ ( is_int @ Z_1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z_1 ) @ one_one_int )
            = Z_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6043]) ).

thf(6270,plain,
    ( ( ! [W: $i,Z1: $i,Z2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ W ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z1 ) @ Z2 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ W ) @ Z1 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ W ) @ Z2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5789]) ).

thf(6271,plain,
    ( ( ! [Z1: $i,Z2: $i,W: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z1 ) @ Z2 ) ) @ W )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z1 ) @ W ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z2 ) @ W ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5788]) ).

thf(6272,plain,
    ( ( ! [V_1: $i,W: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ V_1 ) ) @ ( hAPP_int_int @ number_number_of_int @ W ) )
          = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ V_1 ) @ W ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5787]) ).

thf(6273,plain,
    ( ( ! [Xa: $i,Ya: $i] :
          ( ~ ( is_int @ Xa )
          | ~ ( is_int @ Ya )
          | ( Xa != zero_zero_int )
          | ( Ya != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Xa ) @ Xa ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Ya ) @ Ya ) )
            = zero_zero_int ) )
      & ! [Xa: $i,Ya: $i] :
          ( ~ ( is_int @ Xa )
          | ~ ( is_int @ Ya )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Xa ) @ Xa ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Ya ) @ Ya ) )
           != zero_zero_int )
          | ( Xa = zero_zero_int ) )
      & ! [Xa: $i,Ya: $i] :
          ( ~ ( is_int @ Xa )
          | ~ ( is_int @ Ya )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Xa ) @ Xa ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Ya ) @ Ya ) )
           != zero_zero_int )
          | ( Ya = zero_zero_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6042]) ).

thf(6274,plain,
    ( ( ! [C_35: $i,D_13: $i,A_92: $i,B_63: $i,R_6: $i] :
          ( ~ ( is_int @ C_35 )
          | ~ ( is_int @ D_13 )
          | ~ ( is_int @ R_6 )
          | ( R_6 = zero_zero_int )
          | ( C_35 = D_13 )
          | ( A_92 != B_63 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_92 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ R_6 ) @ C_35 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_63 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ R_6 ) @ D_13 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6041]) ).

thf(6275,plain,
    ( ( ! [V_11: $i,B_62: $i,C_34: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ V_11 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_62 ) @ C_34 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ V_11 ) ) @ B_62 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ V_11 ) ) @ C_34 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5784]) ).

thf(6276,plain,
    ( ( ! [A_91: $i,B_61: $i,V_10: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_91 ) @ B_61 ) ) @ ( hAPP_int_int @ number_number_of_int @ V_10 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_91 ) @ ( hAPP_int_int @ number_number_of_int @ V_10 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_61 ) @ ( hAPP_int_int @ number_number_of_int @ V_10 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5783]) ).

thf(6277,plain,
    ( ( ! [M_15: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ M_15 ) @ M_15 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ one_one_int ) ) @ M_15 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5782]) ).

thf(6278,plain,
    ( ( ! [M_14: $i,A_90: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ M_14 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_90 ) @ M_14 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_90 ) @ one_one_int ) ) @ M_14 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5781]) ).

thf(6279,plain,
    ( ( ! [A_89: $i,M_13: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_89 ) @ M_13 ) ) @ M_13 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_89 ) @ one_one_int ) ) @ M_13 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5780]) ).

thf(6280,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ bit1 @ K_2 ) ) @ L_2 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ L_2 ) ) ) @ L_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5779]) ).

thf(6281,plain,
    ( ( ! [W_5: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ one_one_int ) ) @ ( hAPP_int_int @ number_number_of_int @ W_5 ) )
          = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ W_5 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5778]) ).

thf(6282,plain,
    ( ( ! [A_61: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_61 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_61 ) @ A_61 ) ) @ A_61 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5777]) ).

thf(6283,plain,
    ( ( ! [Z_14: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z_14 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z_14 ) @ Z_14 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5776]) ).

thf(6284,plain,
    ( ( ! [Z_13: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z_13 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z_13 ) @ Z_13 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5775]) ).

thf(6285,plain,
    ( ( ! [Z_12: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ Z_12 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z_12 ) @ Z_12 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5774]) ).

thf(6286,plain,
    ( ( ! [Z_11: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ Z_11 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z_11 ) @ Z_11 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5773]) ).

thf(6287,plain,
    ( ( ! [A_59: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_59 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_59 ) @ A_59 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5772]) ).

thf(6288,plain,
    ( ( ! [X_26: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ X_26 ) @ X_26 )
          = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X_26 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5771]) ).

thf(6289,plain,
    ( ( ! [A_3: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
          = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5770]) ).

thf(6290,plain,
    ( ( ! [W_4: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ number_number_of_int @ W_4 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ W_4 ) ) @ ( hAPP_int_int @ number_number_of_int @ W_4 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5769]) ).

thf(6291,plain,
    ( ( ! [X_15: $i,Y_11: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ X_15 ) @ Y_11 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X_15 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Y_11 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ X_15 ) ) @ Y_11 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5768]) ).

thf(6292,plain,
    ( ( ( hAPP_int_int @ bit1 @ min )
      = min )
    = $true ),
    inference(copy,[status(thm)],[5767]) ).

thf(6293,plain,
    ( ( ! [L: $i] :
          ( ~ ( is_int @ L )
          | ( min
           != ( hAPP_int_int @ bit1 @ L ) )
          | ( min = L ) )
      & ! [L: $i] :
          ( ~ ( is_int @ L )
          | ( min != L )
          | ( min
            = ( hAPP_int_int @ bit1 @ L ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6040]) ).

thf(6294,plain,
    ( ( ! [K: $i] :
          ( ~ ( is_int @ K )
          | ( ( hAPP_int_int @ bit1 @ K )
           != min )
          | ( K = min ) )
      & ! [K: $i] :
          ( ~ ( is_int @ K )
          | ( K != min )
          | ( ( hAPP_int_int @ bit1 @ K )
            = min ) ) )
    = $true ),
    inference(copy,[status(thm)],[6039]) ).

thf(6295,plain,
    ( ( min != pls )
    = $true ),
    inference(copy,[status(thm)],[6038]) ).

thf(6296,plain,
    ( ( pls != min )
    = $true ),
    inference(copy,[status(thm)],[6037]) ).

thf(6297,plain,
    ( ( ! [L_2: $i] :
          ( min
         != ( hAPP_int_int @ bit0 @ L_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6036]) ).

thf(6298,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ bit0 @ K_2 )
         != min ) )
    = $true ),
    inference(copy,[status(thm)],[6035]) ).

thf(6299,plain,
    ( ( ( hAPP_int_int @ number_number_of_int @ pls )
     != ( hAPP_int_int @ number_number_of_int @ min ) )
    = $true ),
    inference(copy,[status(thm)],[6034]) ).

thf(6300,plain,
    ( ( ( hAPP_int_int @ succ @ min )
      = pls )
    = $true ),
    inference(copy,[status(thm)],[5759]) ).

thf(6301,plain,
    ( ( ! [A_1: $i,B_1: $i] :
          ( ! [C: $i,D_1: $i] :
              ( ~ ( is_int @ A_1 )
              | ~ ( is_int @ B_1 )
              | ~ ( is_int @ C )
              | ~ ( is_int @ D_1 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_1 ) @ B_1 )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ C ) @ D_1 ) )
              | ( A_1 != B_1 )
              | ( C = D_1 ) )
          & ! [C: $i,D_1: $i] :
              ( ~ ( is_int @ A_1 )
              | ~ ( is_int @ B_1 )
              | ~ ( is_int @ C )
              | ~ ( is_int @ D_1 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_1 ) @ B_1 )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ C ) @ D_1 ) )
              | ( C != D_1 )
              | ( A_1 = B_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6033]) ).

thf(6302,plain,
    ( ( ! [V_7: $i,W_3: $i] :
          ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ V_7 ) @ W_3 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ number_number_of_int @ V_7 ) ) @ ( hAPP_int_int @ number_number_of_int @ W_3 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5757]) ).

thf(6303,plain,
    ( ( ! [A_1: $i,B_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ~ ( is_int @ B_1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_1 ) @ B_1 )
           != zero_zero_int )
          | ( A_1 = B_1 ) )
      & ! [A_1: $i,B_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ~ ( is_int @ B_1 )
          | ( A_1 != B_1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_1 ) @ B_1 )
            = zero_zero_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6032]) ).

thf(6304,plain,
    ( ( ! [A_1: $i,B_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ~ ( is_int @ B_1 )
          | ( A_1 != B_1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_1 ) @ B_1 )
            = zero_zero_int ) )
      & ! [A_1: $i,B_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ~ ( is_int @ B_1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_1 ) @ B_1 )
           != zero_zero_int )
          | ( A_1 = B_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6031]) ).

thf(6305,plain,
    ( ( ! [A_36: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_36 ) @ A_36 )
          = zero_zero_int ) )
    = $true ),
    inference(copy,[status(thm)],[5754]) ).

thf(6306,plain,
    ( ( ! [A_35: $i] :
          ( ~ ( is_int @ A_35 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_35 ) @ zero_zero_int )
            = A_35 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6030]) ).

thf(6307,plain,
    ( ( ! [A_34: $i] :
          ( ~ ( is_int @ A_34 )
          | ! [B_26: $i] :
              ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_34 ) @ B_26 ) ) @ B_26 )
              = A_34 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6029]) ).

thf(6308,plain,
    ( ( ! [A_33: $i] :
          ( ~ ( is_int @ A_33 )
          | ! [B_25: $i] :
              ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_33 ) @ B_25 ) ) @ B_25 )
              = A_33 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6028]) ).

thf(6309,plain,
    ( ( ! [A_32: $i,C_8: $i,B_24: $i,D_7: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_32 ) @ C_8 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ B_24 ) @ D_7 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_32 ) @ B_24 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ C_8 ) @ D_7 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5750]) ).

thf(6310,plain,
    ( ( ! [K_2: $i] :
          ( ~ ( is_int @ K_2 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ K_2 ) @ pls )
            = K_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6027]) ).

thf(6311,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ bit0 @ K_2 ) ) @ ( hAPP_int_int @ bit0 @ L_2 ) )
          = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ K_2 ) @ L_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5748]) ).

thf(6312,plain,
    ( ( ! [Z1: $i,Z2: $i,W: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ Z1 ) @ Z2 ) ) @ W )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z1 ) @ W ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z2 ) @ W ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5747]) ).

thf(6313,plain,
    ( ( ! [W: $i,Z1: $i,Z2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ W ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ Z1 ) @ Z2 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ W ) @ Z1 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ W ) @ Z2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5746]) ).

thf(6314,plain,
    ( ( ! [X_10: $i,Y_7: $i,A_29: $i,B_22: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ X_10 ) @ Y_7 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_29 ) @ B_22 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ X_10 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ Y_7 ) @ B_22 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ X_10 ) @ A_29 ) ) @ B_22 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5745]) ).

thf(6315,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ bit1 @ K_2 ) ) @ ( hAPP_int_int @ bit1 @ L_2 ) )
          = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ K_2 ) @ L_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5744]) ).

thf(6316,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ bit1 @ K_2 ) ) @ ( hAPP_int_int @ bit0 @ L_2 ) )
          = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ K_2 ) @ L_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5743]) ).

thf(6317,plain,
    ( ( ! [L_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ pls ) @ ( hAPP_int_int @ bit0 @ L_2 ) )
          = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ pls ) @ L_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5742]) ).

thf(6318,plain,
    ( ( ! [X_9: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ X_9 ) @ X_9 ) ) @ one_one_int )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ X_9 ) @ one_one_int ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ X_9 ) @ one_one_int ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5741]) ).

thf(6319,plain,
    ( ( ! [V_4: $i,W_2: $i,C_6: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ V_4 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ number_number_of_int @ W_2 ) ) @ C_6 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ V_4 ) @ W_2 ) ) ) @ C_6 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5740]) ).

thf(6320,plain,
    ( ( ! [L_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ pls ) @ ( hAPP_int_int @ bit1 @ L_2 ) )
          = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ min ) @ L_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5739]) ).

thf(6321,plain,
    ( ( ! [L_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ min ) @ ( hAPP_int_int @ bit1 @ L_2 ) )
          = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ min ) @ L_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5738]) ).

thf(6322,plain,
    ( ( ! [L_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ min ) @ ( hAPP_int_int @ bit0 @ L_2 ) )
          = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ min ) @ L_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5737]) ).

thf(6323,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_3 ) @ B_2 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_3 ) @ B_2 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5736]) ).

thf(6324,plain,
    ( ( ! [A_3: $i] :
          ( ~ ( is_int @ A_3 )
          | ! [B_2: $i,C_1: $i] :
              ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_3 ) @ B_2 )
               != C_1 )
              | ( A_3
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ C_1 ) @ B_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6026]) ).

thf(6325,plain,
    ( ( ! [A_3: $i,R_2: $i,B_2: $i,M: $i,C_1: $i,D_3: $i,N: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ R_2 ) @ B_2 ) ) ) @ M ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ C_1 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ R_2 ) @ D_3 ) ) ) @ N ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ M ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ C_1 ) @ N ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ R_2 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_2 ) @ M ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ D_3 ) @ N ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5734]) ).

thf(6326,plain,
    ( ( ! [N: $i] :
          ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ number_number_of_int @ min ) ) @ N )
            = one_one_int )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ number_number_of_int @ min ) ) @ N )
            = ( hAPP_int_int @ number_number_of_int @ min ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5733]) ).

thf(6327,plain,
    ( ( ! [A_27: $i] :
          ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ abs_abs_int @ A_27 ) )
          = ( hAPP_int_int @ abs_abs_int @ A_27 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5732]) ).

thf(6328,plain,
    ( ( ! [A_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ( ( hAPP_int_int @ abs_abs_int @ A_1 )
           != zero_zero_int )
          | ( A_1 = zero_zero_int ) )
      & ! [A_1: $i] :
          ( ~ ( is_int @ A_1 )
          | ( A_1 != zero_zero_int )
          | ( ( hAPP_int_int @ abs_abs_int @ A_1 )
            = zero_zero_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6025]) ).

thf(6329,plain,
    ( ( ( hAPP_int_int @ abs_abs_int @ zero_zero_int )
      = zero_zero_int )
    = $true ),
    inference(copy,[status(thm)],[5730]) ).

thf(6330,plain,
    ( ( ! [A_24: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ A_24 ) ) @ ( hAPP_int_int @ abs_abs_int @ A_24 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_24 ) @ A_24 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5729]) ).

thf(6331,plain,
    ( ( ! [A_23: $i,B_18: $i] :
          ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_23 ) @ B_18 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ A_23 ) ) @ ( hAPP_int_int @ abs_abs_int @ B_18 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5728]) ).

thf(6332,plain,
    ( ( ! [A_22: $i,B_17: $i] :
          ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ abs_abs_int @ A_22 ) ) @ ( hAPP_int_int @ abs_abs_int @ B_17 ) ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ abs_abs_int @ A_22 ) ) @ ( hAPP_int_int @ abs_abs_int @ B_17 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5727]) ).

thf(6333,plain,
    ( ( ( hAPP_int_int @ abs_abs_int @ one_one_int )
      = one_one_int )
    = $true ),
    inference(copy,[status(thm)],[5726]) ).

thf(6334,plain,
    ( ( ! [A_21: $i,B_16: $i] :
          ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_21 ) @ B_16 ) )
          = ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ B_16 ) @ A_21 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5725]) ).

thf(6335,plain,
    ( ( ! [A_20: $i,N_9: $i] :
          ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_20 ) @ N_9 ) )
          = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ abs_abs_int @ A_20 ) ) @ N_9 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5724]) ).

thf(6336,plain,
    ( ( ! [N_8: $i] :
          ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_nat_int @ semiri1621563631at_int @ N_8 ) )
          = ( hAPP_nat_int @ semiri1621563631at_int @ N_8 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5723]) ).

thf(6337,plain,
    ( ( ! [M: $i] :
          ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_nat_int @ semiri1621563631at_int @ M ) )
          = ( hAPP_nat_int @ semiri1621563631at_int @ M ) ) )
    = $true ),
    inference(copy,[status(thm)],[5722]) ).

thf(6338,plain,
    ( ( ! [N: $i] :
          ( ( hAPP_int_nat @ nat @ ( hAPP_nat_int @ semiri1621563631at_int @ N ) )
          = N ) )
    = $true ),
    inference(copy,[status(thm)],[5721]) ).

thf(6339,plain,
    ( ( ( hAPP_int_nat @ nat @ zero_zero_int )
      = zero_zero_nat )
    = $true ),
    inference(copy,[status(thm)],[5720]) ).

thf(6340,plain,
    ( ( zero_zero_nat
      = ( hAPP_int_nat @ nat @ zero_zero_int ) )
    = $true ),
    inference(copy,[status(thm)],[5719]) ).

thf(6341,plain,
    ( ( ! [M: $i] :
          ( ! [N: $i] :
              ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ M ) @ N ) )
             != one_one_int )
          | ( ( hAPP_int_int @ abs_abs_int @ M )
            = one_one_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6024]) ).

thf(6342,plain,
    ( ( ! [V_1: $i] :
          ( ( hAPP_int_nat @ number_number_of_nat @ V_1 )
          = ( hAPP_int_nat @ nat @ ( hAPP_int_int @ number_number_of_int @ V_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5717]) ).

thf(6343,plain,
    ( ( ! [W: $i] :
          ( ( hAPP_int_nat @ nat @ ( hAPP_int_int @ number_number_of_int @ W ) )
          = ( hAPP_int_nat @ number_number_of_nat @ W ) ) )
    = $true ),
    inference(copy,[status(thm)],[5716]) ).

thf(6344,plain,
    ( ( one_one_nat
      = ( hAPP_int_nat @ nat @ one_one_int ) )
    = $true ),
    inference(copy,[status(thm)],[5715]) ).

thf(6345,plain,
    ( ( ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) )
      = ( hAPP_int_nat @ nat @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5714]) ).

thf(6346,plain,
    ( ( ! [X: $i] :
          ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
          = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ abs_abs_int @ X ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5713]) ).

thf(6347,plain,
    ( ( ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) )
      = ( hAPP_int_nat @ nat @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5712]) ).

thf(6348,plain,
    ( ( ! [A_1: $i,B_1: $i] :
          ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
           != ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
          | ( ( hAPP_int_int @ abs_abs_int @ A_1 )
            = ( hAPP_int_int @ abs_abs_int @ B_1 ) ) )
      & ! [A_1: $i,B_1: $i] :
          ( ( ( hAPP_int_int @ abs_abs_int @ A_1 )
           != ( hAPP_int_int @ abs_abs_int @ B_1 ) )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
            = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6023]) ).

thf(6349,plain,
    ( ( ! [A_3: $i] :
          ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
          = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ abs_abs_int @ A_3 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5710]) ).

thf(6350,plain,
    ( ( ! [A_3: $i] :
          ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
           != one_one_int )
          | ( ( hAPP_int_int @ abs_abs_int @ A_3 )
            = one_one_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6022]) ).

thf(6351,plain,
    ( ( ! [B_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ zero_zero_int ) @ B_2 )
          = zero_zero_int ) )
    = $true ),
    inference(copy,[status(thm)],[5708]) ).

thf(6352,plain,
    ( ( ! [A_3: $i] :
          ( ~ ( is_int @ A_3 )
          | ( A_3 = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ A_3 )
            = one_one_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6021]) ).

thf(6353,plain,
    ( ( ! [V_1: $i,W: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ V_1 ) ) ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ W ) ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ number_number_of_int @ V_1 ) ) @ ( hAPP_int_int @ number_number_of_int @ W ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5706]) ).

thf(6354,plain,
    ( ( ! [X: $i] :
          ( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_int_nat @ nat @ ( hAPP_int_int @ abs_abs_int @ X ) ) )
          = ( hAPP_int_int @ abs_abs_int @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[5705]) ).

thf(6355,plain,
    ( ( ! [M: $i,X: $i] :
          ( ( hAPP_int_int @ ( standardRes @ M ) @ X )
          = ( hAPP_int_int @ ( div_mod_int @ X ) @ M ) ) )
    = $true ),
    inference(copy,[status(thm)],[5704]) ).

thf(6356,plain,
    ( ( ! [A_3: $i] :
          ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ A_3 )
          = zero_zero_int ) )
    = $true ),
    inference(copy,[status(thm)],[5703]) ).

thf(6357,plain,
    ( ( ! [B_2: $i] :
          ( ( hAPP_int_int @ ( div_mod_int @ zero_zero_int ) @ B_2 )
          = zero_zero_int ) )
    = $true ),
    inference(copy,[status(thm)],[5702]) ).

thf(6358,plain,
    ( ( ! [A_3: $i,B_2: $i,C_1: $i] :
          ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ B_2 ) ) @ C_1 )
          = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ ( hAPP_int_int @ ( div_mod_int @ B_2 ) @ C_1 ) ) ) @ C_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5701]) ).

thf(6359,plain,
    ( ( ! [A_3: $i,B_2: $i,C_1: $i] :
          ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ ( hAPP_int_int @ ( div_mod_int @ B_2 ) @ C_1 ) ) ) @ C_1 )
          = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ B_2 ) ) @ C_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5700]) ).

thf(6360,plain,
    ( ( ! [X: $i,M: $i,Y: $i] :
          ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( div_mod_int @ X ) @ M ) ) @ Y ) ) @ M )
          = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ X ) @ Y ) ) @ M ) ) )
    = $true ),
    inference(copy,[status(thm)],[5699]) ).

thf(6361,plain,
    ( ( ! [X: $i,Y: $i,M: $i] :
          ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ X ) @ ( hAPP_int_int @ ( div_mod_int @ Y ) @ M ) ) ) @ M )
          = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ X ) @ Y ) ) @ M ) ) )
    = $true ),
    inference(copy,[status(thm)],[5698]) ).

thf(6362,plain,
    ( ( ! [X: $i,M: $i,Y: $i] :
          ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( div_mod_int @ X ) @ M ) ) @ Y ) ) @ M )
          = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X ) @ Y ) ) @ M ) ) )
    = $true ),
    inference(copy,[status(thm)],[5697]) ).

thf(6363,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 ) ) @ B_2 )
          = zero_zero_int ) )
    = $true ),
    inference(copy,[status(thm)],[5696]) ).

thf(6364,plain,
    ( ( ! [A_3: $i,B_2: $i,C_1: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_3 ) @ B_2 ) ) @ C_1 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ C_1 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ B_2 ) @ C_1 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ C_1 ) ) @ ( hAPP_int_int @ ( div_mod_int @ B_2 ) @ C_1 ) ) ) @ C_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5695]) ).

thf(6365,plain,
    ( ( ! [M: $i] :
          ( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ suc @ M ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ M ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5694]) ).

thf(6366,plain,
    ( ( ! [Xa: $i] :
          ( ( ( hAPP_int_int @ ( div_mod_int @ Xa ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
            = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ Xa ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
            = one_one_int ) )
      & ! [Xa: $i] :
          ( ( ( hAPP_int_int @ ( div_mod_int @ Xa ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
           != one_one_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ Xa ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
           != zero_zero_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6020]) ).

thf(6367,plain,
    ( ( ! [Z_1: $i] :
          ( ~ ( is_int @ Z_1 )
          | ( Z_1
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ ( sK15_M_1 @ Z_1 ) ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ ( sK16_SY717 @ Z_1 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6019]) ).

thf(6368,plain,
    ( ( ! [Z_1: $i] :
          ( ~ ( is_int @ Z_1 )
          | ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ uminus_uminus_int @ Z_1 ) )
            = Z_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[6018]) ).

thf(6369,plain,
    ( ( ( hAPP_int_int @ uminus_uminus_int @ pls )
      = pls )
    = $true ),
    inference(copy,[status(thm)],[5690]) ).

thf(6370,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ bit0 @ K_2 ) )
          = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ uminus_uminus_int @ K_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5689]) ).

thf(6371,plain,
    ( ( ( hAPP_int_int @ uminus_uminus_int @ zero_zero_int )
      = zero_zero_int )
    = $true ),
    inference(copy,[status(thm)],[5688]) ).

thf(6372,plain,
    ( ( ! [Z_1: $i,W: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ uminus_uminus_int @ Z_1 ) ) @ W )
          = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Z_1 ) @ W ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5687]) ).

thf(6373,plain,
    ( ( ! [Z_1: $i,W: $i] :
          ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z_1 ) @ W ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ uminus_uminus_int @ Z_1 ) ) @ ( hAPP_int_int @ uminus_uminus_int @ W ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5686]) ).

thf(6374,plain,
    ( ( ! [W: $i] :
          ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ number_number_of_int @ W ) )
          = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ uminus_uminus_int @ W ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5685]) ).

thf(6375,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) @ ( hAPP_int_int @ uminus_uminus_int @ B_2 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ B_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5684]) ).

thf(6376,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ ( hAPP_int_int @ uminus_uminus_int @ B_2 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) @ B_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5683]) ).

thf(6377,plain,
    ( ( ! [X: $i,M: $i] :
          ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( div_mod_int @ X ) @ M ) ) ) @ M )
          = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ X ) ) @ M ) ) )
    = $true ),
    inference(copy,[status(thm)],[5682]) ).

thf(6378,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) @ ( hAPP_int_int @ uminus_uminus_int @ B_2 ) )
          = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5681]) ).

thf(6379,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ ( hAPP_int_int @ uminus_uminus_int @ B_2 ) )
          = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) @ B_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5680]) ).

thf(6380,plain,
    ( ( ! [Z_1: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ uminus_uminus_int @ Z_1 ) ) @ Z_1 )
          = zero_zero_int ) )
    = $true ),
    inference(copy,[status(thm)],[5679]) ).

thf(6381,plain,
    ( ( ! [Na: $i,Ma: $i] :
          ( ( Na != zero_zero_nat )
          | ( Ma != zero_zero_nat )
          | ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ Na ) )
            = ( hAPP_nat_int @ semiri1621563631at_int @ Ma ) ) )
      & ! [Na: $i] :
          ( ! [Ma: $i] :
              ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ Na ) )
             != ( hAPP_nat_int @ semiri1621563631at_int @ Ma ) )
          | ( Na = zero_zero_nat ) )
      & ! [Na: $i,Ma: $i] :
          ( ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ Na ) )
           != ( hAPP_nat_int @ semiri1621563631at_int @ Ma ) )
          | ( Ma = zero_zero_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[6017]) ).

thf(6382,plain,
    ( ( ! [Z_1: $i,W: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z_1 ) @ ( hAPP_int_int @ uminus_uminus_int @ W ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ Z_1 ) @ W ) ) )
    = $true ),
    inference(copy,[status(thm)],[5677]) ).

thf(6383,plain,
    ( ( ! [Z_1: $i,W: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ Z_1 ) @ W )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ Z_1 ) @ ( hAPP_int_int @ uminus_uminus_int @ W ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5676]) ).

thf(6384,plain,
    ( ( min
      = ( hAPP_int_int @ uminus_uminus_int @ one_one_int ) )
    = $true ),
    inference(copy,[status(thm)],[5675]) ).

thf(6385,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ K_2 ) ) @ L_2 )
            = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ K_2 ) @ L_2 )
           != zero_zero_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6016]) ).

thf(6386,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( ( hAPP_int_int @ ( div_mod_int @ K_2 ) @ ( hAPP_int_int @ uminus_uminus_int @ L_2 ) )
            = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ K_2 ) @ L_2 )
           != zero_zero_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6015]) ).

thf(6387,plain,
    ( ( ( hAPP_int_int @ uminus_uminus_int @ min )
      = ( hAPP_int_int @ bit1 @ pls ) )
    = $true ),
    inference(copy,[status(thm)],[5672]) ).

thf(6388,plain,
    ( ( ! [A_3: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5671]) ).

thf(6389,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ pred @ ( hAPP_int_int @ bit0 @ K_2 ) )
          = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ pred @ K_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5670]) ).

thf(6390,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ pred @ ( hAPP_int_int @ bit1 @ K_2 ) )
          = ( hAPP_int_int @ bit0 @ K_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5669]) ).

thf(6391,plain,
    ( ( ( hAPP_int_int @ pred @ pls )
      = min )
    = $true ),
    inference(copy,[status(thm)],[5668]) ).

thf(6392,plain,
    ( ( ( hAPP_int_int @ pred @ min )
      = ( hAPP_int_int @ bit0 @ min ) )
    = $true ),
    inference(copy,[status(thm)],[5667]) ).

thf(6393,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ pred @ K_2 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ K_2 ) @ one_one_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[5666]) ).

thf(6394,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ bit1 @ K_2 ) )
          = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ pred @ ( hAPP_int_int @ uminus_uminus_int @ K_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5665]) ).

thf(6395,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ K_2 ) @ min )
          = ( hAPP_int_int @ pred @ K_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5664]) ).

thf(6396,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ min ) @ K_2 )
          = ( hAPP_int_int @ pred @ K_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5663]) ).

thf(6397,plain,
    ( ( ! [K_2: $i,L_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ bit0 @ K_2 ) ) @ ( hAPP_int_int @ bit1 @ L_2 ) )
          = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ pred @ K_2 ) ) @ L_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5662]) ).

thf(6398,plain,
    ( ( ! [M: $i,N: $i] :
          ( ( xzgcd @ M @ N )
          = ( xzgcda @ M @ N @ M @ N @ one_one_int @ zero_zero_int @ zero_zero_int @ one_one_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[5661]) ).

thf(6399,plain,
    ( ( ( hAPP_int_int @ fact_fact_int @ one_one_int )
      = one_one_int )
    = $true ),
    inference(copy,[status(thm)],[5660]) ).

thf(6400,plain,
    ( ( ( hAPP_int_int @ fact_fact_int @ zero_zero_int )
      = one_one_int )
    = $true ),
    inference(copy,[status(thm)],[5659]) ).

thf(6401,plain,
    ( ( ! [M: $i,K_2: $i,N: $i] :
          ( ( ( hAPP_int_int @ ( legacy_zgcd @ K_2 ) @ N )
           != one_one_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ M ) ) @ N )
            = ( hAPP_int_int @ ( legacy_zgcd @ M ) @ N ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6014]) ).

thf(6402,plain,
    ( ( ! [N: $i,K_2: $i,M: $i] :
          ( ( ( hAPP_int_int @ ( legacy_zgcd @ K_2 ) @ M )
           != one_one_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ N ) @ M )
           != one_one_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ N ) ) @ M )
            = one_one_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6013]) ).

thf(6403,plain,
    ( ( ! [M: $i] :
          ( ( hAPP_int_int @ ( legacy_zgcd @ M ) @ one_one_int )
          = one_one_int ) )
    = $true ),
    inference(copy,[status(thm)],[5656]) ).

thf(6404,plain,
    ( ( ! [M: $i] :
          ( ( hAPP_int_int @ ( legacy_zgcd @ one_one_int ) @ M )
          = one_one_int ) )
    = $true ),
    inference(copy,[status(thm)],[5655]) ).

thf(6405,plain,
    ( ( ! [I_1: $i,J: $i] :
          ( ~ ( is_int @ I_1 )
          | ~ ( is_int @ J )
          | ( I_1 != zero_zero_int )
          | ( J != zero_zero_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ I_1 ) @ J )
            = zero_zero_int ) )
      & ! [I_1: $i,J: $i] :
          ( ~ ( is_int @ I_1 )
          | ~ ( is_int @ J )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ I_1 ) @ J )
           != zero_zero_int )
          | ( I_1 = zero_zero_int ) )
      & ! [I_1: $i,J: $i] :
          ( ~ ( is_int @ I_1 )
          | ~ ( is_int @ J )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ I_1 ) @ J )
           != zero_zero_int )
          | ( J = zero_zero_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6012]) ).

thf(6406,plain,
    ( ( ! [M: $i,N: $i] :
          ( ( hAPP_int_int @ ( legacy_zgcd @ M ) @ N )
          = ( hAPP_int_int @ ( legacy_zgcd @ N ) @ ( hAPP_int_int @ ( div_mod_int @ M ) @ N ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5653]) ).

thf(6407,plain,
    ( ( ! [A_3: $i,B_2: $i,N: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 ) ) @ N )
          = ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ N ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ N ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5652]) ).

thf(6408,plain,
    ( ( ! [I: $i,J_2: $i] :
          ( ( hAPP_int_int @ ( legacy_zgcd @ I ) @ J_2 )
          = ( hAPP_int_int @ ( legacy_zgcd @ J_2 ) @ I ) ) )
    = $true ),
    inference(copy,[status(thm)],[5651]) ).

thf(6409,plain,
    ( ( ! [K_2: $i,M: $i,N: $i] :
          ( ( hAPP_int_int @ ( legacy_zgcd @ K_2 ) @ ( hAPP_int_int @ ( legacy_zgcd @ M ) @ N ) )
          = ( hAPP_int_int @ ( legacy_zgcd @ M ) @ ( hAPP_int_int @ ( legacy_zgcd @ K_2 ) @ N ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5650]) ).

thf(6410,plain,
    ( ( ! [K_2: $i,M: $i,N: $i] :
          ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( legacy_zgcd @ K_2 ) @ M ) ) @ N )
          = ( hAPP_int_int @ ( legacy_zgcd @ K_2 ) @ ( hAPP_int_int @ ( legacy_zgcd @ M ) @ N ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5649]) ).

thf(6411,plain,
    ( ( ! [I: $i,J_2: $i] :
          ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ uminus_uminus_int @ I ) ) @ J_2 )
          = ( hAPP_int_int @ ( legacy_zgcd @ I ) @ J_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5648]) ).

thf(6412,plain,
    ( ( ! [I: $i,J_2: $i] :
          ( ( hAPP_int_int @ ( legacy_zgcd @ I ) @ ( hAPP_int_int @ uminus_uminus_int @ J_2 ) )
          = ( hAPP_int_int @ ( legacy_zgcd @ I ) @ J_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5647]) ).

thf(6413,plain,
    ( ( ! [M: $i,N: $i,K_2: $i] :
          ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ M ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ N ) @ K_2 ) ) ) @ N )
          = ( hAPP_int_int @ ( legacy_zgcd @ M ) @ N ) ) )
    = $true ),
    inference(copy,[status(thm)],[5646]) ).

thf(6414,plain,
    ( ( ! [N: $i,A_3: $i,B_2: $i] :
          ( ( ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 )
           != one_one_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ N ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ N ) )
            = one_one_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6011]) ).

thf(6415,plain,
    ( ( ! [N: $i,A_3: $i,B_2: $i] :
          ( ( ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 )
           != one_one_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ N ) ) @ B_2 )
            = one_one_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6010]) ).

thf(6416,plain,
    ( ( ! [M: $i] :
          ( ( hAPP_int_int @ ( legacy_zgcd @ zero_zero_int ) @ M )
          = ( hAPP_int_int @ abs_abs_int @ M ) ) )
    = $true ),
    inference(copy,[status(thm)],[5643]) ).

thf(6417,plain,
    ( ( ! [M: $i] :
          ( ( hAPP_int_int @ ( legacy_zgcd @ M ) @ zero_zero_int )
          = ( hAPP_int_int @ abs_abs_int @ M ) ) )
    = $true ),
    inference(copy,[status(thm)],[5642]) ).

thf(6418,plain,
    ( ( ! [Ma: $i] :
          ( ( ( hAPP_int_int @ ( legacy_zgcd @ zero_zero_int ) @ Ma )
           != one_one_int )
          | ( ( hAPP_int_int @ abs_abs_int @ Ma )
            = one_one_int ) )
      & ! [Ma: $i] :
          ( ( ( hAPP_int_int @ abs_abs_int @ Ma )
           != one_one_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ zero_zero_int ) @ Ma )
            = one_one_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6009]) ).

thf(6419,plain,
    ( ( ! [W: $i] :
          ( ( hAPP_int_int @ number_number_of_int @ W )
          = ( hAPP_int_int @ ring_1_of_int_int @ W ) ) )
    = $true ),
    inference(copy,[status(thm)],[5640]) ).

thf(6420,plain,
    ( ( ! [N: $i] :
          ( ( hAPP_int_int @ ring_1_of_int_int @ ( hAPP_nat_int @ semiri1621563631at_int @ N ) )
          = ( hAPP_nat_int @ semiri1621563631at_int @ N ) ) )
    = $true ),
    inference(copy,[status(thm)],[5639]) ).

thf(6421,plain,
    ( ( ! [A: $i,B: $i] :
          ( ( A != B )
          | ( ( image_nat_int @ semiri1621563631at_int @ A )
            = ( image_nat_int @ semiri1621563631at_int @ B ) ) )
      & ! [A: $i,B: $i] :
          ( ( ( image_nat_int @ semiri1621563631at_int @ A )
           != ( image_nat_int @ semiri1621563631at_int @ B ) )
          | ( A = B ) ) )
    = $true ),
    inference(copy,[status(thm)],[6008]) ).

thf(6422,plain,
    ( ( ! [Z_1: $i,W: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Z_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ W ) ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Z_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ W ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Z_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ W ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5637]) ).

thf(6423,plain,
    ( ( ! [N: $i,M: $i,A_3: $i,B_2: $i] :
          ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 )
           != one_one_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ N ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ M ) )
            = one_one_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6007]) ).

thf(6424,plain,
    ( ( ! [X: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ zero_zero_int )
          = ( hAPP_int_int @ abs_abs_int @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[5635]) ).

thf(6425,plain,
    ( ( ! [X: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ zero_zero_int ) @ X )
          = ( hAPP_int_int @ abs_abs_int @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[5634]) ).

thf(6426,plain,
    ( ( ! [M: $i,K_2: $i,N: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ M ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ M ) ) @ N ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ M ) @ N ) ) )
    = $true ),
    inference(copy,[status(thm)],[5633]) ).

thf(6427,plain,
    ( ( ! [M: $i,N: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ M ) @ N ) ) @ N )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ M ) @ N ) ) )
    = $true ),
    inference(copy,[status(thm)],[5632]) ).

thf(6428,plain,
    ( ( ! [M: $i,N: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ M ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ M ) @ N ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ M ) @ N ) ) )
    = $true ),
    inference(copy,[status(thm)],[5631]) ).

thf(6429,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ Y ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[5630]) ).

thf(6430,plain,
    ( ( ! [X: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ X )
          = ( hAPP_int_int @ abs_abs_int @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[5629]) ).

thf(6431,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ Y )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ abs_abs_int @ X ) ) @ ( hAPP_int_int @ abs_abs_int @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5628]) ).

thf(6432,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ ( hAPP_int_int @ abs_abs_int @ Y ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[5627]) ).

thf(6433,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ abs_abs_int @ X ) ) @ Y )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[5626]) ).

thf(6434,plain,
    ( ( ! [N: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ N ) @ one_one_int ) ) @ N )
          = one_one_int ) )
    = $true ),
    inference(copy,[status(thm)],[5625]) ).

thf(6435,plain,
    ( ( ! [N: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ N ) @ one_one_int ) ) @ N )
          = one_one_int ) )
    = $true ),
    inference(copy,[status(thm)],[5624]) ).

thf(6436,plain,
    ( ( ! [M: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ M ) @ one_one_int )
          = one_one_int ) )
    = $true ),
    inference(copy,[status(thm)],[5623]) ).

thf(6437,plain,
    ( ( ! [N: $i,D_3: $i,A_3: $i] :
          ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ A_3 )
           != one_one_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ N ) )
            = one_one_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6006]) ).

thf(6438,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ Y )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ Y ) @ ( hAPP_int_int @ ( div_mod_int @ X ) @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5621]) ).

thf(6439,plain,
    ( ( ! [A_3: $i,N: $i,B_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ N ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ N ) )
          = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) @ N ) ) )
    = $true ),
    inference(copy,[status(thm)],[5620]) ).

thf(6440,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ B_2 ) @ A_3 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5619]) ).

thf(6441,plain,
    ( ( ! [B_2: $i,A_3: $i,C_1: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ B_2 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ C_1 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ B_2 ) @ C_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5618]) ).

thf(6442,plain,
    ( ( ! [A_3: $i,B_2: $i,C_1: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) @ C_1 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ B_2 ) @ C_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5617]) ).

thf(6443,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ ( hAPP_int_int @ uminus_uminus_int @ Y ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[5616]) ).

thf(6444,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ uminus_uminus_int @ X ) ) @ Y )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[5615]) ).

thf(6445,plain,
    ( ( ! [Ma: $i,Na: $i] :
          ( ~ ( is_int @ Ma )
          | ~ ( is_int @ Na )
          | ( Ma != zero_zero_int )
          | ( Na != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ Ma ) @ Na )
            = zero_zero_int ) )
      & ! [Ma: $i,Na: $i] :
          ( ~ ( is_int @ Ma )
          | ~ ( is_int @ Na )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ Ma ) @ Na )
           != zero_zero_int )
          | ( Ma = zero_zero_int ) )
      & ! [Ma: $i,Na: $i] :
          ( ~ ( is_int @ Ma )
          | ~ ( is_int @ Na )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ Ma ) @ Na )
           != zero_zero_int )
          | ( Na = zero_zero_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6005]) ).

thf(6446,plain,
    ( ( ! [D_1: $i] :
          ( ! [A_1: $i,B_1: $i] :
              ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_1 ) @ A_1 )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_1 ) @ B_1 )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_1 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ B_1 ) )
                = one_one_int ) )
          & ! [A_1: $i] :
              ( ! [B_1: $i] :
                  ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_1 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ B_1 ) )
                 != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_1 ) @ A_1 )
                = one_one_int ) )
          & ! [A_1: $i,B_1: $i] :
              ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_1 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ B_1 ) )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_1 ) @ B_1 )
                = one_one_int ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6004]) ).

thf(6447,plain,
    ( ( ! [M: $i,K_2: $i,N: $i] :
          ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ K_2 ) @ N )
           != one_one_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ M ) ) @ N )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ M ) @ N ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[6003]) ).

thf(6448,plain,
    ( ( ! [B_2: $i,D_3: $i,A_3: $i] :
          ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ A_3 )
           != one_one_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ B_2 )
           != one_one_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ B_2 ) )
            = one_one_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6002]) ).

thf(6449,plain,
    ( ( ! [D_3: $i,A_3: $i] :
          ( ! [B_2: $i] :
              ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ B_2 ) )
             != one_one_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ A_3 )
            = one_one_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6001]) ).

thf(6450,plain,
    ( ( ! [D_3: $i,A_3: $i,B_2: $i] :
          ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ B_2 ) )
           != one_one_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ D_3 ) @ B_2 )
            = one_one_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[6000]) ).

thf(6451,plain,
    ( ( ! [B_5: $i,A_5: $i,A_3: $i,B_2: $i] :
          ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 )
            = zero_zero_int )
          | ( A_3
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_5 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) )
          | ( B_2
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_5 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_5 ) @ B_5 )
            = one_one_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[5999]) ).

thf(6452,plain,
    ( ( ! [P: $i] :
          ( ~ ( is_int @ P )
          | ( ( hAPP_int_int @ cOMBI_int @ P )
            = P ) ) )
    = $true ),
    inference(copy,[status(thm)],[5998]) ).

thf(6453,plain,
    ( ( ! [P: $i,Q: $i,R: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ ( hAPP_f2135977429nt_int @ cOMBC_int_int_int @ P ) @ Q ) @ R )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ P @ R ) @ Q ) ) )
    = $true ),
    inference(copy,[status(thm)],[5606]) ).

thf(6454,plain,
    ( ( ! [B_1_1: $i] : ( is_int @ ( archim856651990g_real @ B_1_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5605]) ).

thf(6455,plain,
    ( ( ! [B_1_1: $i] : ( is_int @ ( archim791455193or_rat @ B_1_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5604]) ).

thf(6456,plain,
    ( ( ! [B_1_1: $i] : ( is_int @ ( archim1246769320r_real @ B_1_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5603]) ).

thf(6457,plain,
    ( ( ! [B_1_1: $i,B_2_1: $i] : ( is_int @ ( big_co1548731110nt_int @ B_1_1 @ B_2_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5602]) ).

thf(6458,plain,
    ( ( ! [B_1_1: $i] : ( is_int @ ( code_int_of @ B_1_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5601]) ).

thf(6459,plain,
    ( ( ! [B_1_1: $i] : ( is_int @ ( the_int @ B_1_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5600]) ).

thf(6460,plain,
    ( ( ! [B_1_1: $i] : ( is_int @ ( hilbert_Eps_int @ B_1_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5599]) ).

thf(6461,plain,
    ( ( is_int @ min )
    = $true ),
    inference(copy,[status(thm)],[5598]) ).

thf(6462,plain,
    ( ( ! [B_1_1: $i] : ( is_int @ ( quickcheck_int_of @ B_1_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5597]) ).

thf(6463,plain,
    ( ( ! [B_1_1: $i,B_2_1: $i] : ( is_int @ ( hAPP_f1594865479ol_int @ B_1_1 @ B_2_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5596]) ).

thf(6464,plain,
    ( ( ! [B_1_1: $i,B_2_1: $i] : ( is_int @ ( hAPP_f659380387ol_int @ B_1_1 @ B_2_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5595]) ).

thf(6465,plain,
    ( ( ! [B_1_1: $i,B_2_1: $i] : ( is_int @ ( hAPP_P1175774780nt_int @ B_1_1 @ B_2_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5594]) ).

thf(6466,plain,
    ( ( is_int @ m )
    = $true ),
    inference(copy,[status(thm)],[5593]) ).

thf(6467,plain,
    ( ( is_int @ m1 )
    = $true ),
    inference(copy,[status(thm)],[5592]) ).

thf(6468,plain,
    ( ( is_int @ r )
    = $true ),
    inference(copy,[status(thm)],[5591]) ).

thf(6469,plain,
    ( ( is_int @ s1 )
    = $true ),
    inference(copy,[status(thm)],[5590]) ).

thf(6470,plain,
    ( ( is_int @ s )
    = $true ),
    inference(copy,[status(thm)],[5589]) ).

thf(6471,plain,
    ( ( is_int @ sa )
    = $true ),
    inference(copy,[status(thm)],[5588]) ).

thf(6472,plain,
    ( ( is_int @ t )
    = $true ),
    inference(copy,[status(thm)],[5587]) ).

thf(6473,plain,
    ( ( is_int @ v )
    = $true ),
    inference(copy,[status(thm)],[5586]) ).

thf(6474,plain,
    ( ( is_int @ w )
    = $true ),
    inference(copy,[status(thm)],[5585]) ).

thf(6475,plain,
    ( ( is_int @ x )
    = $true ),
    inference(copy,[status(thm)],[5584]) ).

thf(6476,plain,
    ( ( is_int @ y )
    = $true ),
    inference(copy,[status(thm)],[5583]) ).

thf(6477,plain,
    ( ( one_one_nat != zero_zero_nat )
    = $true ),
    inference(copy,[status(thm)],[5997]) ).

thf(6478,plain,
    ( ( zero_zero_nat != one_one_nat )
    = $true ),
    inference(copy,[status(thm)],[5996]) ).

thf(6479,plain,
    ( ( ( hAPP_nat_nat @ semiri984289939at_nat @ one_one_nat )
      = one_one_nat )
    = $true ),
    inference(copy,[status(thm)],[5580]) ).

thf(6480,plain,
    ( ( ( hAPP_nat_nat @ semiri984289939at_nat @ zero_zero_nat )
      = zero_zero_nat )
    = $true ),
    inference(copy,[status(thm)],[5579]) ).

thf(6481,plain,
    ( ( ! [Xa: $i] :
          ( ( zero_zero_nat != Xa )
          | ( Xa = zero_zero_nat ) )
      & ! [Xa: $i] :
          ( ( Xa != zero_zero_nat )
          | ( zero_zero_nat = Xa ) ) )
    = $true ),
    inference(copy,[status(thm)],[5995]) ).

thf(6482,plain,
    ( ( ! [Xa: $i] :
          ( ( one_one_nat != Xa )
          | ( Xa = one_one_nat ) )
      & ! [Xa: $i] :
          ( ( Xa != one_one_nat )
          | ( one_one_nat = Xa ) ) )
    = $true ),
    inference(copy,[status(thm)],[5994]) ).

thf(6483,plain,
    ( ( ! [A_75: $i] :
          ( ~ ( is_int @ A_75 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_75 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ pls ) ) )
            = A_75 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5993]) ).

thf(6484,plain,
    ( ( ! [A_74: $i] :
          ( ~ ( is_int @ A_74 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ pls ) ) ) @ A_74 )
            = A_74 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5992]) ).

thf(6485,plain,
    ( ( ( is_int @ sK13_X_1 )
      & ( is_int @ sK14_SY716 )
      & ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ sK13_X_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ sK14_SY716 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5991]) ).

thf(6486,plain,
    ( ( ! [M: $i] :
          ( ~ ( is_int @ M )
          | ! [N: $i] :
              ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ M ) @ N )
             != one_one_int )
          | ( M = one_one_int )
          | ( M
            = ( hAPP_int_int @ number_number_of_int @ min ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5990]) ).

thf(6487,plain,
    ( ( ! [Ma: $i,Na: $i] :
          ( ~ ( is_int @ Ma )
          | ~ ( is_int @ Na )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Ma ) @ Na )
           != one_one_int )
          | ( Ma = one_one_int )
          | ( Ma
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
      & ! [Ma: $i,Na: $i] :
          ( ~ ( is_int @ Ma )
          | ~ ( is_int @ Na )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Ma ) @ Na )
           != one_one_int )
          | ( Ma = one_one_int )
          | ( Na
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
      & ! [Ma: $i,Na: $i] :
          ( ~ ( is_int @ Ma )
          | ~ ( is_int @ Na )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Ma ) @ Na )
           != one_one_int )
          | ( Na = one_one_int )
          | ( Ma
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
      & ! [Ma: $i,Na: $i] :
          ( ~ ( is_int @ Ma )
          | ~ ( is_int @ Na )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Ma ) @ Na )
           != one_one_int )
          | ( Na = one_one_int )
          | ( Na
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
      & ! [Ma: $i,Na: $i] :
          ( ~ ( is_int @ Ma )
          | ~ ( is_int @ Na )
          | ( Ma != one_one_int )
          | ( Na != one_one_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Ma ) @ Na )
            = one_one_int ) )
      & ! [Ma: $i,Na: $i] :
          ( ~ ( is_int @ Ma )
          | ~ ( is_int @ Na )
          | ( Ma
           != ( hAPP_int_int @ number_number_of_int @ min ) )
          | ( Na
           != ( hAPP_int_int @ number_number_of_int @ min ) )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ Ma ) @ Na )
            = one_one_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[5989]) ).

thf(6488,plain,
    ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ s ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_int_int @ number_number_of_int @ min ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ s ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ one_one_int ) )
    = $true ),
    inference(copy,[status(thm)],[5571]) ).

thf(6489,plain,
    ( ( ! [A_1: $i,E_2: $i,C: $i] :
          ( ! [B_1: $i,D_1: $i] :
              ( ~ ( is_int @ D_1 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ E_2 ) ) @ C )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_1 ) @ E_2 ) ) @ D_1 ) )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_1 ) @ B_1 ) ) @ E_2 ) ) @ C )
                = D_1 ) )
          & ! [B_1: $i,D_1: $i] :
              ( ~ ( is_int @ D_1 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_1 ) @ B_1 ) ) @ E_2 ) ) @ C )
               != D_1 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ E_2 ) ) @ C )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_1 ) @ E_2 ) ) @ D_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5988]) ).

thf(6490,plain,
    ( ( ! [A_1: $i,E_2: $i,C: $i] :
          ( ( ~ ( is_int @ C )
            | ! [B_1: $i,D_1: $i] :
                ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ E_2 ) ) @ C )
                 != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_1 ) @ E_2 ) ) @ D_1 ) )
                | ( C
                  = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ B_1 ) @ A_1 ) ) @ E_2 ) ) @ D_1 ) ) ) )
          & ( ~ ( is_int @ C )
            | ! [B_1: $i,D_1: $i] :
                ( ( C
                 != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ B_1 ) @ A_1 ) ) @ E_2 ) ) @ D_1 ) )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_1 ) @ E_2 ) ) @ C )
                  = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_1 ) @ E_2 ) ) @ D_1 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5987]) ).

thf(6491,plain,
    ( ( ! [V_6: $i,B_21: $i,C_7: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ V_6 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ B_21 ) @ C_7 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ V_6 ) ) @ B_21 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ V_6 ) ) @ C_7 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5568]) ).

thf(6492,plain,
    ( ( ! [A_28: $i,B_20: $i,V_5: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_28 ) @ B_20 ) ) @ ( hAPP_int_int @ number_number_of_int @ V_5 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_28 ) @ ( hAPP_int_int @ number_number_of_int @ V_5 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_20 ) @ ( hAPP_int_int @ number_number_of_int @ V_5 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5567]) ).

thf(6493,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ K_2 ) @ min )
          = ( hAPP_int_int @ succ @ K_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5566]) ).

thf(6494,plain,
    ( ( ! [X_7: $i,Y_6: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ X_7 ) @ Y_6 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X_7 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ Y_6 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ X_7 ) ) @ Y_6 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5565]) ).

thf(6495,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_3 ) @ B_2 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) @ B_2 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ A_3 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5564]) ).

thf(6496,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_3 ) @ B_2 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ A_3 ) ) @ B_2 ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ B_2 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5563]) ).

thf(6497,plain,
    ( ( ! [Z_2: $i] :
          ( ~ ( is_int @ Z_2 )
          | ( ( hAPP_int_int @ abs_abs_int @ Z_2 )
           != one_one_int )
          | ( Z_2 = one_one_int )
          | ( Z_2
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
      & ! [Z_2: $i] :
          ( ~ ( is_int @ Z_2 )
          | ( Z_2 != one_one_int )
          | ( ( hAPP_int_int @ abs_abs_int @ Z_2 )
            = one_one_int ) )
      & ! [Z_2: $i] :
          ( ~ ( is_int @ Z_2 )
          | ( Z_2
           != ( hAPP_int_int @ number_number_of_int @ min ) )
          | ( ( hAPP_int_int @ abs_abs_int @ Z_2 )
            = one_one_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[5986]) ).

thf(6498,plain,
    ( ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ number_number_of_int @ min ) )
      = one_one_int )
    = $true ),
    inference(copy,[status(thm)],[5561]) ).

thf(6499,plain,
    ( ( ! [P_3: $i,X: $i] :
          ( ( hAPP_int_int @ ( multInv @ P_3 ) @ X )
          = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ X ) @ ( hAPP_int_nat @ nat @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ P_3 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5560]) ).

thf(6500,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( ( hAPP_nat_nat @ suc @ X )
           != ( hAPP_nat_nat @ suc @ Y ) )
          | ( X = Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[5985]) ).

thf(6501,plain,
    ( ( ! [Nat_5: $i,Nat_4: $i] :
          ( ( ( hAPP_nat_nat @ suc @ Nat_5 )
           != ( hAPP_nat_nat @ suc @ Nat_4 ) )
          | ( Nat_5 = Nat_4 ) )
      & ! [Nat_5: $i,Nat_4: $i] :
          ( ( Nat_5 != Nat_4 )
          | ( ( hAPP_nat_nat @ suc @ Nat_5 )
            = ( hAPP_nat_nat @ suc @ Nat_4 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5984]) ).

thf(6502,plain,
    ( ( ! [N: $i] :
          ( ( hAPP_nat_nat @ suc @ N )
         != N ) )
    = $true ),
    inference(copy,[status(thm)],[5983]) ).

thf(6503,plain,
    ( ( ! [N: $i] :
          ( N
         != ( hAPP_nat_nat @ suc @ N ) ) )
    = $true ),
    inference(copy,[status(thm)],[5982]) ).

thf(6504,plain,
    ( ( ! [M: $i] :
          ( zero_zero_nat
         != ( hAPP_nat_nat @ suc @ M ) ) )
    = $true ),
    inference(copy,[status(thm)],[5981]) ).

thf(6505,plain,
    ( ( ! [Nat_3: $i] :
          ( zero_zero_nat
         != ( hAPP_nat_nat @ suc @ Nat_3 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5980]) ).

thf(6506,plain,
    ( ( ! [M: $i] :
          ( ( hAPP_nat_nat @ suc @ M )
         != zero_zero_nat ) )
    = $true ),
    inference(copy,[status(thm)],[5979]) ).

thf(6507,plain,
    ( ( ! [Nat_2: $i] :
          ( ( hAPP_nat_nat @ suc @ Nat_2 )
         != zero_zero_nat ) )
    = $true ),
    inference(copy,[status(thm)],[5978]) ).

thf(6508,plain,
    ( ( ! [M: $i] :
          ( zero_zero_nat
         != ( hAPP_nat_nat @ suc @ M ) ) )
    = $true ),
    inference(copy,[status(thm)],[5977]) ).

thf(6509,plain,
    ( ( ! [M: $i] :
          ( ( hAPP_nat_nat @ suc @ M )
         != zero_zero_nat ) )
    = $true ),
    inference(copy,[status(thm)],[5976]) ).

thf(6510,plain,
    ( ( ! [Ma: $i] :
          ( ~ ( is_int @ Ma )
          | ! [D_1: $i] :
              ( ( ( hAPP_int_int @ ( div_mod_int @ Ma ) @ D_1 )
               != zero_zero_int )
              | ( ( Ma
                  = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ D_1 ) @ ( sK12_Q_4 @ D_1 @ Ma ) ) )
                & ( is_int @ ( sK12_Q_4 @ D_1 @ Ma ) ) ) ) )
      & ! [Ma: $i] :
          ( ~ ( is_int @ Ma )
          | ! [D_1: $i] :
              ( ! [Q_4: $i] :
                  ( ( Ma
                   != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ D_1 ) @ Q_4 ) )
                  | ~ ( is_int @ Q_4 ) )
              | ( ( hAPP_int_int @ ( div_mod_int @ Ma ) @ D_1 )
                = zero_zero_int ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5975]) ).

thf(6511,plain,
    ( ( ! [A_3: $i] :
          ( ~ ( is_int @ A_3 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ zero_zero_int )
            = zero_zero_int ) )
      & ! [A_3: $i] :
          ( ~ ( is_int @ A_3 )
          | ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ zero_zero_int )
            = A_3 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5974]) ).

thf(6512,plain,
    ( ( one_one_nat
      = ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
    = $true ),
    inference(copy,[status(thm)],[5547]) ).

thf(6513,plain,
    ( ( ! [A_3: $i] :
          ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ ( hAPP_int_int @ number_number_of_int @ min ) )
          = zero_zero_int ) )
    = $true ),
    inference(copy,[status(thm)],[5546]) ).

thf(6514,plain,
    ( ( ! [A_3: $i] :
          ( ~ ( is_int @ A_3 )
          | ! [B_2: $i] :
              ( A_3
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_2 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ B_2 ) ) ) @ ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5973]) ).

thf(6515,plain,
    ( ( ! [A_3: $i,B_2: $i,C_1: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ B_2 ) ) @ C_1 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ B_2 ) @ C_1 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ A_3 ) @ ( hAPP_int_int @ ( div_mod_int @ B_2 ) @ C_1 ) ) ) @ C_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5544]) ).

thf(6516,plain,
    ( ( ! [B_2: $i,A_3: $i,K_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ B_2 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ B_2 ) ) ) @ ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 ) ) ) @ K_2 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_3 ) @ K_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5543]) ).

thf(6517,plain,
    ( ( ! [A_3: $i,B_2: $i,K_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ B_2 ) ) @ B_2 ) ) @ ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 ) ) ) @ K_2 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ A_3 ) @ K_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5542]) ).

thf(6518,plain,
    ( ( ! [N: $i,M: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ N ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ M ) @ N ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ M ) @ ( hAPP_int_int @ ( div_mod_int @ M ) @ N ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5541]) ).

thf(6519,plain,
    ( ( ! [M: $i,N: $i] :
          ( ( hAPP_int_int @ ( div_mod_int @ M ) @ N )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ M ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ M ) @ N ) ) @ N ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5540]) ).

thf(6520,plain,
    ( ( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
      = one_one_int )
    = $true ),
    inference(copy,[status(thm)],[5539]) ).

thf(6521,plain,
    ( ( ( hAPP_int_nat @ nat @ one_one_int )
      = ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
    = $true ),
    inference(copy,[status(thm)],[5538]) ).

thf(6522,plain,
    ( ( ! [R_2: $i,S_1: $i,T_1: $i,R_4: $i,S_3: $i,M: $i,T_2: $i,N: $i] :
          ( ( R_4
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ S_3 ) @ M ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ T_2 ) @ N ) ) )
          | ( R_2
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ S_1 ) @ M ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ T_1 ) @ N ) ) )
          | ( ( hAPP_int_int @ ( div_mod_int @ R_4 ) @ R_2 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ S_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ R_4 ) @ R_2 ) ) @ S_1 ) ) ) @ M ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ T_2 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ R_4 ) @ R_2 ) ) @ T_1 ) ) ) @ N ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5972]) ).

thf(6523,plain,
    ( ( ! [A_3: $i,B_2: $i,M: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ A_3 ) @ B_2 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ M ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ M ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ B_2 ) @ M ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ M ) ) @ ( hAPP_int_int @ ( div_mod_int @ B_2 ) @ M ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5536]) ).

thf(6524,plain,
    ( ( ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) )
      = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5535]) ).

thf(6525,plain,
    ( ( ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ pls ) )
      = ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
    = $true ),
    inference(copy,[status(thm)],[5534]) ).

thf(6526,plain,
    ( ( ! [V_1: $i,W: $i] :
          ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ V_1 ) ) ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ W ) ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ number_number_of_int @ V_1 ) ) @ ( hAPP_int_int @ number_number_of_int @ W ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5533]) ).

thf(6527,plain,
    ( ( ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) )
      = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[5532]) ).

thf(6528,plain,
    ( ( ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
      = ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5531]) ).

thf(6529,plain,
    ( ( ( hAPP_int_nat @ nat @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
      = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[5530]) ).

thf(6530,plain,
    ( ( ! [P_3: $i,A_3: $i] :
          ( ( hAPP_int_int @ ( inv @ P_3 ) @ A_3 )
          = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ A_3 ) @ ( hAPP_int_nat @ nat @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ P_3 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) ) @ P_3 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5529]) ).

thf(6531,plain,
    ( ( ! [M_5: $i] :
          ( ~ ( is_int @ M_5 )
          | ! [D_4: $i] :
              ( ( ( hAPP_int_int @ ( div_mod_int @ M_5 ) @ D_4 )
               != zero_zero_int )
              | ( ( M_5
                  = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ D_4 ) @ ( sK11_Q_4 @ D_4 @ M_5 ) ) )
                & ( is_int @ ( sK11_Q_4 @ D_4 @ M_5 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5971]) ).

thf(6532,plain,
    ( ( ! [M: $i,N: $i] :
          ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ M ) ) @ N )
          = ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ N ) ) ) @ N ) ) )
    = $true ),
    inference(copy,[status(thm)],[5527]) ).

thf(6533,plain,
    ( ( ! [M: $i] :
          ( ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
          = zero_zero_nat ) )
    = $true ),
    inference(copy,[status(thm)],[5526]) ).

thf(6534,plain,
    ( ( ! [M: $i,N: $i] :
          ( ( ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ N ) )
           != N )
          | ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ M ) ) @ N )
            = zero_zero_nat ) )
      & ! [M: $i,N: $i] :
          ( ( ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ N ) )
            = N )
          | ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ M ) ) @ N )
            = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ N ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5970]) ).

thf(6535,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_nat_int @ semiri1621563631at_int @ X ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ Y ) )
          = ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( div_mod_nat @ X ) @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5524]) ).

thf(6536,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( div_mod_nat @ A_3 ) @ B_2 ) )
          = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_nat_int @ semiri1621563631at_int @ A_3 ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ B_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5523]) ).

thf(6537,plain,
    ( ( ! [M: $i] :
          ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ suc @ M ) ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5522]) ).

thf(6538,plain,
    ( ( ! [M: $i] :
          ( ( ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
            = ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          | ( ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
            = ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          | ( ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
            = zero_zero_nat )
          | ( ( hAPP_nat_nat @ ( div_mod_nat @ M ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
            = one_one_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[5969]) ).

thf(6539,plain,
    ( ( ! [K_2: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ min ) @ K_2 )
          = ( hAPP_int_int @ uminus_uminus_int @ K_2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5520]) ).

thf(6540,plain,
    ( ( ! [N: $i] :
          ( ( hAPP_int_nat @ nat @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ N ) ) )
          = zero_zero_nat ) )
    = $true ),
    inference(copy,[status(thm)],[5519]) ).

thf(6541,plain,
    ( ( ! [V_1: $i,W: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ number_number_of_int @ V_1 ) ) @ ( hAPP_int_int @ number_number_of_int @ W ) )
          = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ V_1 ) @ ( hAPP_int_int @ uminus_uminus_int @ W ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5518]) ).

thf(6542,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
           != zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) @ B_2 )
            = zero_zero_int ) )
      & ! [A_3: $i,B_2: $i] :
          ( ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
            = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) @ B_2 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ B_2 ) @ ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5968]) ).

thf(6543,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
           != zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ ( hAPP_int_int @ uminus_uminus_int @ B_2 ) )
            = zero_zero_int ) )
      & ! [A_3: $i,B_2: $i] :
          ( ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
            = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ ( hAPP_int_int @ uminus_uminus_int @ B_2 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 ) ) @ B_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5967]) ).

thf(6544,plain,
    ( ( ! [A_3: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ ( hAPP_int_int @ number_number_of_int @ min ) )
          = ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) )
    = $true ),
    inference(copy,[status(thm)],[5515]) ).

thf(6545,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ~ ( is_int @ B_2 )
          | ( B_2 = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
           != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ ( hAPP_int_int @ uminus_uminus_int @ B_2 ) )
            = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ B_2 ) ) ) )
      & ! [A_3: $i,B_2: $i] :
          ( ~ ( is_int @ B_2 )
          | ( B_2 = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
            = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ ( hAPP_int_int @ uminus_uminus_int @ B_2 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ B_2 ) ) ) @ one_one_int ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5966]) ).

thf(6546,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ~ ( is_int @ B_2 )
          | ( B_2 = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
           != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) @ B_2 )
            = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ B_2 ) ) ) )
      & ! [A_3: $i,B_2: $i] :
          ( ~ ( is_int @ B_2 )
          | ( B_2 = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ A_3 ) @ B_2 )
            = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ A_3 ) ) @ B_2 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ B_2 ) ) ) @ one_one_int ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5965]) ).

thf(6547,plain,
    ( ( ! [N: $i] :
          ( ( hAPP_nat_nat @ fact_fact_nat @ N )
         != zero_zero_nat ) )
    = $true ),
    inference(copy,[status(thm)],[5964]) ).

thf(6548,plain,
    ( ( ( hAPP_nat_nat @ fact_fact_nat @ one_one_nat )
      = one_one_nat )
    = $true ),
    inference(copy,[status(thm)],[5511]) ).

thf(6549,plain,
    ( ( ( hAPP_nat_nat @ fact_fact_nat @ zero_zero_nat )
      = ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
    = $true ),
    inference(copy,[status(thm)],[5510]) ).

thf(6550,plain,
    ( ( ( hAPP_nat_nat @ fact_fact_nat @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
      = ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
    = $true ),
    inference(copy,[status(thm)],[5509]) ).

thf(6551,plain,
    ( ( ! [N: $i] :
          ( ( N = zero_zero_nat )
          | ( N
            = ( hAPP_nat_nat @ suc @ ( sK10_M_1 @ N ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5963]) ).

thf(6552,plain,
    ( ( ! [Y: $i] :
          ( ( Y = zero_zero_nat )
          | ( Y
            = ( hAPP_nat_nat @ suc @ ( sK9_Nat_1 @ Y ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5962]) ).

thf(6553,plain,
    ( ( ! [X: $i] :
          ( ~ ( is_int @ X )
          | ( ( hAPP_int_int @ succ @ ( hAPP_int_int @ pred @ X ) )
            = X ) ) )
    = $true ),
    inference(copy,[status(thm)],[5961]) ).

thf(6554,plain,
    ( ( ! [N: $i] :
          ( ( hAPP_nat_nat @ size_size_nat @ N )
          = N ) )
    = $true ),
    inference(copy,[status(thm)],[5505]) ).

thf(6555,plain,
    ( ( ( hAPP_nat_nat @ size_size_nat @ zero_zero_nat )
      = zero_zero_nat )
    = $true ),
    inference(copy,[status(thm)],[5504]) ).

thf(6556,plain,
    ( ( ( hAPP_nat_nat @ nat_size @ zero_zero_nat )
      = zero_zero_nat )
    = $true ),
    inference(copy,[status(thm)],[5503]) ).

thf(6557,plain,
    ( ( ! [X: $i] :
          ( ( hAPP_int_int @ fact_fact_int @ ( hAPP_nat_int @ semiri1621563631at_int @ X ) )
          = ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ fact_fact_nat @ X ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5502]) ).

thf(6558,plain,
    ( ( ! [K_2: $i,M: $i,N: $i] :
          ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ M ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ N ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ K_2 ) ) @ ( hAPP_int_int @ ( legacy_zgcd @ M ) @ N ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5501]) ).

thf(6559,plain,
    ( ( ! [B_2: $i,A_3: $i] :
          ( ~ ( is_int @ B_2 )
          | ~ ( is_int @ A_3 )
          | ( A_3 = zero_zero_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ B_2 ) @ ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 ) ) )
            = one_one_int ) )
      & ! [B_2: $i,A_3: $i] :
          ( ~ ( is_int @ B_2 )
          | ~ ( is_int @ A_3 )
          | ( B_2 = zero_zero_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ B_2 ) @ ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 ) ) )
            = one_one_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[5960]) ).

thf(6560,plain,
    ( ( ! [B_2: $i,A_3: $i] :
          ( ~ ( is_int @ B_2 )
          | ~ ( is_int @ A_3 )
          | ( A_3 = zero_zero_int )
          | ( ( is_int @ ( sK7_C_3 @ A_3 @ B_2 ) )
            & ( is_int @ ( sK8_SY715 @ A_3 @ B_2 ) )
            & ( A_3
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 ) ) @ ( sK7_C_3 @ A_3 @ B_2 ) ) )
            & ( B_2
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 ) ) @ ( sK8_SY715 @ A_3 @ B_2 ) ) )
            & ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK7_C_3 @ A_3 @ B_2 ) ) @ ( sK8_SY715 @ A_3 @ B_2 ) )
              = one_one_int ) ) )
      & ! [B_2: $i,A_3: $i] :
          ( ~ ( is_int @ B_2 )
          | ~ ( is_int @ A_3 )
          | ( B_2 = zero_zero_int )
          | ( ( is_int @ ( sK5_C_3 @ A_3 @ B_2 ) )
            & ( is_int @ ( sK6_SY714 @ A_3 @ B_2 ) )
            & ( A_3
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 ) ) @ ( sK5_C_3 @ A_3 @ B_2 ) ) )
            & ( B_2
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ A_3 ) @ B_2 ) ) @ ( sK6_SY714 @ A_3 @ B_2 ) ) )
            & ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK5_C_3 @ A_3 @ B_2 ) ) @ ( sK6_SY714 @ A_3 @ B_2 ) )
              = one_one_int ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5959]) ).

thf(6561,plain,
    ( ( ! [Z_1: $i] :
          ( ~ ( is_int @ Z_1 )
          | ( Z_1
            = ( hAPP_nat_int @ semiri1621563631at_int @ ( sK4_N_1 @ Z_1 ) ) )
          | ( Z_1
            = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ suc @ ( sK3_N_1 @ Z_1 ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5958]) ).

thf(6562,plain,
    ( ( ( hAPP_nat_nat @ fact @ zero_zero_nat )
      = one_one_nat )
    = $true ),
    inference(copy,[status(thm)],[5497]) ).

thf(6563,plain,
    ( ( ! [A: $i] :
          ( ( image_int_nat @ nat @ ( image_nat_int @ semiri1621563631at_int @ A ) )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[5496]) ).

thf(6564,plain,
    ( ( ! [B_2: $i,A_3: $i] :
          ( ~ ( is_int @ B_2 )
          | ~ ( is_int @ A_3 )
          | ( A_3 = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ B_2 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) )
            = one_one_int ) )
      & ! [B_2: $i,A_3: $i] :
          ( ~ ( is_int @ B_2 )
          | ~ ( is_int @ A_3 )
          | ( B_2 = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ A_3 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ B_2 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) )
            = one_one_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[5957]) ).

thf(6565,plain,
    ( ( ! [K_2: $i,M: $i,N: $i] :
          ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ K_2 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ M ) @ N ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ M ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ K_2 ) @ N ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5494]) ).

thf(6566,plain,
    ( ( ! [X: $i,Y: $i,M: $i] :
          ( ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ X ) @ Y ) ) @ M )
           != one_one_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ X ) @ M )
            = one_one_int ) ) )
    = $true ),
    inference(copy,[status(thm)],[5956]) ).

thf(6567,plain,
    ( ( ! [B_1: $i,C: $i] :
          ( ! [A_1: $i,D_1: $i] :
              ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_1 ) @ D_1 )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ B_1 ) @ C )
               != one_one_int )
              | ( ( hAPP_int_int @ abs_abs_int @ A_1 )
               != ( hAPP_int_int @ abs_abs_int @ B_1 ) )
              | ( ( hAPP_int_int @ abs_abs_int @ C )
               != ( hAPP_int_int @ abs_abs_int @ D_1 ) )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ A_1 ) ) @ ( hAPP_int_int @ abs_abs_int @ C ) )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ B_1 ) ) @ ( hAPP_int_int @ abs_abs_int @ D_1 ) ) ) )
          & ! [A_1: $i,D_1: $i] :
              ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_1 ) @ D_1 )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ B_1 ) @ C )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ A_1 ) ) @ ( hAPP_int_int @ abs_abs_int @ C ) )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ B_1 ) ) @ ( hAPP_int_int @ abs_abs_int @ D_1 ) ) )
              | ( ( hAPP_int_int @ abs_abs_int @ A_1 )
                = ( hAPP_int_int @ abs_abs_int @ B_1 ) ) )
          & ! [A_1: $i,D_1: $i] :
              ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_1 ) @ D_1 )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ B_1 ) @ C )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ A_1 ) ) @ ( hAPP_int_int @ abs_abs_int @ C ) )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ B_1 ) ) @ ( hAPP_int_int @ abs_abs_int @ D_1 ) ) )
              | ( ( hAPP_int_int @ abs_abs_int @ C )
                = ( hAPP_int_int @ abs_abs_int @ D_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5955]) ).

thf(6568,plain,
    ( ( ! [A_3: $i,B_2: $i] :
          ( ~ ( is_int @ A_3 )
          | ~ ( is_int @ B_2 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 )
            = zero_zero_int )
          | ( ( is_int @ ( sK1_A_4 @ B_2 @ A_3 ) )
            & ( is_int @ ( sK2_SY713 @ B_2 @ A_3 ) )
            & ( A_3
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK1_A_4 @ B_2 @ A_3 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) )
            & ( B_2
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK2_SY713 @ B_2 @ A_3 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ A_3 ) @ B_2 ) ) )
            & ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( sK1_A_4 @ B_2 @ A_3 ) ) @ ( sK2_SY713 @ B_2 @ A_3 ) )
              = one_one_int ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[5954]) ).

thf(6569,plain,
    ( ( ! [P: $i] :
          ( ( hAPP_nat_nat @ cOMBI_nat @ P )
          = P ) )
    = $true ),
    inference(copy,[status(thm)],[5490]) ).

thf(6570,plain,
    ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
      = zero_zero_int )
    = $true ),
    inference(copy,[status(thm)],[5953]) ).

thf(6571,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ( ( hAPP_int_int @ ( legacy_zgcd @ zero_zero_int ) @ SX0 )
                 != one_one_int )
                | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
                  = one_one_int ) )
          | ~ ! [SX0: $i] :
                ( ( ( hAPP_int_int @ abs_abs_int @ SX0 )
                 != one_one_int )
                | ( ( hAPP_int_int @ ( legacy_zgcd @ zero_zero_int ) @ SX0 )
                  = one_one_int ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6418]) ).

thf(6572,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ( one_one_int != SX0 )
                | ( SX0 = one_one_int ) )
          | ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ( SX0 != one_one_int )
                | ( one_one_int = SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6214]) ).

thf(6573,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
                 != zero_zero_int )
                | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ ( hAPP_int_int @ uminus_uminus_int @ SX1 ) )
                  = zero_zero_int ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
                  = zero_zero_int )
                | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ ( hAPP_int_int @ uminus_uminus_int @ SX1 ) )
                  = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 ) ) @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6543]) ).

thf(6574,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ( SX0 != SX1 )
                | ( ( image_nat_int @ semiri1621563631at_int @ SX0 )
                  = ( image_nat_int @ semiri1621563631at_int @ SX1 ) ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ( ( image_nat_int @ semiri1621563631at_int @ SX0 )
                 != ( image_nat_int @ semiri1621563631at_int @ SX1 ) )
                | ( SX0 = SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6421]) ).

thf(6575,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
                  = zero_zero_int )
                | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
                  = one_one_int ) )
          | ~ ! [SX0: $i] :
                ( ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
                 != one_one_int )
                | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
                 != zero_zero_int ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6366]) ).

thf(6576,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ( SX0 != zero_zero_nat )
                | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ SX0 )
                  = one_one_int ) )
          | ~ ! [SX0: $i] :
                ( ( SX0 = zero_zero_nat )
                | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ SX0 )
                  = zero_zero_int ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6182]) ).

thf(6577,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ( ( hAPP_int_nat @ number_number_of_nat @ SX0 )
                 != zero_zero_nat )
                | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ ( hAPP_int_nat @ number_number_of_nat @ SX0 ) )
                  = one_one_int ) )
          | ~ ! [SX0: $i] :
                ( ( ( hAPP_int_nat @ number_number_of_nat @ SX0 )
                  = zero_zero_nat )
                | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ ( hAPP_int_nat @ number_number_of_nat @ SX0 ) )
                  = zero_zero_int ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6122]) ).

thf(6578,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ( pls
                 != ( hAPP_int_int @ bit0 @ SX0 ) )
                | ( pls = SX0 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ( pls != SX0 )
                | ( pls
                  = ( hAPP_int_int @ bit0 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6150]) ).

thf(6579,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
                 != zero_zero_int )
                | ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ SX0 ) ) @ SX1 )
                  = zero_zero_int ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
                  = zero_zero_int )
                | ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ SX0 ) ) @ SX1 )
                  = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SX1 ) @ ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6542]) ).

thf(6580,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                 != zero_zero_int )
                | ( SX0 = zero_zero_int )
                | ( SX1 = zero_zero_int ) )
          | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                      ( ~ ( is_int @ SX0 )
                      | ~ ( is_int @ SX1 )
                      | ( SX0 != zero_zero_int )
                      | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                        = zero_zero_int ) )
                | ~ ! [SX0: $i,SX1: $i] :
                      ( ~ ( is_int @ SX0 )
                      | ~ ( is_int @ SX1 )
                      | ( SX1 != zero_zero_int )
                      | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                        = zero_zero_int ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6245]) ).

thf(6581,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ! [SX1: $i] :
                    ( ( ( hAPP_int_nat @ number_number_of_nat @ SX1 )
                      = zero_zero_nat )
                    | ( SX0 != zero_zero_int )
                    | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ SX1 ) )
                      = zero_zero_int ) ) )
          | ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( is_int @ SX0 )
                      | ! [SX1: $i] :
                          ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ SX1 ) )
                           != zero_zero_int )
                          | ( ( hAPP_int_nat @ number_number_of_nat @ SX1 )
                           != zero_zero_nat ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( is_int @ SX0 )
                      | ! [SX1: $i] :
                          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ SX1 ) )
                         != zero_zero_int )
                      | ( SX0 = zero_zero_int ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6166]) ).

thf(6582,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ! [SX1: $i] :
              ( ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
               != zero_zero_int )
              | ~ ( ( SX0
                   != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX1 ) @ ( sK11_Q_4 @ SX1 @ SX0 ) ) )
                  | ~ ( is_int @ ( sK11_Q_4 @ SX1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6531]) ).

thf(6583,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
                 != ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
                | ( SX0 = SX1 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ( SX0 != SX1 )
                | ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
                  = ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6186]) ).

thf(6584,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ( zero_zero_nat != SX0 )
                | ( SX0 = zero_zero_nat ) )
          | ~ ! [SX0: $i] :
                ( ( SX0 != zero_zero_nat )
                | ( zero_zero_nat = SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6481]) ).

thf(6585,plain,
    ( ( ~ ( ~ ~ ( ~ ( is_int @ sK13_X_1 )
                | ~ ( is_int @ sK14_SY716 ) )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ sK13_X_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ sK14_SY716 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6485]) ).

thf(6586,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX1 )
                | ( SX1 = zero_zero_int )
                | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
                 != zero_zero_int )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ SX0 ) ) @ SX1 )
                  = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ SX1 ) ) ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX1 )
                | ( SX1 = zero_zero_int )
                | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
                  = zero_zero_int )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ SX0 ) ) @ SX1 )
                  = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ SX1 ) ) ) @ one_one_int ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6546]) ).

thf(6587,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
                 != zero_zero_int )
                | ( SX0 = zero_zero_int ) )
          | ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ( SX0 != zero_zero_int )
                | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
                  = zero_zero_int ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6328]) ).

thf(6588,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ( ( hAPP_int_int @ bit1 @ SX0 )
                 != min )
                | ( SX0 = min ) )
          | ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ( SX0 != min )
                | ( ( hAPP_int_int @ bit1 @ SX0 )
                  = min ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6294]) ).

thf(6589,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX0 ) @ SX1 )
            = zero_zero_int )
          | ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK1_A_4 @ SX1 @ SX0 ) )
                                | ~ ( is_int @ ( sK2_SY713 @ SX1 @ SX0 ) ) )
                          | ( SX0
                           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK1_A_4 @ SX1 @ SX0 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX0 ) @ SX1 ) ) ) )
                    | ( SX1
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK2_SY713 @ SX1 @ SX0 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX0 ) @ SX1 ) ) ) )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( sK1_A_4 @ SX1 @ SX0 ) ) @ ( sK2_SY713 @ SX1 @ SX0 ) )
               != one_one_int ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6568]) ).

thf(6590,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( ( hAPP_int_int @ number_number_of_int @ SX0 )
                 != ( hAPP_int_int @ number_number_of_int @ SX1 ) )
                | ( SX0 = SX1 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( SX0 != SX1 )
                | ( ( hAPP_int_int @ number_number_of_int @ SX0 )
                  = ( hAPP_int_int @ number_number_of_int @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6135]) ).

thf(6591,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
                 != ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
                | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
                  = ( hAPP_int_int @ abs_abs_int @ SX1 ) ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ( ( hAPP_int_int @ abs_abs_int @ SX0 )
                 != ( hAPP_int_int @ abs_abs_int @ SX1 ) )
                | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
                  = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6348]) ).

thf(6592,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ! [SX1: $i] :
                    ( ( SX1 = zero_zero_nat )
                    | ( SX0 != zero_zero_int )
                    | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ SX1 )
                      = zero_zero_int ) ) )
          | ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( is_int @ SX0 )
                      | ! [SX1: $i] :
                          ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ SX1 )
                           != zero_zero_int )
                          | ( SX1 != zero_zero_nat ) ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( is_int @ SX0 )
                      | ! [SX1: $i] :
                          ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ SX1 )
                         != zero_zero_int )
                      | ( SX0 = zero_zero_int ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6194]) ).

thf(6593,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ! [SX2: $i,SX3: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ~ ( is_int @ SX2 )
                  | ~ ( is_int @ SX3 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX2 ) @ SX3 ) )
                   != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX3 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX2 ) @ SX1 ) ) )
                  | ( SX0 = SX2 )
                  | ( SX1 = SX3 ) )
            | ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
                        ( ~ ( is_int @ SX0 )
                        | ~ ( is_int @ SX1 )
                        | ~ ( is_int @ SX2 )
                        | ~ ( is_int @ SX3 )
                        | ( SX0 != SX2 )
                        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX2 ) @ SX3 ) )
                          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX3 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX2 ) @ SX1 ) ) ) )
                  | ~ ! [SX2: $i,SX3: $i] :
                        ( ~ ( is_int @ SX0 )
                        | ~ ( is_int @ SX1 )
                        | ~ ( is_int @ SX2 )
                        | ~ ( is_int @ SX3 )
                        | ( SX1 != SX3 )
                        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX2 ) @ SX3 ) )
                          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX3 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX2 ) @ SX1 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6256]) ).

thf(6594,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( SX0
                 != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX0 ) @ SX1 ) )
                | ( SX1 = zero_zero_int ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( SX1 != zero_zero_int )
                | ( SX0
                  = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX0 ) @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6218]) ).

thf(6595,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ( ( hAPP_int_nat @ number_number_of_nat @ SX0 )
                 != SX1 )
                | ( SX1
                  = ( hAPP_int_nat @ number_number_of_nat @ SX0 ) ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ( SX1
                 != ( hAPP_int_nat @ number_number_of_nat @ SX0 ) )
                | ( ( hAPP_int_nat @ number_number_of_nat @ SX0 )
                  = SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6137]) ).

thf(6596,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ( zero_zero_int != SX0 )
                | ( SX0 = zero_zero_int ) )
          | ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ( SX0 != zero_zero_int )
                | ( zero_zero_int = SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6198]) ).

thf(6597,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( is_int @ SX1 )
                  | ~ ( is_int @ SX2 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX0 ) @ SX1 )
                   != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX0 ) @ SX2 ) )
                  | ( SX1 = SX2 ) )
            | ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( is_int @ SX1 )
                  | ~ ( is_int @ SX2 )
                  | ( SX1 != SX2 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX0 ) @ SX1 )
                    = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX0 ) @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6207]) ).

thf(6598,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( SX1 = zero_zero_int )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX1 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX1 ) @ SX0 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX1 ) @ SX0 ) ) )
                  = one_one_int ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( SX0 = zero_zero_int )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX1 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX1 ) @ SX0 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX1 ) @ SX0 ) ) )
                  = one_one_int ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6564]) ).

thf(6599,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( ( hAPP_int_int @ bit1 @ SX0 )
                 != ( hAPP_int_int @ bit1 @ SX1 ) )
                | ( SX0 = SX1 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( SX0 != SX1 )
                | ( ( hAPP_int_int @ bit1 @ SX0 )
                  = ( hAPP_int_int @ bit1 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6138]) ).

thf(6600,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ( SX0 != zero_zero_nat )
                | ( SX1 != zero_zero_nat )
                | ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SX0 ) )
                  = ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) ) )
          | ~ ~ ( ~ ! [SX0: $i] :
                      ( ! [SX1: $i] :
                          ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SX0 ) )
                         != ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
                      | ( SX0 = zero_zero_nat ) )
                | ~ ! [SX0: $i,SX1: $i] :
                      ( ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SX0 ) )
                       != ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
                      | ( SX1 = zero_zero_nat ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6381]) ).

thf(6601,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( SX1 = zero_zero_int )
                | ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK7_C_3 @ SX1 @ SX0 ) )
                                      | ~ ( is_int @ ( sK8_SY715 @ SX1 @ SX0 ) ) )
                                | ( SX1
                                 != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) @ ( sK7_C_3 @ SX1 @ SX0 ) ) ) )
                          | ( SX0
                           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) @ ( sK8_SY715 @ SX1 @ SX0 ) ) ) )
                    | ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK7_C_3 @ SX1 @ SX0 ) ) @ ( sK8_SY715 @ SX1 @ SX0 ) )
                     != one_one_int ) ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( SX0 = zero_zero_int )
                | ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK5_C_3 @ SX1 @ SX0 ) )
                                      | ~ ( is_int @ ( sK6_SY714 @ SX1 @ SX0 ) ) )
                                | ( SX1
                                 != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) @ ( sK5_C_3 @ SX1 @ SX0 ) ) ) )
                          | ( SX0
                           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) @ ( sK6_SY714 @ SX1 @ SX0 ) ) ) )
                    | ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK5_C_3 @ SX1 @ SX0 ) ) @ ( sK6_SY714 @ SX1 @ SX0 ) )
                     != one_one_int ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6560]) ).

thf(6602,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX1 )
                | ( ( hAPP_int_int @ number_number_of_int @ SX0 )
                 != SX1 )
                | ( SX1
                  = ( hAPP_int_int @ number_number_of_int @ SX0 ) ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX1 )
                | ( SX1
                 != ( hAPP_int_int @ number_number_of_int @ SX0 ) )
                | ( ( hAPP_int_int @ number_number_of_int @ SX0 )
                  = SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6136]) ).

thf(6603,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX2 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX0 ) @ SX1 )
                   != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX2 ) @ SX1 ) )
                  | ( SX0 = SX2 ) )
            | ~ ! [SX1: $i,SX2: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX2 )
                  | ( SX0 != SX2 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX0 ) @ SX1 )
                    = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX2 ) @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6206]) ).

thf(6604,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( SX1 = zero_zero_int )
                | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX1 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) )
                  = one_one_int ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( SX0 = zero_zero_int )
                | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX1 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) )
                  = one_one_int ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6559]) ).

thf(6605,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ~ ( ~ ( ~ ( is_int @ SX2 )
                | ! [SX3: $i,SX4: $i] :
                    ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 ) ) @ SX2 )
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX3 ) @ SX1 ) ) @ SX4 ) )
                    | ( SX2
                      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SX3 ) @ SX0 ) ) @ SX1 ) ) @ SX4 ) ) ) )
            | ~ ( ~ ( is_int @ SX2 )
                | ! [SX3: $i,SX4: $i] :
                    ( ( SX2
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SX3 ) @ SX0 ) ) @ SX1 ) ) @ SX4 ) )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 ) ) @ SX2 )
                      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX3 ) @ SX1 ) ) @ SX4 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6490]) ).

thf(6606,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ! [SX2: $i,SX3: $i] :
                  ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX2 ) @ SX3 )
                   != one_one_int )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX0 ) @ SX1 )
                   != one_one_int )
                  | ( ( hAPP_int_int @ abs_abs_int @ SX2 )
                   != ( hAPP_int_int @ abs_abs_int @ SX0 ) )
                  | ( ( hAPP_int_int @ abs_abs_int @ SX1 )
                   != ( hAPP_int_int @ abs_abs_int @ SX3 ) )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SX2 ) ) @ ( hAPP_int_int @ abs_abs_int @ SX1 ) )
                    = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SX0 ) ) @ ( hAPP_int_int @ abs_abs_int @ SX3 ) ) ) )
            | ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
                        ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX2 ) @ SX3 )
                         != one_one_int )
                        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX0 ) @ SX1 )
                         != one_one_int )
                        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SX2 ) ) @ ( hAPP_int_int @ abs_abs_int @ SX1 ) )
                         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SX0 ) ) @ ( hAPP_int_int @ abs_abs_int @ SX3 ) ) )
                        | ( ( hAPP_int_int @ abs_abs_int @ SX2 )
                          = ( hAPP_int_int @ abs_abs_int @ SX0 ) ) )
                  | ~ ! [SX2: $i,SX3: $i] :
                        ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX2 ) @ SX3 )
                         != one_one_int )
                        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX0 ) @ SX1 )
                         != one_one_int )
                        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SX2 ) ) @ ( hAPP_int_int @ abs_abs_int @ SX1 ) )
                         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SX0 ) ) @ ( hAPP_int_int @ abs_abs_int @ SX3 ) ) )
                        | ( ( hAPP_int_int @ abs_abs_int @ SX1 )
                          = ( hAPP_int_int @ abs_abs_int @ SX3 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6567]) ).

thf(6607,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ! [SX2: $i,SX3: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ~ ( is_int @ SX2 )
                  | ~ ( is_int @ SX3 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SX0 ) @ SX1 )
                   != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SX2 ) @ SX3 ) )
                  | ( SX0 != SX1 )
                  | ( SX2 = SX3 ) )
            | ~ ! [SX2: $i,SX3: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ~ ( is_int @ SX2 )
                  | ~ ( is_int @ SX3 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SX0 ) @ SX1 )
                   != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SX2 ) @ SX3 ) )
                  | ( SX2 != SX3 )
                  | ( SX0 = SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6301]) ).

thf(6608,plain,
    ( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                            ( ~ ( is_int @ SX0 )
                            | ~ ( is_int @ SX1 )
                            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                             != one_one_int )
                            | ( SX0 = one_one_int )
                            | ( SX0
                              = ( hAPP_int_int @ number_number_of_int @ min ) ) )
                      | ~ ! [SX0: $i,SX1: $i] :
                            ( ~ ( is_int @ SX0 )
                            | ~ ( is_int @ SX1 )
                            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                             != one_one_int )
                            | ( SX0 = one_one_int )
                            | ( SX1
                              = ( hAPP_int_int @ number_number_of_int @ min ) ) ) )
                | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                            ( ~ ( is_int @ SX0 )
                            | ~ ( is_int @ SX1 )
                            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                             != one_one_int )
                            | ( SX1 = one_one_int )
                            | ( SX0
                              = ( hAPP_int_int @ number_number_of_int @ min ) ) )
                      | ~ ! [SX0: $i,SX1: $i] :
                            ( ~ ( is_int @ SX0 )
                            | ~ ( is_int @ SX1 )
                            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                             != one_one_int )
                            | ( SX1 = one_one_int )
                            | ( SX1
                              = ( hAPP_int_int @ number_number_of_int @ min ) ) ) ) )
          | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                      ( ~ ( is_int @ SX0 )
                      | ~ ( is_int @ SX1 )
                      | ( SX0 != one_one_int )
                      | ( SX1 != one_one_int )
                      | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                        = one_one_int ) )
                | ~ ! [SX0: $i,SX1: $i] :
                      ( ~ ( is_int @ SX0 )
                      | ~ ( is_int @ SX1 )
                      | ( SX0
                       != ( hAPP_int_int @ number_number_of_int @ min ) )
                      | ( SX1
                       != ( hAPP_int_int @ number_number_of_int @ min ) )
                      | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                        = one_one_int ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6487]) ).

thf(6609,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
                 != one_one_int )
                | ( SX0 = one_one_int )
                | ( SX0
                  = ( hAPP_int_int @ number_number_of_int @ min ) ) )
          | ~ ~ ( ~ ! [SX0: $i] :
                      ( ~ ( is_int @ SX0 )
                      | ( SX0 != one_one_int )
                      | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
                        = one_one_int ) )
                | ~ ! [SX0: $i] :
                      ( ~ ( is_int @ SX0 )
                      | ( SX0
                       != ( hAPP_int_int @ number_number_of_int @ min ) )
                      | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
                        = one_one_int ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6497]) ).

thf(6610,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ( ( hAPP_int_int @ bit0 @ SX0 )
                 != pls )
                | ( SX0 = pls ) )
          | ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ( SX0 != pls )
                | ( ( hAPP_int_int @ bit0 @ SX0 )
                  = pls ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6149]) ).

thf(6611,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ~ ( ~ ! [SX2: $i,SX3: $i] :
                        ( ~ ( is_int @ SX0 )
                        | ~ ( is_int @ SX1 )
                        | ~ ( is_int @ SX2 )
                        | ~ ( is_int @ SX3 )
                        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX2 ) @ SX0 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX3 ) @ SX1 ) )
                          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX2 ) @ SX1 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX3 ) @ SX0 ) ) )
                        | ( SX2 != SX3 ) )
                  | ~ ! [SX2: $i,SX3: $i] :
                        ( ~ ( is_int @ SX0 )
                        | ~ ( is_int @ SX1 )
                        | ~ ( is_int @ SX2 )
                        | ~ ( is_int @ SX3 )
                        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX2 ) @ SX0 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX3 ) @ SX1 ) )
                          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX2 ) @ SX1 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX3 ) @ SX0 ) ) )
                        | ( SX0 != SX1 ) ) )
            | ~ ! [SX2: $i,SX3: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ~ ( is_int @ SX2 )
                  | ~ ( is_int @ SX3 )
                  | ( SX2 = SX3 )
                  | ( SX0 = SX1 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX2 ) @ SX0 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX3 ) @ SX1 ) )
                   != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX2 ) @ SX1 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX3 ) @ SX0 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6253]) ).

thf(6612,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( SX0 != zero_zero_int )
                | ( SX1 != zero_zero_int )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX0 ) @ SX1 )
                  = zero_zero_int ) )
          | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                      ( ~ ( is_int @ SX0 )
                      | ~ ( is_int @ SX1 )
                      | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX0 ) @ SX1 )
                       != zero_zero_int )
                      | ( SX0 = zero_zero_int ) )
                | ~ ! [SX0: $i,SX1: $i] :
                      ( ~ ( is_int @ SX0 )
                      | ~ ( is_int @ SX1 )
                      | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX0 ) @ SX1 )
                       != zero_zero_int )
                      | ( SX1 = zero_zero_int ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6445]) ).

thf(6613,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX1 )
                | ( SX1 = zero_zero_int )
                | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
                 != zero_zero_int )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ ( hAPP_int_int @ uminus_uminus_int @ SX1 ) )
                  = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ SX1 ) ) ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX1 )
                | ( SX1 = zero_zero_int )
                | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
                  = zero_zero_int )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ ( hAPP_int_int @ uminus_uminus_int @ SX1 ) )
                  = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ SX1 ) ) ) @ one_one_int ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6545]) ).

thf(6614,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
                 != ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
                | ( SX0 = SX1 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ( SX0 != SX1 )
                | ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
                  = ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6143]) ).

thf(6615,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ! [SX1: $i,SX2: $i] :
                  ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX0 ) @ SX1 )
                   != one_one_int )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX0 ) @ SX2 )
                   != one_one_int )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX0 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX1 ) @ SX2 ) )
                    = one_one_int ) )
            | ~ ~ ( ~ ! [SX1: $i] :
                        ( ! [SX2: $i] :
                            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX0 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX1 ) @ SX2 ) )
                           != one_one_int )
                        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX0 ) @ SX1 )
                          = one_one_int ) )
                  | ~ ! [SX1: $i,SX2: $i] :
                        ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX0 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX1 ) @ SX2 ) )
                         != one_one_int )
                        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX0 ) @ SX2 )
                          = one_one_int ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6446]) ).

thf(6616,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
                 != zero_zero_int )
                | ( SX0 = zero_zero_nat ) )
          | ~ ! [SX0: $i] :
                ( ( SX0 != zero_zero_nat )
                | ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
                  = zero_zero_int ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6130]) ).

thf(6617,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ~ ( ~ ! [SX3: $i,SX4: $i] :
                  ( ~ ( is_int @ SX4 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 ) ) @ SX2 )
                   != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX3 ) @ SX1 ) ) @ SX4 ) )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SX0 ) @ SX3 ) ) @ SX1 ) ) @ SX2 )
                    = SX4 ) )
            | ~ ! [SX3: $i,SX4: $i] :
                  ( ~ ( is_int @ SX4 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SX0 ) @ SX3 ) ) @ SX1 ) ) @ SX2 )
                   != SX4 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 ) ) @ SX2 )
                    = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX3 ) @ SX1 ) ) @ SX4 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6489]) ).

thf(6618,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ! [SX1: $i] :
                    ( ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
                     != zero_zero_int )
                    | ~ ( ( SX0
                         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX1 ) @ ( sK12_Q_4 @ SX1 @ SX0 ) ) )
                        | ~ ( is_int @ ( sK12_Q_4 @ SX1 @ SX0 ) ) ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ! [SX1: $i] :
                    ( ! [SX2: $i] :
                        ( ( SX0
                         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX1 ) @ SX2 ) )
                        | ~ ( is_int @ SX2 ) )
                    | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
                      = zero_zero_int ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6510]) ).

thf(6619,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
                 != ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
                | ( SX0 = SX1 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ( SX0 != SX1 )
                | ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
                  = ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6187]) ).

thf(6620,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( ( hAPP_int_int @ bit0 @ SX0 )
                 != ( hAPP_int_int @ bit0 @ SX1 ) )
                | ( SX0 = SX1 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( SX0 != SX1 )
                | ( ( hAPP_int_int @ bit0 @ SX0 )
                  = ( hAPP_int_int @ bit0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6139]) ).

thf(6621,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ( min
                 != ( hAPP_int_int @ bit1 @ SX0 ) )
                | ( min = SX0 ) )
          | ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ( min != SX0 )
                | ( min
                  = ( hAPP_int_int @ bit1 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6293]) ).

thf(6622,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ( ( hAPP_nat_nat @ suc @ SX0 )
                 != ( hAPP_nat_nat @ suc @ SX1 ) )
                | ( SX0 = SX1 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ( SX0 != SX1 )
                | ( ( hAPP_nat_nat @ suc @ SX0 )
                  = ( hAPP_nat_nat @ suc @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6501]) ).

thf(6623,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX0 ) @ SX0 )
                 != zero_zero_int )
                | ( SX0 = zero_zero_int ) )
          | ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ( SX0 != zero_zero_int )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX0 ) @ SX0 )
                  = zero_zero_int ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6144]) ).

thf(6624,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SX0 ) @ SX1 )
                 != zero_zero_int )
                | ( SX0 = SX1 ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( SX0 != SX1 )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SX0 ) @ SX1 )
                  = zero_zero_int ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6303]) ).

thf(6625,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( SX0 != SX1 )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SX0 ) @ SX1 )
                  = zero_zero_int ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SX0 ) @ SX1 )
                 != zero_zero_int )
                | ( SX0 = SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6304]) ).

thf(6626,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ( zero_zero_int
                 != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX0 ) @ SX0 ) )
                | ( SX0 = zero_zero_int ) )
          | ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ( SX0 != zero_zero_int )
                | ( zero_zero_int
                  = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX0 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6222]) ).

thf(6627,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
                 != zero_zero_int )
                | ( SX0 = zero_zero_int ) )
          | ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ( SX0 != zero_zero_int )
                | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
                  = zero_zero_int ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6116]) ).

thf(6628,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ( one_one_nat != SX0 )
                | ( SX0 = one_one_nat ) )
          | ~ ! [SX0: $i] :
                ( ( SX0 != one_one_nat )
                | ( one_one_nat = SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6482]) ).

thf(6629,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ( ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ SX0 ) @ SX1 ) )
                 != SX1 )
                | ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ SX0 ) ) @ SX1 )
                  = zero_zero_nat ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ( ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ SX0 ) @ SX1 ) )
                  = SX1 )
                | ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ SX0 ) ) @ SX1 )
                  = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ SX0 ) @ SX1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6534]) ).

thf(6630,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ zero_zero_int )
                  = zero_zero_int ) )
          | ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ zero_zero_int )
                  = SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6511]) ).

thf(6631,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( SX0 != zero_zero_int )
                | ( SX1 != zero_zero_int )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
                  = zero_zero_int ) )
          | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                      ( ~ ( is_int @ SX0 )
                      | ~ ( is_int @ SX1 )
                      | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
                       != zero_zero_int )
                      | ( SX0 = zero_zero_int ) )
                | ~ ! [SX0: $i,SX1: $i] :
                      ( ~ ( is_int @ SX0 )
                      | ~ ( is_int @ SX1 )
                      | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
                       != zero_zero_int )
                      | ( SX1 = zero_zero_int ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6113]) ).

thf(6632,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( SX0 != zero_zero_int )
                | ( SX1 != zero_zero_int )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX0 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX1 ) @ SX1 ) )
                  = zero_zero_int ) )
          | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                      ( ~ ( is_int @ SX0 )
                      | ~ ( is_int @ SX1 )
                      | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX0 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX1 ) @ SX1 ) )
                       != zero_zero_int )
                      | ( SX0 = zero_zero_int ) )
                | ~ ! [SX0: $i,SX1: $i] :
                      ( ~ ( is_int @ SX0 )
                      | ~ ( is_int @ SX1 )
                      | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX0 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX1 ) @ SX1 ) )
                       != zero_zero_int )
                      | ( SX1 = zero_zero_int ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6273]) ).

thf(6633,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( SX0 != zero_zero_int )
                | ( SX1 != zero_zero_int )
                | ( ( hAPP_int_int @ ( legacy_zgcd @ SX0 ) @ SX1 )
                  = zero_zero_int ) )
          | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                      ( ~ ( is_int @ SX0 )
                      | ~ ( is_int @ SX1 )
                      | ( ( hAPP_int_int @ ( legacy_zgcd @ SX0 ) @ SX1 )
                       != zero_zero_int )
                      | ( SX0 = zero_zero_int ) )
                | ~ ! [SX0: $i,SX1: $i] :
                      ( ~ ( is_int @ SX0 )
                      | ~ ( is_int @ SX1 )
                      | ( ( hAPP_int_int @ ( legacy_zgcd @ SX0 ) @ SX1 )
                       != zero_zero_int )
                      | ( SX1 = zero_zero_int ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6405]) ).

thf(6634,plain,
    ! [SV1: $i] :
      ( ( ! [SY718: $i] :
            ( ~ ( is_int @ SY718 )
            | ( is_int @ ( hAPP_int_int @ SV1 @ SY718 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6111]) ).

thf(6635,plain,
    ! [SV2: $i] :
      ( ( ! [SY719: $i] : ( is_int @ ( hAPP_nat_int @ SV2 @ SY719 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6112]) ).

thf(6636,plain,
    ! [SV3: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ ( hAPP_int_int @ number_number_of_int @ SV3 ) )
        = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ bit1 @ pls ) ) @ SV3 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6117]) ).

thf(6637,plain,
    ! [SV4: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ SV4 ) ) @ one_one_int )
        = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV4 ) @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6118]) ).

thf(6638,plain,
    ! [SV5: $i] :
      ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV5 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
        = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV5 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6121]) ).

thf(6639,plain,
    ! [SV6: $i] :
      ( ( ! [SY720: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ SV6 ) ) @ ( hAPP_int_int @ number_number_of_int @ SY720 ) )
            = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV6 ) @ SY720 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6125]) ).

thf(6640,plain,
    ! [SV7: $i] :
      ( ( ! [SY721: $i,SY722: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV7 ) @ SY721 ) ) @ SY722 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV7 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY721 ) @ SY722 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6140]) ).

thf(6641,plain,
    ! [SV8: $i] :
      ( ( ! [SY723: $i,SY724: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV8 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY723 ) @ SY724 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY723 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV8 ) @ SY724 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6141]) ).

thf(6642,plain,
    ! [SV9: $i] :
      ( ( ! [SY725: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV9 ) @ SY725 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY725 ) @ SV9 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6142]) ).

thf(6643,plain,
    ! [SV10: $i] :
      ( ( ( hAPP_int_int @ bit1 @ SV10 )
       != pls )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6145]) ).

thf(6644,plain,
    ! [SV11: $i] :
      ( ( pls
       != ( hAPP_int_int @ bit1 @ SV11 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6146]) ).

thf(6645,plain,
    ! [SV12: $i] :
      ( ( ! [SY726: $i] :
            ( ( hAPP_int_int @ bit1 @ SV12 )
           != ( hAPP_int_int @ bit0 @ SY726 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6147]) ).

thf(6646,plain,
    ! [SV13: $i] :
      ( ( ! [SY727: $i] :
            ( ( hAPP_int_int @ bit0 @ SV13 )
           != ( hAPP_int_int @ bit1 @ SY727 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6148]) ).

thf(6647,plain,
    ( ( zero_zero_int = one_one_int )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6153]) ).

thf(6648,plain,
    ! [SV14: $i] :
      ( ( ~ ( is_int @ SV14 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV14 ) @ pls )
          = SV14 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6154]) ).

thf(6649,plain,
    ! [SV15: $i] :
      ( ( ~ ( is_int @ SV15 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ pls ) @ SV15 )
          = SV15 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6155]) ).

thf(6650,plain,
    ! [SV16: $i] :
      ( ( ! [SY728: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ bit0 @ SV16 ) ) @ ( hAPP_int_int @ bit0 @ SY728 ) )
            = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV16 ) @ SY728 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6156]) ).

thf(6651,plain,
    ! [SV17: $i] :
      ( ( ( hAPP_int_int @ bit0 @ SV17 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV17 ) @ SV17 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6157]) ).

thf(6652,plain,
    ! [SV18: $i] :
      ( ( ~ ( is_int @ SV18 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV18 ) @ zero_zero_int )
          = SV18 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6158]) ).

thf(6653,plain,
    ! [SV19: $i] :
      ( ( ~ ( is_int @ SV19 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ SV19 )
          = SV19 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6159]) ).

thf(6654,plain,
    ! [SV20: $i] :
      ( ( ~ ( is_int @ SV20 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ pls ) ) @ SV20 )
          = SV20 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6164]) ).

thf(6655,plain,
    ! [SV21: $i] :
      ( ( ~ ( is_int @ SV21 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV21 ) @ ( hAPP_int_int @ number_number_of_int @ pls ) )
          = SV21 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6165]) ).

thf(6656,plain,
    ! [SV22: $i] :
      ( ( ! [SY729: $i,SY730: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ SV22 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ SY729 ) ) @ SY730 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV22 ) @ SY729 ) ) ) @ SY730 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6167]) ).

thf(6657,plain,
    ! [SV23: $i] :
      ( ( ! [SY731: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ SV23 ) ) @ ( hAPP_int_int @ number_number_of_int @ SY731 ) )
            = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV23 ) @ SY731 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6168]) ).

thf(6658,plain,
    ! [SV24: $i] :
      ( ( ! [SY732: $i] :
            ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV24 ) @ SY732 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ SV24 ) ) @ ( hAPP_int_int @ number_number_of_int @ SY732 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6169]) ).

thf(6659,plain,
    ! [SV25: $i] :
      ( ( ! [SY733: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ bit1 @ SV25 ) ) @ ( hAPP_int_int @ bit0 @ SY733 ) )
            = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV25 ) @ SY733 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6170]) ).

thf(6660,plain,
    ! [SV26: $i] :
      ( ( ! [SY734: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ bit0 @ SV26 ) ) @ ( hAPP_int_int @ bit1 @ SY734 ) )
            = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV26 ) @ SY734 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6171]) ).

thf(6661,plain,
    ! [SV27: $i] :
      ( ( ( hAPP_int_int @ bit1 @ SV27 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ SV27 ) ) @ SV27 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6172]) ).

thf(6662,plain,
    ! [SV28: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ SV28 ) ) @ SV28 )
       != zero_zero_int )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6173]) ).

thf(6663,plain,
    ! [SV29: $i] :
      ( ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV29 ) )
        = ( hAPP_nat_int @ semiri1621563631at_int @ SV29 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6174]) ).

thf(6664,plain,
    ! [SV30: $i] :
      ( ( ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_nat_int @ semiri1621563631at_int @ SV30 ) )
        = ( hAPP_nat_nat @ semiri984289939at_nat @ SV30 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6175]) ).

thf(6665,plain,
    ! [SV31: $i] :
      ( ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ SV31 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ ( hAPP_int_int @ number_number_of_int @ SV31 ) ) ) @ ( hAPP_int_int @ number_number_of_int @ SV31 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6176]) ).

thf(6666,plain,
    ! [SV32: $i] :
      ( ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ SV32 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ ( hAPP_int_int @ number_number_of_int @ SV32 ) ) ) @ ( hAPP_int_int @ number_number_of_int @ SV32 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6177]) ).

thf(6667,plain,
    ! [SV33: $i] :
      ( ( ~ ( is_int @ SV33 )
        | ( ( hAPP_int_int @ number_number_of_int @ SV33 )
          = SV33 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6184]) ).

thf(6668,plain,
    ! [SV34: $i] :
      ( ( ~ ( is_int @ SV34 )
        | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV34 ) @ one_one_nat )
          = SV34 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6185]) ).

thf(6669,plain,
    ( ( one_one_int = zero_zero_int )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6188]) ).

thf(6670,plain,
    ( ( zero_zero_int = one_one_int )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6189]) ).

thf(6671,plain,
    ! [SV35: $i] :
      ( ( ! [SY735: $i] :
            ( ~ ( is_int @ SY735 )
            | ( SY735 = zero_zero_int )
            | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY735 ) @ SV35 )
             != zero_zero_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6190]) ).

thf(6672,plain,
    ! [SV36: $i] :
      ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ one_one_int ) @ SV36 )
        = one_one_int )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6191]) ).

thf(6673,plain,
    ! [SV37: $i] :
      ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV37 ) @ zero_zero_nat )
        = one_one_int )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6195]) ).

thf(6674,plain,
    ! [SV38: $i] :
      ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV38 ) @ zero_zero_nat )
        = one_one_int )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6197]) ).

thf(6675,plain,
    ! [SV39: $i] :
      ( ( ( hAPP_int_int @ succ @ ( hAPP_int_int @ bit1 @ SV39 ) )
        = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ succ @ SV39 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6200]) ).

thf(6676,plain,
    ! [SV40: $i] :
      ( ( ( hAPP_int_int @ succ @ ( hAPP_int_int @ bit0 @ SV40 ) )
        = ( hAPP_int_int @ bit1 @ SV40 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6201]) ).

thf(6677,plain,
    ! [SV41: $i] :
      ( ( ! [SY736: $i,SY737: $i] :
            ( ~ ( is_int @ SV41 )
            | ~ ( is_int @ SY737 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV41 ) @ SY736 )
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY737 ) @ SY736 ) )
            | ( SV41 = SY737 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6202]) ).

thf(6678,plain,
    ! [SV42: $i] :
      ( ( ! [SY738: $i,SY739: $i] :
            ( ~ ( is_int @ SY738 )
            | ~ ( is_int @ SY739 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV42 ) @ SY738 )
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV42 ) @ SY739 ) )
            | ( SY738 = SY739 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6203]) ).

thf(6679,plain,
    ! [SV43: $i] :
      ( ( ! [SY740: $i,SY741: $i] :
            ( ~ ( is_int @ SY740 )
            | ~ ( is_int @ SY741 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV43 ) @ SY740 )
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV43 ) @ SY741 ) )
            | ( SY740 = SY741 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6204]) ).

thf(6680,plain,
    ! [SV44: $i] :
      ( ( ! [SY742: $i,SY743: $i,SY744: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV44 ) @ SY742 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY743 ) @ SY744 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV44 ) @ SY743 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY742 ) @ SY744 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6205]) ).

thf(6681,plain,
    ! [SV45: $i] :
      ( ( ! [SY745: $i,SY746: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV45 ) @ SY745 ) ) @ SY746 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV45 ) @ SY746 ) ) @ SY745 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6208]) ).

thf(6682,plain,
    ! [SV46: $i] :
      ( ( ! [SY747: $i,SY748: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV46 ) @ SY747 ) ) @ SY748 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV46 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY747 ) @ SY748 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6209]) ).

thf(6683,plain,
    ! [SV47: $i] :
      ( ( ! [SY749: $i,SY750: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV47 ) @ SY749 ) ) @ SY750 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV47 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY749 ) @ SY750 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6210]) ).

thf(6684,plain,
    ! [SV48: $i] :
      ( ( ! [SY751: $i,SY752: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV48 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY751 ) @ SY752 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV48 ) @ SY751 ) ) @ SY752 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6211]) ).

thf(6685,plain,
    ! [SV49: $i] :
      ( ( ! [SY753: $i,SY754: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV49 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY753 ) @ SY754 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY753 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV49 ) @ SY754 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6212]) ).

thf(6686,plain,
    ! [SV50: $i] :
      ( ( ! [SY755: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV50 ) @ SY755 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY755 ) @ SV50 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6213]) ).

thf(6687,plain,
    ! [SV51: $i] :
      ( ( ( hAPP_int_int @ succ @ SV51 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV51 ) @ one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6215]) ).

thf(6688,plain,
    ! [SV52: $i] :
      ( ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ succ @ SV52 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ ( hAPP_int_int @ number_number_of_int @ SV52 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6216]) ).

thf(6689,plain,
    ! [SV53: $i] :
      ( ( ! [SY756: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ bit1 @ SV53 ) ) @ ( hAPP_int_int @ bit1 @ SY756 ) )
            = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV53 ) @ ( hAPP_int_int @ succ @ SY756 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6217]) ).

thf(6690,plain,
    ! [SV54: $i] :
      ( ( ~ ( is_int @ SV54 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV54 ) @ zero_zero_int )
          = SV54 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6219]) ).

thf(6691,plain,
    ! [SV55: $i] :
      ( ( ~ ( is_int @ SV55 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV55 ) @ zero_zero_int )
          = SV55 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6220]) ).

thf(6692,plain,
    ! [SV56: $i] :
      ( ( ~ ( is_int @ SV56 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV56 ) @ zero_zero_int )
          = SV56 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6221]) ).

thf(6693,plain,
    ! [SV57: $i] :
      ( ( ~ ( is_int @ SV57 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ SV57 )
          = SV57 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6223]) ).

thf(6694,plain,
    ! [SV58: $i] :
      ( ( ~ ( is_int @ SV58 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ SV58 )
          = SV58 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6224]) ).

thf(6695,plain,
    ! [SV59: $i] :
      ( ( ~ ( is_int @ SV59 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ SV59 )
          = SV59 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6225]) ).

thf(6696,plain,
    ! [SV60: $i] :
      ( ( ~ ( is_int @ SV60 )
        | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV60 ) @ one_one_nat )
          = SV60 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6226]) ).

thf(6697,plain,
    ! [SV61: $i] :
      ( ( ! [SY757: $i] :
            ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV61 ) @ SY757 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV61 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV61 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) @ SY757 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ SV61 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY757 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY757 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6227]) ).

thf(6698,plain,
    ! [SV62: $i] :
      ( ( ! [SY758: $i] :
            ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV62 ) @ SY758 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV62 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ SV62 ) ) @ SY758 ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY758 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6228]) ).

thf(6699,plain,
    ! [SV63: $i] :
      ( ( ! [SY759: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV63 ) @ SY759 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY759 ) @ SV63 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6229]) ).

thf(6700,plain,
    ! [SV64: $i] :
      ( ( ! [SY760: $i,SY761: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV64 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY760 ) @ SY761 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY760 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV64 ) @ SY761 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6230]) ).

thf(6701,plain,
    ! [SV65: $i] :
      ( ( ! [SY762: $i,SY763: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV65 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY762 ) @ SY763 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV65 ) @ SY762 ) ) @ SY763 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6231]) ).

thf(6702,plain,
    ! [SV66: $i] :
      ( ( ! [SY764: $i,SY765: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV66 ) @ SY764 ) ) @ SY765 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV66 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY764 ) @ SY765 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6232]) ).

thf(6703,plain,
    ! [SV67: $i] :
      ( ( ! [SY766: $i,SY767: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV67 ) @ SY766 ) ) @ SY767 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV67 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY766 ) @ SY767 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6233]) ).

thf(6704,plain,
    ! [SV68: $i] :
      ( ( ! [SY768: $i,SY769: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV68 ) @ SY768 ) ) @ SY769 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV68 ) @ SY769 ) ) @ SY768 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6234]) ).

thf(6705,plain,
    ! [SV69: $i] :
      ( ( ! [SY770: $i,SY771: $i,SY772: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV69 ) @ SY770 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY771 ) @ SY772 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV69 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY770 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY771 ) @ SY772 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6235]) ).

thf(6706,plain,
    ! [SV70: $i] :
      ( ( ! [SY773: $i,SY774: $i,SY775: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV70 ) @ SY773 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY774 ) @ SY775 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY774 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV70 ) @ SY773 ) ) @ SY775 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6236]) ).

thf(6707,plain,
    ! [SV71: $i] :
      ( ( ! [SY776: $i,SY777: $i,SY778: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV71 ) @ SY776 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY777 ) @ SY778 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV71 ) @ SY777 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY776 ) @ SY778 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6237]) ).

thf(6708,plain,
    ! [SV72: $i] :
      ( ( ! [SY779: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV72 ) @ SY779 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY779 ) @ SV72 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6238]) ).

thf(6709,plain,
    ! [SV73: $i] :
      ( ( ! [SY780: $i,SY781: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV73 ) @ SY780 ) ) @ SY781 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV73 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY780 ) @ SY781 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6239]) ).

thf(6710,plain,
    ! [SV74: $i] :
      ( ( ! [SY782: $i,SY783: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ SV74 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ SY782 ) ) @ SY783 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV74 ) @ SY782 ) ) ) @ SY783 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6240]) ).

thf(6711,plain,
    ! [SV75: $i] :
      ( ( ! [SY784: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ SV75 ) ) @ ( hAPP_int_int @ number_number_of_int @ SY784 ) )
            = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV75 ) @ SY784 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6241]) ).

thf(6712,plain,
    ! [SV76: $i] :
      ( ( ! [SY785: $i] :
            ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV76 ) @ SY785 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ SV76 ) ) @ ( hAPP_int_int @ number_number_of_int @ SY785 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6242]) ).

thf(6713,plain,
    ! [SV77: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ zero_zero_int ) @ SV77 )
        = zero_zero_int )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6243]) ).

thf(6714,plain,
    ! [SV78: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV78 ) @ zero_zero_int )
        = zero_zero_int )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6244]) ).

thf(6715,plain,
    ! [SV79: $i] :
      ( ( ! [SY786: $i] :
            ( ~ ( is_int @ SV79 )
            | ~ ( is_int @ SY786 )
            | ( SY786 = zero_zero_int )
            | ( SV79 = zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY786 ) @ SV79 )
             != zero_zero_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6246]) ).

thf(6716,plain,
    ! [SV80: $i] :
      ( ( ! [SY787: $i] :
            ( ~ ( is_int @ SV80 )
            | ~ ( is_int @ SY787 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV80 ) @ SY787 )
             != zero_zero_int )
            | ( SV80 = zero_zero_int )
            | ( SY787 = zero_zero_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6247]) ).

thf(6717,plain,
    ! [SV81: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ zero_zero_int ) @ SV81 )
        = zero_zero_int )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6248]) ).

thf(6718,plain,
    ! [SV82: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV82 ) @ zero_zero_int )
        = zero_zero_int )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6249]) ).

thf(6719,plain,
    ! [SV83: $i] :
      ( ( ! [SY788: $i,SY789: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV83 ) @ SY788 ) ) @ SY789 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV83 ) @ SY789 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY788 ) @ SY789 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6250]) ).

thf(6720,plain,
    ! [SV84: $i] :
      ( ( ! [SY790: $i,SY791: $i,SY792: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV84 ) @ SY790 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY791 ) @ SY790 ) ) @ SY792 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV84 ) @ SY791 ) ) @ SY790 ) ) @ SY792 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6251]) ).

thf(6721,plain,
    ! [SV85: $i] :
      ( ( ! [SY793: $i,SY794: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV85 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY793 ) @ SY794 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV85 ) @ SY793 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV85 ) @ SY794 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6252]) ).

thf(6722,plain,
    ! [SV86: $i] :
      ( ( ! [SY795: $i,SY796: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV86 ) @ SY795 ) ) @ SY796 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV86 ) @ SY796 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY795 ) @ SY796 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6254]) ).

thf(6723,plain,
    ! [SV87: $i] :
      ( ( ! [SY797: $i,SY798: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV87 ) @ SY797 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY798 ) @ SY797 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV87 ) @ SY798 ) ) @ SY797 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6255]) ).

thf(6724,plain,
    ! [SV88: $i] :
      ( ( ~ ( is_int @ SV88 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ one_one_int ) @ SV88 )
          = SV88 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6257]) ).

thf(6725,plain,
    ! [SV89: $i] :
      ( ( ~ ( is_int @ SV89 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ one_one_int ) @ SV89 )
          = SV89 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6258]) ).

thf(6726,plain,
    ! [SV90: $i] :
      ( ( ~ ( is_int @ SV90 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ one_one_int ) @ SV90 )
          = SV90 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6259]) ).

thf(6727,plain,
    ! [SV91: $i] :
      ( ( ~ ( is_int @ SV91 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV91 ) @ one_one_int )
          = SV91 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6260]) ).

thf(6728,plain,
    ! [SV92: $i] :
      ( ( ~ ( is_int @ SV92 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV92 ) @ one_one_int )
          = SV92 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6261]) ).

thf(6729,plain,
    ! [SV93: $i] :
      ( ( ~ ( is_int @ SV93 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV93 ) @ one_one_int )
          = SV93 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6262]) ).

thf(6730,plain,
    ! [SV94: $i] :
      ( ( ! [SY799: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV94 ) @ SY799 ) ) @ SV94 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV94 ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV94 ) @ SY799 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6263]) ).

thf(6731,plain,
    ! [SV95: $i] :
      ( ( ! [SY800: $i,SY801: $i] :
            ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV95 ) @ SY800 ) ) @ SY801 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV95 ) @ SY801 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY800 ) @ SY801 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6264]) ).

thf(6732,plain,
    ! [SV96: $i] :
      ( ( ! [SY802: $i,SY803: $i] :
            ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV96 ) @ SY802 ) ) @ SY803 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV96 ) @ SY803 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY802 ) @ SY803 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6265]) ).

thf(6733,plain,
    ! [SV97: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ pls ) @ SV97 )
        = pls )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6266]) ).

thf(6734,plain,
    ! [SV98: $i] :
      ( ( ! [SY804: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ bit0 @ SV98 ) ) @ SY804 )
            = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV98 ) @ SY804 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6267]) ).

thf(6735,plain,
    ! [SV99: $i] :
      ( ( ~ ( is_int @ SV99 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ one_one_int ) @ SV99 )
          = SV99 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6268]) ).

thf(6736,plain,
    ! [SV100: $i] :
      ( ( ~ ( is_int @ SV100 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV100 ) @ one_one_int )
          = SV100 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6269]) ).

thf(6737,plain,
    ! [SV101: $i] :
      ( ( ! [SY805: $i,SY806: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV101 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY805 ) @ SY806 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV101 ) @ SY805 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV101 ) @ SY806 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6270]) ).

thf(6738,plain,
    ! [SV102: $i] :
      ( ( ! [SY807: $i,SY808: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV102 ) @ SY807 ) ) @ SY808 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV102 ) @ SY808 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY807 ) @ SY808 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6271]) ).

thf(6739,plain,
    ! [SV103: $i] :
      ( ( ! [SY809: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ SV103 ) ) @ ( hAPP_int_int @ number_number_of_int @ SY809 ) )
            = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV103 ) @ SY809 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6272]) ).

thf(6740,plain,
    ! [SV104: $i] :
      ( ( ! [SY810: $i,SY811: $i,SY812: $i,SY813: $i] :
            ( ~ ( is_int @ SV104 )
            | ~ ( is_int @ SY810 )
            | ~ ( is_int @ SY813 )
            | ( SY813 = zero_zero_int )
            | ( SV104 = SY810 )
            | ( SY811 != SY812 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY811 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY813 ) @ SV104 ) )
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY812 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY813 ) @ SY810 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6274]) ).

thf(6741,plain,
    ! [SV105: $i] :
      ( ( ! [SY814: $i,SY815: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ SV105 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY814 ) @ SY815 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ SV105 ) ) @ SY814 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ SV105 ) ) @ SY815 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6275]) ).

thf(6742,plain,
    ! [SV106: $i] :
      ( ( ! [SY816: $i,SY817: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV106 ) @ SY816 ) ) @ ( hAPP_int_int @ number_number_of_int @ SY817 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV106 ) @ ( hAPP_int_int @ number_number_of_int @ SY817 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY816 ) @ ( hAPP_int_int @ number_number_of_int @ SY817 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6276]) ).

thf(6743,plain,
    ! [SV107: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV107 ) @ SV107 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ one_one_int ) ) @ SV107 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6277]) ).

thf(6744,plain,
    ! [SV108: $i] :
      ( ( ! [SY818: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV108 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY818 ) @ SV108 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY818 ) @ one_one_int ) ) @ SV108 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6278]) ).

thf(6745,plain,
    ! [SV109: $i] :
      ( ( ! [SY819: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV109 ) @ SY819 ) ) @ SY819 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV109 ) @ one_one_int ) ) @ SY819 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6279]) ).

thf(6746,plain,
    ! [SV110: $i] :
      ( ( ! [SY820: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ bit1 @ SV110 ) ) @ SY820 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV110 ) @ SY820 ) ) ) @ SY820 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6280]) ).

thf(6747,plain,
    ! [SV111: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ one_one_int ) ) @ ( hAPP_int_int @ number_number_of_int @ SV111 ) )
        = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ SV111 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6281]) ).

thf(6748,plain,
    ! [SV112: $i] :
      ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV112 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV112 ) @ SV112 ) ) @ SV112 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6282]) ).

thf(6749,plain,
    ! [SV113: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV113 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV113 ) @ SV113 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6283]) ).

thf(6750,plain,
    ! [SV114: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV114 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV114 ) @ SV114 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6284]) ).

thf(6751,plain,
    ! [SV115: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ SV115 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV115 ) @ SV115 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6285]) ).

thf(6752,plain,
    ! [SV116: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ SV116 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV116 ) @ SV116 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6286]) ).

thf(6753,plain,
    ! [SV117: $i] :
      ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV117 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV117 ) @ SV117 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6287]) ).

thf(6754,plain,
    ! [SV118: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV118 ) @ SV118 )
        = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV118 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6288]) ).

thf(6755,plain,
    ! [SV119: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV119 ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV119 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
        = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV119 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6289]) ).

thf(6756,plain,
    ! [SV120: $i] :
      ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ number_number_of_int @ SV120 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ SV120 ) ) @ ( hAPP_int_int @ number_number_of_int @ SV120 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6290]) ).

thf(6757,plain,
    ! [SV121: $i] :
      ( ( ! [SY821: $i] :
            ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV121 ) @ SY821 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV121 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY821 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ SV121 ) ) @ SY821 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6291]) ).

thf(6758,plain,
    ( ( min = pls )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6295]) ).

thf(6759,plain,
    ( ( pls = min )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6296]) ).

thf(6760,plain,
    ! [SV122: $i] :
      ( ( min
       != ( hAPP_int_int @ bit0 @ SV122 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6297]) ).

thf(6761,plain,
    ! [SV123: $i] :
      ( ( ( hAPP_int_int @ bit0 @ SV123 )
       != min )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6298]) ).

thf(6762,plain,
    ( ( ( hAPP_int_int @ number_number_of_int @ pls )
      = ( hAPP_int_int @ number_number_of_int @ min ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6299]) ).

thf(6763,plain,
    ! [SV124: $i] :
      ( ( ! [SY822: $i] :
            ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV124 ) @ SY822 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ number_number_of_int @ SV124 ) ) @ ( hAPP_int_int @ number_number_of_int @ SY822 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6302]) ).

thf(6764,plain,
    ! [SV125: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV125 ) @ SV125 )
        = zero_zero_int )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6305]) ).

thf(6765,plain,
    ! [SV126: $i] :
      ( ( ~ ( is_int @ SV126 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV126 ) @ zero_zero_int )
          = SV126 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6306]) ).

thf(6766,plain,
    ! [SV127: $i] :
      ( ( ~ ( is_int @ SV127 )
        | ! [SY823: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV127 ) @ SY823 ) ) @ SY823 )
            = SV127 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6307]) ).

thf(6767,plain,
    ! [SV128: $i] :
      ( ( ~ ( is_int @ SV128 )
        | ! [SY824: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV128 ) @ SY824 ) ) @ SY824 )
            = SV128 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6308]) ).

thf(6768,plain,
    ! [SV129: $i] :
      ( ( ! [SY825: $i,SY826: $i,SY827: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV129 ) @ SY825 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY826 ) @ SY827 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV129 ) @ SY826 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY825 ) @ SY827 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6309]) ).

thf(6769,plain,
    ! [SV130: $i] :
      ( ( ~ ( is_int @ SV130 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV130 ) @ pls )
          = SV130 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6310]) ).

thf(6770,plain,
    ! [SV131: $i] :
      ( ( ! [SY828: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ bit0 @ SV131 ) ) @ ( hAPP_int_int @ bit0 @ SY828 ) )
            = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV131 ) @ SY828 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6311]) ).

thf(6771,plain,
    ! [SV132: $i] :
      ( ( ! [SY829: $i,SY830: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV132 ) @ SY829 ) ) @ SY830 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV132 ) @ SY830 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY829 ) @ SY830 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6312]) ).

thf(6772,plain,
    ! [SV133: $i] :
      ( ( ! [SY831: $i,SY832: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV133 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY831 ) @ SY832 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV133 ) @ SY831 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV133 ) @ SY832 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6313]) ).

thf(6773,plain,
    ! [SV134: $i] :
      ( ( ! [SY833: $i,SY834: $i,SY835: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV134 ) @ SY833 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY834 ) @ SY835 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV134 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY833 ) @ SY835 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV134 ) @ SY834 ) ) @ SY835 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6314]) ).

thf(6774,plain,
    ! [SV135: $i] :
      ( ( ! [SY836: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ bit1 @ SV135 ) ) @ ( hAPP_int_int @ bit1 @ SY836 ) )
            = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV135 ) @ SY836 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6315]) ).

thf(6775,plain,
    ! [SV136: $i] :
      ( ( ! [SY837: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ bit1 @ SV136 ) ) @ ( hAPP_int_int @ bit0 @ SY837 ) )
            = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV136 ) @ SY837 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6316]) ).

thf(6776,plain,
    ! [SV137: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ pls ) @ ( hAPP_int_int @ bit0 @ SV137 ) )
        = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ pls ) @ SV137 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6317]) ).

thf(6777,plain,
    ! [SV138: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV138 ) @ SV138 ) ) @ one_one_int )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV138 ) @ one_one_int ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV138 ) @ one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6318]) ).

thf(6778,plain,
    ! [SV139: $i] :
      ( ( ! [SY838: $i,SY839: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ SV139 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ number_number_of_int @ SY838 ) ) @ SY839 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV139 ) @ SY838 ) ) ) @ SY839 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6319]) ).

thf(6779,plain,
    ! [SV140: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ pls ) @ ( hAPP_int_int @ bit1 @ SV140 ) )
        = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ min ) @ SV140 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6320]) ).

thf(6780,plain,
    ! [SV141: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ min ) @ ( hAPP_int_int @ bit1 @ SV141 ) )
        = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ min ) @ SV141 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6321]) ).

thf(6781,plain,
    ! [SV142: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ min ) @ ( hAPP_int_int @ bit0 @ SV142 ) )
        = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ min ) @ SV142 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6322]) ).

thf(6782,plain,
    ! [SV143: $i] :
      ( ( ! [SY840: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV143 ) @ SY840 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV143 ) @ SY840 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV143 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY840 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6323]) ).

thf(6783,plain,
    ! [SV144: $i] :
      ( ( ~ ( is_int @ SV144 )
        | ! [SY841: $i,SY842: $i] :
            ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV144 ) @ SY841 )
             != SY842 )
            | ( SV144
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY842 ) @ SY841 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6324]) ).

thf(6784,plain,
    ! [SV145: $i] :
      ( ( ! [SY843: $i,SY844: $i,SY845: $i,SY846: $i,SY847: $i,SY848: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV145 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY843 ) @ SY844 ) ) ) @ SY845 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY846 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY843 ) @ SY847 ) ) ) @ SY848 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV145 ) @ SY845 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY846 ) @ SY848 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY843 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY844 ) @ SY845 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY847 ) @ SY848 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6325]) ).

thf(6785,plain,
    ! [SV146: $i] :
      ( ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ number_number_of_int @ min ) ) @ SV146 )
          = one_one_int )
        | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ number_number_of_int @ min ) ) @ SV146 )
          = ( hAPP_int_int @ number_number_of_int @ min ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6326]) ).

thf(6786,plain,
    ! [SV147: $i] :
      ( ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ abs_abs_int @ SV147 ) )
        = ( hAPP_int_int @ abs_abs_int @ SV147 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6327]) ).

thf(6787,plain,
    ! [SV148: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV148 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV148 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV148 ) @ SV148 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6330]) ).

thf(6788,plain,
    ! [SV149: $i] :
      ( ( ! [SY849: $i] :
            ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV149 ) @ SY849 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV149 ) ) @ ( hAPP_int_int @ abs_abs_int @ SY849 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6331]) ).

thf(6789,plain,
    ! [SV150: $i] :
      ( ( ! [SY850: $i] :
            ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ abs_abs_int @ SV150 ) ) @ ( hAPP_int_int @ abs_abs_int @ SY850 ) ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ abs_abs_int @ SV150 ) ) @ ( hAPP_int_int @ abs_abs_int @ SY850 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6332]) ).

thf(6790,plain,
    ! [SV151: $i] :
      ( ( ! [SY851: $i] :
            ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV151 ) @ SY851 ) )
            = ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY851 ) @ SV151 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6334]) ).

thf(6791,plain,
    ! [SV152: $i] :
      ( ( ! [SY852: $i] :
            ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV152 ) @ SY852 ) )
            = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ abs_abs_int @ SV152 ) ) @ SY852 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6335]) ).

thf(6792,plain,
    ! [SV153: $i] :
      ( ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV153 ) )
        = ( hAPP_nat_int @ semiri1621563631at_int @ SV153 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6336]) ).

thf(6793,plain,
    ! [SV154: $i] :
      ( ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV154 ) )
        = ( hAPP_nat_int @ semiri1621563631at_int @ SV154 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6337]) ).

thf(6794,plain,
    ! [SV155: $i] :
      ( ( ( hAPP_int_nat @ nat @ ( hAPP_nat_int @ semiri1621563631at_int @ SV155 ) )
        = SV155 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6338]) ).

thf(6795,plain,
    ! [SV156: $i] :
      ( ( ! [SY853: $i] :
            ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV156 ) @ SY853 ) )
           != one_one_int )
        | ( ( hAPP_int_int @ abs_abs_int @ SV156 )
          = one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6341]) ).

thf(6796,plain,
    ! [SV157: $i] :
      ( ( ( hAPP_int_nat @ number_number_of_nat @ SV157 )
        = ( hAPP_int_nat @ nat @ ( hAPP_int_int @ number_number_of_int @ SV157 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6342]) ).

thf(6797,plain,
    ! [SV158: $i] :
      ( ( ( hAPP_int_nat @ nat @ ( hAPP_int_int @ number_number_of_int @ SV158 ) )
        = ( hAPP_int_nat @ number_number_of_nat @ SV158 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6343]) ).

thf(6798,plain,
    ! [SV159: $i] :
      ( ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV159 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
        = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ abs_abs_int @ SV159 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6346]) ).

thf(6799,plain,
    ! [SV160: $i] :
      ( ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV160 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
        = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ abs_abs_int @ SV160 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6349]) ).

thf(6800,plain,
    ! [SV161: $i] :
      ( ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV161 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
         != one_one_int )
        | ( ( hAPP_int_int @ abs_abs_int @ SV161 )
          = one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6350]) ).

thf(6801,plain,
    ! [SV162: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ zero_zero_int ) @ SV162 )
        = zero_zero_int )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6351]) ).

thf(6802,plain,
    ! [SV163: $i] :
      ( ( ~ ( is_int @ SV163 )
        | ( SV163 = zero_zero_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV163 ) @ SV163 )
          = one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6352]) ).

thf(6803,plain,
    ! [SV164: $i] :
      ( ( ! [SY854: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ SV164 ) ) ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ SY854 ) ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ number_number_of_int @ SV164 ) ) @ ( hAPP_int_int @ number_number_of_int @ SY854 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6353]) ).

thf(6804,plain,
    ! [SV165: $i] :
      ( ( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_int_nat @ nat @ ( hAPP_int_int @ abs_abs_int @ SV165 ) ) )
        = ( hAPP_int_int @ abs_abs_int @ SV165 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6354]) ).

thf(6805,plain,
    ! [SV166: $i] :
      ( ( ! [SY855: $i] :
            ( ( hAPP_int_int @ ( standardRes @ SV166 ) @ SY855 )
            = ( hAPP_int_int @ ( div_mod_int @ SY855 ) @ SV166 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6355]) ).

thf(6806,plain,
    ! [SV167: $i] :
      ( ( ( hAPP_int_int @ ( div_mod_int @ SV167 ) @ SV167 )
        = zero_zero_int )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6356]) ).

thf(6807,plain,
    ! [SV168: $i] :
      ( ( ( hAPP_int_int @ ( div_mod_int @ zero_zero_int ) @ SV168 )
        = zero_zero_int )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6357]) ).

thf(6808,plain,
    ! [SV169: $i] :
      ( ( ! [SY856: $i,SY857: $i] :
            ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV169 ) @ SY856 ) ) @ SY857 )
            = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV169 ) @ ( hAPP_int_int @ ( div_mod_int @ SY856 ) @ SY857 ) ) ) @ SY857 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6358]) ).

thf(6809,plain,
    ! [SV170: $i] :
      ( ( ! [SY858: $i,SY859: $i] :
            ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV170 ) @ ( hAPP_int_int @ ( div_mod_int @ SY858 ) @ SY859 ) ) ) @ SY859 )
            = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV170 ) @ SY858 ) ) @ SY859 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6359]) ).

thf(6810,plain,
    ! [SV171: $i] :
      ( ( ! [SY860: $i,SY861: $i] :
            ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( div_mod_int @ SV171 ) @ SY860 ) ) @ SY861 ) ) @ SY860 )
            = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV171 ) @ SY861 ) ) @ SY860 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6360]) ).

thf(6811,plain,
    ! [SV172: $i] :
      ( ( ! [SY862: $i,SY863: $i] :
            ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV172 ) @ ( hAPP_int_int @ ( div_mod_int @ SY862 ) @ SY863 ) ) ) @ SY863 )
            = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV172 ) @ SY862 ) ) @ SY863 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6361]) ).

thf(6812,plain,
    ! [SV173: $i] :
      ( ( ! [SY864: $i,SY865: $i] :
            ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( div_mod_int @ SV173 ) @ SY864 ) ) @ SY865 ) ) @ SY864 )
            = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV173 ) @ SY865 ) ) @ SY864 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6362]) ).

thf(6813,plain,
    ! [SV174: $i] :
      ( ( ! [SY866: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ ( div_mod_int @ SV174 ) @ SY866 ) ) @ SY866 )
            = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6363]) ).

thf(6814,plain,
    ! [SV175: $i] :
      ( ( ! [SY867: $i,SY868: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV175 ) @ SY867 ) ) @ SY868 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV175 ) @ SY868 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SY867 ) @ SY868 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( div_mod_int @ SV175 ) @ SY868 ) ) @ ( hAPP_int_int @ ( div_mod_int @ SY867 ) @ SY868 ) ) ) @ SY868 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6364]) ).

thf(6815,plain,
    ! [SV176: $i] :
      ( ( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ suc @ SV176 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ SV176 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6365]) ).

thf(6816,plain,
    ! [SV177: $i] :
      ( ( ~ ( is_int @ SV177 )
        | ( SV177
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ ( sK15_M_1 @ SV177 ) ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ ( sK16_SY717 @ SV177 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6367]) ).

thf(6817,plain,
    ! [SV178: $i] :
      ( ( ~ ( is_int @ SV178 )
        | ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ uminus_uminus_int @ SV178 ) )
          = SV178 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6368]) ).

thf(6818,plain,
    ! [SV179: $i] :
      ( ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ bit0 @ SV179 ) )
        = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ uminus_uminus_int @ SV179 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6370]) ).

thf(6819,plain,
    ! [SV180: $i] :
      ( ( ! [SY869: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ uminus_uminus_int @ SV180 ) ) @ SY869 )
            = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV180 ) @ SY869 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6372]) ).

thf(6820,plain,
    ! [SV181: $i] :
      ( ( ! [SY870: $i] :
            ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV181 ) @ SY870 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ uminus_uminus_int @ SV181 ) ) @ ( hAPP_int_int @ uminus_uminus_int @ SY870 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6373]) ).

thf(6821,plain,
    ! [SV182: $i] :
      ( ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ number_number_of_int @ SV182 ) )
        = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ uminus_uminus_int @ SV182 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6374]) ).

thf(6822,plain,
    ! [SV183: $i] :
      ( ( ! [SY871: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ SV183 ) ) @ ( hAPP_int_int @ uminus_uminus_int @ SY871 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV183 ) @ SY871 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6375]) ).

thf(6823,plain,
    ! [SV184: $i] :
      ( ( ! [SY872: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV184 ) @ ( hAPP_int_int @ uminus_uminus_int @ SY872 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ SV184 ) ) @ SY872 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6376]) ).

thf(6824,plain,
    ! [SV185: $i] :
      ( ( ! [SY873: $i] :
            ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( div_mod_int @ SV185 ) @ SY873 ) ) ) @ SY873 )
            = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ SV185 ) ) @ SY873 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6377]) ).

thf(6825,plain,
    ! [SV186: $i] :
      ( ( ! [SY874: $i] :
            ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ SV186 ) ) @ ( hAPP_int_int @ uminus_uminus_int @ SY874 ) )
            = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( div_mod_int @ SV186 ) @ SY874 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6378]) ).

thf(6826,plain,
    ! [SV187: $i] :
      ( ( ! [SY875: $i] :
            ( ( hAPP_int_int @ ( div_mod_int @ SV187 ) @ ( hAPP_int_int @ uminus_uminus_int @ SY875 ) )
            = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ SV187 ) ) @ SY875 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6379]) ).

thf(6827,plain,
    ! [SV188: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ uminus_uminus_int @ SV188 ) ) @ SV188 )
        = zero_zero_int )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6380]) ).

thf(6828,plain,
    ! [SV189: $i] :
      ( ( ! [SY876: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV189 ) @ ( hAPP_int_int @ uminus_uminus_int @ SY876 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV189 ) @ SY876 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6382]) ).

thf(6829,plain,
    ! [SV190: $i] :
      ( ( ! [SY877: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV190 ) @ SY877 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV190 ) @ ( hAPP_int_int @ uminus_uminus_int @ SY877 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6383]) ).

thf(6830,plain,
    ! [SV191: $i] :
      ( ( ! [SY878: $i] :
            ( ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ SV191 ) ) @ SY878 )
              = zero_zero_int )
            | ( ( hAPP_int_int @ ( div_mod_int @ SV191 ) @ SY878 )
             != zero_zero_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6385]) ).

thf(6831,plain,
    ! [SV192: $i] :
      ( ( ! [SY879: $i] :
            ( ( ( hAPP_int_int @ ( div_mod_int @ SV192 ) @ ( hAPP_int_int @ uminus_uminus_int @ SY879 ) )
              = zero_zero_int )
            | ( ( hAPP_int_int @ ( div_mod_int @ SV192 ) @ SY879 )
             != zero_zero_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6386]) ).

thf(6832,plain,
    ! [SV193: $i] :
      ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ uminus_uminus_int @ SV193 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
        = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV193 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6388]) ).

thf(6833,plain,
    ! [SV194: $i] :
      ( ( ( hAPP_int_int @ pred @ ( hAPP_int_int @ bit0 @ SV194 ) )
        = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ pred @ SV194 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6389]) ).

thf(6834,plain,
    ! [SV195: $i] :
      ( ( ( hAPP_int_int @ pred @ ( hAPP_int_int @ bit1 @ SV195 ) )
        = ( hAPP_int_int @ bit0 @ SV195 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6390]) ).

thf(6835,plain,
    ! [SV196: $i] :
      ( ( ( hAPP_int_int @ pred @ SV196 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV196 ) @ one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6393]) ).

thf(6836,plain,
    ! [SV197: $i] :
      ( ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ bit1 @ SV197 ) )
        = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ pred @ ( hAPP_int_int @ uminus_uminus_int @ SV197 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6394]) ).

thf(6837,plain,
    ! [SV198: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV198 ) @ min )
        = ( hAPP_int_int @ pred @ SV198 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6395]) ).

thf(6838,plain,
    ! [SV199: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ min ) @ SV199 )
        = ( hAPP_int_int @ pred @ SV199 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6396]) ).

thf(6839,plain,
    ! [SV200: $i] :
      ( ( ! [SY880: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ bit0 @ SV200 ) ) @ ( hAPP_int_int @ bit1 @ SY880 ) )
            = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ pred @ SV200 ) ) @ SY880 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6397]) ).

thf(6840,plain,
    ! [SV201: $i] :
      ( ( ! [SY881: $i] :
            ( ( xzgcd @ SV201 @ SY881 )
            = ( xzgcda @ SV201 @ SY881 @ SV201 @ SY881 @ one_one_int @ zero_zero_int @ zero_zero_int @ one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6398]) ).

thf(6841,plain,
    ! [SV202: $i] :
      ( ( ! [SY882: $i,SY883: $i] :
            ( ( ( hAPP_int_int @ ( legacy_zgcd @ SY882 ) @ SY883 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY882 ) @ SV202 ) ) @ SY883 )
              = ( hAPP_int_int @ ( legacy_zgcd @ SV202 ) @ SY883 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6401]) ).

thf(6842,plain,
    ! [SV203: $i] :
      ( ( ! [SY884: $i,SY885: $i] :
            ( ( ( hAPP_int_int @ ( legacy_zgcd @ SY884 ) @ SY885 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( legacy_zgcd @ SV203 ) @ SY885 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY884 ) @ SV203 ) ) @ SY885 )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6402]) ).

thf(6843,plain,
    ! [SV204: $i] :
      ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV204 ) @ one_one_int )
        = one_one_int )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6403]) ).

thf(6844,plain,
    ! [SV205: $i] :
      ( ( ( hAPP_int_int @ ( legacy_zgcd @ one_one_int ) @ SV205 )
        = one_one_int )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6404]) ).

thf(6845,plain,
    ! [SV206: $i] :
      ( ( ! [SY886: $i] :
            ( ( hAPP_int_int @ ( legacy_zgcd @ SV206 ) @ SY886 )
            = ( hAPP_int_int @ ( legacy_zgcd @ SY886 ) @ ( hAPP_int_int @ ( div_mod_int @ SV206 ) @ SY886 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6406]) ).

thf(6846,plain,
    ! [SV207: $i] :
      ( ( ! [SY887: $i,SY888: $i] :
            ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV207 ) @ SY887 ) ) @ SY888 )
            = ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV207 ) @ SY888 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY887 ) @ SY888 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6407]) ).

thf(6847,plain,
    ! [SV208: $i] :
      ( ( ! [SY889: $i] :
            ( ( hAPP_int_int @ ( legacy_zgcd @ SV208 ) @ SY889 )
            = ( hAPP_int_int @ ( legacy_zgcd @ SY889 ) @ SV208 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6408]) ).

thf(6848,plain,
    ! [SV209: $i] :
      ( ( ! [SY890: $i,SY891: $i] :
            ( ( hAPP_int_int @ ( legacy_zgcd @ SV209 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SY890 ) @ SY891 ) )
            = ( hAPP_int_int @ ( legacy_zgcd @ SY890 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV209 ) @ SY891 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6409]) ).

thf(6849,plain,
    ! [SV210: $i] :
      ( ( ! [SY892: $i,SY893: $i] :
            ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( legacy_zgcd @ SV210 ) @ SY892 ) ) @ SY893 )
            = ( hAPP_int_int @ ( legacy_zgcd @ SV210 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SY892 ) @ SY893 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6410]) ).

thf(6850,plain,
    ! [SV211: $i] :
      ( ( ! [SY894: $i] :
            ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ uminus_uminus_int @ SV211 ) ) @ SY894 )
            = ( hAPP_int_int @ ( legacy_zgcd @ SV211 ) @ SY894 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6411]) ).

thf(6851,plain,
    ! [SV212: $i] :
      ( ( ! [SY895: $i] :
            ( ( hAPP_int_int @ ( legacy_zgcd @ SV212 ) @ ( hAPP_int_int @ uminus_uminus_int @ SY895 ) )
            = ( hAPP_int_int @ ( legacy_zgcd @ SV212 ) @ SY895 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6412]) ).

thf(6852,plain,
    ! [SV213: $i] :
      ( ( ! [SY896: $i,SY897: $i] :
            ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV213 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY896 ) @ SY897 ) ) ) @ SY896 )
            = ( hAPP_int_int @ ( legacy_zgcd @ SV213 ) @ SY896 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6413]) ).

thf(6853,plain,
    ! [SV214: $i] :
      ( ( ! [SY898: $i,SY899: $i] :
            ( ( ( hAPP_int_int @ ( legacy_zgcd @ SY898 ) @ SY899 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY898 ) @ SV214 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY899 ) @ SV214 ) )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6414]) ).

thf(6854,plain,
    ! [SV215: $i] :
      ( ( ! [SY900: $i,SY901: $i] :
            ( ( ( hAPP_int_int @ ( legacy_zgcd @ SY900 ) @ SY901 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY900 ) @ SV215 ) ) @ SY901 )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6415]) ).

thf(6855,plain,
    ! [SV216: $i] :
      ( ( ( hAPP_int_int @ ( legacy_zgcd @ zero_zero_int ) @ SV216 )
        = ( hAPP_int_int @ abs_abs_int @ SV216 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6416]) ).

thf(6856,plain,
    ! [SV217: $i] :
      ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV217 ) @ zero_zero_int )
        = ( hAPP_int_int @ abs_abs_int @ SV217 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6417]) ).

thf(6857,plain,
    ! [SV218: $i] :
      ( ( ( hAPP_int_int @ number_number_of_int @ SV218 )
        = ( hAPP_int_int @ ring_1_of_int_int @ SV218 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6419]) ).

thf(6858,plain,
    ! [SV219: $i] :
      ( ( ( hAPP_int_int @ ring_1_of_int_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV219 ) )
        = ( hAPP_nat_int @ semiri1621563631at_int @ SV219 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6420]) ).

thf(6859,plain,
    ! [SV220: $i] :
      ( ( ! [SY902: $i] :
            ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV220 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ SY902 ) ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV220 ) @ ( hAPP_int_nat @ number_number_of_nat @ SY902 ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV220 ) @ ( hAPP_int_nat @ number_number_of_nat @ SY902 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6422]) ).

thf(6860,plain,
    ! [SV221: $i] :
      ( ( ! [SY903: $i,SY904: $i,SY905: $i] :
            ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY904 ) @ SY905 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY904 ) @ SV221 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY905 ) @ SY903 ) )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6423]) ).

thf(6861,plain,
    ! [SV222: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV222 ) @ zero_zero_int )
        = ( hAPP_int_int @ abs_abs_int @ SV222 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6424]) ).

thf(6862,plain,
    ! [SV223: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ zero_zero_int ) @ SV223 )
        = ( hAPP_int_int @ abs_abs_int @ SV223 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6425]) ).

thf(6863,plain,
    ! [SV224: $i] :
      ( ( ! [SY906: $i,SY907: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV224 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY906 ) @ SV224 ) ) @ SY907 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV224 ) @ SY907 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6426]) ).

thf(6864,plain,
    ! [SV225: $i] :
      ( ( ! [SY908: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV225 ) @ SY908 ) ) @ SY908 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV225 ) @ SY908 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6427]) ).

thf(6865,plain,
    ! [SV226: $i] :
      ( ( ! [SY909: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV226 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV226 ) @ SY909 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV226 ) @ SY909 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6428]) ).

thf(6866,plain,
    ! [SV227: $i] :
      ( ( ! [SY910: $i] :
            ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV227 ) @ SY910 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV227 ) @ SY910 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6429]) ).

thf(6867,plain,
    ! [SV228: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV228 ) @ SV228 )
        = ( hAPP_int_int @ abs_abs_int @ SV228 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6430]) ).

thf(6868,plain,
    ! [SV229: $i] :
      ( ( ! [SY911: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV229 ) @ SY911 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ abs_abs_int @ SV229 ) ) @ ( hAPP_int_int @ abs_abs_int @ SY911 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6431]) ).

thf(6869,plain,
    ! [SV230: $i] :
      ( ( ! [SY912: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV230 ) @ ( hAPP_int_int @ abs_abs_int @ SY912 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV230 ) @ SY912 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6432]) ).

thf(6870,plain,
    ! [SV231: $i] :
      ( ( ! [SY913: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ abs_abs_int @ SV231 ) ) @ SY913 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV231 ) @ SY913 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6433]) ).

thf(6871,plain,
    ! [SV232: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV232 ) @ one_one_int ) ) @ SV232 )
        = one_one_int )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6434]) ).

thf(6872,plain,
    ! [SV233: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV233 ) @ one_one_int ) ) @ SV233 )
        = one_one_int )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6435]) ).

thf(6873,plain,
    ! [SV234: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV234 ) @ one_one_int )
        = one_one_int )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6436]) ).

thf(6874,plain,
    ! [SV235: $i] :
      ( ( ! [SY914: $i,SY915: $i] :
            ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY914 ) @ SY915 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY914 ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY915 ) @ SV235 ) )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6437]) ).

thf(6875,plain,
    ! [SV236: $i] :
      ( ( ! [SY916: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV236 ) @ SY916 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY916 ) @ ( hAPP_int_int @ ( div_mod_int @ SV236 ) @ SY916 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6438]) ).

thf(6876,plain,
    ! [SV237: $i] :
      ( ( ! [SY917: $i,SY918: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV237 ) @ SY917 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY918 ) @ SY917 ) )
            = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV237 ) @ SY918 ) ) @ SY917 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6439]) ).

thf(6877,plain,
    ! [SV238: $i] :
      ( ( ! [SY919: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV238 ) @ SY919 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY919 ) @ SV238 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6440]) ).

thf(6878,plain,
    ! [SV239: $i] :
      ( ( ! [SY920: $i,SY921: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV239 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY920 ) @ SY921 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY920 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV239 ) @ SY921 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6441]) ).

thf(6879,plain,
    ! [SV240: $i] :
      ( ( ! [SY922: $i,SY923: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV240 ) @ SY922 ) ) @ SY923 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV240 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY922 ) @ SY923 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6442]) ).

thf(6880,plain,
    ! [SV241: $i] :
      ( ( ! [SY924: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV241 ) @ ( hAPP_int_int @ uminus_uminus_int @ SY924 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV241 ) @ SY924 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6443]) ).

thf(6881,plain,
    ! [SV242: $i] :
      ( ( ! [SY925: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ uminus_uminus_int @ SV242 ) ) @ SY925 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV242 ) @ SY925 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6444]) ).

thf(6882,plain,
    ! [SV243: $i] :
      ( ( ! [SY926: $i,SY927: $i] :
            ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY926 ) @ SY927 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY926 ) @ SV243 ) ) @ SY927 )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV243 ) @ SY927 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6447]) ).

thf(6883,plain,
    ! [SV244: $i] :
      ( ( ! [SY928: $i,SY929: $i] :
            ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY928 ) @ SY929 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY928 ) @ SV244 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY928 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY929 ) @ SV244 ) )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6448]) ).

thf(6884,plain,
    ! [SV245: $i] :
      ( ( ! [SY930: $i] :
            ( ! [SY931: $i] :
                ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV245 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY930 ) @ SY931 ) )
               != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV245 ) @ SY930 )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6449]) ).

thf(6885,plain,
    ! [SV246: $i] :
      ( ( ! [SY932: $i,SY933: $i] :
            ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV246 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY932 ) @ SY933 ) )
             != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV246 ) @ SY933 )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6450]) ).

thf(6886,plain,
    ! [SV247: $i] :
      ( ( ! [SY934: $i,SY935: $i,SY936: $i] :
            ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY935 ) @ SY936 )
              = zero_zero_int )
            | ( SY935
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY934 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY935 ) @ SY936 ) ) )
            | ( SY936
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV247 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY935 ) @ SY936 ) ) )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY934 ) @ SV247 )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6451]) ).

thf(6887,plain,
    ! [SV248: $i] :
      ( ( ~ ( is_int @ SV248 )
        | ( ( hAPP_int_int @ cOMBI_int @ SV248 )
          = SV248 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6452]) ).

thf(6888,plain,
    ! [SV249: $i] :
      ( ( ! [SY937: $i,SY938: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ ( hAPP_f2135977429nt_int @ cOMBC_int_int_int @ SV249 ) @ SY937 ) @ SY938 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ SV249 @ SY938 ) @ SY937 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6453]) ).

thf(6889,plain,
    ! [SV250: $i] :
      ( ( is_int @ ( archim856651990g_real @ SV250 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6454]) ).

thf(6890,plain,
    ! [SV251: $i] :
      ( ( is_int @ ( archim791455193or_rat @ SV251 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6455]) ).

thf(6891,plain,
    ! [SV252: $i] :
      ( ( is_int @ ( archim1246769320r_real @ SV252 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6456]) ).

thf(6892,plain,
    ! [SV253: $i] :
      ( ( ! [SY939: $i] : ( is_int @ ( big_co1548731110nt_int @ SV253 @ SY939 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6457]) ).

thf(6893,plain,
    ! [SV254: $i] :
      ( ( is_int @ ( code_int_of @ SV254 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6458]) ).

thf(6894,plain,
    ! [SV255: $i] :
      ( ( is_int @ ( the_int @ SV255 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6459]) ).

thf(6895,plain,
    ! [SV256: $i] :
      ( ( is_int @ ( hilbert_Eps_int @ SV256 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6460]) ).

thf(6896,plain,
    ! [SV257: $i] :
      ( ( is_int @ ( quickcheck_int_of @ SV257 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6462]) ).

thf(6897,plain,
    ! [SV258: $i] :
      ( ( ! [SY940: $i] : ( is_int @ ( hAPP_f1594865479ol_int @ SV258 @ SY940 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6463]) ).

thf(6898,plain,
    ! [SV259: $i] :
      ( ( ! [SY941: $i] : ( is_int @ ( hAPP_f659380387ol_int @ SV259 @ SY941 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6464]) ).

thf(6899,plain,
    ! [SV260: $i] :
      ( ( ! [SY942: $i] : ( is_int @ ( hAPP_P1175774780nt_int @ SV260 @ SY942 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6465]) ).

thf(6900,plain,
    ( ( one_one_nat = zero_zero_nat )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6477]) ).

thf(6901,plain,
    ( ( zero_zero_nat = one_one_nat )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6478]) ).

thf(6902,plain,
    ! [SV261: $i] :
      ( ( ~ ( is_int @ SV261 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV261 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ pls ) ) )
          = SV261 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6483]) ).

thf(6903,plain,
    ! [SV262: $i] :
      ( ( ~ ( is_int @ SV262 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ pls ) ) ) @ SV262 )
          = SV262 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6484]) ).

thf(6904,plain,
    ! [SV263: $i] :
      ( ( ~ ( is_int @ SV263 )
        | ! [SY943: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV263 ) @ SY943 )
           != one_one_int )
        | ( SV263 = one_one_int )
        | ( SV263
          = ( hAPP_int_int @ number_number_of_int @ min ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6486]) ).

thf(6905,plain,
    ! [SV264: $i] :
      ( ( ! [SY944: $i,SY945: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ SV264 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY944 ) @ SY945 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ SV264 ) ) @ SY944 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ SV264 ) ) @ SY945 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6491]) ).

thf(6906,plain,
    ! [SV265: $i] :
      ( ( ! [SY946: $i,SY947: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV265 ) @ SY946 ) ) @ ( hAPP_int_int @ number_number_of_int @ SY947 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV265 ) @ ( hAPP_int_int @ number_number_of_int @ SY947 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY946 ) @ ( hAPP_int_int @ number_number_of_int @ SY947 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6492]) ).

thf(6907,plain,
    ! [SV266: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV266 ) @ min )
        = ( hAPP_int_int @ succ @ SV266 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6493]) ).

thf(6908,plain,
    ! [SV267: $i] :
      ( ( ! [SY948: $i] :
            ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV267 ) @ SY948 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV267 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY948 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ SV267 ) ) @ SY948 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6494]) ).

thf(6909,plain,
    ! [SV268: $i] :
      ( ( ! [SY949: $i] :
            ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV268 ) @ SY949 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV268 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV268 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) @ SY949 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ SV268 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY949 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY949 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6495]) ).

thf(6910,plain,
    ! [SV269: $i] :
      ( ( ! [SY950: $i] :
            ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV269 ) @ SY950 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV269 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ SV269 ) ) @ SY950 ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY950 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6496]) ).

thf(6911,plain,
    ! [SV270: $i] :
      ( ( ! [SY951: $i] :
            ( ( hAPP_int_int @ ( multInv @ SV270 ) @ SY951 )
            = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY951 ) @ ( hAPP_int_nat @ nat @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV270 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6499]) ).

thf(6912,plain,
    ! [SV271: $i] :
      ( ( ! [SY952: $i] :
            ( ( ( hAPP_nat_nat @ suc @ SV271 )
             != ( hAPP_nat_nat @ suc @ SY952 ) )
            | ( SV271 = SY952 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6500]) ).

thf(6913,plain,
    ! [SV272: $i] :
      ( ( ( hAPP_nat_nat @ suc @ SV272 )
       != SV272 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6502]) ).

thf(6914,plain,
    ! [SV273: $i] :
      ( ( SV273
       != ( hAPP_nat_nat @ suc @ SV273 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6503]) ).

thf(6915,plain,
    ! [SV274: $i] :
      ( ( zero_zero_nat
       != ( hAPP_nat_nat @ suc @ SV274 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6504]) ).

thf(6916,plain,
    ! [SV275: $i] :
      ( ( zero_zero_nat
       != ( hAPP_nat_nat @ suc @ SV275 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6505]) ).

thf(6917,plain,
    ! [SV276: $i] :
      ( ( ( hAPP_nat_nat @ suc @ SV276 )
       != zero_zero_nat )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6506]) ).

thf(6918,plain,
    ! [SV277: $i] :
      ( ( ( hAPP_nat_nat @ suc @ SV277 )
       != zero_zero_nat )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6507]) ).

thf(6919,plain,
    ! [SV278: $i] :
      ( ( zero_zero_nat
       != ( hAPP_nat_nat @ suc @ SV278 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6508]) ).

thf(6920,plain,
    ! [SV279: $i] :
      ( ( ( hAPP_nat_nat @ suc @ SV279 )
       != zero_zero_nat )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6509]) ).

thf(6921,plain,
    ! [SV280: $i] :
      ( ( ( hAPP_int_int @ ( div_mod_int @ SV280 ) @ ( hAPP_int_int @ number_number_of_int @ min ) )
        = zero_zero_int )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6513]) ).

thf(6922,plain,
    ! [SV281: $i] :
      ( ( ~ ( is_int @ SV281 )
        | ! [SY953: $i] :
            ( SV281
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY953 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV281 ) @ SY953 ) ) ) @ ( hAPP_int_int @ ( div_mod_int @ SV281 ) @ SY953 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6514]) ).

thf(6923,plain,
    ! [SV282: $i] :
      ( ( ! [SY954: $i,SY955: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV282 ) @ SY954 ) ) @ SY955 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV282 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SY954 ) @ SY955 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV282 ) @ ( hAPP_int_int @ ( div_mod_int @ SY954 ) @ SY955 ) ) ) @ SY955 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6515]) ).

thf(6924,plain,
    ! [SV283: $i] :
      ( ( ! [SY956: $i,SY957: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV283 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SY956 ) @ SV283 ) ) ) @ ( hAPP_int_int @ ( div_mod_int @ SY956 ) @ SV283 ) ) ) @ SY957 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY956 ) @ SY957 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6516]) ).

thf(6925,plain,
    ! [SV284: $i] :
      ( ( ! [SY958: $i,SY959: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV284 ) @ SY958 ) ) @ SY958 ) ) @ ( hAPP_int_int @ ( div_mod_int @ SV284 ) @ SY958 ) ) ) @ SY959 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV284 ) @ SY959 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6517]) ).

thf(6926,plain,
    ! [SV285: $i] :
      ( ( ! [SY960: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV285 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SY960 ) @ SV285 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY960 ) @ ( hAPP_int_int @ ( div_mod_int @ SY960 ) @ SV285 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6518]) ).

thf(6927,plain,
    ! [SV286: $i] :
      ( ( ! [SY961: $i] :
            ( ( hAPP_int_int @ ( div_mod_int @ SV286 ) @ SY961 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV286 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV286 ) @ SY961 ) ) @ SY961 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6519]) ).

thf(6928,plain,
    ! [SV287: $i] :
      ( ( ! [SY962: $i,SY963: $i,SY964: $i,SY965: $i,SY966: $i,SY967: $i,SY968: $i] :
            ( ( SY964
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY965 ) @ SY966 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY967 ) @ SY968 ) ) )
            | ( SV287
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY962 ) @ SY966 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY963 ) @ SY968 ) ) )
            | ( ( hAPP_int_int @ ( div_mod_int @ SY964 ) @ SV287 )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY965 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SY964 ) @ SV287 ) ) @ SY962 ) ) ) @ SY966 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY967 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SY964 ) @ SV287 ) ) @ SY963 ) ) ) @ SY968 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6522]) ).

thf(6929,plain,
    ! [SV288: $i] :
      ( ( ! [SY969: $i,SY970: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV288 ) @ SY969 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY970 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV288 ) @ SY970 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SY969 ) @ SY970 ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( div_mod_int @ SV288 ) @ SY970 ) ) @ ( hAPP_int_int @ ( div_mod_int @ SY969 ) @ SY970 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6523]) ).

thf(6930,plain,
    ! [SV289: $i] :
      ( ( ! [SY971: $i] :
            ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ SV289 ) ) ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ SY971 ) ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ number_number_of_int @ SV289 ) ) @ ( hAPP_int_int @ number_number_of_int @ SY971 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6526]) ).

thf(6931,plain,
    ! [SV290: $i] :
      ( ( ! [SY972: $i] :
            ( ( hAPP_int_int @ ( inv @ SV290 ) @ SY972 )
            = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY972 ) @ ( hAPP_int_nat @ nat @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV290 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) ) @ SV290 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6530]) ).

thf(6932,plain,
    ! [SV291: $i] :
      ( ( ! [SY973: $i] :
            ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ SV291 ) ) @ SY973 )
            = ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ SV291 ) @ SY973 ) ) ) @ SY973 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6532]) ).

thf(6933,plain,
    ! [SV292: $i] :
      ( ( ( hAPP_nat_nat @ ( div_mod_nat @ SV292 ) @ ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
        = zero_zero_nat )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6533]) ).

thf(6934,plain,
    ! [SV293: $i] :
      ( ( ! [SY974: $i] :
            ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV293 ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ SY974 ) )
            = ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( div_mod_nat @ SV293 ) @ SY974 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6535]) ).

thf(6935,plain,
    ! [SV294: $i] :
      ( ( ! [SY975: $i] :
            ( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( div_mod_nat @ SV294 ) @ SY975 ) )
            = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV294 ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ SY975 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6536]) ).

thf(6936,plain,
    ! [SV295: $i] :
      ( ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ suc @ SV295 ) ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
        = ( hAPP_nat_nat @ ( div_mod_nat @ SV295 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6537]) ).

thf(6937,plain,
    ! [SV296: $i] :
      ( ( ( ( hAPP_nat_nat @ ( div_mod_nat @ SV296 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
          = ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
        | ( ( hAPP_nat_nat @ ( div_mod_nat @ SV296 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
          = ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
        | ( ( hAPP_nat_nat @ ( div_mod_nat @ SV296 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
          = zero_zero_nat )
        | ( ( hAPP_nat_nat @ ( div_mod_nat @ SV296 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
          = one_one_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6538]) ).

thf(6938,plain,
    ! [SV297: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ min ) @ SV297 )
        = ( hAPP_int_int @ uminus_uminus_int @ SV297 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6539]) ).

thf(6939,plain,
    ! [SV298: $i] :
      ( ( ( hAPP_int_nat @ nat @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV298 ) ) )
        = zero_zero_nat )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6540]) ).

thf(6940,plain,
    ! [SV299: $i] :
      ( ( ! [SY976: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ number_number_of_int @ SV299 ) ) @ ( hAPP_int_int @ number_number_of_int @ SY976 ) )
            = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV299 ) @ ( hAPP_int_int @ uminus_uminus_int @ SY976 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6541]) ).

thf(6941,plain,
    ! [SV300: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV300 ) @ ( hAPP_int_int @ number_number_of_int @ min ) )
        = ( hAPP_int_int @ uminus_uminus_int @ SV300 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6544]) ).

thf(6942,plain,
    ! [SV301: $i] :
      ( ( ( hAPP_nat_nat @ fact_fact_nat @ SV301 )
       != zero_zero_nat )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6547]) ).

thf(6943,plain,
    ! [SV302: $i] :
      ( ( ( SV302 = zero_zero_nat )
        | ( SV302
          = ( hAPP_nat_nat @ suc @ ( sK10_M_1 @ SV302 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6551]) ).

thf(6944,plain,
    ! [SV303: $i] :
      ( ( ( SV303 = zero_zero_nat )
        | ( SV303
          = ( hAPP_nat_nat @ suc @ ( sK9_Nat_1 @ SV303 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6552]) ).

thf(6945,plain,
    ! [SV304: $i] :
      ( ( ~ ( is_int @ SV304 )
        | ( ( hAPP_int_int @ succ @ ( hAPP_int_int @ pred @ SV304 ) )
          = SV304 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6553]) ).

thf(6946,plain,
    ! [SV305: $i] :
      ( ( ( hAPP_nat_nat @ size_size_nat @ SV305 )
        = SV305 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6554]) ).

thf(6947,plain,
    ! [SV306: $i] :
      ( ( ( hAPP_int_int @ fact_fact_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV306 ) )
        = ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ fact_fact_nat @ SV306 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6557]) ).

thf(6948,plain,
    ! [SV307: $i] :
      ( ( ! [SY977: $i,SY978: $i] :
            ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV307 ) @ SY977 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV307 ) @ SY978 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV307 ) ) @ ( hAPP_int_int @ ( legacy_zgcd @ SY977 ) @ SY978 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6558]) ).

thf(6949,plain,
    ! [SV308: $i] :
      ( ( ~ ( is_int @ SV308 )
        | ( SV308
          = ( hAPP_nat_int @ semiri1621563631at_int @ ( sK4_N_1 @ SV308 ) ) )
        | ( SV308
          = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ suc @ ( sK3_N_1 @ SV308 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6561]) ).

thf(6950,plain,
    ! [SV309: $i] :
      ( ( ( image_int_nat @ nat @ ( image_nat_int @ semiri1621563631at_int @ SV309 ) )
        = SV309 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6563]) ).

thf(6951,plain,
    ! [SV310: $i] :
      ( ( ! [SY979: $i,SY980: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV310 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY979 ) @ SY980 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV310 ) @ SY979 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV310 ) @ SY980 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6565]) ).

thf(6952,plain,
    ! [SV311: $i] :
      ( ( ! [SY981: $i,SY982: $i] :
            ( ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV311 ) @ SY981 ) ) @ SY982 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV311 ) @ SY982 )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6566]) ).

thf(6953,plain,
    ! [SV312: $i] :
      ( ( ( hAPP_nat_nat @ cOMBI_nat @ SV312 )
        = SV312 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6569]) ).

thf(6954,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( ( hAPP_int_int @ ( legacy_zgcd @ zero_zero_int ) @ SX0 )
             != one_one_int )
            | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
              = one_one_int ) )
      | ~ ! [SX0: $i] :
            ( ( ( hAPP_int_int @ abs_abs_int @ SX0 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( legacy_zgcd @ zero_zero_int ) @ SX0 )
              = one_one_int ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6571]) ).

thf(6955,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( one_one_int != SX0 )
            | ( SX0 = one_one_int ) )
      | ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( SX0 != one_one_int )
            | ( one_one_int = SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6572]) ).

thf(6956,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
             != zero_zero_int )
            | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ ( hAPP_int_int @ uminus_uminus_int @ SX1 ) )
              = zero_zero_int ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
              = zero_zero_int )
            | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ ( hAPP_int_int @ uminus_uminus_int @ SX1 ) )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 ) ) @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6573]) ).

thf(6957,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( SX0 != SX1 )
            | ( ( image_nat_int @ semiri1621563631at_int @ SX0 )
              = ( image_nat_int @ semiri1621563631at_int @ SX1 ) ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ( ( image_nat_int @ semiri1621563631at_int @ SX0 )
             != ( image_nat_int @ semiri1621563631at_int @ SX1 ) )
            | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6574]) ).

thf(6958,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
              = zero_zero_int )
            | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
              = one_one_int ) )
      | ~ ! [SX0: $i] :
            ( ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
             != one_one_int )
            | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
             != zero_zero_int ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6575]) ).

thf(6959,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( SX0 != zero_zero_nat )
            | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ SX0 )
              = one_one_int ) )
      | ~ ! [SX0: $i] :
            ( ( SX0 = zero_zero_nat )
            | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ SX0 )
              = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6576]) ).

thf(6960,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( ( hAPP_int_nat @ number_number_of_nat @ SX0 )
             != zero_zero_nat )
            | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ ( hAPP_int_nat @ number_number_of_nat @ SX0 ) )
              = one_one_int ) )
      | ~ ! [SX0: $i] :
            ( ( ( hAPP_int_nat @ number_number_of_nat @ SX0 )
              = zero_zero_nat )
            | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ ( hAPP_int_nat @ number_number_of_nat @ SX0 ) )
              = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6577]) ).

thf(6961,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( pls
             != ( hAPP_int_int @ bit0 @ SX0 ) )
            | ( pls = SX0 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( pls != SX0 )
            | ( pls
              = ( hAPP_int_int @ bit0 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6578]) ).

thf(6962,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
             != zero_zero_int )
            | ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ SX0 ) ) @ SX1 )
              = zero_zero_int ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
              = zero_zero_int )
            | ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ SX0 ) ) @ SX1 )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SX1 ) @ ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6579]) ).

thf(6963,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
             != zero_zero_int )
            | ( SX0 = zero_zero_int )
            | ( SX1 = zero_zero_int ) )
      | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( SX0 != zero_zero_int )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                    = zero_zero_int ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( SX1 != zero_zero_int )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                    = zero_zero_int ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6580]) ).

thf(6964,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ! [SX1: $i] :
                ( ( ( hAPP_int_nat @ number_number_of_nat @ SX1 )
                  = zero_zero_nat )
                | ( SX0 != zero_zero_int )
                | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ SX1 ) )
                  = zero_zero_int ) ) )
      | ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ SX1 ) )
                       != zero_zero_int )
                      | ( ( hAPP_int_nat @ number_number_of_nat @ SX1 )
                       != zero_zero_nat ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ! [SX1: $i] :
                      ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ SX1 ) )
                     != zero_zero_int )
                  | ( SX0 = zero_zero_int ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6581]) ).

thf(6965,plain,
    ! [SV313: $i] :
      ( ( ~ ( is_int @ SV313 )
        | ! [SY983: $i] :
            ( ( ( hAPP_int_int @ ( div_mod_int @ SV313 ) @ SY983 )
             != zero_zero_int )
            | ~ ( ( SV313
                 != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY983 ) @ ( sK11_Q_4 @ SY983 @ SV313 ) ) )
                | ~ ( is_int @ ( sK11_Q_4 @ SY983 @ SV313 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6582]) ).

thf(6966,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
             != ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ( SX0 != SX1 )
            | ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
              = ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6583]) ).

thf(6967,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( zero_zero_nat != SX0 )
            | ( SX0 = zero_zero_nat ) )
      | ~ ! [SX0: $i] :
            ( ( SX0 != zero_zero_nat )
            | ( zero_zero_nat = SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6584]) ).

thf(6968,plain,
    ( ( ~ ~ ( ~ ( is_int @ sK13_X_1 )
            | ~ ( is_int @ sK14_SY716 ) )
      | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ sK13_X_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ sK14_SY716 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
       != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6585]) ).

thf(6969,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX1 )
            | ( SX1 = zero_zero_int )
            | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
             != zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ SX0 ) ) @ SX1 )
              = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ SX1 ) ) ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX1 )
            | ( SX1 = zero_zero_int )
            | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
              = zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ SX0 ) ) @ SX1 )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ SX1 ) ) ) @ one_one_int ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6586]) ).

thf(6970,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
             != zero_zero_int )
            | ( SX0 = zero_zero_int ) )
      | ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( SX0 != zero_zero_int )
            | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
              = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6587]) ).

thf(6971,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( ( hAPP_int_int @ bit1 @ SX0 )
             != min )
            | ( SX0 = min ) )
      | ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( SX0 != min )
            | ( ( hAPP_int_int @ bit1 @ SX0 )
              = min ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6588]) ).

thf(6972,plain,
    ! [SV314: $i] :
      ( ( ! [SY984: $i] :
            ( ~ ( is_int @ SV314 )
            | ~ ( is_int @ SY984 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SY984 )
              = zero_zero_int )
            | ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK1_A_4 @ SY984 @ SV314 ) )
                                  | ~ ( is_int @ ( sK2_SY713 @ SY984 @ SV314 ) ) )
                            | ( SV314
                             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK1_A_4 @ SY984 @ SV314 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SY984 ) ) ) )
                      | ( SY984
                       != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK2_SY713 @ SY984 @ SV314 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SY984 ) ) ) )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( sK1_A_4 @ SY984 @ SV314 ) ) @ ( sK2_SY713 @ SY984 @ SV314 ) )
                 != one_one_int ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6589]) ).

thf(6973,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ number_number_of_int @ SX0 )
             != ( hAPP_int_int @ number_number_of_int @ SX1 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0 != SX1 )
            | ( ( hAPP_int_int @ number_number_of_int @ SX0 )
              = ( hAPP_int_int @ number_number_of_int @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6590]) ).

thf(6974,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
             != ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
            | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
              = ( hAPP_int_int @ abs_abs_int @ SX1 ) ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ( ( hAPP_int_int @ abs_abs_int @ SX0 )
             != ( hAPP_int_int @ abs_abs_int @ SX1 ) )
            | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
              = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6591]) ).

thf(6975,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ! [SX1: $i] :
                ( ( SX1 = zero_zero_nat )
                | ( SX0 != zero_zero_int )
                | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ SX1 )
                  = zero_zero_int ) ) )
      | ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ SX1 )
                       != zero_zero_int )
                      | ( SX1 != zero_zero_nat ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ! [SX1: $i] :
                      ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ SX1 )
                     != zero_zero_int )
                  | ( SX0 = zero_zero_int ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6592]) ).

thf(6976,plain,
    ! [SV315: $i] :
      ( ( ! [SY985: $i] :
            ~ ( ~ ! [SY986: $i,SY987: $i] :
                    ( ~ ( is_int @ SV315 )
                    | ~ ( is_int @ SY985 )
                    | ~ ( is_int @ SY986 )
                    | ~ ( is_int @ SY987 )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SY985 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY986 ) @ SY987 ) )
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SY987 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY986 ) @ SY985 ) ) )
                    | ( SV315 = SY986 )
                    | ( SY985 = SY987 ) )
              | ~ ~ ( ~ ! [SY988: $i,SY989: $i] :
                          ( ~ ( is_int @ SV315 )
                          | ~ ( is_int @ SY985 )
                          | ~ ( is_int @ SY988 )
                          | ~ ( is_int @ SY989 )
                          | ( SV315 != SY988 )
                          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SY985 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY988 ) @ SY989 ) )
                            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SY989 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY988 ) @ SY985 ) ) ) )
                    | ~ ! [SY990: $i,SY991: $i] :
                          ( ~ ( is_int @ SV315 )
                          | ~ ( is_int @ SY985 )
                          | ~ ( is_int @ SY990 )
                          | ~ ( is_int @ SY991 )
                          | ( SY985 != SY991 )
                          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SY985 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY990 ) @ SY991 ) )
                            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SY991 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY990 ) @ SY985 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6593]) ).

thf(6977,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX0 ) @ SX1 ) )
            | ( SX1 = zero_zero_int ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX1 != zero_zero_int )
            | ( SX0
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX0 ) @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6594]) ).

thf(6978,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( hAPP_int_nat @ number_number_of_nat @ SX0 )
             != SX1 )
            | ( SX1
              = ( hAPP_int_nat @ number_number_of_nat @ SX0 ) ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ( SX1
             != ( hAPP_int_nat @ number_number_of_nat @ SX0 ) )
            | ( ( hAPP_int_nat @ number_number_of_nat @ SX0 )
              = SX1 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6595]) ).

thf(6979,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( zero_zero_int != SX0 )
            | ( SX0 = zero_zero_int ) )
      | ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( SX0 != zero_zero_int )
            | ( zero_zero_int = SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6596]) ).

thf(6980,plain,
    ! [SV316: $i] :
      ( ( ~ ( ~ ! [SY992: $i,SY993: $i] :
                  ( ~ ( is_int @ SY992 )
                  | ~ ( is_int @ SY993 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SY992 )
                   != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SY993 ) )
                  | ( SY992 = SY993 ) )
            | ~ ! [SY994: $i,SY995: $i] :
                  ( ~ ( is_int @ SY994 )
                  | ~ ( is_int @ SY995 )
                  | ( SY994 != SY995 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SY994 )
                    = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SY995 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6597]) ).

thf(6981,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX1 = zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX1 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX1 ) @ SX0 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX1 ) @ SX0 ) ) )
              = one_one_int ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0 = zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX1 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX1 ) @ SX0 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX1 ) @ SX0 ) ) )
              = one_one_int ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6598]) ).

thf(6982,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ bit1 @ SX0 )
             != ( hAPP_int_int @ bit1 @ SX1 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0 != SX1 )
            | ( ( hAPP_int_int @ bit1 @ SX0 )
              = ( hAPP_int_int @ bit1 @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6599]) ).

thf(6983,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( SX0 != zero_zero_nat )
            | ( SX1 != zero_zero_nat )
            | ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SX0 ) )
              = ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) ) )
      | ~ ~ ( ~ ! [SX0: $i] :
                  ( ! [SX1: $i] :
                      ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SX0 ) )
                     != ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
                  | ( SX0 = zero_zero_nat ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SX0 ) )
                   != ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
                  | ( SX1 = zero_zero_nat ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6600]) ).

thf(6984,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX1 = zero_zero_int )
            | ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK7_C_3 @ SX1 @ SX0 ) )
                                  | ~ ( is_int @ ( sK8_SY715 @ SX1 @ SX0 ) ) )
                            | ( SX1
                             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) @ ( sK7_C_3 @ SX1 @ SX0 ) ) ) )
                      | ( SX0
                       != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) @ ( sK8_SY715 @ SX1 @ SX0 ) ) ) )
                | ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK7_C_3 @ SX1 @ SX0 ) ) @ ( sK8_SY715 @ SX1 @ SX0 ) )
                 != one_one_int ) ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0 = zero_zero_int )
            | ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK5_C_3 @ SX1 @ SX0 ) )
                                  | ~ ( is_int @ ( sK6_SY714 @ SX1 @ SX0 ) ) )
                            | ( SX1
                             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) @ ( sK5_C_3 @ SX1 @ SX0 ) ) ) )
                      | ( SX0
                       != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) @ ( sK6_SY714 @ SX1 @ SX0 ) ) ) )
                | ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK5_C_3 @ SX1 @ SX0 ) ) @ ( sK6_SY714 @ SX1 @ SX0 ) )
                 != one_one_int ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6601]) ).

thf(6985,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ number_number_of_int @ SX0 )
             != SX1 )
            | ( SX1
              = ( hAPP_int_int @ number_number_of_int @ SX0 ) ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX1 )
            | ( SX1
             != ( hAPP_int_int @ number_number_of_int @ SX0 ) )
            | ( ( hAPP_int_int @ number_number_of_int @ SX0 )
              = SX1 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6602]) ).

thf(6986,plain,
    ! [SV317: $i] :
      ( ( ~ ( ~ ! [SY996: $i,SY997: $i] :
                  ( ~ ( is_int @ SV317 )
                  | ~ ( is_int @ SY997 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV317 ) @ SY996 )
                   != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY997 ) @ SY996 ) )
                  | ( SV317 = SY997 ) )
            | ~ ! [SY998: $i,SY999: $i] :
                  ( ~ ( is_int @ SV317 )
                  | ~ ( is_int @ SY999 )
                  | ( SV317 != SY999 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV317 ) @ SY998 )
                    = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY999 ) @ SY998 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6603]) ).

thf(6987,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX1 = zero_zero_int )
            | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX1 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) )
              = one_one_int ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0 = zero_zero_int )
            | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX1 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) )
              = one_one_int ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6604]) ).

thf(6988,plain,
    ! [SV318: $i] :
      ( ( ! [SY1000: $i,SY1001: $i] :
            ~ ( ~ ( ~ ( is_int @ SY1001 )
                  | ! [SY1002: $i,SY1003: $i] :
                      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV318 ) @ SY1000 ) ) @ SY1001 )
                       != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1002 ) @ SY1000 ) ) @ SY1003 ) )
                      | ( SY1001
                        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1002 ) @ SV318 ) ) @ SY1000 ) ) @ SY1003 ) ) ) )
              | ~ ( ~ ( is_int @ SY1001 )
                  | ! [SY1004: $i,SY1005: $i] :
                      ( ( SY1001
                       != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1004 ) @ SV318 ) ) @ SY1000 ) ) @ SY1005 ) )
                      | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV318 ) @ SY1000 ) ) @ SY1001 )
                        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1004 ) @ SY1000 ) ) @ SY1005 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6605]) ).

thf(6989,plain,
    ! [SV319: $i] :
      ( ( ! [SY1006: $i] :
            ~ ( ~ ! [SY1007: $i,SY1008: $i] :
                    ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY1007 ) @ SY1008 )
                     != one_one_int )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SY1006 )
                     != one_one_int )
                    | ( ( hAPP_int_int @ abs_abs_int @ SY1007 )
                     != ( hAPP_int_int @ abs_abs_int @ SV319 ) )
                    | ( ( hAPP_int_int @ abs_abs_int @ SY1006 )
                     != ( hAPP_int_int @ abs_abs_int @ SY1008 ) )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SY1007 ) ) @ ( hAPP_int_int @ abs_abs_int @ SY1006 ) )
                      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SY1008 ) ) ) )
              | ~ ~ ( ~ ! [SY1009: $i,SY1010: $i] :
                          ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY1009 ) @ SY1010 )
                           != one_one_int )
                          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SY1006 )
                           != one_one_int )
                          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SY1009 ) ) @ ( hAPP_int_int @ abs_abs_int @ SY1006 ) )
                           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SY1010 ) ) )
                          | ( ( hAPP_int_int @ abs_abs_int @ SY1009 )
                            = ( hAPP_int_int @ abs_abs_int @ SV319 ) ) )
                    | ~ ! [SY1011: $i,SY1012: $i] :
                          ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY1011 ) @ SY1012 )
                           != one_one_int )
                          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SY1006 )
                           != one_one_int )
                          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SY1011 ) ) @ ( hAPP_int_int @ abs_abs_int @ SY1006 ) )
                           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SY1012 ) ) )
                          | ( ( hAPP_int_int @ abs_abs_int @ SY1006 )
                            = ( hAPP_int_int @ abs_abs_int @ SY1012 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6606]) ).

thf(6990,plain,
    ! [SV320: $i] :
      ( ( ! [SY1013: $i] :
            ~ ( ~ ! [SY1014: $i,SY1015: $i] :
                    ( ~ ( is_int @ SV320 )
                    | ~ ( is_int @ SY1013 )
                    | ~ ( is_int @ SY1014 )
                    | ~ ( is_int @ SY1015 )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SY1013 )
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1014 ) @ SY1015 ) )
                    | ( SV320 != SY1013 )
                    | ( SY1014 = SY1015 ) )
              | ~ ! [SY1016: $i,SY1017: $i] :
                    ( ~ ( is_int @ SV320 )
                    | ~ ( is_int @ SY1013 )
                    | ~ ( is_int @ SY1016 )
                    | ~ ( is_int @ SY1017 )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SY1013 )
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1016 ) @ SY1017 ) )
                    | ( SY1016 != SY1017 )
                    | ( SV320 = SY1013 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6607]) ).

thf(6991,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                        ( ~ ( is_int @ SX0 )
                        | ~ ( is_int @ SX1 )
                        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                         != one_one_int )
                        | ( SX0 = one_one_int )
                        | ( SX0
                          = ( hAPP_int_int @ number_number_of_int @ min ) ) )
                  | ~ ! [SX0: $i,SX1: $i] :
                        ( ~ ( is_int @ SX0 )
                        | ~ ( is_int @ SX1 )
                        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                         != one_one_int )
                        | ( SX0 = one_one_int )
                        | ( SX1
                          = ( hAPP_int_int @ number_number_of_int @ min ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                        ( ~ ( is_int @ SX0 )
                        | ~ ( is_int @ SX1 )
                        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                         != one_one_int )
                        | ( SX1 = one_one_int )
                        | ( SX0
                          = ( hAPP_int_int @ number_number_of_int @ min ) ) )
                  | ~ ! [SX0: $i,SX1: $i] :
                        ( ~ ( is_int @ SX0 )
                        | ~ ( is_int @ SX1 )
                        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                         != one_one_int )
                        | ( SX1 = one_one_int )
                        | ( SX1
                          = ( hAPP_int_int @ number_number_of_int @ min ) ) ) ) )
      | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( SX0 != one_one_int )
                  | ( SX1 != one_one_int )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                    = one_one_int ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( SX0
                   != ( hAPP_int_int @ number_number_of_int @ min ) )
                  | ( SX1
                   != ( hAPP_int_int @ number_number_of_int @ min ) )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                    = one_one_int ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6608]) ).

thf(6992,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
             != one_one_int )
            | ( SX0 = one_one_int )
            | ( SX0
              = ( hAPP_int_int @ number_number_of_int @ min ) ) )
      | ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ( SX0 != one_one_int )
                  | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
                    = one_one_int ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ( SX0
                   != ( hAPP_int_int @ number_number_of_int @ min ) )
                  | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
                    = one_one_int ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6609]) ).

thf(6993,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( ( hAPP_int_int @ bit0 @ SX0 )
             != pls )
            | ( SX0 = pls ) )
      | ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( SX0 != pls )
            | ( ( hAPP_int_int @ bit0 @ SX0 )
              = pls ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6610]) ).

thf(6994,plain,
    ! [SV321: $i] :
      ( ( ! [SY1018: $i] :
            ~ ( ~ ~ ( ~ ! [SY1019: $i,SY1020: $i] :
                          ( ~ ( is_int @ SV321 )
                          | ~ ( is_int @ SY1018 )
                          | ~ ( is_int @ SY1019 )
                          | ~ ( is_int @ SY1020 )
                          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1019 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1020 ) @ SY1018 ) )
                            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1019 ) @ SY1018 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1020 ) @ SV321 ) ) )
                          | ( SY1019 != SY1020 ) )
                    | ~ ! [SY1021: $i,SY1022: $i] :
                          ( ~ ( is_int @ SV321 )
                          | ~ ( is_int @ SY1018 )
                          | ~ ( is_int @ SY1021 )
                          | ~ ( is_int @ SY1022 )
                          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1021 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1022 ) @ SY1018 ) )
                            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1021 ) @ SY1018 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1022 ) @ SV321 ) ) )
                          | ( SV321 != SY1018 ) ) )
              | ~ ! [SY1023: $i,SY1024: $i] :
                    ( ~ ( is_int @ SV321 )
                    | ~ ( is_int @ SY1018 )
                    | ~ ( is_int @ SY1023 )
                    | ~ ( is_int @ SY1024 )
                    | ( SY1023 = SY1024 )
                    | ( SV321 = SY1018 )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1023 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1024 ) @ SY1018 ) )
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1023 ) @ SY1018 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1024 ) @ SV321 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6611]) ).

thf(6995,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0 != zero_zero_int )
            | ( SX1 != zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX0 ) @ SX1 )
              = zero_zero_int ) )
      | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX0 ) @ SX1 )
                   != zero_zero_int )
                  | ( SX0 = zero_zero_int ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX0 ) @ SX1 )
                   != zero_zero_int )
                  | ( SX1 = zero_zero_int ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6612]) ).

thf(6996,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX1 )
            | ( SX1 = zero_zero_int )
            | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
             != zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ ( hAPP_int_int @ uminus_uminus_int @ SX1 ) )
              = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ SX1 ) ) ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX1 )
            | ( SX1 = zero_zero_int )
            | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
              = zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ ( hAPP_int_int @ uminus_uminus_int @ SX1 ) )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ SX1 ) ) ) @ one_one_int ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6613]) ).

thf(6997,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
             != ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ( SX0 != SX1 )
            | ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
              = ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6614]) ).

thf(6998,plain,
    ! [SV322: $i] :
      ( ( ~ ( ~ ! [SY1025: $i,SY1026: $i] :
                  ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SY1025 )
                   != one_one_int )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SY1026 )
                   != one_one_int )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1025 ) @ SY1026 ) )
                    = one_one_int ) )
            | ~ ~ ( ~ ! [SY1027: $i] :
                        ( ! [SY1028: $i] :
                            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1027 ) @ SY1028 ) )
                           != one_one_int )
                        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SY1027 )
                          = one_one_int ) )
                  | ~ ! [SY1029: $i,SY1030: $i] :
                        ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1029 ) @ SY1030 ) )
                         != one_one_int )
                        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SY1030 )
                          = one_one_int ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6615]) ).

thf(6999,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
             != zero_zero_int )
            | ( SX0 = zero_zero_nat ) )
      | ~ ! [SX0: $i] :
            ( ( SX0 != zero_zero_nat )
            | ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
              = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6616]) ).

thf(7000,plain,
    ! [SV323: $i] :
      ( ( ! [SY1031: $i,SY1032: $i] :
            ~ ( ~ ! [SY1033: $i,SY1034: $i] :
                    ( ~ ( is_int @ SY1034 )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV323 ) @ SY1031 ) ) @ SY1032 )
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1033 ) @ SY1031 ) ) @ SY1034 ) )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV323 ) @ SY1033 ) ) @ SY1031 ) ) @ SY1032 )
                      = SY1034 ) )
              | ~ ! [SY1035: $i,SY1036: $i] :
                    ( ~ ( is_int @ SY1036 )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV323 ) @ SY1035 ) ) @ SY1031 ) ) @ SY1032 )
                     != SY1036 )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV323 ) @ SY1031 ) ) @ SY1032 )
                      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1035 ) @ SY1031 ) ) @ SY1036 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6617]) ).

thf(7001,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ! [SX1: $i] :
                ( ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
                 != zero_zero_int )
                | ~ ( ( SX0
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX1 ) @ ( sK12_Q_4 @ SX1 @ SX0 ) ) )
                    | ~ ( is_int @ ( sK12_Q_4 @ SX1 @ SX0 ) ) ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ! [SX1: $i] :
                ( ! [SX2: $i] :
                    ( ( SX0
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX1 ) @ SX2 ) )
                    | ~ ( is_int @ SX2 ) )
                | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
                  = zero_zero_int ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6618]) ).

thf(7002,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
             != ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ( SX0 != SX1 )
            | ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
              = ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6619]) ).

thf(7003,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ bit0 @ SX0 )
             != ( hAPP_int_int @ bit0 @ SX1 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0 != SX1 )
            | ( ( hAPP_int_int @ bit0 @ SX0 )
              = ( hAPP_int_int @ bit0 @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6620]) ).

thf(7004,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( min
             != ( hAPP_int_int @ bit1 @ SX0 ) )
            | ( min = SX0 ) )
      | ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( min != SX0 )
            | ( min
              = ( hAPP_int_int @ bit1 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6621]) ).

thf(7005,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( hAPP_nat_nat @ suc @ SX0 )
             != ( hAPP_nat_nat @ suc @ SX1 ) )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ( SX0 != SX1 )
            | ( ( hAPP_nat_nat @ suc @ SX0 )
              = ( hAPP_nat_nat @ suc @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6622]) ).

thf(7006,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX0 ) @ SX0 )
             != zero_zero_int )
            | ( SX0 = zero_zero_int ) )
      | ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( SX0 != zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX0 ) @ SX0 )
              = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6623]) ).

thf(7007,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SX0 ) @ SX1 )
             != zero_zero_int )
            | ( SX0 = SX1 ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0 != SX1 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SX0 ) @ SX1 )
              = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6624]) ).

thf(7008,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0 != SX1 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SX0 ) @ SX1 )
              = zero_zero_int ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SX0 ) @ SX1 )
             != zero_zero_int )
            | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6625]) ).

thf(7009,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( zero_zero_int
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX0 ) @ SX0 ) )
            | ( SX0 = zero_zero_int ) )
      | ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( SX0 != zero_zero_int )
            | ( zero_zero_int
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX0 ) @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6626]) ).

thf(7010,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
             != zero_zero_int )
            | ( SX0 = zero_zero_int ) )
      | ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( SX0 != zero_zero_int )
            | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
              = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6627]) ).

thf(7011,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( one_one_nat != SX0 )
            | ( SX0 = one_one_nat ) )
      | ~ ! [SX0: $i] :
            ( ( SX0 != one_one_nat )
            | ( one_one_nat = SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6628]) ).

thf(7012,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ SX0 ) @ SX1 ) )
             != SX1 )
            | ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ SX0 ) ) @ SX1 )
              = zero_zero_nat ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ( ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ SX0 ) @ SX1 ) )
              = SX1 )
            | ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ SX0 ) ) @ SX1 )
              = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ SX0 ) @ SX1 ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6629]) ).

thf(7013,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ zero_zero_int )
              = zero_zero_int ) )
      | ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ zero_zero_int )
              = SX0 ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6630]) ).

thf(7014,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0 != zero_zero_int )
            | ( SX1 != zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
              = zero_zero_int ) )
      | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
                   != zero_zero_int )
                  | ( SX0 = zero_zero_int ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
                   != zero_zero_int )
                  | ( SX1 = zero_zero_int ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6631]) ).

thf(7015,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0 != zero_zero_int )
            | ( SX1 != zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX0 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX1 ) @ SX1 ) )
              = zero_zero_int ) )
      | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX0 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX1 ) @ SX1 ) )
                   != zero_zero_int )
                  | ( SX0 = zero_zero_int ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX0 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX1 ) @ SX1 ) )
                   != zero_zero_int )
                  | ( SX1 = zero_zero_int ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6632]) ).

thf(7016,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0 != zero_zero_int )
            | ( SX1 != zero_zero_int )
            | ( ( hAPP_int_int @ ( legacy_zgcd @ SX0 ) @ SX1 )
              = zero_zero_int ) )
      | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( ( hAPP_int_int @ ( legacy_zgcd @ SX0 ) @ SX1 )
                   != zero_zero_int )
                  | ( SX0 = zero_zero_int ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( ( hAPP_int_int @ ( legacy_zgcd @ SX0 ) @ SX1 )
                   != zero_zero_int )
                  | ( SX1 = zero_zero_int ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[6633]) ).

thf(7017,plain,
    ! [SV1: $i,SV324: $i] :
      ( ( ~ ( is_int @ SV324 )
        | ( is_int @ ( hAPP_int_int @ SV1 @ SV324 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6634]) ).

thf(7018,plain,
    ! [SV325: $i,SV2: $i] :
      ( ( is_int @ ( hAPP_nat_int @ SV2 @ SV325 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6635]) ).

thf(7019,plain,
    ! [SV326: $i,SV6: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ SV6 ) ) @ ( hAPP_int_int @ number_number_of_int @ SV326 ) )
        = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV6 ) @ SV326 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6639]) ).

thf(7020,plain,
    ! [SV327: $i,SV7: $i] :
      ( ( ! [SY1037: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV7 ) @ SV327 ) ) @ SY1037 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV7 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV327 ) @ SY1037 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6640]) ).

thf(7021,plain,
    ! [SV328: $i,SV8: $i] :
      ( ( ! [SY1038: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV8 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV328 ) @ SY1038 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV328 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV8 ) @ SY1038 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6641]) ).

thf(7022,plain,
    ! [SV329: $i,SV9: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV9 ) @ SV329 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV329 ) @ SV9 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6642]) ).

thf(7023,plain,
    ! [SV10: $i] :
      ( ( ( hAPP_int_int @ bit1 @ SV10 )
        = pls )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6643]) ).

thf(7024,plain,
    ! [SV11: $i] :
      ( ( pls
        = ( hAPP_int_int @ bit1 @ SV11 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6644]) ).

thf(7025,plain,
    ! [SV330: $i,SV12: $i] :
      ( ( ( hAPP_int_int @ bit1 @ SV12 )
       != ( hAPP_int_int @ bit0 @ SV330 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6645]) ).

thf(7026,plain,
    ! [SV331: $i,SV13: $i] :
      ( ( ( hAPP_int_int @ bit0 @ SV13 )
       != ( hAPP_int_int @ bit1 @ SV331 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6646]) ).

thf(7027,plain,
    ! [SV14: $i] :
      ( ( ( ~ ( is_int @ SV14 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV14 ) @ pls )
          = SV14 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6648]) ).

thf(7028,plain,
    ! [SV15: $i] :
      ( ( ( ~ ( is_int @ SV15 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ pls ) @ SV15 )
          = SV15 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6649]) ).

thf(7029,plain,
    ! [SV332: $i,SV16: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ bit0 @ SV16 ) ) @ ( hAPP_int_int @ bit0 @ SV332 ) )
        = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV16 ) @ SV332 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6650]) ).

thf(7030,plain,
    ! [SV18: $i] :
      ( ( ( ~ ( is_int @ SV18 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV18 ) @ zero_zero_int )
          = SV18 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6652]) ).

thf(7031,plain,
    ! [SV19: $i] :
      ( ( ( ~ ( is_int @ SV19 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ SV19 )
          = SV19 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6653]) ).

thf(7032,plain,
    ! [SV20: $i] :
      ( ( ( ~ ( is_int @ SV20 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ pls ) ) @ SV20 )
          = SV20 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6654]) ).

thf(7033,plain,
    ! [SV21: $i] :
      ( ( ( ~ ( is_int @ SV21 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV21 ) @ ( hAPP_int_int @ number_number_of_int @ pls ) )
          = SV21 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6655]) ).

thf(7034,plain,
    ! [SV333: $i,SV22: $i] :
      ( ( ! [SY1039: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ SV22 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ SV333 ) ) @ SY1039 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV22 ) @ SV333 ) ) ) @ SY1039 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6656]) ).

thf(7035,plain,
    ! [SV334: $i,SV23: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ SV23 ) ) @ ( hAPP_int_int @ number_number_of_int @ SV334 ) )
        = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV23 ) @ SV334 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6657]) ).

thf(7036,plain,
    ! [SV335: $i,SV24: $i] :
      ( ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV24 ) @ SV335 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ SV24 ) ) @ ( hAPP_int_int @ number_number_of_int @ SV335 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6658]) ).

thf(7037,plain,
    ! [SV336: $i,SV25: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ bit1 @ SV25 ) ) @ ( hAPP_int_int @ bit0 @ SV336 ) )
        = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV25 ) @ SV336 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6659]) ).

thf(7038,plain,
    ! [SV337: $i,SV26: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ bit0 @ SV26 ) ) @ ( hAPP_int_int @ bit1 @ SV337 ) )
        = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV26 ) @ SV337 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6660]) ).

thf(7039,plain,
    ! [SV28: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ SV28 ) ) @ SV28 )
        = zero_zero_int )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6662]) ).

thf(7040,plain,
    ! [SV33: $i] :
      ( ( ( ~ ( is_int @ SV33 ) )
        = $true )
      | ( ( ( hAPP_int_int @ number_number_of_int @ SV33 )
          = SV33 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6667]) ).

thf(7041,plain,
    ! [SV34: $i] :
      ( ( ( ~ ( is_int @ SV34 ) )
        = $true )
      | ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV34 ) @ one_one_nat )
          = SV34 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6668]) ).

thf(7042,plain,
    ! [SV35: $i,SV338: $i] :
      ( ( ~ ( is_int @ SV338 )
        | ( SV338 = zero_zero_int )
        | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV338 ) @ SV35 )
         != zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6671]) ).

thf(7043,plain,
    ! [SV339: $i,SV41: $i] :
      ( ( ! [SY1040: $i] :
            ( ~ ( is_int @ SV41 )
            | ~ ( is_int @ SY1040 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV41 ) @ SV339 )
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY1040 ) @ SV339 ) )
            | ( SV41 = SY1040 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6677]) ).

thf(7044,plain,
    ! [SV42: $i,SV340: $i] :
      ( ( ! [SY1041: $i] :
            ( ~ ( is_int @ SV340 )
            | ~ ( is_int @ SY1041 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV42 ) @ SV340 )
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV42 ) @ SY1041 ) )
            | ( SV340 = SY1041 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6678]) ).

thf(7045,plain,
    ! [SV43: $i,SV341: $i] :
      ( ( ! [SY1042: $i] :
            ( ~ ( is_int @ SV341 )
            | ~ ( is_int @ SY1042 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV43 ) @ SV341 )
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV43 ) @ SY1042 ) )
            | ( SV341 = SY1042 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6679]) ).

thf(7046,plain,
    ! [SV342: $i,SV44: $i] :
      ( ( ! [SY1043: $i,SY1044: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV44 ) @ SV342 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY1043 ) @ SY1044 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV44 ) @ SY1043 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV342 ) @ SY1044 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6680]) ).

thf(7047,plain,
    ! [SV343: $i,SV45: $i] :
      ( ( ! [SY1045: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV45 ) @ SV343 ) ) @ SY1045 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV45 ) @ SY1045 ) ) @ SV343 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6681]) ).

thf(7048,plain,
    ! [SV344: $i,SV46: $i] :
      ( ( ! [SY1046: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV46 ) @ SV344 ) ) @ SY1046 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV46 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV344 ) @ SY1046 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6682]) ).

thf(7049,plain,
    ! [SV345: $i,SV47: $i] :
      ( ( ! [SY1047: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV47 ) @ SV345 ) ) @ SY1047 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV47 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV345 ) @ SY1047 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6683]) ).

thf(7050,plain,
    ! [SV346: $i,SV48: $i] :
      ( ( ! [SY1048: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV48 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV346 ) @ SY1048 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV48 ) @ SV346 ) ) @ SY1048 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6684]) ).

thf(7051,plain,
    ! [SV347: $i,SV49: $i] :
      ( ( ! [SY1049: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV49 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV347 ) @ SY1049 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV347 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV49 ) @ SY1049 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6685]) ).

thf(7052,plain,
    ! [SV348: $i,SV50: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV50 ) @ SV348 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV348 ) @ SV50 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6686]) ).

thf(7053,plain,
    ! [SV349: $i,SV53: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ bit1 @ SV53 ) ) @ ( hAPP_int_int @ bit1 @ SV349 ) )
        = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV53 ) @ ( hAPP_int_int @ succ @ SV349 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6689]) ).

thf(7054,plain,
    ! [SV54: $i] :
      ( ( ( ~ ( is_int @ SV54 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV54 ) @ zero_zero_int )
          = SV54 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6690]) ).

thf(7055,plain,
    ! [SV55: $i] :
      ( ( ( ~ ( is_int @ SV55 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV55 ) @ zero_zero_int )
          = SV55 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6691]) ).

thf(7056,plain,
    ! [SV56: $i] :
      ( ( ( ~ ( is_int @ SV56 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV56 ) @ zero_zero_int )
          = SV56 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6692]) ).

thf(7057,plain,
    ! [SV57: $i] :
      ( ( ( ~ ( is_int @ SV57 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ SV57 )
          = SV57 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6693]) ).

thf(7058,plain,
    ! [SV58: $i] :
      ( ( ( ~ ( is_int @ SV58 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ SV58 )
          = SV58 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6694]) ).

thf(7059,plain,
    ! [SV59: $i] :
      ( ( ( ~ ( is_int @ SV59 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ SV59 )
          = SV59 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6695]) ).

thf(7060,plain,
    ! [SV60: $i] :
      ( ( ( ~ ( is_int @ SV60 ) )
        = $true )
      | ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV60 ) @ one_one_nat )
          = SV60 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6696]) ).

thf(7061,plain,
    ! [SV350: $i,SV61: $i] :
      ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV61 ) @ SV350 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV61 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV61 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) @ SV350 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ SV61 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV350 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV350 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6697]) ).

thf(7062,plain,
    ! [SV351: $i,SV62: $i] :
      ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV62 ) @ SV351 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV62 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ SV62 ) ) @ SV351 ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV351 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6698]) ).

thf(7063,plain,
    ! [SV352: $i,SV63: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV63 ) @ SV352 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV352 ) @ SV63 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6699]) ).

thf(7064,plain,
    ! [SV353: $i,SV64: $i] :
      ( ( ! [SY1050: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV64 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV353 ) @ SY1050 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV353 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV64 ) @ SY1050 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6700]) ).

thf(7065,plain,
    ! [SV354: $i,SV65: $i] :
      ( ( ! [SY1051: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV65 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV354 ) @ SY1051 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV65 ) @ SV354 ) ) @ SY1051 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6701]) ).

thf(7066,plain,
    ! [SV355: $i,SV66: $i] :
      ( ( ! [SY1052: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV66 ) @ SV355 ) ) @ SY1052 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV66 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV355 ) @ SY1052 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6702]) ).

thf(7067,plain,
    ! [SV356: $i,SV67: $i] :
      ( ( ! [SY1053: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV67 ) @ SV356 ) ) @ SY1053 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV67 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV356 ) @ SY1053 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6703]) ).

thf(7068,plain,
    ! [SV357: $i,SV68: $i] :
      ( ( ! [SY1054: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV68 ) @ SV357 ) ) @ SY1054 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV68 ) @ SY1054 ) ) @ SV357 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6704]) ).

thf(7069,plain,
    ! [SV358: $i,SV69: $i] :
      ( ( ! [SY1055: $i,SY1056: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV69 ) @ SV358 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1055 ) @ SY1056 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV69 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV358 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1055 ) @ SY1056 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6705]) ).

thf(7070,plain,
    ! [SV359: $i,SV70: $i] :
      ( ( ! [SY1057: $i,SY1058: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV70 ) @ SV359 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1057 ) @ SY1058 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1057 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV70 ) @ SV359 ) ) @ SY1058 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6706]) ).

thf(7071,plain,
    ! [SV360: $i,SV71: $i] :
      ( ( ! [SY1059: $i,SY1060: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV71 ) @ SV360 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1059 ) @ SY1060 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV71 ) @ SY1059 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV360 ) @ SY1060 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6707]) ).

thf(7072,plain,
    ! [SV361: $i,SV72: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV72 ) @ SV361 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV361 ) @ SV72 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6708]) ).

thf(7073,plain,
    ! [SV362: $i,SV73: $i] :
      ( ( ! [SY1061: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV73 ) @ SV362 ) ) @ SY1061 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV73 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV362 ) @ SY1061 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6709]) ).

thf(7074,plain,
    ! [SV363: $i,SV74: $i] :
      ( ( ! [SY1062: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ SV74 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ SV363 ) ) @ SY1062 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV74 ) @ SV363 ) ) ) @ SY1062 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6710]) ).

thf(7075,plain,
    ! [SV364: $i,SV75: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ SV75 ) ) @ ( hAPP_int_int @ number_number_of_int @ SV364 ) )
        = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV75 ) @ SV364 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6711]) ).

thf(7076,plain,
    ! [SV365: $i,SV76: $i] :
      ( ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV76 ) @ SV365 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ SV76 ) ) @ ( hAPP_int_int @ number_number_of_int @ SV365 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6712]) ).

thf(7077,plain,
    ! [SV366: $i,SV79: $i] :
      ( ( ~ ( is_int @ SV79 )
        | ~ ( is_int @ SV366 )
        | ( SV366 = zero_zero_int )
        | ( SV79 = zero_zero_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV366 ) @ SV79 )
         != zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6715]) ).

thf(7078,plain,
    ! [SV367: $i,SV80: $i] :
      ( ( ~ ( is_int @ SV80 )
        | ~ ( is_int @ SV367 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV80 ) @ SV367 )
         != zero_zero_int )
        | ( SV80 = zero_zero_int )
        | ( SV367 = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6716]) ).

thf(7079,plain,
    ! [SV368: $i,SV83: $i] :
      ( ( ! [SY1063: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV83 ) @ SV368 ) ) @ SY1063 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV83 ) @ SY1063 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV368 ) @ SY1063 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6719]) ).

thf(7080,plain,
    ! [SV369: $i,SV84: $i] :
      ( ( ! [SY1064: $i,SY1065: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV84 ) @ SV369 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1064 ) @ SV369 ) ) @ SY1065 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV84 ) @ SY1064 ) ) @ SV369 ) ) @ SY1065 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6720]) ).

thf(7081,plain,
    ! [SV370: $i,SV85: $i] :
      ( ( ! [SY1066: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV85 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV370 ) @ SY1066 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV85 ) @ SV370 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV85 ) @ SY1066 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6721]) ).

thf(7082,plain,
    ! [SV371: $i,SV86: $i] :
      ( ( ! [SY1067: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV86 ) @ SV371 ) ) @ SY1067 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV86 ) @ SY1067 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV371 ) @ SY1067 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6722]) ).

thf(7083,plain,
    ! [SV372: $i,SV87: $i] :
      ( ( ! [SY1068: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV87 ) @ SV372 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1068 ) @ SV372 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV87 ) @ SY1068 ) ) @ SV372 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6723]) ).

thf(7084,plain,
    ! [SV88: $i] :
      ( ( ( ~ ( is_int @ SV88 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ one_one_int ) @ SV88 )
          = SV88 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6724]) ).

thf(7085,plain,
    ! [SV89: $i] :
      ( ( ( ~ ( is_int @ SV89 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ one_one_int ) @ SV89 )
          = SV89 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6725]) ).

thf(7086,plain,
    ! [SV90: $i] :
      ( ( ( ~ ( is_int @ SV90 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ one_one_int ) @ SV90 )
          = SV90 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6726]) ).

thf(7087,plain,
    ! [SV91: $i] :
      ( ( ( ~ ( is_int @ SV91 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV91 ) @ one_one_int )
          = SV91 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6727]) ).

thf(7088,plain,
    ! [SV92: $i] :
      ( ( ( ~ ( is_int @ SV92 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV92 ) @ one_one_int )
          = SV92 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6728]) ).

thf(7089,plain,
    ! [SV93: $i] :
      ( ( ( ~ ( is_int @ SV93 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV93 ) @ one_one_int )
          = SV93 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6729]) ).

thf(7090,plain,
    ! [SV373: $i,SV94: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV94 ) @ SV373 ) ) @ SV94 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV94 ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV94 ) @ SV373 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6730]) ).

thf(7091,plain,
    ! [SV374: $i,SV95: $i] :
      ( ( ! [SY1069: $i] :
            ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV95 ) @ SV374 ) ) @ SY1069 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV95 ) @ SY1069 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV374 ) @ SY1069 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6731]) ).

thf(7092,plain,
    ! [SV375: $i,SV96: $i] :
      ( ( ! [SY1070: $i] :
            ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV96 ) @ SV375 ) ) @ SY1070 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV96 ) @ SY1070 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV375 ) @ SY1070 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6732]) ).

thf(7093,plain,
    ! [SV376: $i,SV98: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ bit0 @ SV98 ) ) @ SV376 )
        = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV98 ) @ SV376 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6734]) ).

thf(7094,plain,
    ! [SV99: $i] :
      ( ( ( ~ ( is_int @ SV99 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ one_one_int ) @ SV99 )
          = SV99 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6735]) ).

thf(7095,plain,
    ! [SV100: $i] :
      ( ( ( ~ ( is_int @ SV100 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV100 ) @ one_one_int )
          = SV100 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6736]) ).

thf(7096,plain,
    ! [SV377: $i,SV101: $i] :
      ( ( ! [SY1071: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV101 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV377 ) @ SY1071 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV101 ) @ SV377 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV101 ) @ SY1071 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6737]) ).

thf(7097,plain,
    ! [SV378: $i,SV102: $i] :
      ( ( ! [SY1072: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV102 ) @ SV378 ) ) @ SY1072 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV102 ) @ SY1072 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV378 ) @ SY1072 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6738]) ).

thf(7098,plain,
    ! [SV379: $i,SV103: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ SV103 ) ) @ ( hAPP_int_int @ number_number_of_int @ SV379 ) )
        = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV103 ) @ SV379 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6739]) ).

thf(7099,plain,
    ! [SV380: $i,SV104: $i] :
      ( ( ! [SY1073: $i,SY1074: $i,SY1075: $i] :
            ( ~ ( is_int @ SV104 )
            | ~ ( is_int @ SV380 )
            | ~ ( is_int @ SY1075 )
            | ( SY1075 = zero_zero_int )
            | ( SV104 = SV380 )
            | ( SY1073 != SY1074 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY1073 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1075 ) @ SV104 ) )
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY1074 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1075 ) @ SV380 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6740]) ).

thf(7100,plain,
    ! [SV381: $i,SV105: $i] :
      ( ( ! [SY1076: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ SV105 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV381 ) @ SY1076 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ SV105 ) ) @ SV381 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ SV105 ) ) @ SY1076 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6741]) ).

thf(7101,plain,
    ! [SV382: $i,SV106: $i] :
      ( ( ! [SY1077: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV106 ) @ SV382 ) ) @ ( hAPP_int_int @ number_number_of_int @ SY1077 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV106 ) @ ( hAPP_int_int @ number_number_of_int @ SY1077 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV382 ) @ ( hAPP_int_int @ number_number_of_int @ SY1077 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6742]) ).

thf(7102,plain,
    ! [SV383: $i,SV108: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV108 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV383 ) @ SV108 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV383 ) @ one_one_int ) ) @ SV108 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6744]) ).

thf(7103,plain,
    ! [SV384: $i,SV109: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV109 ) @ SV384 ) ) @ SV384 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV109 ) @ one_one_int ) ) @ SV384 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6745]) ).

thf(7104,plain,
    ! [SV385: $i,SV110: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ bit1 @ SV110 ) ) @ SV385 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV110 ) @ SV385 ) ) ) @ SV385 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6746]) ).

thf(7105,plain,
    ! [SV386: $i,SV121: $i] :
      ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV121 ) @ SV386 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV121 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV386 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ SV121 ) ) @ SV386 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6757]) ).

thf(7106,plain,
    ! [SV122: $i] :
      ( ( min
        = ( hAPP_int_int @ bit0 @ SV122 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6760]) ).

thf(7107,plain,
    ! [SV123: $i] :
      ( ( ( hAPP_int_int @ bit0 @ SV123 )
        = min )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6761]) ).

thf(7108,plain,
    ! [SV387: $i,SV124: $i] :
      ( ( ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV124 ) @ SV387 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ number_number_of_int @ SV124 ) ) @ ( hAPP_int_int @ number_number_of_int @ SV387 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6763]) ).

thf(7109,plain,
    ! [SV126: $i] :
      ( ( ( ~ ( is_int @ SV126 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV126 ) @ zero_zero_int )
          = SV126 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6765]) ).

thf(7110,plain,
    ! [SV127: $i] :
      ( ( ( ~ ( is_int @ SV127 ) )
        = $true )
      | ( ( ! [SY823: $i] :
              ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV127 ) @ SY823 ) ) @ SY823 )
              = SV127 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6766]) ).

thf(7111,plain,
    ! [SV128: $i] :
      ( ( ( ~ ( is_int @ SV128 ) )
        = $true )
      | ( ( ! [SY824: $i] :
              ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV128 ) @ SY824 ) ) @ SY824 )
              = SV128 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6767]) ).

thf(7112,plain,
    ! [SV388: $i,SV129: $i] :
      ( ( ! [SY1078: $i,SY1079: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV129 ) @ SV388 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY1078 ) @ SY1079 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV129 ) @ SY1078 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV388 ) @ SY1079 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6768]) ).

thf(7113,plain,
    ! [SV130: $i] :
      ( ( ( ~ ( is_int @ SV130 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV130 ) @ pls )
          = SV130 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6769]) ).

thf(7114,plain,
    ! [SV389: $i,SV131: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ bit0 @ SV131 ) ) @ ( hAPP_int_int @ bit0 @ SV389 ) )
        = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV131 ) @ SV389 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6770]) ).

thf(7115,plain,
    ! [SV390: $i,SV132: $i] :
      ( ( ! [SY1080: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV132 ) @ SV390 ) ) @ SY1080 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV132 ) @ SY1080 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV390 ) @ SY1080 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6771]) ).

thf(7116,plain,
    ! [SV391: $i,SV133: $i] :
      ( ( ! [SY1081: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV133 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV391 ) @ SY1081 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV133 ) @ SV391 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV133 ) @ SY1081 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6772]) ).

thf(7117,plain,
    ! [SV392: $i,SV134: $i] :
      ( ( ! [SY1082: $i,SY1083: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV134 ) @ SV392 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1082 ) @ SY1083 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV134 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV392 ) @ SY1083 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV134 ) @ SY1082 ) ) @ SY1083 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6773]) ).

thf(7118,plain,
    ! [SV393: $i,SV135: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ bit1 @ SV135 ) ) @ ( hAPP_int_int @ bit1 @ SV393 ) )
        = ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV135 ) @ SV393 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6774]) ).

thf(7119,plain,
    ! [SV394: $i,SV136: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ bit1 @ SV136 ) ) @ ( hAPP_int_int @ bit0 @ SV394 ) )
        = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV136 ) @ SV394 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6775]) ).

thf(7120,plain,
    ! [SV395: $i,SV139: $i] :
      ( ( ! [SY1084: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ SV139 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ number_number_of_int @ SV395 ) ) @ SY1084 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV139 ) @ SV395 ) ) ) @ SY1084 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6778]) ).

thf(7121,plain,
    ! [SV396: $i,SV143: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV143 ) @ SV396 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV143 ) @ SV396 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV143 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV396 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6782]) ).

thf(7122,plain,
    ! [SV144: $i] :
      ( ( ( ~ ( is_int @ SV144 ) )
        = $true )
      | ( ( ! [SY841: $i,SY842: $i] :
              ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV144 ) @ SY841 )
               != SY842 )
              | ( SV144
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY842 ) @ SY841 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6783]) ).

thf(7123,plain,
    ! [SV397: $i,SV145: $i] :
      ( ( ! [SY1085: $i,SY1086: $i,SY1087: $i,SY1088: $i,SY1089: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV145 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV397 ) @ SY1085 ) ) ) @ SY1086 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1087 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV397 ) @ SY1088 ) ) ) @ SY1089 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV145 ) @ SY1086 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1087 ) @ SY1089 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV397 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1085 ) @ SY1086 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1088 ) @ SY1089 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6784]) ).

thf(7124,plain,
    ! [SV146: $i] :
      ( ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ number_number_of_int @ min ) ) @ SV146 )
          = one_one_int )
        = $true )
      | ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ number_number_of_int @ min ) ) @ SV146 )
          = ( hAPP_int_int @ number_number_of_int @ min ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6785]) ).

thf(7125,plain,
    ! [SV398: $i,SV149: $i] :
      ( ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV149 ) @ SV398 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV149 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV398 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6788]) ).

thf(7126,plain,
    ! [SV399: $i,SV150: $i] :
      ( ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ abs_abs_int @ SV150 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV399 ) ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ abs_abs_int @ SV150 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV399 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6789]) ).

thf(7127,plain,
    ! [SV400: $i,SV151: $i] :
      ( ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV151 ) @ SV400 ) )
        = ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV400 ) @ SV151 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6790]) ).

thf(7128,plain,
    ! [SV401: $i,SV152: $i] :
      ( ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV152 ) @ SV401 ) )
        = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ abs_abs_int @ SV152 ) ) @ SV401 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6791]) ).

thf(7129,plain,
    ! [SV156: $i] :
      ( ( ( ! [SY853: $i] :
              ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV156 ) @ SY853 ) )
             != one_one_int ) )
        = $true )
      | ( ( ( hAPP_int_int @ abs_abs_int @ SV156 )
          = one_one_int )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6795]) ).

thf(7130,plain,
    ! [SV161: $i] :
      ( ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV161 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
         != one_one_int )
        = $true )
      | ( ( ( hAPP_int_int @ abs_abs_int @ SV161 )
          = one_one_int )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6800]) ).

thf(7131,plain,
    ! [SV163: $i] :
      ( ( ( ~ ( is_int @ SV163 ) )
        = $true )
      | ( ( ( SV163 = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV163 ) @ SV163 )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6802]) ).

thf(7132,plain,
    ! [SV402: $i,SV164: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ SV164 ) ) ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ SV402 ) ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ number_number_of_int @ SV164 ) ) @ ( hAPP_int_int @ number_number_of_int @ SV402 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6803]) ).

thf(7133,plain,
    ! [SV403: $i,SV166: $i] :
      ( ( ( hAPP_int_int @ ( standardRes @ SV166 ) @ SV403 )
        = ( hAPP_int_int @ ( div_mod_int @ SV403 ) @ SV166 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6805]) ).

thf(7134,plain,
    ! [SV404: $i,SV169: $i] :
      ( ( ! [SY1090: $i] :
            ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV169 ) @ SV404 ) ) @ SY1090 )
            = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV169 ) @ ( hAPP_int_int @ ( div_mod_int @ SV404 ) @ SY1090 ) ) ) @ SY1090 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6808]) ).

thf(7135,plain,
    ! [SV405: $i,SV170: $i] :
      ( ( ! [SY1091: $i] :
            ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV170 ) @ ( hAPP_int_int @ ( div_mod_int @ SV405 ) @ SY1091 ) ) ) @ SY1091 )
            = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV170 ) @ SV405 ) ) @ SY1091 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6809]) ).

thf(7136,plain,
    ! [SV406: $i,SV171: $i] :
      ( ( ! [SY1092: $i] :
            ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( div_mod_int @ SV171 ) @ SV406 ) ) @ SY1092 ) ) @ SV406 )
            = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV171 ) @ SY1092 ) ) @ SV406 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6810]) ).

thf(7137,plain,
    ! [SV407: $i,SV172: $i] :
      ( ( ! [SY1093: $i] :
            ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV172 ) @ ( hAPP_int_int @ ( div_mod_int @ SV407 ) @ SY1093 ) ) ) @ SY1093 )
            = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV172 ) @ SV407 ) ) @ SY1093 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6811]) ).

thf(7138,plain,
    ! [SV408: $i,SV173: $i] :
      ( ( ! [SY1094: $i] :
            ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( div_mod_int @ SV173 ) @ SV408 ) ) @ SY1094 ) ) @ SV408 )
            = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV173 ) @ SY1094 ) ) @ SV408 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6812]) ).

thf(7139,plain,
    ! [SV409: $i,SV174: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ ( div_mod_int @ SV174 ) @ SV409 ) ) @ SV409 )
        = zero_zero_int )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6813]) ).

thf(7140,plain,
    ! [SV410: $i,SV175: $i] :
      ( ( ! [SY1095: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV175 ) @ SV410 ) ) @ SY1095 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV175 ) @ SY1095 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV410 ) @ SY1095 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( div_mod_int @ SV175 ) @ SY1095 ) ) @ ( hAPP_int_int @ ( div_mod_int @ SV410 ) @ SY1095 ) ) ) @ SY1095 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6814]) ).

thf(7141,plain,
    ! [SV177: $i] :
      ( ( ( ~ ( is_int @ SV177 ) )
        = $true )
      | ( ( SV177
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ ( sK15_M_1 @ SV177 ) ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ ( sK16_SY717 @ SV177 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6816]) ).

thf(7142,plain,
    ! [SV178: $i] :
      ( ( ( ~ ( is_int @ SV178 ) )
        = $true )
      | ( ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ uminus_uminus_int @ SV178 ) )
          = SV178 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6817]) ).

thf(7143,plain,
    ! [SV411: $i,SV180: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ uminus_uminus_int @ SV180 ) ) @ SV411 )
        = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV180 ) @ SV411 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6819]) ).

thf(7144,plain,
    ! [SV412: $i,SV181: $i] :
      ( ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV181 ) @ SV412 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ uminus_uminus_int @ SV181 ) ) @ ( hAPP_int_int @ uminus_uminus_int @ SV412 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6820]) ).

thf(7145,plain,
    ! [SV413: $i,SV183: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ SV183 ) ) @ ( hAPP_int_int @ uminus_uminus_int @ SV413 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV183 ) @ SV413 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6822]) ).

thf(7146,plain,
    ! [SV414: $i,SV184: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV184 ) @ ( hAPP_int_int @ uminus_uminus_int @ SV414 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ SV184 ) ) @ SV414 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6823]) ).

thf(7147,plain,
    ! [SV415: $i,SV185: $i] :
      ( ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( div_mod_int @ SV185 ) @ SV415 ) ) ) @ SV415 )
        = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ SV185 ) ) @ SV415 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6824]) ).

thf(7148,plain,
    ! [SV416: $i,SV186: $i] :
      ( ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ SV186 ) ) @ ( hAPP_int_int @ uminus_uminus_int @ SV416 ) )
        = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( div_mod_int @ SV186 ) @ SV416 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6825]) ).

thf(7149,plain,
    ! [SV417: $i,SV187: $i] :
      ( ( ( hAPP_int_int @ ( div_mod_int @ SV187 ) @ ( hAPP_int_int @ uminus_uminus_int @ SV417 ) )
        = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ SV187 ) ) @ SV417 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6826]) ).

thf(7150,plain,
    ! [SV418: $i,SV189: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV189 ) @ ( hAPP_int_int @ uminus_uminus_int @ SV418 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV189 ) @ SV418 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6828]) ).

thf(7151,plain,
    ! [SV419: $i,SV190: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV190 ) @ SV419 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV190 ) @ ( hAPP_int_int @ uminus_uminus_int @ SV419 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6829]) ).

thf(7152,plain,
    ! [SV420: $i,SV191: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ SV191 ) ) @ SV420 )
          = zero_zero_int )
        | ( ( hAPP_int_int @ ( div_mod_int @ SV191 ) @ SV420 )
         != zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6830]) ).

thf(7153,plain,
    ! [SV421: $i,SV192: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV192 ) @ ( hAPP_int_int @ uminus_uminus_int @ SV421 ) )
          = zero_zero_int )
        | ( ( hAPP_int_int @ ( div_mod_int @ SV192 ) @ SV421 )
         != zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6831]) ).

thf(7154,plain,
    ! [SV422: $i,SV200: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ bit0 @ SV200 ) ) @ ( hAPP_int_int @ bit1 @ SV422 ) )
        = ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ pred @ SV200 ) ) @ SV422 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6839]) ).

thf(7155,plain,
    ! [SV423: $i,SV201: $i] :
      ( ( ( xzgcd @ SV201 @ SV423 )
        = ( xzgcda @ SV201 @ SV423 @ SV201 @ SV423 @ one_one_int @ zero_zero_int @ zero_zero_int @ one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6840]) ).

thf(7156,plain,
    ! [SV202: $i,SV424: $i] :
      ( ( ! [SY1096: $i] :
            ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV424 ) @ SY1096 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV424 ) @ SV202 ) ) @ SY1096 )
              = ( hAPP_int_int @ ( legacy_zgcd @ SV202 ) @ SY1096 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6841]) ).

thf(7157,plain,
    ! [SV203: $i,SV425: $i] :
      ( ( ! [SY1097: $i] :
            ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV425 ) @ SY1097 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( legacy_zgcd @ SV203 ) @ SY1097 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV425 ) @ SV203 ) ) @ SY1097 )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6842]) ).

thf(7158,plain,
    ! [SV426: $i,SV206: $i] :
      ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV206 ) @ SV426 )
        = ( hAPP_int_int @ ( legacy_zgcd @ SV426 ) @ ( hAPP_int_int @ ( div_mod_int @ SV206 ) @ SV426 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6845]) ).

thf(7159,plain,
    ! [SV427: $i,SV207: $i] :
      ( ( ! [SY1098: $i] :
            ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV207 ) @ SV427 ) ) @ SY1098 )
            = ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV207 ) @ SY1098 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV427 ) @ SY1098 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6846]) ).

thf(7160,plain,
    ! [SV428: $i,SV208: $i] :
      ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV208 ) @ SV428 )
        = ( hAPP_int_int @ ( legacy_zgcd @ SV428 ) @ SV208 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6847]) ).

thf(7161,plain,
    ! [SV429: $i,SV209: $i] :
      ( ( ! [SY1099: $i] :
            ( ( hAPP_int_int @ ( legacy_zgcd @ SV209 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV429 ) @ SY1099 ) )
            = ( hAPP_int_int @ ( legacy_zgcd @ SV429 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV209 ) @ SY1099 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6848]) ).

thf(7162,plain,
    ! [SV430: $i,SV210: $i] :
      ( ( ! [SY1100: $i] :
            ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( legacy_zgcd @ SV210 ) @ SV430 ) ) @ SY1100 )
            = ( hAPP_int_int @ ( legacy_zgcd @ SV210 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV430 ) @ SY1100 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6849]) ).

thf(7163,plain,
    ! [SV431: $i,SV211: $i] :
      ( ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ uminus_uminus_int @ SV211 ) ) @ SV431 )
        = ( hAPP_int_int @ ( legacy_zgcd @ SV211 ) @ SV431 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6850]) ).

thf(7164,plain,
    ! [SV432: $i,SV212: $i] :
      ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV212 ) @ ( hAPP_int_int @ uminus_uminus_int @ SV432 ) )
        = ( hAPP_int_int @ ( legacy_zgcd @ SV212 ) @ SV432 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6851]) ).

thf(7165,plain,
    ! [SV433: $i,SV213: $i] :
      ( ( ! [SY1101: $i] :
            ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV213 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV433 ) @ SY1101 ) ) ) @ SV433 )
            = ( hAPP_int_int @ ( legacy_zgcd @ SV213 ) @ SV433 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6852]) ).

thf(7166,plain,
    ! [SV214: $i,SV434: $i] :
      ( ( ! [SY1102: $i] :
            ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV434 ) @ SY1102 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV434 ) @ SV214 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY1102 ) @ SV214 ) )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6853]) ).

thf(7167,plain,
    ! [SV215: $i,SV435: $i] :
      ( ( ! [SY1103: $i] :
            ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV435 ) @ SY1103 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV435 ) @ SV215 ) ) @ SY1103 )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6854]) ).

thf(7168,plain,
    ! [SV436: $i,SV220: $i] :
      ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV220 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ SV436 ) ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV220 ) @ ( hAPP_int_nat @ number_number_of_nat @ SV436 ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV220 ) @ ( hAPP_int_nat @ number_number_of_nat @ SV436 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6859]) ).

thf(7169,plain,
    ! [SV437: $i,SV221: $i] :
      ( ( ! [SY1104: $i,SY1105: $i] :
            ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY1104 ) @ SY1105 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY1104 ) @ SV221 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY1105 ) @ SV437 ) )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6860]) ).

thf(7170,plain,
    ! [SV438: $i,SV224: $i] :
      ( ( ! [SY1106: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV224 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV438 ) @ SV224 ) ) @ SY1106 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV224 ) @ SY1106 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6863]) ).

thf(7171,plain,
    ! [SV439: $i,SV225: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV225 ) @ SV439 ) ) @ SV439 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV225 ) @ SV439 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6864]) ).

thf(7172,plain,
    ! [SV440: $i,SV226: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV226 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV226 ) @ SV440 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV226 ) @ SV440 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6865]) ).

thf(7173,plain,
    ! [SV441: $i,SV227: $i] :
      ( ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV227 ) @ SV441 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV227 ) @ SV441 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6866]) ).

thf(7174,plain,
    ! [SV442: $i,SV229: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV229 ) @ SV442 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ abs_abs_int @ SV229 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV442 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6868]) ).

thf(7175,plain,
    ! [SV443: $i,SV230: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV230 ) @ ( hAPP_int_int @ abs_abs_int @ SV443 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV230 ) @ SV443 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6869]) ).

thf(7176,plain,
    ! [SV444: $i,SV231: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ abs_abs_int @ SV231 ) ) @ SV444 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV231 ) @ SV444 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6870]) ).

thf(7177,plain,
    ! [SV235: $i,SV445: $i] :
      ( ( ! [SY1107: $i] :
            ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV445 ) @ SY1107 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV445 ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY1107 ) @ SV235 ) )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6874]) ).

thf(7178,plain,
    ! [SV446: $i,SV236: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV236 ) @ SV446 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV446 ) @ ( hAPP_int_int @ ( div_mod_int @ SV236 ) @ SV446 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6875]) ).

thf(7179,plain,
    ! [SV447: $i,SV237: $i] :
      ( ( ! [SY1108: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV237 ) @ SV447 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY1108 ) @ SV447 ) )
            = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV237 ) @ SY1108 ) ) @ SV447 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6876]) ).

thf(7180,plain,
    ! [SV448: $i,SV238: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV238 ) @ SV448 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV448 ) @ SV238 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6877]) ).

thf(7181,plain,
    ! [SV449: $i,SV239: $i] :
      ( ( ! [SY1109: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV239 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV449 ) @ SY1109 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV449 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV239 ) @ SY1109 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6878]) ).

thf(7182,plain,
    ! [SV450: $i,SV240: $i] :
      ( ( ! [SY1110: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV240 ) @ SV450 ) ) @ SY1110 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV240 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV450 ) @ SY1110 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6879]) ).

thf(7183,plain,
    ! [SV451: $i,SV241: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV241 ) @ ( hAPP_int_int @ uminus_uminus_int @ SV451 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV241 ) @ SV451 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6880]) ).

thf(7184,plain,
    ! [SV452: $i,SV242: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ uminus_uminus_int @ SV242 ) ) @ SV452 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV242 ) @ SV452 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6881]) ).

thf(7185,plain,
    ! [SV243: $i,SV453: $i] :
      ( ( ! [SY1111: $i] :
            ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV453 ) @ SY1111 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV453 ) @ SV243 ) ) @ SY1111 )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV243 ) @ SY1111 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6882]) ).

thf(7186,plain,
    ! [SV244: $i,SV454: $i] :
      ( ( ! [SY1112: $i] :
            ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV454 ) @ SY1112 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV454 ) @ SV244 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV454 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1112 ) @ SV244 ) )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6883]) ).

thf(7187,plain,
    ! [SV455: $i,SV245: $i] :
      ( ( ! [SY1113: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV245 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV455 ) @ SY1113 ) )
           != one_one_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV245 ) @ SV455 )
          = one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6884]) ).

thf(7188,plain,
    ! [SV456: $i,SV246: $i] :
      ( ( ! [SY1114: $i] :
            ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV246 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV456 ) @ SY1114 ) )
             != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV246 ) @ SY1114 )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6885]) ).

thf(7189,plain,
    ! [SV247: $i,SV457: $i] :
      ( ( ! [SY1115: $i,SY1116: $i] :
            ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY1115 ) @ SY1116 )
              = zero_zero_int )
            | ( SY1115
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV457 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY1115 ) @ SY1116 ) ) )
            | ( SY1116
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV247 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY1115 ) @ SY1116 ) ) )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV457 ) @ SV247 )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6886]) ).

thf(7190,plain,
    ! [SV248: $i] :
      ( ( ( ~ ( is_int @ SV248 ) )
        = $true )
      | ( ( ( hAPP_int_int @ cOMBI_int @ SV248 )
          = SV248 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6887]) ).

thf(7191,plain,
    ! [SV458: $i,SV249: $i] :
      ( ( ! [SY1117: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ ( hAPP_f2135977429nt_int @ cOMBC_int_int_int @ SV249 ) @ SV458 ) @ SY1117 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ SV249 @ SY1117 ) @ SV458 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6888]) ).

thf(7192,plain,
    ! [SV459: $i,SV253: $i] :
      ( ( is_int @ ( big_co1548731110nt_int @ SV253 @ SV459 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6892]) ).

thf(7193,plain,
    ! [SV460: $i,SV258: $i] :
      ( ( is_int @ ( hAPP_f1594865479ol_int @ SV258 @ SV460 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6897]) ).

thf(7194,plain,
    ! [SV461: $i,SV259: $i] :
      ( ( is_int @ ( hAPP_f659380387ol_int @ SV259 @ SV461 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6898]) ).

thf(7195,plain,
    ! [SV462: $i,SV260: $i] :
      ( ( is_int @ ( hAPP_P1175774780nt_int @ SV260 @ SV462 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6899]) ).

thf(7196,plain,
    ! [SV261: $i] :
      ( ( ( ~ ( is_int @ SV261 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV261 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ pls ) ) )
          = SV261 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6902]) ).

thf(7197,plain,
    ! [SV262: $i] :
      ( ( ( ~ ( is_int @ SV262 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ pls ) ) ) @ SV262 )
          = SV262 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6903]) ).

thf(7198,plain,
    ! [SV263: $i] :
      ( ( ( ~ ( is_int @ SV263 ) )
        = $true )
      | ( ( ! [SY943: $i] :
              ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV263 ) @ SY943 )
             != one_one_int )
          | ( SV263 = one_one_int )
          | ( SV263
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6904]) ).

thf(7199,plain,
    ! [SV463: $i,SV264: $i] :
      ( ( ! [SY1118: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ SV264 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV463 ) @ SY1118 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ SV264 ) ) @ SV463 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ SV264 ) ) @ SY1118 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6905]) ).

thf(7200,plain,
    ! [SV464: $i,SV265: $i] :
      ( ( ! [SY1119: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV265 ) @ SV464 ) ) @ ( hAPP_int_int @ number_number_of_int @ SY1119 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV265 ) @ ( hAPP_int_int @ number_number_of_int @ SY1119 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV464 ) @ ( hAPP_int_int @ number_number_of_int @ SY1119 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6906]) ).

thf(7201,plain,
    ! [SV465: $i,SV267: $i] :
      ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV267 ) @ SV465 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV267 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV465 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ SV267 ) ) @ SV465 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6908]) ).

thf(7202,plain,
    ! [SV466: $i,SV268: $i] :
      ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV268 ) @ SV466 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV268 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV268 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) @ SV466 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ SV268 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV466 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV466 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6909]) ).

thf(7203,plain,
    ! [SV467: $i,SV269: $i] :
      ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV269 ) @ SV467 ) ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV269 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ SV269 ) ) @ SV467 ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV467 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6910]) ).

thf(7204,plain,
    ! [SV468: $i,SV270: $i] :
      ( ( ( hAPP_int_int @ ( multInv @ SV270 ) @ SV468 )
        = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV468 ) @ ( hAPP_int_nat @ nat @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV270 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6911]) ).

thf(7205,plain,
    ! [SV469: $i,SV271: $i] :
      ( ( ( ( hAPP_nat_nat @ suc @ SV271 )
         != ( hAPP_nat_nat @ suc @ SV469 ) )
        | ( SV271 = SV469 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6912]) ).

thf(7206,plain,
    ! [SV272: $i] :
      ( ( ( hAPP_nat_nat @ suc @ SV272 )
        = SV272 )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6913]) ).

thf(7207,plain,
    ! [SV273: $i] :
      ( ( SV273
        = ( hAPP_nat_nat @ suc @ SV273 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6914]) ).

thf(7208,plain,
    ! [SV274: $i] :
      ( ( zero_zero_nat
        = ( hAPP_nat_nat @ suc @ SV274 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6915]) ).

thf(7209,plain,
    ! [SV275: $i] :
      ( ( zero_zero_nat
        = ( hAPP_nat_nat @ suc @ SV275 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6916]) ).

thf(7210,plain,
    ! [SV276: $i] :
      ( ( ( hAPP_nat_nat @ suc @ SV276 )
        = zero_zero_nat )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6917]) ).

thf(7211,plain,
    ! [SV277: $i] :
      ( ( ( hAPP_nat_nat @ suc @ SV277 )
        = zero_zero_nat )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6918]) ).

thf(7212,plain,
    ! [SV278: $i] :
      ( ( zero_zero_nat
        = ( hAPP_nat_nat @ suc @ SV278 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6919]) ).

thf(7213,plain,
    ! [SV279: $i] :
      ( ( ( hAPP_nat_nat @ suc @ SV279 )
        = zero_zero_nat )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6920]) ).

thf(7214,plain,
    ! [SV281: $i] :
      ( ( ( ~ ( is_int @ SV281 ) )
        = $true )
      | ( ( ! [SY953: $i] :
              ( SV281
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY953 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV281 ) @ SY953 ) ) ) @ ( hAPP_int_int @ ( div_mod_int @ SV281 ) @ SY953 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6922]) ).

thf(7215,plain,
    ! [SV470: $i,SV282: $i] :
      ( ( ! [SY1120: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV282 ) @ SV470 ) ) @ SY1120 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV282 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV470 ) @ SY1120 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV282 ) @ ( hAPP_int_int @ ( div_mod_int @ SV470 ) @ SY1120 ) ) ) @ SY1120 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6923]) ).

thf(7216,plain,
    ! [SV471: $i,SV283: $i] :
      ( ( ! [SY1121: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV283 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV471 ) @ SV283 ) ) ) @ ( hAPP_int_int @ ( div_mod_int @ SV471 ) @ SV283 ) ) ) @ SY1121 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV471 ) @ SY1121 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6924]) ).

thf(7217,plain,
    ! [SV472: $i,SV284: $i] :
      ( ( ! [SY1122: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV284 ) @ SV472 ) ) @ SV472 ) ) @ ( hAPP_int_int @ ( div_mod_int @ SV284 ) @ SV472 ) ) ) @ SY1122 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV284 ) @ SY1122 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6925]) ).

thf(7218,plain,
    ! [SV473: $i,SV285: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV285 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV473 ) @ SV285 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV473 ) @ ( hAPP_int_int @ ( div_mod_int @ SV473 ) @ SV285 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6926]) ).

thf(7219,plain,
    ! [SV474: $i,SV286: $i] :
      ( ( ( hAPP_int_int @ ( div_mod_int @ SV286 ) @ SV474 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV286 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV286 ) @ SV474 ) ) @ SV474 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6927]) ).

thf(7220,plain,
    ! [SV475: $i,SV287: $i] :
      ( ( ! [SY1123: $i,SY1124: $i,SY1125: $i,SY1126: $i,SY1127: $i,SY1128: $i] :
            ( ( SY1124
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1125 ) @ SY1126 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1127 ) @ SY1128 ) ) )
            | ( SV287
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV475 ) @ SY1126 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1123 ) @ SY1128 ) ) )
            | ( ( hAPP_int_int @ ( div_mod_int @ SY1124 ) @ SV287 )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1125 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SY1124 ) @ SV287 ) ) @ SV475 ) ) ) @ SY1126 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1127 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SY1124 ) @ SV287 ) ) @ SY1123 ) ) ) @ SY1128 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6928]) ).

thf(7221,plain,
    ! [SV476: $i,SV288: $i] :
      ( ( ! [SY1129: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV288 ) @ SV476 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1129 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV288 ) @ SY1129 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV476 ) @ SY1129 ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( div_mod_int @ SV288 ) @ SY1129 ) ) @ ( hAPP_int_int @ ( div_mod_int @ SV476 ) @ SY1129 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6929]) ).

thf(7222,plain,
    ! [SV477: $i,SV289: $i] :
      ( ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ SV289 ) ) ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ SV477 ) ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) @ ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ number_number_of_int @ SV289 ) ) @ ( hAPP_int_int @ number_number_of_int @ SV477 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6930]) ).

thf(7223,plain,
    ! [SV478: $i,SV290: $i] :
      ( ( ( hAPP_int_int @ ( inv @ SV290 ) @ SV478 )
        = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV478 ) @ ( hAPP_int_nat @ nat @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV290 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) ) @ SV290 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6931]) ).

thf(7224,plain,
    ! [SV479: $i,SV291: $i] :
      ( ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ SV291 ) ) @ SV479 )
        = ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ SV291 ) @ SV479 ) ) ) @ SV479 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6932]) ).

thf(7225,plain,
    ! [SV480: $i,SV293: $i] :
      ( ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV293 ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ SV480 ) )
        = ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( div_mod_nat @ SV293 ) @ SV480 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6934]) ).

thf(7226,plain,
    ! [SV481: $i,SV294: $i] :
      ( ( ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ ( div_mod_nat @ SV294 ) @ SV481 ) )
        = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV294 ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ SV481 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6935]) ).

thf(7227,plain,
    ! [SV296: $i] :
      ( ( ( ( hAPP_nat_nat @ ( div_mod_nat @ SV296 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
          = ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
        = $true )
      | ( ( ( ( hAPP_nat_nat @ ( div_mod_nat @ SV296 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
            = ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          | ( ( hAPP_nat_nat @ ( div_mod_nat @ SV296 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
            = zero_zero_nat )
          | ( ( hAPP_nat_nat @ ( div_mod_nat @ SV296 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
            = one_one_nat ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6937]) ).

thf(7228,plain,
    ! [SV482: $i,SV299: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ number_number_of_int @ SV299 ) ) @ ( hAPP_int_int @ number_number_of_int @ SV482 ) )
        = ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV299 ) @ ( hAPP_int_int @ uminus_uminus_int @ SV482 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6940]) ).

thf(7229,plain,
    ! [SV301: $i] :
      ( ( ( hAPP_nat_nat @ fact_fact_nat @ SV301 )
        = zero_zero_nat )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6942]) ).

thf(7230,plain,
    ! [SV302: $i] :
      ( ( ( SV302 = zero_zero_nat )
        = $true )
      | ( ( SV302
          = ( hAPP_nat_nat @ suc @ ( sK10_M_1 @ SV302 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6943]) ).

thf(7231,plain,
    ! [SV303: $i] :
      ( ( ( SV303 = zero_zero_nat )
        = $true )
      | ( ( SV303
          = ( hAPP_nat_nat @ suc @ ( sK9_Nat_1 @ SV303 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6944]) ).

thf(7232,plain,
    ! [SV304: $i] :
      ( ( ( ~ ( is_int @ SV304 ) )
        = $true )
      | ( ( ( hAPP_int_int @ succ @ ( hAPP_int_int @ pred @ SV304 ) )
          = SV304 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6945]) ).

thf(7233,plain,
    ! [SV483: $i,SV307: $i] :
      ( ( ! [SY1130: $i] :
            ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV307 ) @ SV483 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV307 ) @ SY1130 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV307 ) ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV483 ) @ SY1130 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6948]) ).

thf(7234,plain,
    ! [SV308: $i] :
      ( ( ( ~ ( is_int @ SV308 ) )
        = $true )
      | ( ( ( SV308
            = ( hAPP_nat_int @ semiri1621563631at_int @ ( sK4_N_1 @ SV308 ) ) )
          | ( SV308
            = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ suc @ ( sK3_N_1 @ SV308 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6949]) ).

thf(7235,plain,
    ! [SV484: $i,SV310: $i] :
      ( ( ! [SY1131: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV310 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV484 ) @ SY1131 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV310 ) @ SV484 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV310 ) @ SY1131 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6951]) ).

thf(7236,plain,
    ! [SV485: $i,SV311: $i] :
      ( ( ! [SY1132: $i] :
            ( ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV311 ) @ SV485 ) ) @ SY1132 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV311 ) @ SY1132 )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6952]) ).

thf(7237,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( ( hAPP_int_int @ ( legacy_zgcd @ zero_zero_int ) @ SX0 )
             != one_one_int )
            | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
              = one_one_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6954]) ).

thf(7238,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( ( hAPP_int_int @ abs_abs_int @ SX0 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( legacy_zgcd @ zero_zero_int ) @ SX0 )
              = one_one_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6954]) ).

thf(7239,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( one_one_int != SX0 )
            | ( SX0 = one_one_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6955]) ).

thf(7240,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( SX0 != one_one_int )
            | ( one_one_int = SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6955]) ).

thf(7241,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
             != zero_zero_int )
            | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ ( hAPP_int_int @ uminus_uminus_int @ SX1 ) )
              = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6956]) ).

thf(7242,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
              = zero_zero_int )
            | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ ( hAPP_int_int @ uminus_uminus_int @ SX1 ) )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 ) ) @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6956]) ).

thf(7243,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( SX0 != SX1 )
            | ( ( image_nat_int @ semiri1621563631at_int @ SX0 )
              = ( image_nat_int @ semiri1621563631at_int @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6957]) ).

thf(7244,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( image_nat_int @ semiri1621563631at_int @ SX0 )
             != ( image_nat_int @ semiri1621563631at_int @ SX1 ) )
            | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6957]) ).

thf(7245,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
              = zero_zero_int )
            | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
              = one_one_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6958]) ).

thf(7246,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
             != one_one_int )
            | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
             != zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6958]) ).

thf(7247,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( SX0 != zero_zero_nat )
            | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ SX0 )
              = one_one_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6959]) ).

thf(7248,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( SX0 = zero_zero_nat )
            | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ SX0 )
              = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6959]) ).

thf(7249,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( ( hAPP_int_nat @ number_number_of_nat @ SX0 )
             != zero_zero_nat )
            | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ ( hAPP_int_nat @ number_number_of_nat @ SX0 ) )
              = one_one_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6960]) ).

thf(7250,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( ( hAPP_int_nat @ number_number_of_nat @ SX0 )
              = zero_zero_nat )
            | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ ( hAPP_int_nat @ number_number_of_nat @ SX0 ) )
              = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6960]) ).

thf(7251,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( pls
             != ( hAPP_int_int @ bit0 @ SX0 ) )
            | ( pls = SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6961]) ).

thf(7252,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( pls != SX0 )
            | ( pls
              = ( hAPP_int_int @ bit0 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6961]) ).

thf(7253,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
             != zero_zero_int )
            | ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ SX0 ) ) @ SX1 )
              = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6962]) ).

thf(7254,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
              = zero_zero_int )
            | ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ SX0 ) ) @ SX1 )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SX1 ) @ ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6962]) ).

thf(7255,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
             != zero_zero_int )
            | ( SX0 = zero_zero_int )
            | ( SX1 = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6963]) ).

thf(7256,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( SX0 != zero_zero_int )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                    = zero_zero_int ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( SX1 != zero_zero_int )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                    = zero_zero_int ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6963]) ).

thf(7257,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ! [SX1: $i] :
                ( ( ( hAPP_int_nat @ number_number_of_nat @ SX1 )
                  = zero_zero_nat )
                | ( SX0 != zero_zero_int )
                | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ SX1 ) )
                  = zero_zero_int ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6964]) ).

thf(7258,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ SX1 ) )
                       != zero_zero_int )
                      | ( ( hAPP_int_nat @ number_number_of_nat @ SX1 )
                       != zero_zero_nat ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ! [SX1: $i] :
                      ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ SX1 ) )
                     != zero_zero_int )
                  | ( SX0 = zero_zero_int ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6964]) ).

thf(7259,plain,
    ! [SV313: $i] :
      ( ( ( ~ ( is_int @ SV313 ) )
        = $true )
      | ( ( ! [SY983: $i] :
              ( ( ( hAPP_int_int @ ( div_mod_int @ SV313 ) @ SY983 )
               != zero_zero_int )
              | ~ ( ( SV313
                   != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY983 ) @ ( sK11_Q_4 @ SY983 @ SV313 ) ) )
                  | ~ ( is_int @ ( sK11_Q_4 @ SY983 @ SV313 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[6965]) ).

thf(7260,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
             != ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
            | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6966]) ).

thf(7261,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( SX0 != SX1 )
            | ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
              = ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6966]) ).

thf(7262,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( zero_zero_nat != SX0 )
            | ( SX0 = zero_zero_nat ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6967]) ).

thf(7263,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( SX0 != zero_zero_nat )
            | ( zero_zero_nat = SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6967]) ).

thf(7264,plain,
    ( ( ~ ~ ( ~ ( is_int @ sK13_X_1 )
            | ~ ( is_int @ sK14_SY716 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6968]) ).

thf(7265,plain,
    ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ sK13_X_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ sK14_SY716 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6968]) ).

thf(7266,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX1 )
            | ( SX1 = zero_zero_int )
            | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
             != zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ SX0 ) ) @ SX1 )
              = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ SX1 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6969]) ).

thf(7267,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX1 )
            | ( SX1 = zero_zero_int )
            | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
              = zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ SX0 ) ) @ SX1 )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ SX1 ) ) ) @ one_one_int ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6969]) ).

thf(7268,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
             != zero_zero_int )
            | ( SX0 = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6970]) ).

thf(7269,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( SX0 != zero_zero_int )
            | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
              = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6970]) ).

thf(7270,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( ( hAPP_int_int @ bit1 @ SX0 )
             != min )
            | ( SX0 = min ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6971]) ).

thf(7271,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( SX0 != min )
            | ( ( hAPP_int_int @ bit1 @ SX0 )
              = min ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6971]) ).

thf(7272,plain,
    ! [SV486: $i,SV314: $i] :
      ( ( ~ ( is_int @ SV314 )
        | ~ ( is_int @ SV486 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 )
          = zero_zero_int )
        | ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK1_A_4 @ SV486 @ SV314 ) )
                              | ~ ( is_int @ ( sK2_SY713 @ SV486 @ SV314 ) ) )
                        | ( SV314
                         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK1_A_4 @ SV486 @ SV314 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 ) ) ) )
                  | ( SV486
                   != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK2_SY713 @ SV486 @ SV314 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 ) ) ) )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( sK1_A_4 @ SV486 @ SV314 ) ) @ ( sK2_SY713 @ SV486 @ SV314 ) )
             != one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6972]) ).

thf(7273,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ number_number_of_int @ SX0 )
             != ( hAPP_int_int @ number_number_of_int @ SX1 ) )
            | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6973]) ).

thf(7274,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0 != SX1 )
            | ( ( hAPP_int_int @ number_number_of_int @ SX0 )
              = ( hAPP_int_int @ number_number_of_int @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6973]) ).

thf(7275,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
             != ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
            | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
              = ( hAPP_int_int @ abs_abs_int @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6974]) ).

thf(7276,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( hAPP_int_int @ abs_abs_int @ SX0 )
             != ( hAPP_int_int @ abs_abs_int @ SX1 ) )
            | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
              = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6974]) ).

thf(7277,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ! [SX1: $i] :
                ( ( SX1 = zero_zero_nat )
                | ( SX0 != zero_zero_int )
                | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ SX1 )
                  = zero_zero_int ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6975]) ).

thf(7278,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ! [SX1: $i] :
                      ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ SX1 )
                       != zero_zero_int )
                      | ( SX1 != zero_zero_nat ) ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ! [SX1: $i] :
                      ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ SX1 )
                     != zero_zero_int )
                  | ( SX0 = zero_zero_int ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6975]) ).

thf(7279,plain,
    ! [SV487: $i,SV315: $i] :
      ( ( ~ ( ~ ! [SY1133: $i,SY1134: $i] :
                  ( ~ ( is_int @ SV315 )
                  | ~ ( is_int @ SV487 )
                  | ~ ( is_int @ SY1133 )
                  | ~ ( is_int @ SY1134 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1133 ) @ SY1134 ) )
                   != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SY1134 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1133 ) @ SV487 ) ) )
                  | ( SV315 = SY1133 )
                  | ( SV487 = SY1134 ) )
            | ~ ~ ( ~ ! [SY1135: $i,SY1136: $i] :
                        ( ~ ( is_int @ SV315 )
                        | ~ ( is_int @ SV487 )
                        | ~ ( is_int @ SY1135 )
                        | ~ ( is_int @ SY1136 )
                        | ( SV315 != SY1135 )
                        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1135 ) @ SY1136 ) )
                          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SY1136 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1135 ) @ SV487 ) ) ) )
                  | ~ ! [SY1137: $i,SY1138: $i] :
                        ( ~ ( is_int @ SV315 )
                        | ~ ( is_int @ SV487 )
                        | ~ ( is_int @ SY1137 )
                        | ~ ( is_int @ SY1138 )
                        | ( SV487 != SY1138 )
                        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1137 ) @ SY1138 ) )
                          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SY1138 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1137 ) @ SV487 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6976]) ).

thf(7280,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX0 ) @ SX1 ) )
            | ( SX1 = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6977]) ).

thf(7281,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX1 != zero_zero_int )
            | ( SX0
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX0 ) @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6977]) ).

thf(7282,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( hAPP_int_nat @ number_number_of_nat @ SX0 )
             != SX1 )
            | ( SX1
              = ( hAPP_int_nat @ number_number_of_nat @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6978]) ).

thf(7283,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( SX1
             != ( hAPP_int_nat @ number_number_of_nat @ SX0 ) )
            | ( ( hAPP_int_nat @ number_number_of_nat @ SX0 )
              = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6978]) ).

thf(7284,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( zero_zero_int != SX0 )
            | ( SX0 = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6979]) ).

thf(7285,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( SX0 != zero_zero_int )
            | ( zero_zero_int = SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6979]) ).

thf(7286,plain,
    ! [SV316: $i] :
      ( ( ~ ! [SY992: $i,SY993: $i] :
              ( ~ ( is_int @ SY992 )
              | ~ ( is_int @ SY993 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SY992 )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SY993 ) )
              | ( SY992 = SY993 ) )
        | ~ ! [SY994: $i,SY995: $i] :
              ( ~ ( is_int @ SY994 )
              | ~ ( is_int @ SY995 )
              | ( SY994 != SY995 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SY994 )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SY995 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6980]) ).

thf(7287,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX1 = zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX1 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX1 ) @ SX0 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX1 ) @ SX0 ) ) )
              = one_one_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6981]) ).

thf(7288,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0 = zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX1 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX1 ) @ SX0 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX1 ) @ SX0 ) ) )
              = one_one_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6981]) ).

thf(7289,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ bit1 @ SX0 )
             != ( hAPP_int_int @ bit1 @ SX1 ) )
            | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6982]) ).

thf(7290,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0 != SX1 )
            | ( ( hAPP_int_int @ bit1 @ SX0 )
              = ( hAPP_int_int @ bit1 @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6982]) ).

thf(7291,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( SX0 != zero_zero_nat )
            | ( SX1 != zero_zero_nat )
            | ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SX0 ) )
              = ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6983]) ).

thf(7292,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ! [SX1: $i] :
                      ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SX0 ) )
                     != ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
                  | ( SX0 = zero_zero_nat ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SX0 ) )
                   != ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
                  | ( SX1 = zero_zero_nat ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6983]) ).

thf(7293,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX1 = zero_zero_int )
            | ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK7_C_3 @ SX1 @ SX0 ) )
                                  | ~ ( is_int @ ( sK8_SY715 @ SX1 @ SX0 ) ) )
                            | ( SX1
                             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) @ ( sK7_C_3 @ SX1 @ SX0 ) ) ) )
                      | ( SX0
                       != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) @ ( sK8_SY715 @ SX1 @ SX0 ) ) ) )
                | ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK7_C_3 @ SX1 @ SX0 ) ) @ ( sK8_SY715 @ SX1 @ SX0 ) )
                 != one_one_int ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6984]) ).

thf(7294,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0 = zero_zero_int )
            | ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK5_C_3 @ SX1 @ SX0 ) )
                                  | ~ ( is_int @ ( sK6_SY714 @ SX1 @ SX0 ) ) )
                            | ( SX1
                             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) @ ( sK5_C_3 @ SX1 @ SX0 ) ) ) )
                      | ( SX0
                       != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) @ ( sK6_SY714 @ SX1 @ SX0 ) ) ) )
                | ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK5_C_3 @ SX1 @ SX0 ) ) @ ( sK6_SY714 @ SX1 @ SX0 ) )
                 != one_one_int ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6984]) ).

thf(7295,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ number_number_of_int @ SX0 )
             != SX1 )
            | ( SX1
              = ( hAPP_int_int @ number_number_of_int @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6985]) ).

thf(7296,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX1 )
            | ( SX1
             != ( hAPP_int_int @ number_number_of_int @ SX0 ) )
            | ( ( hAPP_int_int @ number_number_of_int @ SX0 )
              = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6985]) ).

thf(7297,plain,
    ! [SV317: $i] :
      ( ( ~ ! [SY996: $i,SY997: $i] :
              ( ~ ( is_int @ SV317 )
              | ~ ( is_int @ SY997 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV317 ) @ SY996 )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY997 ) @ SY996 ) )
              | ( SV317 = SY997 ) )
        | ~ ! [SY998: $i,SY999: $i] :
              ( ~ ( is_int @ SV317 )
              | ~ ( is_int @ SY999 )
              | ( SV317 != SY999 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV317 ) @ SY998 )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY999 ) @ SY998 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6986]) ).

thf(7298,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX1 = zero_zero_int )
            | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX1 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) )
              = one_one_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6987]) ).

thf(7299,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0 = zero_zero_int )
            | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX1 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) )
              = one_one_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6987]) ).

thf(7300,plain,
    ! [SV488: $i,SV318: $i] :
      ( ( ! [SY1139: $i] :
            ~ ( ~ ( ~ ( is_int @ SY1139 )
                  | ! [SY1140: $i,SY1141: $i] :
                      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV318 ) @ SV488 ) ) @ SY1139 )
                       != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1140 ) @ SV488 ) ) @ SY1141 ) )
                      | ( SY1139
                        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1140 ) @ SV318 ) ) @ SV488 ) ) @ SY1141 ) ) ) )
              | ~ ( ~ ( is_int @ SY1139 )
                  | ! [SY1142: $i,SY1143: $i] :
                      ( ( SY1139
                       != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1142 ) @ SV318 ) ) @ SV488 ) ) @ SY1143 ) )
                      | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV318 ) @ SV488 ) ) @ SY1139 )
                        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1142 ) @ SV488 ) ) @ SY1143 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6988]) ).

thf(7301,plain,
    ! [SV489: $i,SV319: $i] :
      ( ( ~ ( ~ ! [SY1144: $i,SY1145: $i] :
                  ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY1144 ) @ SY1145 )
                   != one_one_int )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
                   != one_one_int )
                  | ( ( hAPP_int_int @ abs_abs_int @ SY1144 )
                   != ( hAPP_int_int @ abs_abs_int @ SV319 ) )
                  | ( ( hAPP_int_int @ abs_abs_int @ SV489 )
                   != ( hAPP_int_int @ abs_abs_int @ SY1145 ) )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SY1144 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
                    = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SY1145 ) ) ) )
            | ~ ~ ( ~ ! [SY1146: $i,SY1147: $i] :
                        ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY1146 ) @ SY1147 )
                         != one_one_int )
                        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
                         != one_one_int )
                        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SY1146 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
                         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SY1147 ) ) )
                        | ( ( hAPP_int_int @ abs_abs_int @ SY1146 )
                          = ( hAPP_int_int @ abs_abs_int @ SV319 ) ) )
                  | ~ ! [SY1148: $i,SY1149: $i] :
                        ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY1148 ) @ SY1149 )
                         != one_one_int )
                        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
                         != one_one_int )
                        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SY1148 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
                         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SY1149 ) ) )
                        | ( ( hAPP_int_int @ abs_abs_int @ SV489 )
                          = ( hAPP_int_int @ abs_abs_int @ SY1149 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6989]) ).

thf(7302,plain,
    ! [SV490: $i,SV320: $i] :
      ( ( ~ ( ~ ! [SY1150: $i,SY1151: $i] :
                  ( ~ ( is_int @ SV320 )
                  | ~ ( is_int @ SV490 )
                  | ~ ( is_int @ SY1150 )
                  | ~ ( is_int @ SY1151 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
                   != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1150 ) @ SY1151 ) )
                  | ( SV320 != SV490 )
                  | ( SY1150 = SY1151 ) )
            | ~ ! [SY1152: $i,SY1153: $i] :
                  ( ~ ( is_int @ SV320 )
                  | ~ ( is_int @ SV490 )
                  | ~ ( is_int @ SY1152 )
                  | ~ ( is_int @ SY1153 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
                   != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1152 ) @ SY1153 ) )
                  | ( SY1152 != SY1153 )
                  | ( SV320 = SV490 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6990]) ).

thf(7303,plain,
    ( ( ~ ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                        ( ~ ( is_int @ SX0 )
                        | ~ ( is_int @ SX1 )
                        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                         != one_one_int )
                        | ( SX0 = one_one_int )
                        | ( SX0
                          = ( hAPP_int_int @ number_number_of_int @ min ) ) )
                  | ~ ! [SX0: $i,SX1: $i] :
                        ( ~ ( is_int @ SX0 )
                        | ~ ( is_int @ SX1 )
                        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                         != one_one_int )
                        | ( SX0 = one_one_int )
                        | ( SX1
                          = ( hAPP_int_int @ number_number_of_int @ min ) ) ) )
            | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                        ( ~ ( is_int @ SX0 )
                        | ~ ( is_int @ SX1 )
                        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                         != one_one_int )
                        | ( SX1 = one_one_int )
                        | ( SX0
                          = ( hAPP_int_int @ number_number_of_int @ min ) ) )
                  | ~ ! [SX0: $i,SX1: $i] :
                        ( ~ ( is_int @ SX0 )
                        | ~ ( is_int @ SX1 )
                        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                         != one_one_int )
                        | ( SX1 = one_one_int )
                        | ( SX1
                          = ( hAPP_int_int @ number_number_of_int @ min ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6991]) ).

thf(7304,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( SX0 != one_one_int )
                  | ( SX1 != one_one_int )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                    = one_one_int ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( SX0
                   != ( hAPP_int_int @ number_number_of_int @ min ) )
                  | ( SX1
                   != ( hAPP_int_int @ number_number_of_int @ min ) )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                    = one_one_int ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6991]) ).

thf(7305,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
             != one_one_int )
            | ( SX0 = one_one_int )
            | ( SX0
              = ( hAPP_int_int @ number_number_of_int @ min ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6992]) ).

thf(7306,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ( SX0 != one_one_int )
                  | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
                    = one_one_int ) )
            | ~ ! [SX0: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ( SX0
                   != ( hAPP_int_int @ number_number_of_int @ min ) )
                  | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
                    = one_one_int ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6992]) ).

thf(7307,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( ( hAPP_int_int @ bit0 @ SX0 )
             != pls )
            | ( SX0 = pls ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6993]) ).

thf(7308,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( SX0 != pls )
            | ( ( hAPP_int_int @ bit0 @ SX0 )
              = pls ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6993]) ).

thf(7309,plain,
    ! [SV491: $i,SV321: $i] :
      ( ( ~ ( ~ ~ ( ~ ! [SY1154: $i,SY1155: $i] :
                        ( ~ ( is_int @ SV321 )
                        | ~ ( is_int @ SV491 )
                        | ~ ( is_int @ SY1154 )
                        | ~ ( is_int @ SY1155 )
                        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1154 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1155 ) @ SV491 ) )
                          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1154 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1155 ) @ SV321 ) ) )
                        | ( SY1154 != SY1155 ) )
                  | ~ ! [SY1156: $i,SY1157: $i] :
                        ( ~ ( is_int @ SV321 )
                        | ~ ( is_int @ SV491 )
                        | ~ ( is_int @ SY1156 )
                        | ~ ( is_int @ SY1157 )
                        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1156 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1157 ) @ SV491 ) )
                          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1156 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1157 ) @ SV321 ) ) )
                        | ( SV321 != SV491 ) ) )
            | ~ ! [SY1158: $i,SY1159: $i] :
                  ( ~ ( is_int @ SV321 )
                  | ~ ( is_int @ SV491 )
                  | ~ ( is_int @ SY1158 )
                  | ~ ( is_int @ SY1159 )
                  | ( SY1158 = SY1159 )
                  | ( SV321 = SV491 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1158 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1159 ) @ SV491 ) )
                   != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1158 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1159 ) @ SV321 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[6994]) ).

thf(7310,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0 != zero_zero_int )
            | ( SX1 != zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX0 ) @ SX1 )
              = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6995]) ).

thf(7311,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX0 ) @ SX1 )
                   != zero_zero_int )
                  | ( SX0 = zero_zero_int ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX0 ) @ SX1 )
                   != zero_zero_int )
                  | ( SX1 = zero_zero_int ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6995]) ).

thf(7312,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX1 )
            | ( SX1 = zero_zero_int )
            | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
             != zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ ( hAPP_int_int @ uminus_uminus_int @ SX1 ) )
              = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ SX1 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6996]) ).

thf(7313,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX1 )
            | ( SX1 = zero_zero_int )
            | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
              = zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ ( hAPP_int_int @ uminus_uminus_int @ SX1 ) )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ SX1 ) ) ) @ one_one_int ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6996]) ).

thf(7314,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
             != ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
            | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6997]) ).

thf(7315,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( SX0 != SX1 )
            | ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
              = ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6997]) ).

thf(7316,plain,
    ! [SV322: $i] :
      ( ( ~ ! [SY1025: $i,SY1026: $i] :
              ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SY1025 )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SY1026 )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1025 ) @ SY1026 ) )
                = one_one_int ) )
        | ~ ~ ( ~ ! [SY1027: $i] :
                    ( ! [SY1028: $i] :
                        ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1027 ) @ SY1028 ) )
                       != one_one_int )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SY1027 )
                      = one_one_int ) )
              | ~ ! [SY1029: $i,SY1030: $i] :
                    ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1029 ) @ SY1030 ) )
                     != one_one_int )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SY1030 )
                      = one_one_int ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[6998]) ).

thf(7317,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
             != zero_zero_int )
            | ( SX0 = zero_zero_nat ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6999]) ).

thf(7318,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( SX0 != zero_zero_nat )
            | ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
              = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[6999]) ).

thf(7319,plain,
    ! [SV492: $i,SV323: $i] :
      ( ( ! [SY1160: $i] :
            ~ ( ~ ! [SY1161: $i,SY1162: $i] :
                    ( ~ ( is_int @ SY1162 )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV323 ) @ SV492 ) ) @ SY1160 )
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1161 ) @ SV492 ) ) @ SY1162 ) )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV323 ) @ SY1161 ) ) @ SV492 ) ) @ SY1160 )
                      = SY1162 ) )
              | ~ ! [SY1163: $i,SY1164: $i] :
                    ( ~ ( is_int @ SY1164 )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV323 ) @ SY1163 ) ) @ SV492 ) ) @ SY1160 )
                     != SY1164 )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV323 ) @ SV492 ) ) @ SY1160 )
                      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1163 ) @ SV492 ) ) @ SY1164 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7000]) ).

thf(7320,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ! [SX1: $i] :
                ( ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
                 != zero_zero_int )
                | ~ ( ( SX0
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX1 ) @ ( sK12_Q_4 @ SX1 @ SX0 ) ) )
                    | ~ ( is_int @ ( sK12_Q_4 @ SX1 @ SX0 ) ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7001]) ).

thf(7321,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ! [SX1: $i] :
                ( ! [SX2: $i] :
                    ( ( SX0
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX1 ) @ SX2 ) )
                    | ~ ( is_int @ SX2 ) )
                | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
                  = zero_zero_int ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7001]) ).

thf(7322,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
             != ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
            | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7002]) ).

thf(7323,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( SX0 != SX1 )
            | ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
              = ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7002]) ).

thf(7324,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ bit0 @ SX0 )
             != ( hAPP_int_int @ bit0 @ SX1 ) )
            | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7003]) ).

thf(7325,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0 != SX1 )
            | ( ( hAPP_int_int @ bit0 @ SX0 )
              = ( hAPP_int_int @ bit0 @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7003]) ).

thf(7326,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( min
             != ( hAPP_int_int @ bit1 @ SX0 ) )
            | ( min = SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7004]) ).

thf(7327,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( min != SX0 )
            | ( min
              = ( hAPP_int_int @ bit1 @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7004]) ).

thf(7328,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( hAPP_nat_nat @ suc @ SX0 )
             != ( hAPP_nat_nat @ suc @ SX1 ) )
            | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7005]) ).

thf(7329,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( SX0 != SX1 )
            | ( ( hAPP_nat_nat @ suc @ SX0 )
              = ( hAPP_nat_nat @ suc @ SX1 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7005]) ).

thf(7330,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX0 ) @ SX0 )
             != zero_zero_int )
            | ( SX0 = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7006]) ).

thf(7331,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( SX0 != zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX0 ) @ SX0 )
              = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7006]) ).

thf(7332,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SX0 ) @ SX1 )
             != zero_zero_int )
            | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7007]) ).

thf(7333,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0 != SX1 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SX0 ) @ SX1 )
              = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7007]) ).

thf(7334,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0 != SX1 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SX0 ) @ SX1 )
              = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7008]) ).

thf(7335,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SX0 ) @ SX1 )
             != zero_zero_int )
            | ( SX0 = SX1 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7008]) ).

thf(7336,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( zero_zero_int
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX0 ) @ SX0 ) )
            | ( SX0 = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7009]) ).

thf(7337,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( SX0 != zero_zero_int )
            | ( zero_zero_int
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX0 ) @ SX0 ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7009]) ).

thf(7338,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
             != zero_zero_int )
            | ( SX0 = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7010]) ).

thf(7339,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( SX0 != zero_zero_int )
            | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
              = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7010]) ).

thf(7340,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( one_one_nat != SX0 )
            | ( SX0 = one_one_nat ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7011]) ).

thf(7341,plain,
    ( ( ~ ! [SX0: $i] :
            ( ( SX0 != one_one_nat )
            | ( one_one_nat = SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7011]) ).

thf(7342,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ SX0 ) @ SX1 ) )
             != SX1 )
            | ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ SX0 ) ) @ SX1 )
              = zero_zero_nat ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7012]) ).

thf(7343,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ SX0 ) @ SX1 ) )
              = SX1 )
            | ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ SX0 ) ) @ SX1 )
              = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ SX0 ) @ SX1 ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7012]) ).

thf(7344,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ zero_zero_int )
              = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7013]) ).

thf(7345,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ zero_zero_int )
              = SX0 ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7013]) ).

thf(7346,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0 != zero_zero_int )
            | ( SX1 != zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
              = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7014]) ).

thf(7347,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
                   != zero_zero_int )
                  | ( SX0 = zero_zero_int ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
                   != zero_zero_int )
                  | ( SX1 = zero_zero_int ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7014]) ).

thf(7348,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0 != zero_zero_int )
            | ( SX1 != zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX0 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX1 ) @ SX1 ) )
              = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7015]) ).

thf(7349,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX0 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX1 ) @ SX1 ) )
                   != zero_zero_int )
                  | ( SX0 = zero_zero_int ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX0 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX1 ) @ SX1 ) )
                   != zero_zero_int )
                  | ( SX1 = zero_zero_int ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7015]) ).

thf(7350,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0 != zero_zero_int )
            | ( SX1 != zero_zero_int )
            | ( ( hAPP_int_int @ ( legacy_zgcd @ SX0 ) @ SX1 )
              = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7016]) ).

thf(7351,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( ( hAPP_int_int @ ( legacy_zgcd @ SX0 ) @ SX1 )
                   != zero_zero_int )
                  | ( SX0 = zero_zero_int ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( ( hAPP_int_int @ ( legacy_zgcd @ SX0 ) @ SX1 )
                   != zero_zero_int )
                  | ( SX1 = zero_zero_int ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7016]) ).

thf(7352,plain,
    ! [SV1: $i,SV324: $i] :
      ( ( ( ~ ( is_int @ SV324 ) )
        = $true )
      | ( ( is_int @ ( hAPP_int_int @ SV1 @ SV324 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7017]) ).

thf(7353,plain,
    ! [SV493: $i,SV327: $i,SV7: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV7 ) @ SV327 ) ) @ SV493 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV7 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV327 ) @ SV493 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7020]) ).

thf(7354,plain,
    ! [SV494: $i,SV328: $i,SV8: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV8 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV328 ) @ SV494 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV328 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV8 ) @ SV494 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7021]) ).

thf(7355,plain,
    ! [SV330: $i,SV12: $i] :
      ( ( ( hAPP_int_int @ bit1 @ SV12 )
        = ( hAPP_int_int @ bit0 @ SV330 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[7025]) ).

thf(7356,plain,
    ! [SV331: $i,SV13: $i] :
      ( ( ( hAPP_int_int @ bit0 @ SV13 )
        = ( hAPP_int_int @ bit1 @ SV331 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[7026]) ).

thf(7357,plain,
    ! [SV14: $i] :
      ( ( ( is_int @ SV14 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV14 ) @ pls )
          = SV14 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7027]) ).

thf(7358,plain,
    ! [SV15: $i] :
      ( ( ( is_int @ SV15 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ pls ) @ SV15 )
          = SV15 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7028]) ).

thf(7359,plain,
    ! [SV18: $i] :
      ( ( ( is_int @ SV18 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV18 ) @ zero_zero_int )
          = SV18 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7030]) ).

thf(7360,plain,
    ! [SV19: $i] :
      ( ( ( is_int @ SV19 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ SV19 )
          = SV19 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7031]) ).

thf(7361,plain,
    ! [SV20: $i] :
      ( ( ( is_int @ SV20 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ pls ) ) @ SV20 )
          = SV20 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7032]) ).

thf(7362,plain,
    ! [SV21: $i] :
      ( ( ( is_int @ SV21 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV21 ) @ ( hAPP_int_int @ number_number_of_int @ pls ) )
          = SV21 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7033]) ).

thf(7363,plain,
    ! [SV495: $i,SV333: $i,SV22: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ SV22 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ SV333 ) ) @ SV495 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV22 ) @ SV333 ) ) ) @ SV495 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7034]) ).

thf(7364,plain,
    ! [SV33: $i] :
      ( ( ( is_int @ SV33 )
        = $false )
      | ( ( ( hAPP_int_int @ number_number_of_int @ SV33 )
          = SV33 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7040]) ).

thf(7365,plain,
    ! [SV34: $i] :
      ( ( ( is_int @ SV34 )
        = $false )
      | ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV34 ) @ one_one_nat )
          = SV34 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7041]) ).

thf(7366,plain,
    ! [SV35: $i,SV338: $i] :
      ( ( ( ~ ( is_int @ SV338 ) )
        = $true )
      | ( ( ( SV338 = zero_zero_int )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV338 ) @ SV35 )
           != zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7042]) ).

thf(7367,plain,
    ! [SV339: $i,SV496: $i,SV41: $i] :
      ( ( ~ ( is_int @ SV41 )
        | ~ ( is_int @ SV496 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV41 ) @ SV339 )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV496 ) @ SV339 ) )
        | ( SV41 = SV496 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7043]) ).

thf(7368,plain,
    ! [SV42: $i,SV497: $i,SV340: $i] :
      ( ( ~ ( is_int @ SV340 )
        | ~ ( is_int @ SV497 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV42 ) @ SV340 )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV42 ) @ SV497 ) )
        | ( SV340 = SV497 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7044]) ).

thf(7369,plain,
    ! [SV43: $i,SV498: $i,SV341: $i] :
      ( ( ~ ( is_int @ SV341 )
        | ~ ( is_int @ SV498 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV43 ) @ SV341 )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV43 ) @ SV498 ) )
        | ( SV341 = SV498 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7045]) ).

thf(7370,plain,
    ! [SV499: $i,SV342: $i,SV44: $i] :
      ( ( ! [SY1165: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV44 ) @ SV342 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV499 ) @ SY1165 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV44 ) @ SV499 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV342 ) @ SY1165 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7046]) ).

thf(7371,plain,
    ! [SV500: $i,SV343: $i,SV45: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV45 ) @ SV343 ) ) @ SV500 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV45 ) @ SV500 ) ) @ SV343 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7047]) ).

thf(7372,plain,
    ! [SV501: $i,SV344: $i,SV46: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV46 ) @ SV344 ) ) @ SV501 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV46 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV344 ) @ SV501 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7048]) ).

thf(7373,plain,
    ! [SV502: $i,SV345: $i,SV47: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV47 ) @ SV345 ) ) @ SV502 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV47 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV345 ) @ SV502 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7049]) ).

thf(7374,plain,
    ! [SV503: $i,SV346: $i,SV48: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV48 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV346 ) @ SV503 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV48 ) @ SV346 ) ) @ SV503 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7050]) ).

thf(7375,plain,
    ! [SV504: $i,SV347: $i,SV49: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV49 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV347 ) @ SV504 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV347 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV49 ) @ SV504 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7051]) ).

thf(7376,plain,
    ! [SV54: $i] :
      ( ( ( is_int @ SV54 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV54 ) @ zero_zero_int )
          = SV54 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7054]) ).

thf(7377,plain,
    ! [SV55: $i] :
      ( ( ( is_int @ SV55 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV55 ) @ zero_zero_int )
          = SV55 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7055]) ).

thf(7378,plain,
    ! [SV56: $i] :
      ( ( ( is_int @ SV56 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV56 ) @ zero_zero_int )
          = SV56 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7056]) ).

thf(7379,plain,
    ! [SV57: $i] :
      ( ( ( is_int @ SV57 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ SV57 )
          = SV57 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7057]) ).

thf(7380,plain,
    ! [SV58: $i] :
      ( ( ( is_int @ SV58 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ SV58 )
          = SV58 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7058]) ).

thf(7381,plain,
    ! [SV59: $i] :
      ( ( ( is_int @ SV59 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ zero_zero_int ) @ SV59 )
          = SV59 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7059]) ).

thf(7382,plain,
    ! [SV60: $i] :
      ( ( ( is_int @ SV60 )
        = $false )
      | ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV60 ) @ one_one_nat )
          = SV60 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7060]) ).

thf(7383,plain,
    ! [SV505: $i,SV353: $i,SV64: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV64 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV353 ) @ SV505 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV353 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV64 ) @ SV505 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7064]) ).

thf(7384,plain,
    ! [SV506: $i,SV354: $i,SV65: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV65 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV354 ) @ SV506 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV65 ) @ SV354 ) ) @ SV506 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7065]) ).

thf(7385,plain,
    ! [SV507: $i,SV355: $i,SV66: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV66 ) @ SV355 ) ) @ SV507 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV66 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV355 ) @ SV507 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7066]) ).

thf(7386,plain,
    ! [SV508: $i,SV356: $i,SV67: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV67 ) @ SV356 ) ) @ SV508 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV67 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV356 ) @ SV508 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7067]) ).

thf(7387,plain,
    ! [SV509: $i,SV357: $i,SV68: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV68 ) @ SV357 ) ) @ SV509 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV68 ) @ SV509 ) ) @ SV357 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7068]) ).

thf(7388,plain,
    ! [SV510: $i,SV358: $i,SV69: $i] :
      ( ( ! [SY1166: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV69 ) @ SV358 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV510 ) @ SY1166 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV69 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV358 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV510 ) @ SY1166 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7069]) ).

thf(7389,plain,
    ! [SV511: $i,SV359: $i,SV70: $i] :
      ( ( ! [SY1167: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV70 ) @ SV359 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV511 ) @ SY1167 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV511 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV70 ) @ SV359 ) ) @ SY1167 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7070]) ).

thf(7390,plain,
    ! [SV512: $i,SV360: $i,SV71: $i] :
      ( ( ! [SY1168: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV71 ) @ SV360 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV512 ) @ SY1168 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV71 ) @ SV512 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV360 ) @ SY1168 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7071]) ).

thf(7391,plain,
    ! [SV513: $i,SV362: $i,SV73: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV73 ) @ SV362 ) ) @ SV513 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV73 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV362 ) @ SV513 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7073]) ).

thf(7392,plain,
    ! [SV514: $i,SV363: $i,SV74: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ SV74 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ SV363 ) ) @ SV514 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV74 ) @ SV363 ) ) ) @ SV514 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7074]) ).

thf(7393,plain,
    ! [SV366: $i,SV79: $i] :
      ( ( ( ~ ( is_int @ SV79 )
          | ~ ( is_int @ SV366 ) )
        = $true )
      | ( ( ( SV366 = zero_zero_int )
          | ( SV79 = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV366 ) @ SV79 )
           != zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7077]) ).

thf(7394,plain,
    ! [SV367: $i,SV80: $i] :
      ( ( ( ~ ( is_int @ SV80 )
          | ~ ( is_int @ SV367 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV80 ) @ SV367 )
           != zero_zero_int )
          | ( SV80 = zero_zero_int )
          | ( SV367 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7078]) ).

thf(7395,plain,
    ! [SV515: $i,SV368: $i,SV83: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV83 ) @ SV368 ) ) @ SV515 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV83 ) @ SV515 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV368 ) @ SV515 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7079]) ).

thf(7396,plain,
    ! [SV516: $i,SV369: $i,SV84: $i] :
      ( ( ! [SY1169: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV84 ) @ SV369 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV516 ) @ SV369 ) ) @ SY1169 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV84 ) @ SV516 ) ) @ SV369 ) ) @ SY1169 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7080]) ).

thf(7397,plain,
    ! [SV517: $i,SV370: $i,SV85: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV85 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV370 ) @ SV517 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV85 ) @ SV370 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV85 ) @ SV517 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7081]) ).

thf(7398,plain,
    ! [SV518: $i,SV371: $i,SV86: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV86 ) @ SV371 ) ) @ SV518 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV86 ) @ SV518 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV371 ) @ SV518 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7082]) ).

thf(7399,plain,
    ! [SV519: $i,SV372: $i,SV87: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV87 ) @ SV372 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV519 ) @ SV372 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV87 ) @ SV519 ) ) @ SV372 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7083]) ).

thf(7400,plain,
    ! [SV88: $i] :
      ( ( ( is_int @ SV88 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ one_one_int ) @ SV88 )
          = SV88 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7084]) ).

thf(7401,plain,
    ! [SV89: $i] :
      ( ( ( is_int @ SV89 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ one_one_int ) @ SV89 )
          = SV89 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7085]) ).

thf(7402,plain,
    ! [SV90: $i] :
      ( ( ( is_int @ SV90 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ one_one_int ) @ SV90 )
          = SV90 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7086]) ).

thf(7403,plain,
    ! [SV91: $i] :
      ( ( ( is_int @ SV91 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV91 ) @ one_one_int )
          = SV91 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7087]) ).

thf(7404,plain,
    ! [SV92: $i] :
      ( ( ( is_int @ SV92 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV92 ) @ one_one_int )
          = SV92 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7088]) ).

thf(7405,plain,
    ! [SV93: $i] :
      ( ( ( is_int @ SV93 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV93 ) @ one_one_int )
          = SV93 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7089]) ).

thf(7406,plain,
    ! [SV520: $i,SV374: $i,SV95: $i] :
      ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV95 ) @ SV374 ) ) @ SV520 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV95 ) @ SV520 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV374 ) @ SV520 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7091]) ).

thf(7407,plain,
    ! [SV521: $i,SV375: $i,SV96: $i] :
      ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV96 ) @ SV375 ) ) @ SV521 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV96 ) @ SV521 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV375 ) @ SV521 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7092]) ).

thf(7408,plain,
    ! [SV99: $i] :
      ( ( ( is_int @ SV99 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ one_one_int ) @ SV99 )
          = SV99 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7094]) ).

thf(7409,plain,
    ! [SV100: $i] :
      ( ( ( is_int @ SV100 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV100 ) @ one_one_int )
          = SV100 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7095]) ).

thf(7410,plain,
    ! [SV522: $i,SV377: $i,SV101: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV101 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV377 ) @ SV522 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV101 ) @ SV377 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV101 ) @ SV522 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7096]) ).

thf(7411,plain,
    ! [SV523: $i,SV378: $i,SV102: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV102 ) @ SV378 ) ) @ SV523 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV102 ) @ SV523 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV378 ) @ SV523 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7097]) ).

thf(7412,plain,
    ! [SV524: $i,SV380: $i,SV104: $i] :
      ( ( ! [SY1170: $i,SY1171: $i] :
            ( ~ ( is_int @ SV104 )
            | ~ ( is_int @ SV380 )
            | ~ ( is_int @ SY1171 )
            | ( SY1171 = zero_zero_int )
            | ( SV104 = SV380 )
            | ( SV524 != SY1170 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV524 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1171 ) @ SV104 ) )
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY1170 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1171 ) @ SV380 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7099]) ).

thf(7413,plain,
    ! [SV525: $i,SV381: $i,SV105: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ SV105 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV381 ) @ SV525 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ SV105 ) ) @ SV381 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ SV105 ) ) @ SV525 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7100]) ).

thf(7414,plain,
    ! [SV526: $i,SV382: $i,SV106: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV106 ) @ SV382 ) ) @ ( hAPP_int_int @ number_number_of_int @ SV526 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV106 ) @ ( hAPP_int_int @ number_number_of_int @ SV526 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV382 ) @ ( hAPP_int_int @ number_number_of_int @ SV526 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7101]) ).

thf(7415,plain,
    ! [SV126: $i] :
      ( ( ( is_int @ SV126 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV126 ) @ zero_zero_int )
          = SV126 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7109]) ).

thf(7416,plain,
    ! [SV127: $i] :
      ( ( ( is_int @ SV127 )
        = $false )
      | ( ( ! [SY823: $i] :
              ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV127 ) @ SY823 ) ) @ SY823 )
              = SV127 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7110]) ).

thf(7417,plain,
    ! [SV128: $i] :
      ( ( ( is_int @ SV128 )
        = $false )
      | ( ( ! [SY824: $i] :
              ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV128 ) @ SY824 ) ) @ SY824 )
              = SV128 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7111]) ).

thf(7418,plain,
    ! [SV527: $i,SV388: $i,SV129: $i] :
      ( ( ! [SY1172: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV129 ) @ SV388 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV527 ) @ SY1172 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV129 ) @ SV527 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV388 ) @ SY1172 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7112]) ).

thf(7419,plain,
    ! [SV130: $i] :
      ( ( ( is_int @ SV130 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV130 ) @ pls )
          = SV130 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7113]) ).

thf(7420,plain,
    ! [SV528: $i,SV390: $i,SV132: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV132 ) @ SV390 ) ) @ SV528 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV132 ) @ SV528 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV390 ) @ SV528 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7115]) ).

thf(7421,plain,
    ! [SV529: $i,SV391: $i,SV133: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV133 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV391 ) @ SV529 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV133 ) @ SV391 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV133 ) @ SV529 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7116]) ).

thf(7422,plain,
    ! [SV530: $i,SV392: $i,SV134: $i] :
      ( ( ! [SY1173: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV134 ) @ SV392 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV530 ) @ SY1173 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV134 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV392 ) @ SY1173 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV134 ) @ SV530 ) ) @ SY1173 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7117]) ).

thf(7423,plain,
    ! [SV531: $i,SV395: $i,SV139: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ number_number_of_int @ SV139 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ number_number_of_int @ SV395 ) ) @ SV531 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV139 ) @ SV395 ) ) ) @ SV531 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7120]) ).

thf(7424,plain,
    ! [SV144: $i] :
      ( ( ( is_int @ SV144 )
        = $false )
      | ( ( ! [SY841: $i,SY842: $i] :
              ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV144 ) @ SY841 )
               != SY842 )
              | ( SV144
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY842 ) @ SY841 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7122]) ).

thf(7425,plain,
    ! [SV532: $i,SV397: $i,SV145: $i] :
      ( ( ! [SY1174: $i,SY1175: $i,SY1176: $i,SY1177: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV145 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV397 ) @ SV532 ) ) ) @ SY1174 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1175 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV397 ) @ SY1176 ) ) ) @ SY1177 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV145 ) @ SY1174 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1175 ) @ SY1177 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV397 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV532 ) @ SY1174 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1176 ) @ SY1177 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7123]) ).

thf(7426,plain,
    ! [SV533: $i,SV156: $i] :
      ( ( ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV156 ) @ SV533 ) )
         != one_one_int )
        = $true )
      | ( ( ( hAPP_int_int @ abs_abs_int @ SV156 )
          = one_one_int )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[7129]) ).

thf(7427,plain,
    ! [SV161: $i] :
      ( ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV161 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ abs_abs_int @ SV161 )
          = one_one_int )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7130]) ).

thf(7428,plain,
    ! [SV163: $i] :
      ( ( ( is_int @ SV163 )
        = $false )
      | ( ( ( SV163 = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV163 ) @ SV163 )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7131]) ).

thf(7429,plain,
    ! [SV534: $i,SV404: $i,SV169: $i] :
      ( ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV169 ) @ SV404 ) ) @ SV534 )
        = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV169 ) @ ( hAPP_int_int @ ( div_mod_int @ SV404 ) @ SV534 ) ) ) @ SV534 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7134]) ).

thf(7430,plain,
    ! [SV535: $i,SV405: $i,SV170: $i] :
      ( ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV170 ) @ ( hAPP_int_int @ ( div_mod_int @ SV405 ) @ SV535 ) ) ) @ SV535 )
        = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV170 ) @ SV405 ) ) @ SV535 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7135]) ).

thf(7431,plain,
    ! [SV536: $i,SV406: $i,SV171: $i] :
      ( ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( div_mod_int @ SV171 ) @ SV406 ) ) @ SV536 ) ) @ SV406 )
        = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV171 ) @ SV536 ) ) @ SV406 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7136]) ).

thf(7432,plain,
    ! [SV537: $i,SV407: $i,SV172: $i] :
      ( ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV172 ) @ ( hAPP_int_int @ ( div_mod_int @ SV407 ) @ SV537 ) ) ) @ SV537 )
        = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV172 ) @ SV407 ) ) @ SV537 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7137]) ).

thf(7433,plain,
    ! [SV538: $i,SV408: $i,SV173: $i] :
      ( ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( div_mod_int @ SV173 ) @ SV408 ) ) @ SV538 ) ) @ SV408 )
        = ( hAPP_int_int @ ( div_mod_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV173 ) @ SV538 ) ) @ SV408 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7138]) ).

thf(7434,plain,
    ! [SV539: $i,SV410: $i,SV175: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV175 ) @ SV410 ) ) @ SV539 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV175 ) @ SV539 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV410 ) @ SV539 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( div_mod_int @ SV175 ) @ SV539 ) ) @ ( hAPP_int_int @ ( div_mod_int @ SV410 ) @ SV539 ) ) ) @ SV539 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7140]) ).

thf(7435,plain,
    ! [SV177: $i] :
      ( ( ( is_int @ SV177 )
        = $false )
      | ( ( SV177
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ ( sK15_M_1 @ SV177 ) ) ) @ ( hAPP_nat_int @ semiri1621563631at_int @ ( sK16_SY717 @ SV177 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7141]) ).

thf(7436,plain,
    ! [SV178: $i] :
      ( ( ( is_int @ SV178 )
        = $false )
      | ( ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ uminus_uminus_int @ SV178 ) )
          = SV178 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7142]) ).

thf(7437,plain,
    ! [SV420: $i,SV191: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ SV191 ) ) @ SV420 )
          = zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ SV191 ) @ SV420 )
         != zero_zero_int )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7152]) ).

thf(7438,plain,
    ! [SV421: $i,SV192: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV192 ) @ ( hAPP_int_int @ uminus_uminus_int @ SV421 ) )
          = zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ SV192 ) @ SV421 )
         != zero_zero_int )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7153]) ).

thf(7439,plain,
    ! [SV202: $i,SV540: $i,SV424: $i] :
      ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV424 ) @ SV540 )
         != one_one_int )
        | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV424 ) @ SV202 ) ) @ SV540 )
          = ( hAPP_int_int @ ( legacy_zgcd @ SV202 ) @ SV540 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7156]) ).

thf(7440,plain,
    ! [SV203: $i,SV541: $i,SV425: $i] :
      ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV425 ) @ SV541 )
         != one_one_int )
        | ( ( hAPP_int_int @ ( legacy_zgcd @ SV203 ) @ SV541 )
         != one_one_int )
        | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV425 ) @ SV203 ) ) @ SV541 )
          = one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7157]) ).

thf(7441,plain,
    ! [SV542: $i,SV427: $i,SV207: $i] :
      ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV207 ) @ SV427 ) ) @ SV542 )
        = ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV207 ) @ SV542 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV427 ) @ SV542 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7159]) ).

thf(7442,plain,
    ! [SV543: $i,SV429: $i,SV209: $i] :
      ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV209 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV429 ) @ SV543 ) )
        = ( hAPP_int_int @ ( legacy_zgcd @ SV429 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV209 ) @ SV543 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7161]) ).

thf(7443,plain,
    ! [SV544: $i,SV430: $i,SV210: $i] :
      ( ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( legacy_zgcd @ SV210 ) @ SV430 ) ) @ SV544 )
        = ( hAPP_int_int @ ( legacy_zgcd @ SV210 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV430 ) @ SV544 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7162]) ).

thf(7444,plain,
    ! [SV545: $i,SV433: $i,SV213: $i] :
      ( ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV213 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV433 ) @ SV545 ) ) ) @ SV433 )
        = ( hAPP_int_int @ ( legacy_zgcd @ SV213 ) @ SV433 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7165]) ).

thf(7445,plain,
    ! [SV214: $i,SV546: $i,SV434: $i] :
      ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV434 ) @ SV546 )
         != one_one_int )
        | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV434 ) @ SV214 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV546 ) @ SV214 ) )
          = one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7166]) ).

thf(7446,plain,
    ! [SV215: $i,SV547: $i,SV435: $i] :
      ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV435 ) @ SV547 )
         != one_one_int )
        | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV435 ) @ SV215 ) ) @ SV547 )
          = one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7167]) ).

thf(7447,plain,
    ! [SV437: $i,SV221: $i,SV548: $i] :
      ( ( ! [SY1178: $i] :
            ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV548 ) @ SY1178 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV548 ) @ SV221 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY1178 ) @ SV437 ) )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7169]) ).

thf(7448,plain,
    ! [SV549: $i,SV438: $i,SV224: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV224 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV438 ) @ SV224 ) ) @ SV549 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV224 ) @ SV549 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7170]) ).

thf(7449,plain,
    ! [SV235: $i,SV550: $i,SV445: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV445 ) @ SV550 )
         != one_one_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV445 ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV550 ) @ SV235 ) )
          = one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7177]) ).

thf(7450,plain,
    ! [SV551: $i,SV447: $i,SV237: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV237 ) @ SV447 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV551 ) @ SV447 ) )
        = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV237 ) @ SV551 ) ) @ SV447 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7179]) ).

thf(7451,plain,
    ! [SV552: $i,SV449: $i,SV239: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV239 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV449 ) @ SV552 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV449 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV239 ) @ SV552 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7181]) ).

thf(7452,plain,
    ! [SV553: $i,SV450: $i,SV240: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV240 ) @ SV450 ) ) @ SV553 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV240 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV450 ) @ SV553 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7182]) ).

thf(7453,plain,
    ! [SV243: $i,SV554: $i,SV453: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV453 ) @ SV554 )
         != one_one_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV453 ) @ SV243 ) ) @ SV554 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV243 ) @ SV554 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7185]) ).

thf(7454,plain,
    ! [SV244: $i,SV555: $i,SV454: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV454 ) @ SV555 )
         != one_one_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV454 ) @ SV244 )
         != one_one_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV454 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV555 ) @ SV244 ) )
          = one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7186]) ).

thf(7455,plain,
    ! [SV455: $i,SV245: $i] :
      ( ( ( ! [SY1113: $i] :
              ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV245 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV455 ) @ SY1113 ) )
             != one_one_int ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV245 ) @ SV455 )
          = one_one_int )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7187]) ).

thf(7456,plain,
    ! [SV556: $i,SV456: $i,SV246: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV246 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV456 ) @ SV556 ) )
         != one_one_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV246 ) @ SV556 )
          = one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7188]) ).

thf(7457,plain,
    ! [SV247: $i,SV457: $i,SV557: $i] :
      ( ( ! [SY1179: $i] :
            ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV557 ) @ SY1179 )
              = zero_zero_int )
            | ( SV557
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV457 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV557 ) @ SY1179 ) ) )
            | ( SY1179
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV247 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV557 ) @ SY1179 ) ) )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV457 ) @ SV247 )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7189]) ).

thf(7458,plain,
    ! [SV248: $i] :
      ( ( ( is_int @ SV248 )
        = $false )
      | ( ( ( hAPP_int_int @ cOMBI_int @ SV248 )
          = SV248 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7190]) ).

thf(7459,plain,
    ! [SV558: $i,SV458: $i,SV249: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ ( hAPP_f2135977429nt_int @ cOMBC_int_int_int @ SV249 ) @ SV458 ) @ SV558 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ SV249 @ SV558 ) @ SV458 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7191]) ).

thf(7460,plain,
    ! [SV261: $i] :
      ( ( ( is_int @ SV261 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV261 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ pls ) ) )
          = SV261 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7196]) ).

thf(7461,plain,
    ! [SV262: $i] :
      ( ( ( is_int @ SV262 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit1 @ pls ) ) ) @ SV262 )
          = SV262 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7197]) ).

thf(7462,plain,
    ! [SV263: $i] :
      ( ( ( is_int @ SV263 )
        = $false )
      | ( ( ! [SY943: $i] :
              ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV263 ) @ SY943 )
             != one_one_int )
          | ( SV263 = one_one_int )
          | ( SV263
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7198]) ).

thf(7463,plain,
    ! [SV559: $i,SV463: $i,SV264: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ SV264 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV463 ) @ SV559 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ SV264 ) ) @ SV463 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ SV264 ) ) @ SV559 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7199]) ).

thf(7464,plain,
    ! [SV560: $i,SV464: $i,SV265: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV265 ) @ SV464 ) ) @ ( hAPP_int_int @ number_number_of_int @ SV560 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV265 ) @ ( hAPP_int_int @ number_number_of_int @ SV560 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV464 ) @ ( hAPP_int_int @ number_number_of_int @ SV560 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7200]) ).

thf(7465,plain,
    ! [SV469: $i,SV271: $i] :
      ( ( ( ( hAPP_nat_nat @ suc @ SV271 )
         != ( hAPP_nat_nat @ suc @ SV469 ) )
        = $true )
      | ( ( SV271 = SV469 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7205]) ).

thf(7466,plain,
    ! [SV281: $i] :
      ( ( ( is_int @ SV281 )
        = $false )
      | ( ( ! [SY953: $i] :
              ( SV281
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY953 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV281 ) @ SY953 ) ) ) @ ( hAPP_int_int @ ( div_mod_int @ SV281 ) @ SY953 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7214]) ).

thf(7467,plain,
    ! [SV561: $i,SV470: $i,SV282: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV282 ) @ SV470 ) ) @ SV561 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV282 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV470 ) @ SV561 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV282 ) @ ( hAPP_int_int @ ( div_mod_int @ SV470 ) @ SV561 ) ) ) @ SV561 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7215]) ).

thf(7468,plain,
    ! [SV562: $i,SV471: $i,SV283: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV283 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV471 ) @ SV283 ) ) ) @ ( hAPP_int_int @ ( div_mod_int @ SV471 ) @ SV283 ) ) ) @ SV562 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV471 ) @ SV562 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7216]) ).

thf(7469,plain,
    ! [SV563: $i,SV472: $i,SV284: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV284 ) @ SV472 ) ) @ SV472 ) ) @ ( hAPP_int_int @ ( div_mod_int @ SV284 ) @ SV472 ) ) ) @ SV563 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV284 ) @ SV563 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7217]) ).

thf(7470,plain,
    ! [SV564: $i,SV475: $i,SV287: $i] :
      ( ( ! [SY1180: $i,SY1181: $i,SY1182: $i,SY1183: $i,SY1184: $i] :
            ( ( SY1180
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1181 ) @ SY1182 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1183 ) @ SY1184 ) ) )
            | ( SV287
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV475 ) @ SY1182 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV564 ) @ SY1184 ) ) )
            | ( ( hAPP_int_int @ ( div_mod_int @ SY1180 ) @ SV287 )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1181 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SY1180 ) @ SV287 ) ) @ SV475 ) ) ) @ SY1182 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1183 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SY1180 ) @ SV287 ) ) @ SV564 ) ) ) @ SY1184 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7220]) ).

thf(7471,plain,
    ! [SV565: $i,SV476: $i,SV288: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV288 ) @ SV476 )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV565 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV288 ) @ SV565 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV476 ) @ SV565 ) ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( div_mod_int @ SV288 ) @ SV565 ) ) @ ( hAPP_int_int @ ( div_mod_int @ SV476 ) @ SV565 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7221]) ).

thf(7472,plain,
    ! [SV296: $i] :
      ( ( ( ( hAPP_nat_nat @ ( div_mod_nat @ SV296 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
          = ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
        = $true )
      | ( ( ( ( hAPP_nat_nat @ ( div_mod_nat @ SV296 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
            = zero_zero_nat )
          | ( ( hAPP_nat_nat @ ( div_mod_nat @ SV296 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
            = one_one_nat ) )
        = $true )
      | ( ( ( hAPP_nat_nat @ ( div_mod_nat @ SV296 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
          = ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7227]) ).

thf(7473,plain,
    ! [SV304: $i] :
      ( ( ( is_int @ SV304 )
        = $false )
      | ( ( ( hAPP_int_int @ succ @ ( hAPP_int_int @ pred @ SV304 ) )
          = SV304 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7232]) ).

thf(7474,plain,
    ! [SV566: $i,SV483: $i,SV307: $i] :
      ( ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV307 ) @ SV483 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV307 ) @ SV566 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV307 ) ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV483 ) @ SV566 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7233]) ).

thf(7475,plain,
    ! [SV308: $i] :
      ( ( ( is_int @ SV308 )
        = $false )
      | ( ( ( SV308
            = ( hAPP_nat_int @ semiri1621563631at_int @ ( sK4_N_1 @ SV308 ) ) )
          | ( SV308
            = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ suc @ ( sK3_N_1 @ SV308 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7234]) ).

thf(7476,plain,
    ! [SV567: $i,SV484: $i,SV310: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV310 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV484 ) @ SV567 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV310 ) @ SV484 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV310 ) @ SV567 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7235]) ).

thf(7477,plain,
    ! [SV568: $i,SV485: $i,SV311: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV311 ) @ SV485 ) ) @ SV568 )
         != one_one_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV311 ) @ SV568 )
          = one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7236]) ).

thf(7478,plain,
    ( ( ! [SX0: $i] :
          ( ( ( hAPP_int_int @ ( legacy_zgcd @ zero_zero_int ) @ SX0 )
           != one_one_int )
          | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
            = one_one_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7237]) ).

thf(7479,plain,
    ( ( ! [SX0: $i] :
          ( ( ( hAPP_int_int @ abs_abs_int @ SX0 )
           != one_one_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ zero_zero_int ) @ SX0 )
            = one_one_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7238]) ).

thf(7480,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ( one_one_int != SX0 )
          | ( SX0 = one_one_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7239]) ).

thf(7481,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ( SX0 != one_one_int )
          | ( one_one_int = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7240]) ).

thf(7482,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
           != zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ ( hAPP_int_int @ uminus_uminus_int @ SX1 ) )
            = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7241]) ).

thf(7483,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
            = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ ( hAPP_int_int @ uminus_uminus_int @ SX1 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 ) ) @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7242]) ).

thf(7484,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( ( image_nat_int @ semiri1621563631at_int @ SX0 )
            = ( image_nat_int @ semiri1621563631at_int @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7243]) ).

thf(7485,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ( image_nat_int @ semiri1621563631at_int @ SX0 )
           != ( image_nat_int @ semiri1621563631at_int @ SX1 ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7244]) ).

thf(7486,plain,
    ( ( ! [SX0: $i] :
          ( ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
            = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
            = one_one_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7245]) ).

thf(7487,plain,
    ( ( ! [SX0: $i] :
          ( ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
           != one_one_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
           != zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7246]) ).

thf(7488,plain,
    ( ( ! [SX0: $i] :
          ( ( SX0 != zero_zero_nat )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ SX0 )
            = one_one_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7247]) ).

thf(7489,plain,
    ( ( ! [SX0: $i] :
          ( ( SX0 = zero_zero_nat )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ SX0 )
            = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7248]) ).

thf(7490,plain,
    ( ( ! [SX0: $i] :
          ( ( ( hAPP_int_nat @ number_number_of_nat @ SX0 )
           != zero_zero_nat )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ ( hAPP_int_nat @ number_number_of_nat @ SX0 ) )
            = one_one_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7249]) ).

thf(7491,plain,
    ( ( ! [SX0: $i] :
          ( ( ( hAPP_int_nat @ number_number_of_nat @ SX0 )
            = zero_zero_nat )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ ( hAPP_int_nat @ number_number_of_nat @ SX0 ) )
            = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7250]) ).

thf(7492,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ( pls
           != ( hAPP_int_int @ bit0 @ SX0 ) )
          | ( pls = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7251]) ).

thf(7493,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ( pls != SX0 )
          | ( pls
            = ( hAPP_int_int @ bit0 @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7252]) ).

thf(7494,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
           != zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ SX0 ) ) @ SX1 )
            = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7253]) ).

thf(7495,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
            = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ SX0 ) ) @ SX1 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SX1 ) @ ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7254]) ).

thf(7496,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
           != zero_zero_int )
          | ( SX0 = zero_zero_int )
          | ( SX1 = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7255]) ).

thf(7497,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( SX0 != zero_zero_int )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                  = zero_zero_int ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( SX1 != zero_zero_int )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                  = zero_zero_int ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7256]) ).

thf(7498,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ! [SX1: $i] :
              ( ( ( hAPP_int_nat @ number_number_of_nat @ SX1 )
                = zero_zero_nat )
              | ( SX0 != zero_zero_int )
              | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ SX1 ) )
                = zero_zero_int ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7257]) ).

thf(7499,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ! [SX1: $i] :
                    ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ SX1 ) )
                     != zero_zero_int )
                    | ( ( hAPP_int_nat @ number_number_of_nat @ SX1 )
                     != zero_zero_nat ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ! [SX1: $i] :
                    ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ SX1 ) )
                   != zero_zero_int )
                | ( SX0 = zero_zero_int ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7258]) ).

thf(7500,plain,
    ! [SV313: $i] :
      ( ( ( is_int @ SV313 )
        = $false )
      | ( ( ! [SY983: $i] :
              ( ( ( hAPP_int_int @ ( div_mod_int @ SV313 ) @ SY983 )
               != zero_zero_int )
              | ~ ( ( SV313
                   != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY983 ) @ ( sK11_Q_4 @ SY983 @ SV313 ) ) )
                  | ~ ( is_int @ ( sK11_Q_4 @ SY983 @ SV313 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7259]) ).

thf(7501,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
           != ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7260]) ).

thf(7502,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
            = ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7261]) ).

thf(7503,plain,
    ( ( ! [SX0: $i] :
          ( ( zero_zero_nat != SX0 )
          | ( SX0 = zero_zero_nat ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7262]) ).

thf(7504,plain,
    ( ( ! [SX0: $i] :
          ( ( SX0 != zero_zero_nat )
          | ( zero_zero_nat = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7263]) ).

thf(7505,plain,
    ( ( ~ ( ~ ( is_int @ sK13_X_1 )
          | ~ ( is_int @ sK14_SY716 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7264]) ).

thf(7506,plain,
    ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ sK13_X_1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ sK14_SY716 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ m ) ) @ one_one_int ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ one_one_int ) @ ( hAPP_nat_int @ semiri1621563631at_int @ n ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7265]) ).

thf(7507,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX1 )
          | ( SX1 = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
           != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ SX0 ) ) @ SX1 )
            = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ SX1 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7266]) ).

thf(7508,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX1 )
          | ( SX1 = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
            = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ SX0 ) ) @ SX1 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ SX1 ) ) ) @ one_one_int ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7267]) ).

thf(7509,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
           != zero_zero_int )
          | ( SX0 = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7268]) ).

thf(7510,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ( SX0 != zero_zero_int )
          | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
            = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7269]) ).

thf(7511,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ( ( hAPP_int_int @ bit1 @ SX0 )
           != min )
          | ( SX0 = min ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7270]) ).

thf(7512,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ( SX0 != min )
          | ( ( hAPP_int_int @ bit1 @ SX0 )
            = min ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7271]) ).

thf(7513,plain,
    ! [SV486: $i,SV314: $i] :
      ( ( ( ~ ( is_int @ SV314 )
          | ~ ( is_int @ SV486 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 )
            = zero_zero_int )
          | ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK1_A_4 @ SV486 @ SV314 ) )
                                | ~ ( is_int @ ( sK2_SY713 @ SV486 @ SV314 ) ) )
                          | ( SV314
                           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK1_A_4 @ SV486 @ SV314 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 ) ) ) )
                    | ( SV486
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK2_SY713 @ SV486 @ SV314 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 ) ) ) )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( sK1_A_4 @ SV486 @ SV314 ) ) @ ( sK2_SY713 @ SV486 @ SV314 ) )
               != one_one_int ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7272]) ).

thf(7514,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( ( hAPP_int_int @ number_number_of_int @ SX0 )
           != ( hAPP_int_int @ number_number_of_int @ SX1 ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7273]) ).

thf(7515,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( SX0 != SX1 )
          | ( ( hAPP_int_int @ number_number_of_int @ SX0 )
            = ( hAPP_int_int @ number_number_of_int @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7274]) ).

thf(7516,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
           != ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
          | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
            = ( hAPP_int_int @ abs_abs_int @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7275]) ).

thf(7517,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ( hAPP_int_int @ abs_abs_int @ SX0 )
           != ( hAPP_int_int @ abs_abs_int @ SX1 ) )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
            = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7276]) ).

thf(7518,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ! [SX1: $i] :
              ( ( SX1 = zero_zero_nat )
              | ( SX0 != zero_zero_int )
              | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ SX1 )
                = zero_zero_int ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7277]) ).

thf(7519,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ! [SX1: $i] :
                    ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ SX1 )
                     != zero_zero_int )
                    | ( SX1 != zero_zero_nat ) ) )
          | ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ! [SX1: $i] :
                    ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ SX1 )
                   != zero_zero_int )
                | ( SX0 = zero_zero_int ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7278]) ).

thf(7520,plain,
    ! [SV487: $i,SV315: $i] :
      ( ( ~ ! [SY1133: $i,SY1134: $i] :
              ( ~ ( is_int @ SV315 )
              | ~ ( is_int @ SV487 )
              | ~ ( is_int @ SY1133 )
              | ~ ( is_int @ SY1134 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1133 ) @ SY1134 ) )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SY1134 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1133 ) @ SV487 ) ) )
              | ( SV315 = SY1133 )
              | ( SV487 = SY1134 ) )
        | ~ ~ ( ~ ! [SY1135: $i,SY1136: $i] :
                    ( ~ ( is_int @ SV315 )
                    | ~ ( is_int @ SV487 )
                    | ~ ( is_int @ SY1135 )
                    | ~ ( is_int @ SY1136 )
                    | ( SV315 != SY1135 )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1135 ) @ SY1136 ) )
                      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SY1136 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1135 ) @ SV487 ) ) ) )
              | ~ ! [SY1137: $i,SY1138: $i] :
                    ( ~ ( is_int @ SV315 )
                    | ~ ( is_int @ SV487 )
                    | ~ ( is_int @ SY1137 )
                    | ~ ( is_int @ SY1138 )
                    | ( SV487 != SY1138 )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1137 ) @ SY1138 ) )
                      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SY1138 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1137 ) @ SV487 ) ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[7279]) ).

thf(7521,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( SX0
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX0 ) @ SX1 ) )
          | ( SX1 = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7280]) ).

thf(7522,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( SX1 != zero_zero_int )
          | ( SX0
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX0 ) @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7281]) ).

thf(7523,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ( hAPP_int_nat @ number_number_of_nat @ SX0 )
           != SX1 )
          | ( SX1
            = ( hAPP_int_nat @ number_number_of_nat @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7282]) ).

thf(7524,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX1
           != ( hAPP_int_nat @ number_number_of_nat @ SX0 ) )
          | ( ( hAPP_int_nat @ number_number_of_nat @ SX0 )
            = SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7283]) ).

thf(7525,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ( zero_zero_int != SX0 )
          | ( SX0 = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7284]) ).

thf(7526,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ( SX0 != zero_zero_int )
          | ( zero_zero_int = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7285]) ).

thf(7527,plain,
    ! [SV316: $i] :
      ( ( ~ ! [SY992: $i,SY993: $i] :
              ( ~ ( is_int @ SY992 )
              | ~ ( is_int @ SY993 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SY992 )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SY993 ) )
              | ( SY992 = SY993 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[7286]) ).

thf(7528,plain,
    ! [SV316: $i] :
      ( ( ~ ! [SY994: $i,SY995: $i] :
              ( ~ ( is_int @ SY994 )
              | ~ ( is_int @ SY995 )
              | ( SY994 != SY995 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SY994 )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SY995 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[7286]) ).

thf(7529,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( SX1 = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX1 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX1 ) @ SX0 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX1 ) @ SX0 ) ) )
            = one_one_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7287]) ).

thf(7530,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( SX0 = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX1 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX1 ) @ SX0 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX1 ) @ SX0 ) ) )
            = one_one_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7288]) ).

thf(7531,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( ( hAPP_int_int @ bit1 @ SX0 )
           != ( hAPP_int_int @ bit1 @ SX1 ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7289]) ).

thf(7532,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( SX0 != SX1 )
          | ( ( hAPP_int_int @ bit1 @ SX0 )
            = ( hAPP_int_int @ bit1 @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7290]) ).

thf(7533,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != zero_zero_nat )
          | ( SX1 != zero_zero_nat )
          | ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SX0 ) )
            = ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7291]) ).

thf(7534,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ! [SX1: $i] :
                    ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SX0 ) )
                   != ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
                | ( SX0 = zero_zero_nat ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SX0 ) )
                 != ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
                | ( SX1 = zero_zero_nat ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7292]) ).

thf(7535,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( SX1 = zero_zero_int )
          | ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK7_C_3 @ SX1 @ SX0 ) )
                                | ~ ( is_int @ ( sK8_SY715 @ SX1 @ SX0 ) ) )
                          | ( SX1
                           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) @ ( sK7_C_3 @ SX1 @ SX0 ) ) ) )
                    | ( SX0
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) @ ( sK8_SY715 @ SX1 @ SX0 ) ) ) )
              | ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK7_C_3 @ SX1 @ SX0 ) ) @ ( sK8_SY715 @ SX1 @ SX0 ) )
               != one_one_int ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7293]) ).

thf(7536,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( SX0 = zero_zero_int )
          | ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK5_C_3 @ SX1 @ SX0 ) )
                                | ~ ( is_int @ ( sK6_SY714 @ SX1 @ SX0 ) ) )
                          | ( SX1
                           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) @ ( sK5_C_3 @ SX1 @ SX0 ) ) ) )
                    | ( SX0
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) @ ( sK6_SY714 @ SX1 @ SX0 ) ) ) )
              | ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK5_C_3 @ SX1 @ SX0 ) ) @ ( sK6_SY714 @ SX1 @ SX0 ) )
               != one_one_int ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7294]) ).

thf(7537,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX1 )
          | ( ( hAPP_int_int @ number_number_of_int @ SX0 )
           != SX1 )
          | ( SX1
            = ( hAPP_int_int @ number_number_of_int @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7295]) ).

thf(7538,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX1 )
          | ( SX1
           != ( hAPP_int_int @ number_number_of_int @ SX0 ) )
          | ( ( hAPP_int_int @ number_number_of_int @ SX0 )
            = SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7296]) ).

thf(7539,plain,
    ! [SV317: $i] :
      ( ( ~ ! [SY996: $i,SY997: $i] :
              ( ~ ( is_int @ SV317 )
              | ~ ( is_int @ SY997 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV317 ) @ SY996 )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY997 ) @ SY996 ) )
              | ( SV317 = SY997 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[7297]) ).

thf(7540,plain,
    ! [SV317: $i] :
      ( ( ~ ! [SY998: $i,SY999: $i] :
              ( ~ ( is_int @ SV317 )
              | ~ ( is_int @ SY999 )
              | ( SV317 != SY999 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV317 ) @ SY998 )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY999 ) @ SY998 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[7297]) ).

thf(7541,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( SX1 = zero_zero_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX1 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) )
            = one_one_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7298]) ).

thf(7542,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( SX0 = zero_zero_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX1 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SX1 ) @ SX0 ) ) )
            = one_one_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7299]) ).

thf(7543,plain,
    ! [SV488: $i,SV318: $i,SV569: $i] :
      ( ( ~ ( ~ ( ~ ( is_int @ SV569 )
                | ! [SY1185: $i,SY1186: $i] :
                    ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV318 ) @ SV488 ) ) @ SV569 )
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1185 ) @ SV488 ) ) @ SY1186 ) )
                    | ( SV569
                      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1185 ) @ SV318 ) ) @ SV488 ) ) @ SY1186 ) ) ) )
            | ~ ( ~ ( is_int @ SV569 )
                | ! [SY1187: $i,SY1188: $i] :
                    ( ( SV569
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1187 ) @ SV318 ) ) @ SV488 ) ) @ SY1188 ) )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV318 ) @ SV488 ) ) @ SV569 )
                      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1187 ) @ SV488 ) ) @ SY1188 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7300]) ).

thf(7544,plain,
    ! [SV489: $i,SV319: $i] :
      ( ( ~ ! [SY1144: $i,SY1145: $i] :
              ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY1144 ) @ SY1145 )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
               != one_one_int )
              | ( ( hAPP_int_int @ abs_abs_int @ SY1144 )
               != ( hAPP_int_int @ abs_abs_int @ SV319 ) )
              | ( ( hAPP_int_int @ abs_abs_int @ SV489 )
               != ( hAPP_int_int @ abs_abs_int @ SY1145 ) )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SY1144 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SY1145 ) ) ) )
        | ~ ~ ( ~ ! [SY1146: $i,SY1147: $i] :
                    ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY1146 ) @ SY1147 )
                     != one_one_int )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
                     != one_one_int )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SY1146 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SY1147 ) ) )
                    | ( ( hAPP_int_int @ abs_abs_int @ SY1146 )
                      = ( hAPP_int_int @ abs_abs_int @ SV319 ) ) )
              | ~ ! [SY1148: $i,SY1149: $i] :
                    ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY1148 ) @ SY1149 )
                     != one_one_int )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
                     != one_one_int )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SY1148 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SY1149 ) ) )
                    | ( ( hAPP_int_int @ abs_abs_int @ SV489 )
                      = ( hAPP_int_int @ abs_abs_int @ SY1149 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[7301]) ).

thf(7545,plain,
    ! [SV490: $i,SV320: $i] :
      ( ( ~ ! [SY1150: $i,SY1151: $i] :
              ( ~ ( is_int @ SV320 )
              | ~ ( is_int @ SV490 )
              | ~ ( is_int @ SY1150 )
              | ~ ( is_int @ SY1151 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1150 ) @ SY1151 ) )
              | ( SV320 != SV490 )
              | ( SY1150 = SY1151 ) )
        | ~ ! [SY1152: $i,SY1153: $i] :
              ( ~ ( is_int @ SV320 )
              | ~ ( is_int @ SV490 )
              | ~ ( is_int @ SY1152 )
              | ~ ( is_int @ SY1153 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1152 ) @ SY1153 ) )
              | ( SY1152 != SY1153 )
              | ( SV320 = SV490 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[7302]) ).

thf(7546,plain,
    ( ( ~ ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                      ( ~ ( is_int @ SX0 )
                      | ~ ( is_int @ SX1 )
                      | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                       != one_one_int )
                      | ( SX0 = one_one_int )
                      | ( SX0
                        = ( hAPP_int_int @ number_number_of_int @ min ) ) )
                | ~ ! [SX0: $i,SX1: $i] :
                      ( ~ ( is_int @ SX0 )
                      | ~ ( is_int @ SX1 )
                      | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                       != one_one_int )
                      | ( SX0 = one_one_int )
                      | ( SX1
                        = ( hAPP_int_int @ number_number_of_int @ min ) ) ) )
          | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                      ( ~ ( is_int @ SX0 )
                      | ~ ( is_int @ SX1 )
                      | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                       != one_one_int )
                      | ( SX1 = one_one_int )
                      | ( SX0
                        = ( hAPP_int_int @ number_number_of_int @ min ) ) )
                | ~ ! [SX0: $i,SX1: $i] :
                      ( ~ ( is_int @ SX0 )
                      | ~ ( is_int @ SX1 )
                      | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                       != one_one_int )
                      | ( SX1 = one_one_int )
                      | ( SX1
                        = ( hAPP_int_int @ number_number_of_int @ min ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7303]) ).

thf(7547,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( SX0 != one_one_int )
                | ( SX1 != one_one_int )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                  = one_one_int ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( SX0
                 != ( hAPP_int_int @ number_number_of_int @ min ) )
                | ( SX1
                 != ( hAPP_int_int @ number_number_of_int @ min ) )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                  = one_one_int ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7304]) ).

thf(7548,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
           != one_one_int )
          | ( SX0 = one_one_int )
          | ( SX0
            = ( hAPP_int_int @ number_number_of_int @ min ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7305]) ).

thf(7549,plain,
    ( ( ~ ( ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ( SX0 != one_one_int )
                | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
                  = one_one_int ) )
          | ~ ! [SX0: $i] :
                ( ~ ( is_int @ SX0 )
                | ( SX0
                 != ( hAPP_int_int @ number_number_of_int @ min ) )
                | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
                  = one_one_int ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7306]) ).

thf(7550,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ( ( hAPP_int_int @ bit0 @ SX0 )
           != pls )
          | ( SX0 = pls ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7307]) ).

thf(7551,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ( SX0 != pls )
          | ( ( hAPP_int_int @ bit0 @ SX0 )
            = pls ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7308]) ).

thf(7552,plain,
    ! [SV491: $i,SV321: $i] :
      ( ( ~ ~ ( ~ ! [SY1154: $i,SY1155: $i] :
                    ( ~ ( is_int @ SV321 )
                    | ~ ( is_int @ SV491 )
                    | ~ ( is_int @ SY1154 )
                    | ~ ( is_int @ SY1155 )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1154 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1155 ) @ SV491 ) )
                      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1154 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1155 ) @ SV321 ) ) )
                    | ( SY1154 != SY1155 ) )
              | ~ ! [SY1156: $i,SY1157: $i] :
                    ( ~ ( is_int @ SV321 )
                    | ~ ( is_int @ SV491 )
                    | ~ ( is_int @ SY1156 )
                    | ~ ( is_int @ SY1157 )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1156 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1157 ) @ SV491 ) )
                      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1156 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1157 ) @ SV321 ) ) )
                    | ( SV321 != SV491 ) ) )
        | ~ ! [SY1158: $i,SY1159: $i] :
              ( ~ ( is_int @ SV321 )
              | ~ ( is_int @ SV491 )
              | ~ ( is_int @ SY1158 )
              | ~ ( is_int @ SY1159 )
              | ( SY1158 = SY1159 )
              | ( SV321 = SV491 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1158 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1159 ) @ SV491 ) )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1158 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1159 ) @ SV321 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[7309]) ).

thf(7553,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( SX0 != zero_zero_int )
          | ( SX1 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX0 ) @ SX1 )
            = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7310]) ).

thf(7554,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX0 ) @ SX1 )
                 != zero_zero_int )
                | ( SX0 = zero_zero_int ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX0 ) @ SX1 )
                 != zero_zero_int )
                | ( SX1 = zero_zero_int ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7311]) ).

thf(7555,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX1 )
          | ( SX1 = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
           != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ ( hAPP_int_int @ uminus_uminus_int @ SX1 ) )
            = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ SX1 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7312]) ).

thf(7556,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX1 )
          | ( SX1 = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
            = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ ( hAPP_int_int @ uminus_uminus_int @ SX1 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ SX1 ) ) ) @ one_one_int ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7313]) ).

thf(7557,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
           != ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7314]) ).

thf(7558,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
            = ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7315]) ).

thf(7559,plain,
    ! [SV322: $i] :
      ( ( ~ ! [SY1025: $i,SY1026: $i] :
              ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SY1025 )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SY1026 )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1025 ) @ SY1026 ) )
                = one_one_int ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[7316]) ).

thf(7560,plain,
    ! [SV322: $i] :
      ( ( ~ ~ ( ~ ! [SY1027: $i] :
                    ( ! [SY1028: $i] :
                        ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1027 ) @ SY1028 ) )
                       != one_one_int )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SY1027 )
                      = one_one_int ) )
              | ~ ! [SY1029: $i,SY1030: $i] :
                    ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1029 ) @ SY1030 ) )
                     != one_one_int )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SY1030 )
                      = one_one_int ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[7316]) ).

thf(7561,plain,
    ( ( ! [SX0: $i] :
          ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
           != zero_zero_int )
          | ( SX0 = zero_zero_nat ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7317]) ).

thf(7562,plain,
    ( ( ! [SX0: $i] :
          ( ( SX0 != zero_zero_nat )
          | ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
            = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7318]) ).

thf(7563,plain,
    ! [SV570: $i,SV492: $i,SV323: $i] :
      ( ( ~ ( ~ ! [SY1189: $i,SY1190: $i] :
                  ( ~ ( is_int @ SY1190 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV323 ) @ SV492 ) ) @ SV570 )
                   != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1189 ) @ SV492 ) ) @ SY1190 ) )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV323 ) @ SY1189 ) ) @ SV492 ) ) @ SV570 )
                    = SY1190 ) )
            | ~ ! [SY1191: $i,SY1192: $i] :
                  ( ~ ( is_int @ SY1192 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV323 ) @ SY1191 ) ) @ SV492 ) ) @ SV570 )
                   != SY1192 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV323 ) @ SV492 ) ) @ SV570 )
                    = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1191 ) @ SV492 ) ) @ SY1192 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7319]) ).

thf(7564,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ! [SX1: $i] :
              ( ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
               != zero_zero_int )
              | ~ ( ( SX0
                   != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX1 ) @ ( sK12_Q_4 @ SX1 @ SX0 ) ) )
                  | ~ ( is_int @ ( sK12_Q_4 @ SX1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7320]) ).

thf(7565,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ! [SX1: $i] :
              ( ! [SX2: $i] :
                  ( ( SX0
                   != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX1 ) @ SX2 ) )
                  | ~ ( is_int @ SX2 ) )
              | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ SX1 )
                = zero_zero_int ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7321]) ).

thf(7566,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
           != ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7322]) ).

thf(7567,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( ( hAPP_nat_int @ semiri1621563631at_int @ SX0 )
            = ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7323]) ).

thf(7568,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( ( hAPP_int_int @ bit0 @ SX0 )
           != ( hAPP_int_int @ bit0 @ SX1 ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7324]) ).

thf(7569,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( SX0 != SX1 )
          | ( ( hAPP_int_int @ bit0 @ SX0 )
            = ( hAPP_int_int @ bit0 @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7325]) ).

thf(7570,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ( min
           != ( hAPP_int_int @ bit1 @ SX0 ) )
          | ( min = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7326]) ).

thf(7571,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ( min != SX0 )
          | ( min
            = ( hAPP_int_int @ bit1 @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7327]) ).

thf(7572,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ( hAPP_nat_nat @ suc @ SX0 )
           != ( hAPP_nat_nat @ suc @ SX1 ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7328]) ).

thf(7573,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( ( hAPP_nat_nat @ suc @ SX0 )
            = ( hAPP_nat_nat @ suc @ SX1 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7329]) ).

thf(7574,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX0 ) @ SX0 )
           != zero_zero_int )
          | ( SX0 = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7330]) ).

thf(7575,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ( SX0 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX0 ) @ SX0 )
            = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7331]) ).

thf(7576,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SX0 ) @ SX1 )
           != zero_zero_int )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7332]) ).

thf(7577,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( SX0 != SX1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SX0 ) @ SX1 )
            = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7333]) ).

thf(7578,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( SX0 != SX1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SX0 ) @ SX1 )
            = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7334]) ).

thf(7579,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SX0 ) @ SX1 )
           != zero_zero_int )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7335]) ).

thf(7580,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ( zero_zero_int
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX0 ) @ SX0 ) )
          | ( SX0 = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7336]) ).

thf(7581,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ( SX0 != zero_zero_int )
          | ( zero_zero_int
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SX0 ) @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7337]) ).

thf(7582,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
           != zero_zero_int )
          | ( SX0 = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7338]) ).

thf(7583,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ( SX0 != zero_zero_int )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
            = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7339]) ).

thf(7584,plain,
    ( ( ! [SX0: $i] :
          ( ( one_one_nat != SX0 )
          | ( SX0 = one_one_nat ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7340]) ).

thf(7585,plain,
    ( ( ! [SX0: $i] :
          ( ( SX0 != one_one_nat )
          | ( one_one_nat = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7341]) ).

thf(7586,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ SX0 ) @ SX1 ) )
           != SX1 )
          | ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ SX0 ) ) @ SX1 )
            = zero_zero_nat ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7342]) ).

thf(7587,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ SX0 ) @ SX1 ) )
            = SX1 )
          | ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ SX0 ) ) @ SX1 )
            = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ SX0 ) @ SX1 ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7343]) ).

thf(7588,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SX0 ) @ zero_zero_int )
            = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7344]) ).

thf(7589,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ( ( hAPP_int_int @ ( div_mod_int @ SX0 ) @ zero_zero_int )
            = SX0 ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7345]) ).

thf(7590,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( SX0 != zero_zero_int )
          | ( SX1 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
            = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7346]) ).

thf(7591,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
                 != zero_zero_int )
                | ( SX0 = zero_zero_int ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
                 != zero_zero_int )
                | ( SX1 = zero_zero_int ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7347]) ).

thf(7592,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( SX0 != zero_zero_int )
          | ( SX1 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX0 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX1 ) @ SX1 ) )
            = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7348]) ).

thf(7593,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX0 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX1 ) @ SX1 ) )
                 != zero_zero_int )
                | ( SX0 = zero_zero_int ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX0 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX1 ) @ SX1 ) )
                 != zero_zero_int )
                | ( SX1 = zero_zero_int ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7349]) ).

thf(7594,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( SX0 != zero_zero_int )
          | ( SX1 != zero_zero_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ SX0 ) @ SX1 )
            = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7350]) ).

thf(7595,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( ( hAPP_int_int @ ( legacy_zgcd @ SX0 ) @ SX1 )
                 != zero_zero_int )
                | ( SX0 = zero_zero_int ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( ( hAPP_int_int @ ( legacy_zgcd @ SX0 ) @ SX1 )
                 != zero_zero_int )
                | ( SX1 = zero_zero_int ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7351]) ).

thf(7596,plain,
    ! [SV1: $i,SV324: $i] :
      ( ( ( is_int @ SV324 )
        = $false )
      | ( ( is_int @ ( hAPP_int_int @ SV1 @ SV324 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7352]) ).

thf(7597,plain,
    ! [SV35: $i,SV338: $i] :
      ( ( ( is_int @ SV338 )
        = $false )
      | ( ( ( SV338 = zero_zero_int )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV338 ) @ SV35 )
           != zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7366]) ).

thf(7598,plain,
    ! [SV339: $i,SV496: $i,SV41: $i] :
      ( ( ( ~ ( is_int @ SV41 )
          | ~ ( is_int @ SV496 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV41 ) @ SV339 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV496 ) @ SV339 ) )
          | ( SV41 = SV496 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7367]) ).

thf(7599,plain,
    ! [SV42: $i,SV497: $i,SV340: $i] :
      ( ( ( ~ ( is_int @ SV340 )
          | ~ ( is_int @ SV497 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV42 ) @ SV340 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV42 ) @ SV497 ) )
          | ( SV340 = SV497 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7368]) ).

thf(7600,plain,
    ! [SV43: $i,SV498: $i,SV341: $i] :
      ( ( ( ~ ( is_int @ SV341 )
          | ~ ( is_int @ SV498 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV43 ) @ SV341 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV43 ) @ SV498 ) )
          | ( SV341 = SV498 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7369]) ).

thf(7601,plain,
    ! [SV571: $i,SV499: $i,SV342: $i,SV44: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV44 ) @ SV342 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV499 ) @ SV571 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV44 ) @ SV499 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV342 ) @ SV571 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7370]) ).

thf(7602,plain,
    ! [SV572: $i,SV510: $i,SV358: $i,SV69: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV69 ) @ SV358 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV510 ) @ SV572 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV69 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV358 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV510 ) @ SV572 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7388]) ).

thf(7603,plain,
    ! [SV573: $i,SV511: $i,SV359: $i,SV70: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV70 ) @ SV359 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV511 ) @ SV573 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV511 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV70 ) @ SV359 ) ) @ SV573 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7389]) ).

thf(7604,plain,
    ! [SV574: $i,SV512: $i,SV360: $i,SV71: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV71 ) @ SV360 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV512 ) @ SV574 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV71 ) @ SV512 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV360 ) @ SV574 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7390]) ).

thf(7605,plain,
    ! [SV366: $i,SV79: $i] :
      ( ( ( ~ ( is_int @ SV79 ) )
        = $true )
      | ( ( ~ ( is_int @ SV366 ) )
        = $true )
      | ( ( ( SV366 = zero_zero_int )
          | ( SV79 = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV366 ) @ SV79 )
           != zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7393]) ).

thf(7606,plain,
    ! [SV367: $i,SV80: $i] :
      ( ( ( ~ ( is_int @ SV80 ) )
        = $true )
      | ( ( ~ ( is_int @ SV367 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV80 ) @ SV367 )
           != zero_zero_int )
          | ( SV80 = zero_zero_int )
          | ( SV367 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7394]) ).

thf(7607,plain,
    ! [SV575: $i,SV516: $i,SV369: $i,SV84: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV84 ) @ SV369 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV516 ) @ SV369 ) ) @ SV575 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV84 ) @ SV516 ) ) @ SV369 ) ) @ SV575 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7396]) ).

thf(7608,plain,
    ! [SV576: $i,SV524: $i,SV380: $i,SV104: $i] :
      ( ( ! [SY1193: $i] :
            ( ~ ( is_int @ SV104 )
            | ~ ( is_int @ SV380 )
            | ~ ( is_int @ SY1193 )
            | ( SY1193 = zero_zero_int )
            | ( SV104 = SV380 )
            | ( SV524 != SV576 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV524 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1193 ) @ SV104 ) )
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV576 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1193 ) @ SV380 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7412]) ).

thf(7609,plain,
    ! [SV577: $i,SV127: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV127 ) @ SV577 ) ) @ SV577 )
          = SV127 )
        = $true )
      | ( ( is_int @ SV127 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[7416]) ).

thf(7610,plain,
    ! [SV578: $i,SV128: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV128 ) @ SV578 ) ) @ SV578 )
          = SV128 )
        = $true )
      | ( ( is_int @ SV128 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[7417]) ).

thf(7611,plain,
    ! [SV579: $i,SV527: $i,SV388: $i,SV129: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV129 ) @ SV388 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV527 ) @ SV579 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV129 ) @ SV527 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV388 ) @ SV579 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7418]) ).

thf(7612,plain,
    ! [SV580: $i,SV530: $i,SV392: $i,SV134: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV134 ) @ SV392 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV530 ) @ SV580 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV134 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV392 ) @ SV580 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV134 ) @ SV530 ) ) @ SV580 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7422]) ).

thf(7613,plain,
    ! [SV581: $i,SV144: $i] :
      ( ( ( ! [SY1194: $i] :
              ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV144 ) @ SV581 )
               != SY1194 )
              | ( SV144
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY1194 ) @ SV581 ) ) ) )
        = $true )
      | ( ( is_int @ SV144 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[7424]) ).

thf(7614,plain,
    ! [SV582: $i,SV532: $i,SV397: $i,SV145: $i] :
      ( ( ! [SY1195: $i,SY1196: $i,SY1197: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV145 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV397 ) @ SV532 ) ) ) @ SV582 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1195 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV397 ) @ SY1196 ) ) ) @ SY1197 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV145 ) @ SV582 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1195 ) @ SY1197 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV397 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV532 ) @ SV582 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1196 ) @ SY1197 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7425]) ).

thf(7615,plain,
    ! [SV533: $i,SV156: $i] :
      ( ( ( ( hAPP_int_int @ abs_abs_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV156 ) @ SV533 ) )
          = one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ abs_abs_int @ SV156 )
          = one_one_int )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7426]) ).

thf(7616,plain,
    ! [SV163: $i] :
      ( ( ( SV163 = zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV163 ) @ SV163 )
          = one_one_int )
        = $true )
      | ( ( is_int @ SV163 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[7428]) ).

thf(7617,plain,
    ! [SV420: $i,SV191: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV191 ) @ SV420 )
          = zero_zero_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ SV191 ) ) @ SV420 )
          = zero_zero_int )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7437]) ).

thf(7618,plain,
    ! [SV421: $i,SV192: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV192 ) @ SV421 )
          = zero_zero_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ SV192 ) @ ( hAPP_int_int @ uminus_uminus_int @ SV421 ) )
          = zero_zero_int )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7438]) ).

thf(7619,plain,
    ! [SV202: $i,SV540: $i,SV424: $i] :
      ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV424 ) @ SV540 )
         != one_one_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV424 ) @ SV202 ) ) @ SV540 )
          = ( hAPP_int_int @ ( legacy_zgcd @ SV202 ) @ SV540 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7439]) ).

thf(7620,plain,
    ! [SV203: $i,SV541: $i,SV425: $i] :
      ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV425 ) @ SV541 )
         != one_one_int )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV203 ) @ SV541 )
           != one_one_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV425 ) @ SV203 ) ) @ SV541 )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7440]) ).

thf(7621,plain,
    ! [SV214: $i,SV546: $i,SV434: $i] :
      ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV434 ) @ SV546 )
         != one_one_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV434 ) @ SV214 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV546 ) @ SV214 ) )
          = one_one_int )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7445]) ).

thf(7622,plain,
    ! [SV215: $i,SV547: $i,SV435: $i] :
      ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV435 ) @ SV547 )
         != one_one_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV435 ) @ SV215 ) ) @ SV547 )
          = one_one_int )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7446]) ).

thf(7623,plain,
    ! [SV437: $i,SV221: $i,SV583: $i,SV548: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV548 ) @ SV583 )
         != one_one_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV548 ) @ SV221 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV583 ) @ SV437 ) )
          = one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7447]) ).

thf(7624,plain,
    ! [SV235: $i,SV550: $i,SV445: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV445 ) @ SV550 )
         != one_one_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV445 ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV550 ) @ SV235 ) )
          = one_one_int )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7449]) ).

thf(7625,plain,
    ! [SV243: $i,SV554: $i,SV453: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV453 ) @ SV554 )
         != one_one_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV453 ) @ SV243 ) ) @ SV554 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV243 ) @ SV554 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7453]) ).

thf(7626,plain,
    ! [SV244: $i,SV555: $i,SV454: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV454 ) @ SV555 )
         != one_one_int )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV454 ) @ SV244 )
           != one_one_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV454 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV555 ) @ SV244 ) )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7454]) ).

thf(7627,plain,
    ! [SV584: $i,SV455: $i,SV245: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV245 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV455 ) @ SV584 ) )
         != one_one_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV245 ) @ SV455 )
          = one_one_int )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[7455]) ).

thf(7628,plain,
    ! [SV556: $i,SV456: $i,SV246: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV246 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV456 ) @ SV556 ) )
         != one_one_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV246 ) @ SV556 )
          = one_one_int )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7456]) ).

thf(7629,plain,
    ! [SV247: $i,SV457: $i,SV585: $i,SV557: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV557 ) @ SV585 )
          = zero_zero_int )
        | ( SV557
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV457 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV557 ) @ SV585 ) ) )
        | ( SV585
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV247 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV557 ) @ SV585 ) ) )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV457 ) @ SV247 )
          = one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7457]) ).

thf(7630,plain,
    ! [SV263: $i] :
      ( ( ( ! [SY943: $i] :
              ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV263 ) @ SY943 )
             != one_one_int ) )
        = $true )
      | ( ( ( SV263 = one_one_int )
          | ( SV263
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true )
      | ( ( is_int @ SV263 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[7462]) ).

thf(7631,plain,
    ! [SV469: $i,SV271: $i] :
      ( ( ( ( hAPP_nat_nat @ suc @ SV271 )
          = ( hAPP_nat_nat @ suc @ SV469 ) )
        = $false )
      | ( ( SV271 = SV469 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7465]) ).

thf(7632,plain,
    ! [SV586: $i,SV281: $i] :
      ( ( ( SV281
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV586 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV281 ) @ SV586 ) ) ) @ ( hAPP_int_int @ ( div_mod_int @ SV281 ) @ SV586 ) ) )
        = $true )
      | ( ( is_int @ SV281 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[7466]) ).

thf(7633,plain,
    ! [SV564: $i,SV475: $i,SV287: $i,SV587: $i] :
      ( ( ! [SY1198: $i,SY1199: $i,SY1200: $i,SY1201: $i] :
            ( ( SV587
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1198 ) @ SY1199 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1200 ) @ SY1201 ) ) )
            | ( SV287
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV475 ) @ SY1199 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV564 ) @ SY1201 ) ) )
            | ( ( hAPP_int_int @ ( div_mod_int @ SV587 ) @ SV287 )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1198 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV587 ) @ SV287 ) ) @ SV475 ) ) ) @ SY1199 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1200 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV587 ) @ SV287 ) ) @ SV564 ) ) ) @ SY1201 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7470]) ).

thf(7634,plain,
    ! [SV296: $i] :
      ( ( ( ( hAPP_nat_nat @ ( div_mod_nat @ SV296 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
          = zero_zero_nat )
        = $true )
      | ( ( ( hAPP_nat_nat @ ( div_mod_nat @ SV296 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
          = one_one_nat )
        = $true )
      | ( ( ( hAPP_nat_nat @ ( div_mod_nat @ SV296 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
          = ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
        = $true )
      | ( ( ( hAPP_nat_nat @ ( div_mod_nat @ SV296 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
          = ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit1 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7472]) ).

thf(7635,plain,
    ! [SV308: $i] :
      ( ( ( SV308
          = ( hAPP_nat_int @ semiri1621563631at_int @ ( sK4_N_1 @ SV308 ) ) )
        = $true )
      | ( ( SV308
          = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ ( hAPP_nat_nat @ suc @ ( sK3_N_1 @ SV308 ) ) ) ) )
        = $true )
      | ( ( is_int @ SV308 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[7475]) ).

thf(7636,plain,
    ! [SV568: $i,SV485: $i,SV311: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV311 ) @ SV485 ) ) @ SV568 )
         != one_one_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV311 ) @ SV568 )
          = one_one_int )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7477]) ).

thf(7637,plain,
    ! [SV588: $i] :
      ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ zero_zero_int ) @ SV588 )
         != one_one_int )
        | ( ( hAPP_int_int @ abs_abs_int @ SV588 )
          = one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7478]) ).

thf(7638,plain,
    ! [SV589: $i] :
      ( ( ( ( hAPP_int_int @ abs_abs_int @ SV589 )
         != one_one_int )
        | ( ( hAPP_int_int @ ( legacy_zgcd @ zero_zero_int ) @ SV589 )
          = one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7479]) ).

thf(7639,plain,
    ! [SV590: $i] :
      ( ( ~ ( is_int @ SV590 )
        | ( one_one_int != SV590 )
        | ( SV590 = one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7480]) ).

thf(7640,plain,
    ! [SV591: $i] :
      ( ( ~ ( is_int @ SV591 )
        | ( SV591 != one_one_int )
        | ( one_one_int = SV591 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7481]) ).

thf(7641,plain,
    ! [SV592: $i] :
      ( ( ! [SY1202: $i] :
            ( ( ( hAPP_int_int @ ( div_mod_int @ SV592 ) @ SY1202 )
             != zero_zero_int )
            | ( ( hAPP_int_int @ ( div_mod_int @ SV592 ) @ ( hAPP_int_int @ uminus_uminus_int @ SY1202 ) )
              = zero_zero_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7482]) ).

thf(7642,plain,
    ! [SV593: $i] :
      ( ( ! [SY1203: $i] :
            ( ( ( hAPP_int_int @ ( div_mod_int @ SV593 ) @ SY1203 )
              = zero_zero_int )
            | ( ( hAPP_int_int @ ( div_mod_int @ SV593 ) @ ( hAPP_int_int @ uminus_uminus_int @ SY1203 ) )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( div_mod_int @ SV593 ) @ SY1203 ) ) @ SY1203 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7483]) ).

thf(7643,plain,
    ! [SV594: $i] :
      ( ( ! [SY1204: $i] :
            ( ( SV594 != SY1204 )
            | ( ( image_nat_int @ semiri1621563631at_int @ SV594 )
              = ( image_nat_int @ semiri1621563631at_int @ SY1204 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7484]) ).

thf(7644,plain,
    ! [SV595: $i] :
      ( ( ! [SY1205: $i] :
            ( ( ( image_nat_int @ semiri1621563631at_int @ SV595 )
             != ( image_nat_int @ semiri1621563631at_int @ SY1205 ) )
            | ( SV595 = SY1205 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7485]) ).

thf(7645,plain,
    ! [SV596: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV596 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = zero_zero_int )
        | ( ( hAPP_int_int @ ( div_mod_int @ SV596 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7486]) ).

thf(7646,plain,
    ! [SV597: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV597 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
         != one_one_int )
        | ( ( hAPP_int_int @ ( div_mod_int @ SV597 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
         != zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7487]) ).

thf(7647,plain,
    ! [SV598: $i] :
      ( ( ( SV598 != zero_zero_nat )
        | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ SV598 )
          = one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7488]) ).

thf(7648,plain,
    ! [SV599: $i] :
      ( ( ( SV599 = zero_zero_nat )
        | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ SV599 )
          = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7489]) ).

thf(7649,plain,
    ! [SV600: $i] :
      ( ( ( ( hAPP_int_nat @ number_number_of_nat @ SV600 )
         != zero_zero_nat )
        | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ ( hAPP_int_nat @ number_number_of_nat @ SV600 ) )
          = one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7490]) ).

thf(7650,plain,
    ! [SV601: $i] :
      ( ( ( ( hAPP_int_nat @ number_number_of_nat @ SV601 )
          = zero_zero_nat )
        | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ ( hAPP_int_nat @ number_number_of_nat @ SV601 ) )
          = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7491]) ).

thf(7651,plain,
    ! [SV602: $i] :
      ( ( ~ ( is_int @ SV602 )
        | ( pls
         != ( hAPP_int_int @ bit0 @ SV602 ) )
        | ( pls = SV602 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7492]) ).

thf(7652,plain,
    ! [SV603: $i] :
      ( ( ~ ( is_int @ SV603 )
        | ( pls != SV603 )
        | ( pls
          = ( hAPP_int_int @ bit0 @ SV603 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7493]) ).

thf(7653,plain,
    ! [SV604: $i] :
      ( ( ! [SY1206: $i] :
            ( ( ( hAPP_int_int @ ( div_mod_int @ SV604 ) @ SY1206 )
             != zero_zero_int )
            | ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ SV604 ) ) @ SY1206 )
              = zero_zero_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7494]) ).

thf(7654,plain,
    ! [SV605: $i] :
      ( ( ! [SY1207: $i] :
            ( ( ( hAPP_int_int @ ( div_mod_int @ SV605 ) @ SY1207 )
              = zero_zero_int )
            | ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ SV605 ) ) @ SY1207 )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1207 ) @ ( hAPP_int_int @ ( div_mod_int @ SV605 ) @ SY1207 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7495]) ).

thf(7655,plain,
    ! [SV606: $i] :
      ( ( ! [SY1208: $i] :
            ( ~ ( is_int @ SV606 )
            | ~ ( is_int @ SY1208 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV606 ) @ SY1208 )
             != zero_zero_int )
            | ( SV606 = zero_zero_int )
            | ( SY1208 = zero_zero_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7496]) ).

thf(7656,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0 != zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
              = zero_zero_int ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX1 != zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
              = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[7497]) ).

thf(7657,plain,
    ! [SV607: $i] :
      ( ( ~ ( is_int @ SV607 )
        | ! [SY1209: $i] :
            ( ( ( hAPP_int_nat @ number_number_of_nat @ SY1209 )
              = zero_zero_nat )
            | ( SV607 != zero_zero_int )
            | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV607 ) @ ( hAPP_int_nat @ number_number_of_nat @ SY1209 ) )
              = zero_zero_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7498]) ).

thf(7658,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ! [SX1: $i] :
                ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ SX1 ) )
                 != zero_zero_int )
                | ( ( hAPP_int_nat @ number_number_of_nat @ SX1 )
                 != zero_zero_nat ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ! [SX1: $i] :
                ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ SX1 ) )
               != zero_zero_int )
            | ( SX0 = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[7499]) ).

thf(7659,plain,
    ! [SV608: $i,SV313: $i] :
      ( ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV313 ) @ SV608 )
           != zero_zero_int )
          | ~ ( ( SV313
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV608 ) @ ( sK11_Q_4 @ SV608 @ SV313 ) ) )
              | ~ ( is_int @ ( sK11_Q_4 @ SV608 @ SV313 ) ) ) )
        = $true )
      | ( ( is_int @ SV313 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[7500]) ).

thf(7660,plain,
    ! [SV609: $i] :
      ( ( ! [SY1210: $i] :
            ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV609 )
             != ( hAPP_nat_int @ semiri1621563631at_int @ SY1210 ) )
            | ( SV609 = SY1210 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7501]) ).

thf(7661,plain,
    ! [SV610: $i] :
      ( ( ! [SY1211: $i] :
            ( ( SV610 != SY1211 )
            | ( ( hAPP_nat_int @ semiri1621563631at_int @ SV610 )
              = ( hAPP_nat_int @ semiri1621563631at_int @ SY1211 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7502]) ).

thf(7662,plain,
    ! [SV611: $i] :
      ( ( ( zero_zero_nat != SV611 )
        | ( SV611 = zero_zero_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7503]) ).

thf(7663,plain,
    ! [SV612: $i] :
      ( ( ( SV612 != zero_zero_nat )
        | ( zero_zero_nat = SV612 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7504]) ).

thf(7664,plain,
    ( ( ~ ( is_int @ sK13_X_1 )
      | ~ ( is_int @ sK14_SY716 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[7505]) ).

thf(7665,plain,
    ! [SV613: $i] :
      ( ( ! [SY1212: $i] :
            ( ~ ( is_int @ SY1212 )
            | ( SY1212 = zero_zero_int )
            | ( ( hAPP_int_int @ ( div_mod_int @ SV613 ) @ SY1212 )
             != zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ SV613 ) ) @ SY1212 )
              = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV613 ) @ SY1212 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7507]) ).

thf(7666,plain,
    ! [SV614: $i] :
      ( ( ! [SY1213: $i] :
            ( ~ ( is_int @ SY1213 )
            | ( SY1213 = zero_zero_int )
            | ( ( hAPP_int_int @ ( div_mod_int @ SV614 ) @ SY1213 )
              = zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ SV614 ) ) @ SY1213 )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV614 ) @ SY1213 ) ) ) @ one_one_int ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7508]) ).

thf(7667,plain,
    ! [SV615: $i] :
      ( ( ~ ( is_int @ SV615 )
        | ( ( hAPP_int_int @ abs_abs_int @ SV615 )
         != zero_zero_int )
        | ( SV615 = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7509]) ).

thf(7668,plain,
    ! [SV616: $i] :
      ( ( ~ ( is_int @ SV616 )
        | ( SV616 != zero_zero_int )
        | ( ( hAPP_int_int @ abs_abs_int @ SV616 )
          = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7510]) ).

thf(7669,plain,
    ! [SV617: $i] :
      ( ( ~ ( is_int @ SV617 )
        | ( ( hAPP_int_int @ bit1 @ SV617 )
         != min )
        | ( SV617 = min ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7511]) ).

thf(7670,plain,
    ! [SV618: $i] :
      ( ( ~ ( is_int @ SV618 )
        | ( SV618 != min )
        | ( ( hAPP_int_int @ bit1 @ SV618 )
          = min ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7512]) ).

thf(7671,plain,
    ! [SV486: $i,SV314: $i] :
      ( ( ( ~ ( is_int @ SV314 ) )
        = $true )
      | ( ( ~ ( is_int @ SV486 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 )
            = zero_zero_int )
          | ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK1_A_4 @ SV486 @ SV314 ) )
                                | ~ ( is_int @ ( sK2_SY713 @ SV486 @ SV314 ) ) )
                          | ( SV314
                           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK1_A_4 @ SV486 @ SV314 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 ) ) ) )
                    | ( SV486
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK2_SY713 @ SV486 @ SV314 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 ) ) ) )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( sK1_A_4 @ SV486 @ SV314 ) ) @ ( sK2_SY713 @ SV486 @ SV314 ) )
               != one_one_int ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7513]) ).

thf(7672,plain,
    ! [SV619: $i] :
      ( ( ! [SY1214: $i] :
            ( ~ ( is_int @ SV619 )
            | ~ ( is_int @ SY1214 )
            | ( ( hAPP_int_int @ number_number_of_int @ SV619 )
             != ( hAPP_int_int @ number_number_of_int @ SY1214 ) )
            | ( SV619 = SY1214 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7514]) ).

thf(7673,plain,
    ! [SV620: $i] :
      ( ( ! [SY1215: $i] :
            ( ~ ( is_int @ SV620 )
            | ~ ( is_int @ SY1215 )
            | ( SV620 != SY1215 )
            | ( ( hAPP_int_int @ number_number_of_int @ SV620 )
              = ( hAPP_int_int @ number_number_of_int @ SY1215 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7515]) ).

thf(7674,plain,
    ! [SV621: $i] :
      ( ( ! [SY1216: $i] :
            ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV621 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
             != ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY1216 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
            | ( ( hAPP_int_int @ abs_abs_int @ SV621 )
              = ( hAPP_int_int @ abs_abs_int @ SY1216 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7516]) ).

thf(7675,plain,
    ! [SV622: $i] :
      ( ( ! [SY1217: $i] :
            ( ( ( hAPP_int_int @ abs_abs_int @ SV622 )
             != ( hAPP_int_int @ abs_abs_int @ SY1217 ) )
            | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV622 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
              = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY1217 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7517]) ).

thf(7676,plain,
    ! [SV623: $i] :
      ( ( ~ ( is_int @ SV623 )
        | ! [SY1218: $i] :
            ( ( SY1218 = zero_zero_nat )
            | ( SV623 != zero_zero_int )
            | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV623 ) @ SY1218 )
              = zero_zero_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7518]) ).

thf(7677,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ! [SX1: $i] :
                ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ SX1 )
                 != zero_zero_int )
                | ( SX1 != zero_zero_nat ) ) )
      | ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ! [SX1: $i] :
                ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ SX1 )
               != zero_zero_int )
            | ( SX0 = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[7519]) ).

thf(7678,plain,
    ! [SV487: $i,SV315: $i] :
      ( ( ~ ! [SY1133: $i,SY1134: $i] :
              ( ~ ( is_int @ SV315 )
              | ~ ( is_int @ SV487 )
              | ~ ( is_int @ SY1133 )
              | ~ ( is_int @ SY1134 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1133 ) @ SY1134 ) )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SY1134 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1133 ) @ SV487 ) ) )
              | ( SV315 = SY1133 )
              | ( SV487 = SY1134 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[7520]) ).

thf(7679,plain,
    ! [SV487: $i,SV315: $i] :
      ( ( ~ ~ ( ~ ! [SY1135: $i,SY1136: $i] :
                    ( ~ ( is_int @ SV315 )
                    | ~ ( is_int @ SV487 )
                    | ~ ( is_int @ SY1135 )
                    | ~ ( is_int @ SY1136 )
                    | ( SV315 != SY1135 )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1135 ) @ SY1136 ) )
                      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SY1136 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1135 ) @ SV487 ) ) ) )
              | ~ ! [SY1137: $i,SY1138: $i] :
                    ( ~ ( is_int @ SV315 )
                    | ~ ( is_int @ SV487 )
                    | ~ ( is_int @ SY1137 )
                    | ~ ( is_int @ SY1138 )
                    | ( SV487 != SY1138 )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1137 ) @ SY1138 ) )
                      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SY1138 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1137 ) @ SV487 ) ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[7520]) ).

thf(7680,plain,
    ! [SV624: $i] :
      ( ( ! [SY1219: $i] :
            ( ~ ( is_int @ SV624 )
            | ~ ( is_int @ SY1219 )
            | ( SV624
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV624 ) @ SY1219 ) )
            | ( SY1219 = zero_zero_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7521]) ).

thf(7681,plain,
    ! [SV625: $i] :
      ( ( ! [SY1220: $i] :
            ( ~ ( is_int @ SV625 )
            | ~ ( is_int @ SY1220 )
            | ( SY1220 != zero_zero_int )
            | ( SV625
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV625 ) @ SY1220 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7522]) ).

thf(7682,plain,
    ! [SV626: $i] :
      ( ( ! [SY1221: $i] :
            ( ( ( hAPP_int_nat @ number_number_of_nat @ SV626 )
             != SY1221 )
            | ( SY1221
              = ( hAPP_int_nat @ number_number_of_nat @ SV626 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7523]) ).

thf(7683,plain,
    ! [SV627: $i] :
      ( ( ! [SY1222: $i] :
            ( ( SY1222
             != ( hAPP_int_nat @ number_number_of_nat @ SV627 ) )
            | ( ( hAPP_int_nat @ number_number_of_nat @ SV627 )
              = SY1222 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7524]) ).

thf(7684,plain,
    ! [SV628: $i] :
      ( ( ~ ( is_int @ SV628 )
        | ( zero_zero_int != SV628 )
        | ( SV628 = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7525]) ).

thf(7685,plain,
    ! [SV629: $i] :
      ( ( ~ ( is_int @ SV629 )
        | ( SV629 != zero_zero_int )
        | ( zero_zero_int = SV629 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7526]) ).

thf(7686,plain,
    ! [SV316: $i] :
      ( ( ! [SY992: $i,SY993: $i] :
            ( ~ ( is_int @ SY992 )
            | ~ ( is_int @ SY993 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SY992 )
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SY993 ) )
            | ( SY992 = SY993 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[7527]) ).

thf(7687,plain,
    ! [SV316: $i] :
      ( ( ! [SY994: $i,SY995: $i] :
            ( ~ ( is_int @ SY994 )
            | ~ ( is_int @ SY995 )
            | ( SY994 != SY995 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SY994 )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SY995 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[7528]) ).

thf(7688,plain,
    ! [SV630: $i] :
      ( ( ! [SY1223: $i] :
            ( ~ ( is_int @ SV630 )
            | ~ ( is_int @ SY1223 )
            | ( SY1223 = zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SY1223 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY1223 ) @ SV630 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV630 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY1223 ) @ SV630 ) ) )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7529]) ).

thf(7689,plain,
    ! [SV631: $i] :
      ( ( ! [SY1224: $i] :
            ( ~ ( is_int @ SV631 )
            | ~ ( is_int @ SY1224 )
            | ( SV631 = zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SY1224 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY1224 ) @ SV631 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV631 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY1224 ) @ SV631 ) ) )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7530]) ).

thf(7690,plain,
    ! [SV632: $i] :
      ( ( ! [SY1225: $i] :
            ( ~ ( is_int @ SV632 )
            | ~ ( is_int @ SY1225 )
            | ( ( hAPP_int_int @ bit1 @ SV632 )
             != ( hAPP_int_int @ bit1 @ SY1225 ) )
            | ( SV632 = SY1225 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7531]) ).

thf(7691,plain,
    ! [SV633: $i] :
      ( ( ! [SY1226: $i] :
            ( ~ ( is_int @ SV633 )
            | ~ ( is_int @ SY1226 )
            | ( SV633 != SY1226 )
            | ( ( hAPP_int_int @ bit1 @ SV633 )
              = ( hAPP_int_int @ bit1 @ SY1226 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7532]) ).

thf(7692,plain,
    ! [SV634: $i] :
      ( ( ! [SY1227: $i] :
            ( ( SV634 != zero_zero_nat )
            | ( SY1227 != zero_zero_nat )
            | ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV634 ) )
              = ( hAPP_nat_int @ semiri1621563631at_int @ SY1227 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7533]) ).

thf(7693,plain,
    ( ( ~ ! [SX0: $i] :
            ( ! [SX1: $i] :
                ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SX0 ) )
               != ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
            | ( SX0 = zero_zero_nat ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SX0 ) )
             != ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
            | ( SX1 = zero_zero_nat ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[7534]) ).

thf(7694,plain,
    ! [SV635: $i] :
      ( ( ! [SY1228: $i] :
            ( ~ ( is_int @ SV635 )
            | ~ ( is_int @ SY1228 )
            | ( SY1228 = zero_zero_int )
            | ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK7_C_3 @ SY1228 @ SV635 ) )
                                  | ~ ( is_int @ ( sK8_SY715 @ SY1228 @ SV635 ) ) )
                            | ( SY1228
                             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SY1228 ) @ SV635 ) ) @ ( sK7_C_3 @ SY1228 @ SV635 ) ) ) )
                      | ( SV635
                       != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SY1228 ) @ SV635 ) ) @ ( sK8_SY715 @ SY1228 @ SV635 ) ) ) )
                | ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK7_C_3 @ SY1228 @ SV635 ) ) @ ( sK8_SY715 @ SY1228 @ SV635 ) )
                 != one_one_int ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7535]) ).

thf(7695,plain,
    ! [SV636: $i] :
      ( ( ! [SY1229: $i] :
            ( ~ ( is_int @ SV636 )
            | ~ ( is_int @ SY1229 )
            | ( SV636 = zero_zero_int )
            | ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK5_C_3 @ SY1229 @ SV636 ) )
                                  | ~ ( is_int @ ( sK6_SY714 @ SY1229 @ SV636 ) ) )
                            | ( SY1229
                             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SY1229 ) @ SV636 ) ) @ ( sK5_C_3 @ SY1229 @ SV636 ) ) ) )
                      | ( SV636
                       != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SY1229 ) @ SV636 ) ) @ ( sK6_SY714 @ SY1229 @ SV636 ) ) ) )
                | ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK5_C_3 @ SY1229 @ SV636 ) ) @ ( sK6_SY714 @ SY1229 @ SV636 ) )
                 != one_one_int ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7536]) ).

thf(7696,plain,
    ! [SV637: $i] :
      ( ( ! [SY1230: $i] :
            ( ~ ( is_int @ SY1230 )
            | ( ( hAPP_int_int @ number_number_of_int @ SV637 )
             != SY1230 )
            | ( SY1230
              = ( hAPP_int_int @ number_number_of_int @ SV637 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7537]) ).

thf(7697,plain,
    ! [SV638: $i] :
      ( ( ! [SY1231: $i] :
            ( ~ ( is_int @ SY1231 )
            | ( SY1231
             != ( hAPP_int_int @ number_number_of_int @ SV638 ) )
            | ( ( hAPP_int_int @ number_number_of_int @ SV638 )
              = SY1231 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7538]) ).

thf(7698,plain,
    ! [SV317: $i] :
      ( ( ! [SY996: $i,SY997: $i] :
            ( ~ ( is_int @ SV317 )
            | ~ ( is_int @ SY997 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV317 ) @ SY996 )
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY997 ) @ SY996 ) )
            | ( SV317 = SY997 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[7539]) ).

thf(7699,plain,
    ! [SV317: $i] :
      ( ( ! [SY998: $i,SY999: $i] :
            ( ~ ( is_int @ SV317 )
            | ~ ( is_int @ SY999 )
            | ( SV317 != SY999 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV317 ) @ SY998 )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY999 ) @ SY998 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[7540]) ).

thf(7700,plain,
    ! [SV639: $i] :
      ( ( ! [SY1232: $i] :
            ( ~ ( is_int @ SV639 )
            | ~ ( is_int @ SY1232 )
            | ( SY1232 = zero_zero_int )
            | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SY1232 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SY1232 ) @ SV639 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV639 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SY1232 ) @ SV639 ) ) )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7541]) ).

thf(7701,plain,
    ! [SV640: $i] :
      ( ( ! [SY1233: $i] :
            ( ~ ( is_int @ SV640 )
            | ~ ( is_int @ SY1233 )
            | ( SV640 = zero_zero_int )
            | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SY1233 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SY1233 ) @ SV640 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV640 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SY1233 ) @ SV640 ) ) )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7542]) ).

thf(7702,plain,
    ! [SV488: $i,SV318: $i,SV569: $i] :
      ( ( ~ ( ~ ( is_int @ SV569 )
            | ! [SY1185: $i,SY1186: $i] :
                ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV318 ) @ SV488 ) ) @ SV569 )
                 != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1185 ) @ SV488 ) ) @ SY1186 ) )
                | ( SV569
                  = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1185 ) @ SV318 ) ) @ SV488 ) ) @ SY1186 ) ) ) )
        | ~ ( ~ ( is_int @ SV569 )
            | ! [SY1187: $i,SY1188: $i] :
                ( ( SV569
                 != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1187 ) @ SV318 ) ) @ SV488 ) ) @ SY1188 ) )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV318 ) @ SV488 ) ) @ SV569 )
                  = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1187 ) @ SV488 ) ) @ SY1188 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[7543]) ).

thf(7703,plain,
    ! [SV489: $i,SV319: $i] :
      ( ( ~ ! [SY1144: $i,SY1145: $i] :
              ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY1144 ) @ SY1145 )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
               != one_one_int )
              | ( ( hAPP_int_int @ abs_abs_int @ SY1144 )
               != ( hAPP_int_int @ abs_abs_int @ SV319 ) )
              | ( ( hAPP_int_int @ abs_abs_int @ SV489 )
               != ( hAPP_int_int @ abs_abs_int @ SY1145 ) )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SY1144 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SY1145 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[7544]) ).

thf(7704,plain,
    ! [SV489: $i,SV319: $i] :
      ( ( ~ ~ ( ~ ! [SY1146: $i,SY1147: $i] :
                    ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY1146 ) @ SY1147 )
                     != one_one_int )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
                     != one_one_int )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SY1146 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SY1147 ) ) )
                    | ( ( hAPP_int_int @ abs_abs_int @ SY1146 )
                      = ( hAPP_int_int @ abs_abs_int @ SV319 ) ) )
              | ~ ! [SY1148: $i,SY1149: $i] :
                    ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY1148 ) @ SY1149 )
                     != one_one_int )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
                     != one_one_int )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SY1148 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SY1149 ) ) )
                    | ( ( hAPP_int_int @ abs_abs_int @ SV489 )
                      = ( hAPP_int_int @ abs_abs_int @ SY1149 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[7544]) ).

thf(7705,plain,
    ! [SV490: $i,SV320: $i] :
      ( ( ~ ! [SY1150: $i,SY1151: $i] :
              ( ~ ( is_int @ SV320 )
              | ~ ( is_int @ SV490 )
              | ~ ( is_int @ SY1150 )
              | ~ ( is_int @ SY1151 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1150 ) @ SY1151 ) )
              | ( SV320 != SV490 )
              | ( SY1150 = SY1151 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[7545]) ).

thf(7706,plain,
    ! [SV490: $i,SV320: $i] :
      ( ( ~ ! [SY1152: $i,SY1153: $i] :
              ( ~ ( is_int @ SV320 )
              | ~ ( is_int @ SV490 )
              | ~ ( is_int @ SY1152 )
              | ~ ( is_int @ SY1153 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1152 ) @ SY1153 ) )
              | ( SY1152 != SY1153 )
              | ( SV320 = SV490 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[7545]) ).

thf(7707,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                   != one_one_int )
                  | ( SX0 = one_one_int )
                  | ( SX0
                    = ( hAPP_int_int @ number_number_of_int @ min ) ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                   != one_one_int )
                  | ( SX0 = one_one_int )
                  | ( SX1
                    = ( hAPP_int_int @ number_number_of_int @ min ) ) ) )
      | ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                   != one_one_int )
                  | ( SX1 = one_one_int )
                  | ( SX0
                    = ( hAPP_int_int @ number_number_of_int @ min ) ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                   != one_one_int )
                  | ( SX1 = one_one_int )
                  | ( SX1
                    = ( hAPP_int_int @ number_number_of_int @ min ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[7546]) ).

thf(7708,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0 != one_one_int )
            | ( SX1 != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
              = one_one_int ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0
             != ( hAPP_int_int @ number_number_of_int @ min ) )
            | ( SX1
             != ( hAPP_int_int @ number_number_of_int @ min ) )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
              = one_one_int ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[7547]) ).

thf(7709,plain,
    ! [SV641: $i] :
      ( ( ~ ( is_int @ SV641 )
        | ( ( hAPP_int_int @ abs_abs_int @ SV641 )
         != one_one_int )
        | ( SV641 = one_one_int )
        | ( SV641
          = ( hAPP_int_int @ number_number_of_int @ min ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7548]) ).

thf(7710,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( SX0 != one_one_int )
            | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
              = one_one_int ) )
      | ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( SX0
             != ( hAPP_int_int @ number_number_of_int @ min ) )
            | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
              = one_one_int ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[7549]) ).

thf(7711,plain,
    ! [SV642: $i] :
      ( ( ~ ( is_int @ SV642 )
        | ( ( hAPP_int_int @ bit0 @ SV642 )
         != pls )
        | ( SV642 = pls ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7550]) ).

thf(7712,plain,
    ! [SV643: $i] :
      ( ( ~ ( is_int @ SV643 )
        | ( SV643 != pls )
        | ( ( hAPP_int_int @ bit0 @ SV643 )
          = pls ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7551]) ).

thf(7713,plain,
    ! [SV491: $i,SV321: $i] :
      ( ( ~ ~ ( ~ ! [SY1154: $i,SY1155: $i] :
                    ( ~ ( is_int @ SV321 )
                    | ~ ( is_int @ SV491 )
                    | ~ ( is_int @ SY1154 )
                    | ~ ( is_int @ SY1155 )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1154 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1155 ) @ SV491 ) )
                      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1154 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1155 ) @ SV321 ) ) )
                    | ( SY1154 != SY1155 ) )
              | ~ ! [SY1156: $i,SY1157: $i] :
                    ( ~ ( is_int @ SV321 )
                    | ~ ( is_int @ SV491 )
                    | ~ ( is_int @ SY1156 )
                    | ~ ( is_int @ SY1157 )
                    | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1156 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1157 ) @ SV491 ) )
                      = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1156 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1157 ) @ SV321 ) ) )
                    | ( SV321 != SV491 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[7552]) ).

thf(7714,plain,
    ! [SV491: $i,SV321: $i] :
      ( ( ~ ! [SY1158: $i,SY1159: $i] :
              ( ~ ( is_int @ SV321 )
              | ~ ( is_int @ SV491 )
              | ~ ( is_int @ SY1158 )
              | ~ ( is_int @ SY1159 )
              | ( SY1158 = SY1159 )
              | ( SV321 = SV491 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1158 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1159 ) @ SV491 ) )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1158 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1159 ) @ SV321 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[7552]) ).

thf(7715,plain,
    ! [SV644: $i] :
      ( ( ! [SY1234: $i] :
            ( ~ ( is_int @ SV644 )
            | ~ ( is_int @ SY1234 )
            | ( SV644 != zero_zero_int )
            | ( SY1234 != zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV644 ) @ SY1234 )
              = zero_zero_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7553]) ).

thf(7716,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX0 ) @ SX1 )
             != zero_zero_int )
            | ( SX0 = zero_zero_int ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX0 ) @ SX1 )
             != zero_zero_int )
            | ( SX1 = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[7554]) ).

thf(7717,plain,
    ! [SV645: $i] :
      ( ( ! [SY1235: $i] :
            ( ~ ( is_int @ SY1235 )
            | ( SY1235 = zero_zero_int )
            | ( ( hAPP_int_int @ ( div_mod_int @ SV645 ) @ SY1235 )
             != zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV645 ) @ ( hAPP_int_int @ uminus_uminus_int @ SY1235 ) )
              = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV645 ) @ SY1235 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7555]) ).

thf(7718,plain,
    ! [SV646: $i] :
      ( ( ! [SY1236: $i] :
            ( ~ ( is_int @ SY1236 )
            | ( SY1236 = zero_zero_int )
            | ( ( hAPP_int_int @ ( div_mod_int @ SV646 ) @ SY1236 )
              = zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV646 ) @ ( hAPP_int_int @ uminus_uminus_int @ SY1236 ) )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV646 ) @ SY1236 ) ) ) @ one_one_int ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7556]) ).

thf(7719,plain,
    ! [SV647: $i] :
      ( ( ! [SY1237: $i] :
            ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV647 )
             != ( hAPP_nat_int @ semiri1621563631at_int @ SY1237 ) )
            | ( SV647 = SY1237 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7557]) ).

thf(7720,plain,
    ! [SV648: $i] :
      ( ( ! [SY1238: $i] :
            ( ( SV648 != SY1238 )
            | ( ( hAPP_nat_int @ semiri1621563631at_int @ SV648 )
              = ( hAPP_nat_int @ semiri1621563631at_int @ SY1238 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7558]) ).

thf(7721,plain,
    ! [SV322: $i] :
      ( ( ! [SY1025: $i,SY1026: $i] :
            ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SY1025 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SY1026 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1025 ) @ SY1026 ) )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[7559]) ).

thf(7722,plain,
    ! [SV322: $i] :
      ( ( ~ ( ~ ! [SY1027: $i] :
                  ( ! [SY1028: $i] :
                      ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1027 ) @ SY1028 ) )
                     != one_one_int )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SY1027 )
                    = one_one_int ) )
            | ~ ! [SY1029: $i,SY1030: $i] :
                  ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1029 ) @ SY1030 ) )
                   != one_one_int )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SY1030 )
                    = one_one_int ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[7560]) ).

thf(7723,plain,
    ! [SV649: $i] :
      ( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV649 )
         != zero_zero_int )
        | ( SV649 = zero_zero_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7561]) ).

thf(7724,plain,
    ! [SV650: $i] :
      ( ( ( SV650 != zero_zero_nat )
        | ( ( hAPP_nat_int @ semiri1621563631at_int @ SV650 )
          = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7562]) ).

thf(7725,plain,
    ! [SV570: $i,SV492: $i,SV323: $i] :
      ( ( ~ ! [SY1189: $i,SY1190: $i] :
              ( ~ ( is_int @ SY1190 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV323 ) @ SV492 ) ) @ SV570 )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1189 ) @ SV492 ) ) @ SY1190 ) )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV323 ) @ SY1189 ) ) @ SV492 ) ) @ SV570 )
                = SY1190 ) )
        | ~ ! [SY1191: $i,SY1192: $i] :
              ( ~ ( is_int @ SY1192 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV323 ) @ SY1191 ) ) @ SV492 ) ) @ SV570 )
               != SY1192 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV323 ) @ SV492 ) ) @ SV570 )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1191 ) @ SV492 ) ) @ SY1192 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[7563]) ).

thf(7726,plain,
    ! [SV651: $i] :
      ( ( ~ ( is_int @ SV651 )
        | ! [SY1239: $i] :
            ( ( ( hAPP_int_int @ ( div_mod_int @ SV651 ) @ SY1239 )
             != zero_zero_int )
            | ~ ( ( SV651
                 != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1239 ) @ ( sK12_Q_4 @ SY1239 @ SV651 ) ) )
                | ~ ( is_int @ ( sK12_Q_4 @ SY1239 @ SV651 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7564]) ).

thf(7727,plain,
    ! [SV652: $i] :
      ( ( ~ ( is_int @ SV652 )
        | ! [SY1240: $i] :
            ( ! [SY1241: $i] :
                ( ( SV652
                 != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1240 ) @ SY1241 ) )
                | ~ ( is_int @ SY1241 ) )
            | ( ( hAPP_int_int @ ( div_mod_int @ SV652 ) @ SY1240 )
              = zero_zero_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7565]) ).

thf(7728,plain,
    ! [SV653: $i] :
      ( ( ! [SY1242: $i] :
            ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV653 )
             != ( hAPP_nat_int @ semiri1621563631at_int @ SY1242 ) )
            | ( SV653 = SY1242 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7566]) ).

thf(7729,plain,
    ! [SV654: $i] :
      ( ( ! [SY1243: $i] :
            ( ( SV654 != SY1243 )
            | ( ( hAPP_nat_int @ semiri1621563631at_int @ SV654 )
              = ( hAPP_nat_int @ semiri1621563631at_int @ SY1243 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7567]) ).

thf(7730,plain,
    ! [SV655: $i] :
      ( ( ! [SY1244: $i] :
            ( ~ ( is_int @ SV655 )
            | ~ ( is_int @ SY1244 )
            | ( ( hAPP_int_int @ bit0 @ SV655 )
             != ( hAPP_int_int @ bit0 @ SY1244 ) )
            | ( SV655 = SY1244 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7568]) ).

thf(7731,plain,
    ! [SV656: $i] :
      ( ( ! [SY1245: $i] :
            ( ~ ( is_int @ SV656 )
            | ~ ( is_int @ SY1245 )
            | ( SV656 != SY1245 )
            | ( ( hAPP_int_int @ bit0 @ SV656 )
              = ( hAPP_int_int @ bit0 @ SY1245 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7569]) ).

thf(7732,plain,
    ! [SV657: $i] :
      ( ( ~ ( is_int @ SV657 )
        | ( min
         != ( hAPP_int_int @ bit1 @ SV657 ) )
        | ( min = SV657 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7570]) ).

thf(7733,plain,
    ! [SV658: $i] :
      ( ( ~ ( is_int @ SV658 )
        | ( min != SV658 )
        | ( min
          = ( hAPP_int_int @ bit1 @ SV658 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7571]) ).

thf(7734,plain,
    ! [SV659: $i] :
      ( ( ! [SY1246: $i] :
            ( ( ( hAPP_nat_nat @ suc @ SV659 )
             != ( hAPP_nat_nat @ suc @ SY1246 ) )
            | ( SV659 = SY1246 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7572]) ).

thf(7735,plain,
    ! [SV660: $i] :
      ( ( ! [SY1247: $i] :
            ( ( SV660 != SY1247 )
            | ( ( hAPP_nat_nat @ suc @ SV660 )
              = ( hAPP_nat_nat @ suc @ SY1247 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7573]) ).

thf(7736,plain,
    ! [SV661: $i] :
      ( ( ~ ( is_int @ SV661 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV661 ) @ SV661 )
         != zero_zero_int )
        | ( SV661 = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7574]) ).

thf(7737,plain,
    ! [SV662: $i] :
      ( ( ~ ( is_int @ SV662 )
        | ( SV662 != zero_zero_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV662 ) @ SV662 )
          = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7575]) ).

thf(7738,plain,
    ! [SV663: $i] :
      ( ( ! [SY1248: $i] :
            ( ~ ( is_int @ SV663 )
            | ~ ( is_int @ SY1248 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV663 ) @ SY1248 )
             != zero_zero_int )
            | ( SV663 = SY1248 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7576]) ).

thf(7739,plain,
    ! [SV664: $i] :
      ( ( ! [SY1249: $i] :
            ( ~ ( is_int @ SV664 )
            | ~ ( is_int @ SY1249 )
            | ( SV664 != SY1249 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV664 ) @ SY1249 )
              = zero_zero_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7577]) ).

thf(7740,plain,
    ! [SV665: $i] :
      ( ( ! [SY1250: $i] :
            ( ~ ( is_int @ SV665 )
            | ~ ( is_int @ SY1250 )
            | ( SV665 != SY1250 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV665 ) @ SY1250 )
              = zero_zero_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7578]) ).

thf(7741,plain,
    ! [SV666: $i] :
      ( ( ! [SY1251: $i] :
            ( ~ ( is_int @ SV666 )
            | ~ ( is_int @ SY1251 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV666 ) @ SY1251 )
             != zero_zero_int )
            | ( SV666 = SY1251 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7579]) ).

thf(7742,plain,
    ! [SV667: $i] :
      ( ( ~ ( is_int @ SV667 )
        | ( zero_zero_int
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV667 ) @ SV667 ) )
        | ( SV667 = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7580]) ).

thf(7743,plain,
    ! [SV668: $i] :
      ( ( ~ ( is_int @ SV668 )
        | ( SV668 != zero_zero_int )
        | ( zero_zero_int
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV668 ) @ SV668 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7581]) ).

thf(7744,plain,
    ! [SV669: $i] :
      ( ( ~ ( is_int @ SV669 )
        | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV669 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
         != zero_zero_int )
        | ( SV669 = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7582]) ).

thf(7745,plain,
    ! [SV670: $i] :
      ( ( ~ ( is_int @ SV670 )
        | ( SV670 != zero_zero_int )
        | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV670 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7583]) ).

thf(7746,plain,
    ! [SV671: $i] :
      ( ( ( one_one_nat != SV671 )
        | ( SV671 = one_one_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7584]) ).

thf(7747,plain,
    ! [SV672: $i] :
      ( ( ( SV672 != one_one_nat )
        | ( one_one_nat = SV672 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7585]) ).

thf(7748,plain,
    ! [SV673: $i] :
      ( ( ! [SY1252: $i] :
            ( ( ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ SV673 ) @ SY1252 ) )
             != SY1252 )
            | ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ SV673 ) ) @ SY1252 )
              = zero_zero_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7586]) ).

thf(7749,plain,
    ! [SV674: $i] :
      ( ( ! [SY1253: $i] :
            ( ( ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ SV674 ) @ SY1253 ) )
              = SY1253 )
            | ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ SV674 ) ) @ SY1253 )
              = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ SV674 ) @ SY1253 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7587]) ).

thf(7750,plain,
    ! [SV675: $i] :
      ( ( ~ ( is_int @ SV675 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV675 ) @ zero_zero_int )
          = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7588]) ).

thf(7751,plain,
    ! [SV676: $i] :
      ( ( ~ ( is_int @ SV676 )
        | ( ( hAPP_int_int @ ( div_mod_int @ SV676 ) @ zero_zero_int )
          = SV676 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7589]) ).

thf(7752,plain,
    ! [SV677: $i] :
      ( ( ! [SY1254: $i] :
            ( ~ ( is_int @ SV677 )
            | ~ ( is_int @ SY1254 )
            | ( SV677 != zero_zero_int )
            | ( SY1254 != zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV677 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY1254 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
              = zero_zero_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7590]) ).

thf(7753,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
             != zero_zero_int )
            | ( SX0 = zero_zero_int ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
             != zero_zero_int )
            | ( SX1 = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[7591]) ).

thf(7754,plain,
    ! [SV678: $i] :
      ( ( ! [SY1255: $i] :
            ( ~ ( is_int @ SV678 )
            | ~ ( is_int @ SY1255 )
            | ( SV678 != zero_zero_int )
            | ( SY1255 != zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV678 ) @ SV678 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1255 ) @ SY1255 ) )
              = zero_zero_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7592]) ).

thf(7755,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX0 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX1 ) @ SX1 ) )
             != zero_zero_int )
            | ( SX0 = zero_zero_int ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX0 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX1 ) @ SX1 ) )
             != zero_zero_int )
            | ( SX1 = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[7593]) ).

thf(7756,plain,
    ! [SV679: $i] :
      ( ( ! [SY1256: $i] :
            ( ~ ( is_int @ SV679 )
            | ~ ( is_int @ SY1256 )
            | ( SV679 != zero_zero_int )
            | ( SY1256 != zero_zero_int )
            | ( ( hAPP_int_int @ ( legacy_zgcd @ SV679 ) @ SY1256 )
              = zero_zero_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7594]) ).

thf(7757,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ ( legacy_zgcd @ SX0 ) @ SX1 )
             != zero_zero_int )
            | ( SX0 = zero_zero_int ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ ( legacy_zgcd @ SX0 ) @ SX1 )
             != zero_zero_int )
            | ( SX1 = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[7595]) ).

thf(7758,plain,
    ! [SV35: $i,SV338: $i] :
      ( ( ( SV338 = zero_zero_int )
        = $true )
      | ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV338 ) @ SV35 )
         != zero_zero_int )
        = $true )
      | ( ( is_int @ SV338 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[7597]) ).

thf(7759,plain,
    ! [SV339: $i,SV496: $i,SV41: $i] :
      ( ( ( ~ ( is_int @ SV41 ) )
        = $true )
      | ( ( ~ ( is_int @ SV496 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV41 ) @ SV339 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV496 ) @ SV339 ) )
          | ( SV41 = SV496 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7598]) ).

thf(7760,plain,
    ! [SV42: $i,SV497: $i,SV340: $i] :
      ( ( ( ~ ( is_int @ SV340 ) )
        = $true )
      | ( ( ~ ( is_int @ SV497 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV42 ) @ SV340 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV42 ) @ SV497 ) )
          | ( SV340 = SV497 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7599]) ).

thf(7761,plain,
    ! [SV43: $i,SV498: $i,SV341: $i] :
      ( ( ( ~ ( is_int @ SV341 ) )
        = $true )
      | ( ( ~ ( is_int @ SV498 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV43 ) @ SV341 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV43 ) @ SV498 ) )
          | ( SV341 = SV498 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7600]) ).

thf(7762,plain,
    ! [SV366: $i,SV79: $i] :
      ( ( ( is_int @ SV79 )
        = $false )
      | ( ( ~ ( is_int @ SV366 ) )
        = $true )
      | ( ( ( SV366 = zero_zero_int )
          | ( SV79 = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV366 ) @ SV79 )
           != zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7605]) ).

thf(7763,plain,
    ! [SV367: $i,SV80: $i] :
      ( ( ( is_int @ SV80 )
        = $false )
      | ( ( ~ ( is_int @ SV367 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV80 ) @ SV367 )
           != zero_zero_int )
          | ( SV80 = zero_zero_int )
          | ( SV367 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7606]) ).

thf(7764,plain,
    ! [SV576: $i,SV524: $i,SV680: $i,SV380: $i,SV104: $i] :
      ( ( ~ ( is_int @ SV104 )
        | ~ ( is_int @ SV380 )
        | ~ ( is_int @ SV680 )
        | ( SV680 = zero_zero_int )
        | ( SV104 = SV380 )
        | ( SV524 != SV576 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV524 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV680 ) @ SV104 ) )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV576 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV680 ) @ SV380 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7608]) ).

thf(7765,plain,
    ! [SV681: $i,SV581: $i,SV144: $i] :
      ( ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV144 ) @ SV581 )
           != SV681 )
          | ( SV144
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV681 ) @ SV581 ) ) )
        = $true )
      | ( ( is_int @ SV144 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[7613]) ).

thf(7766,plain,
    ! [SV682: $i,SV582: $i,SV532: $i,SV397: $i,SV145: $i] :
      ( ( ! [SY1257: $i,SY1258: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV145 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV397 ) @ SV532 ) ) ) @ SV582 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV682 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV397 ) @ SY1257 ) ) ) @ SY1258 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV145 ) @ SV582 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV682 ) @ SY1258 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV397 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV532 ) @ SV582 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1257 ) @ SY1258 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7614]) ).

thf(7767,plain,
    ! [SV202: $i,SV540: $i,SV424: $i] :
      ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV424 ) @ SV540 )
          = one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV424 ) @ SV202 ) ) @ SV540 )
          = ( hAPP_int_int @ ( legacy_zgcd @ SV202 ) @ SV540 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7619]) ).

thf(7768,plain,
    ! [SV203: $i,SV541: $i,SV425: $i] :
      ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV425 ) @ SV541 )
          = one_one_int )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV203 ) @ SV541 )
           != one_one_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV425 ) @ SV203 ) ) @ SV541 )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7620]) ).

thf(7769,plain,
    ! [SV214: $i,SV546: $i,SV434: $i] :
      ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV434 ) @ SV546 )
          = one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV434 ) @ SV214 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV546 ) @ SV214 ) )
          = one_one_int )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7621]) ).

thf(7770,plain,
    ! [SV215: $i,SV547: $i,SV435: $i] :
      ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV435 ) @ SV547 )
          = one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV435 ) @ SV215 ) ) @ SV547 )
          = one_one_int )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7622]) ).

thf(7771,plain,
    ! [SV437: $i,SV221: $i,SV583: $i,SV548: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV548 ) @ SV583 )
         != one_one_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV548 ) @ SV221 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV583 ) @ SV437 ) )
          = one_one_int )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7623]) ).

thf(7772,plain,
    ! [SV235: $i,SV550: $i,SV445: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV445 ) @ SV550 )
          = one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV445 ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV550 ) @ SV235 ) )
          = one_one_int )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7624]) ).

thf(7773,plain,
    ! [SV243: $i,SV554: $i,SV453: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV453 ) @ SV554 )
          = one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV453 ) @ SV243 ) ) @ SV554 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV243 ) @ SV554 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7625]) ).

thf(7774,plain,
    ! [SV244: $i,SV555: $i,SV454: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV454 ) @ SV555 )
          = one_one_int )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV454 ) @ SV244 )
           != one_one_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV454 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV555 ) @ SV244 ) )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7626]) ).

thf(7775,plain,
    ! [SV584: $i,SV455: $i,SV245: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV245 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV455 ) @ SV584 ) )
          = one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV245 ) @ SV455 )
          = one_one_int )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7627]) ).

thf(7776,plain,
    ! [SV556: $i,SV456: $i,SV246: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV246 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV456 ) @ SV556 ) )
          = one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV246 ) @ SV556 )
          = one_one_int )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7628]) ).

thf(7777,plain,
    ! [SV247: $i,SV457: $i,SV585: $i,SV557: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV557 ) @ SV585 )
          = zero_zero_int )
        = $true )
      | ( ( ( SV557
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV457 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV557 ) @ SV585 ) ) )
          | ( SV585
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV247 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV557 ) @ SV585 ) ) )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV457 ) @ SV247 )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7629]) ).

thf(7778,plain,
    ! [SV683: $i,SV263: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV263 ) @ SV683 )
         != one_one_int )
        = $true )
      | ( ( ( SV263 = one_one_int )
          | ( SV263
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true )
      | ( ( is_int @ SV263 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[7630]) ).

thf(7779,plain,
    ! [SV564: $i,SV475: $i,SV287: $i,SV684: $i,SV587: $i] :
      ( ( ! [SY1259: $i,SY1260: $i,SY1261: $i] :
            ( ( SV587
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV684 ) @ SY1259 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1260 ) @ SY1261 ) ) )
            | ( SV287
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV475 ) @ SY1259 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV564 ) @ SY1261 ) ) )
            | ( ( hAPP_int_int @ ( div_mod_int @ SV587 ) @ SV287 )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV684 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV587 ) @ SV287 ) ) @ SV475 ) ) ) @ SY1259 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1260 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV587 ) @ SV287 ) ) @ SV564 ) ) ) @ SY1261 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7633]) ).

thf(7780,plain,
    ! [SV568: $i,SV485: $i,SV311: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV311 ) @ SV485 ) ) @ SV568 )
          = one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV311 ) @ SV568 )
          = one_one_int )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7636]) ).

thf(7781,plain,
    ! [SV588: $i] :
      ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ zero_zero_int ) @ SV588 )
         != one_one_int )
        = $true )
      | ( ( ( hAPP_int_int @ abs_abs_int @ SV588 )
          = one_one_int )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7637]) ).

thf(7782,plain,
    ! [SV589: $i] :
      ( ( ( ( hAPP_int_int @ abs_abs_int @ SV589 )
         != one_one_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( legacy_zgcd @ zero_zero_int ) @ SV589 )
          = one_one_int )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7638]) ).

thf(7783,plain,
    ! [SV590: $i] :
      ( ( ( ~ ( is_int @ SV590 ) )
        = $true )
      | ( ( ( one_one_int != SV590 )
          | ( SV590 = one_one_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7639]) ).

thf(7784,plain,
    ! [SV591: $i] :
      ( ( ( ~ ( is_int @ SV591 ) )
        = $true )
      | ( ( ( SV591 != one_one_int )
          | ( one_one_int = SV591 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7640]) ).

thf(7785,plain,
    ! [SV685: $i,SV592: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV592 ) @ SV685 )
         != zero_zero_int )
        | ( ( hAPP_int_int @ ( div_mod_int @ SV592 ) @ ( hAPP_int_int @ uminus_uminus_int @ SV685 ) )
          = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7641]) ).

thf(7786,plain,
    ! [SV686: $i,SV593: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV593 ) @ SV686 )
          = zero_zero_int )
        | ( ( hAPP_int_int @ ( div_mod_int @ SV593 ) @ ( hAPP_int_int @ uminus_uminus_int @ SV686 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( div_mod_int @ SV593 ) @ SV686 ) ) @ SV686 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7642]) ).

thf(7787,plain,
    ! [SV687: $i,SV594: $i] :
      ( ( ( SV594 != SV687 )
        | ( ( image_nat_int @ semiri1621563631at_int @ SV594 )
          = ( image_nat_int @ semiri1621563631at_int @ SV687 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7643]) ).

thf(7788,plain,
    ! [SV688: $i,SV595: $i] :
      ( ( ( ( image_nat_int @ semiri1621563631at_int @ SV595 )
         != ( image_nat_int @ semiri1621563631at_int @ SV688 ) )
        | ( SV595 = SV688 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7644]) ).

thf(7789,plain,
    ! [SV596: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV596 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ SV596 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = one_one_int )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7645]) ).

thf(7790,plain,
    ! [SV597: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV597 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
         != one_one_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ SV597 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
         != zero_zero_int )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7646]) ).

thf(7791,plain,
    ! [SV598: $i] :
      ( ( ( SV598 != zero_zero_nat )
        = $true )
      | ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ SV598 )
          = one_one_int )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7647]) ).

thf(7792,plain,
    ! [SV599: $i] :
      ( ( ( SV599 = zero_zero_nat )
        = $true )
      | ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ SV599 )
          = zero_zero_int )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7648]) ).

thf(7793,plain,
    ! [SV600: $i] :
      ( ( ( ( hAPP_int_nat @ number_number_of_nat @ SV600 )
         != zero_zero_nat )
        = $true )
      | ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ ( hAPP_int_nat @ number_number_of_nat @ SV600 ) )
          = one_one_int )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7649]) ).

thf(7794,plain,
    ! [SV601: $i] :
      ( ( ( ( hAPP_int_nat @ number_number_of_nat @ SV601 )
          = zero_zero_nat )
        = $true )
      | ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ ( hAPP_int_nat @ number_number_of_nat @ SV601 ) )
          = zero_zero_int )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7650]) ).

thf(7795,plain,
    ! [SV602: $i] :
      ( ( ( ~ ( is_int @ SV602 ) )
        = $true )
      | ( ( ( pls
           != ( hAPP_int_int @ bit0 @ SV602 ) )
          | ( pls = SV602 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7651]) ).

thf(7796,plain,
    ! [SV603: $i] :
      ( ( ( ~ ( is_int @ SV603 ) )
        = $true )
      | ( ( ( pls != SV603 )
          | ( pls
            = ( hAPP_int_int @ bit0 @ SV603 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7652]) ).

thf(7797,plain,
    ! [SV689: $i,SV604: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV604 ) @ SV689 )
         != zero_zero_int )
        | ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ SV604 ) ) @ SV689 )
          = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7653]) ).

thf(7798,plain,
    ! [SV690: $i,SV605: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV605 ) @ SV690 )
          = zero_zero_int )
        | ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ SV605 ) ) @ SV690 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV690 ) @ ( hAPP_int_int @ ( div_mod_int @ SV605 ) @ SV690 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7654]) ).

thf(7799,plain,
    ! [SV691: $i,SV606: $i] :
      ( ( ~ ( is_int @ SV606 )
        | ~ ( is_int @ SV691 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV606 ) @ SV691 )
         != zero_zero_int )
        | ( SV606 = zero_zero_int )
        | ( SV691 = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7655]) ).

thf(7800,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0 != zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
              = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7656]) ).

thf(7801,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX1 != zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
              = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7656]) ).

thf(7802,plain,
    ! [SV607: $i] :
      ( ( ( ~ ( is_int @ SV607 ) )
        = $true )
      | ( ( ! [SY1209: $i] :
              ( ( ( hAPP_int_nat @ number_number_of_nat @ SY1209 )
                = zero_zero_nat )
              | ( SV607 != zero_zero_int )
              | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV607 ) @ ( hAPP_int_nat @ number_number_of_nat @ SY1209 ) )
                = zero_zero_int ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7657]) ).

thf(7803,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ! [SX1: $i] :
                ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ SX1 ) )
                 != zero_zero_int )
                | ( ( hAPP_int_nat @ number_number_of_nat @ SX1 )
                 != zero_zero_nat ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7658]) ).

thf(7804,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ! [SX1: $i] :
                ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ SX1 ) )
               != zero_zero_int )
            | ( SX0 = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7658]) ).

thf(7805,plain,
    ! [SV608: $i,SV313: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV313 ) @ SV608 )
         != zero_zero_int )
        = $true )
      | ( ( ~ ( ( SV313
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV608 ) @ ( sK11_Q_4 @ SV608 @ SV313 ) ) )
              | ~ ( is_int @ ( sK11_Q_4 @ SV608 @ SV313 ) ) ) )
        = $true )
      | ( ( is_int @ SV313 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[7659]) ).

thf(7806,plain,
    ! [SV692: $i,SV609: $i] :
      ( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV609 )
         != ( hAPP_nat_int @ semiri1621563631at_int @ SV692 ) )
        | ( SV609 = SV692 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7660]) ).

thf(7807,plain,
    ! [SV693: $i,SV610: $i] :
      ( ( ( SV610 != SV693 )
        | ( ( hAPP_nat_int @ semiri1621563631at_int @ SV610 )
          = ( hAPP_nat_int @ semiri1621563631at_int @ SV693 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7661]) ).

thf(7808,plain,
    ! [SV611: $i] :
      ( ( ( zero_zero_nat != SV611 )
        = $true )
      | ( ( SV611 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7662]) ).

thf(7809,plain,
    ! [SV612: $i] :
      ( ( ( SV612 != zero_zero_nat )
        = $true )
      | ( ( zero_zero_nat = SV612 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7663]) ).

thf(7810,plain,
    ( ( ~ ( is_int @ sK13_X_1 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7664]) ).

thf(7811,plain,
    ( ( ~ ( is_int @ sK14_SY716 ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7664]) ).

thf(7812,plain,
    ! [SV613: $i,SV694: $i] :
      ( ( ~ ( is_int @ SV694 )
        | ( SV694 = zero_zero_int )
        | ( ( hAPP_int_int @ ( div_mod_int @ SV613 ) @ SV694 )
         != zero_zero_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ SV613 ) ) @ SV694 )
          = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV613 ) @ SV694 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7665]) ).

thf(7813,plain,
    ! [SV614: $i,SV695: $i] :
      ( ( ~ ( is_int @ SV695 )
        | ( SV695 = zero_zero_int )
        | ( ( hAPP_int_int @ ( div_mod_int @ SV614 ) @ SV695 )
          = zero_zero_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ SV614 ) ) @ SV695 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV614 ) @ SV695 ) ) ) @ one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7666]) ).

thf(7814,plain,
    ! [SV615: $i] :
      ( ( ( ~ ( is_int @ SV615 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ abs_abs_int @ SV615 )
           != zero_zero_int )
          | ( SV615 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7667]) ).

thf(7815,plain,
    ! [SV616: $i] :
      ( ( ( ~ ( is_int @ SV616 ) )
        = $true )
      | ( ( ( SV616 != zero_zero_int )
          | ( ( hAPP_int_int @ abs_abs_int @ SV616 )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7668]) ).

thf(7816,plain,
    ! [SV617: $i] :
      ( ( ( ~ ( is_int @ SV617 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ bit1 @ SV617 )
           != min )
          | ( SV617 = min ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7669]) ).

thf(7817,plain,
    ! [SV618: $i] :
      ( ( ( ~ ( is_int @ SV618 ) )
        = $true )
      | ( ( ( SV618 != min )
          | ( ( hAPP_int_int @ bit1 @ SV618 )
            = min ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7670]) ).

thf(7818,plain,
    ! [SV486: $i,SV314: $i] :
      ( ( ( is_int @ SV314 )
        = $false )
      | ( ( ~ ( is_int @ SV486 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 )
            = zero_zero_int )
          | ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK1_A_4 @ SV486 @ SV314 ) )
                                | ~ ( is_int @ ( sK2_SY713 @ SV486 @ SV314 ) ) )
                          | ( SV314
                           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK1_A_4 @ SV486 @ SV314 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 ) ) ) )
                    | ( SV486
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK2_SY713 @ SV486 @ SV314 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 ) ) ) )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( sK1_A_4 @ SV486 @ SV314 ) ) @ ( sK2_SY713 @ SV486 @ SV314 ) )
               != one_one_int ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7671]) ).

thf(7819,plain,
    ! [SV696: $i,SV619: $i] :
      ( ( ~ ( is_int @ SV619 )
        | ~ ( is_int @ SV696 )
        | ( ( hAPP_int_int @ number_number_of_int @ SV619 )
         != ( hAPP_int_int @ number_number_of_int @ SV696 ) )
        | ( SV619 = SV696 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7672]) ).

thf(7820,plain,
    ! [SV697: $i,SV620: $i] :
      ( ( ~ ( is_int @ SV620 )
        | ~ ( is_int @ SV697 )
        | ( SV620 != SV697 )
        | ( ( hAPP_int_int @ number_number_of_int @ SV620 )
          = ( hAPP_int_int @ number_number_of_int @ SV697 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7673]) ).

thf(7821,plain,
    ! [SV698: $i,SV621: $i] :
      ( ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV621 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
         != ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV698 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
        | ( ( hAPP_int_int @ abs_abs_int @ SV621 )
          = ( hAPP_int_int @ abs_abs_int @ SV698 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7674]) ).

thf(7822,plain,
    ! [SV699: $i,SV622: $i] :
      ( ( ( ( hAPP_int_int @ abs_abs_int @ SV622 )
         != ( hAPP_int_int @ abs_abs_int @ SV699 ) )
        | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV622 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV699 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7675]) ).

thf(7823,plain,
    ! [SV623: $i] :
      ( ( ( ~ ( is_int @ SV623 ) )
        = $true )
      | ( ( ! [SY1218: $i] :
              ( ( SY1218 = zero_zero_nat )
              | ( SV623 != zero_zero_int )
              | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV623 ) @ SY1218 )
                = zero_zero_int ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7676]) ).

thf(7824,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ! [SX1: $i] :
                ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ SX1 )
                 != zero_zero_int )
                | ( SX1 != zero_zero_nat ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7677]) ).

thf(7825,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ! [SX1: $i] :
                ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ SX1 )
               != zero_zero_int )
            | ( SX0 = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7677]) ).

thf(7826,plain,
    ! [SV487: $i,SV315: $i] :
      ( ( ! [SY1133: $i,SY1134: $i] :
            ( ~ ( is_int @ SV315 )
            | ~ ( is_int @ SV487 )
            | ~ ( is_int @ SY1133 )
            | ~ ( is_int @ SY1134 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1133 ) @ SY1134 ) )
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SY1134 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1133 ) @ SV487 ) ) )
            | ( SV315 = SY1133 )
            | ( SV487 = SY1134 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[7678]) ).

thf(7827,plain,
    ! [SV487: $i,SV315: $i] :
      ( ( ~ ( ~ ! [SY1135: $i,SY1136: $i] :
                  ( ~ ( is_int @ SV315 )
                  | ~ ( is_int @ SV487 )
                  | ~ ( is_int @ SY1135 )
                  | ~ ( is_int @ SY1136 )
                  | ( SV315 != SY1135 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1135 ) @ SY1136 ) )
                    = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SY1136 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1135 ) @ SV487 ) ) ) )
            | ~ ! [SY1137: $i,SY1138: $i] :
                  ( ~ ( is_int @ SV315 )
                  | ~ ( is_int @ SV487 )
                  | ~ ( is_int @ SY1137 )
                  | ~ ( is_int @ SY1138 )
                  | ( SV487 != SY1138 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1137 ) @ SY1138 ) )
                    = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SY1138 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1137 ) @ SV487 ) ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[7679]) ).

thf(7828,plain,
    ! [SV700: $i,SV624: $i] :
      ( ( ~ ( is_int @ SV624 )
        | ~ ( is_int @ SV700 )
        | ( SV624
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV624 ) @ SV700 ) )
        | ( SV700 = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7680]) ).

thf(7829,plain,
    ! [SV701: $i,SV625: $i] :
      ( ( ~ ( is_int @ SV625 )
        | ~ ( is_int @ SV701 )
        | ( SV701 != zero_zero_int )
        | ( SV625
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV625 ) @ SV701 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7681]) ).

thf(7830,plain,
    ! [SV702: $i,SV626: $i] :
      ( ( ( ( hAPP_int_nat @ number_number_of_nat @ SV626 )
         != SV702 )
        | ( SV702
          = ( hAPP_int_nat @ number_number_of_nat @ SV626 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7682]) ).

thf(7831,plain,
    ! [SV627: $i,SV703: $i] :
      ( ( ( SV703
         != ( hAPP_int_nat @ number_number_of_nat @ SV627 ) )
        | ( ( hAPP_int_nat @ number_number_of_nat @ SV627 )
          = SV703 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7683]) ).

thf(7832,plain,
    ! [SV628: $i] :
      ( ( ( ~ ( is_int @ SV628 ) )
        = $true )
      | ( ( ( zero_zero_int != SV628 )
          | ( SV628 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7684]) ).

thf(7833,plain,
    ! [SV629: $i] :
      ( ( ( ~ ( is_int @ SV629 ) )
        = $true )
      | ( ( ( SV629 != zero_zero_int )
          | ( zero_zero_int = SV629 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7685]) ).

thf(7834,plain,
    ! [SV316: $i,SV704: $i] :
      ( ( ! [SY1262: $i] :
            ( ~ ( is_int @ SV704 )
            | ~ ( is_int @ SY1262 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SV704 )
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SY1262 ) )
            | ( SV704 = SY1262 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7686]) ).

thf(7835,plain,
    ! [SV316: $i,SV705: $i] :
      ( ( ! [SY1263: $i] :
            ( ~ ( is_int @ SV705 )
            | ~ ( is_int @ SY1263 )
            | ( SV705 != SY1263 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SV705 )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SY1263 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7687]) ).

thf(7836,plain,
    ! [SV706: $i,SV630: $i] :
      ( ( ~ ( is_int @ SV630 )
        | ~ ( is_int @ SV706 )
        | ( SV706 = zero_zero_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV706 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV706 ) @ SV630 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV630 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV706 ) @ SV630 ) ) )
          = one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7688]) ).

thf(7837,plain,
    ! [SV707: $i,SV631: $i] :
      ( ( ~ ( is_int @ SV631 )
        | ~ ( is_int @ SV707 )
        | ( SV631 = zero_zero_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV707 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV707 ) @ SV631 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV631 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV707 ) @ SV631 ) ) )
          = one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7689]) ).

thf(7838,plain,
    ! [SV708: $i,SV632: $i] :
      ( ( ~ ( is_int @ SV632 )
        | ~ ( is_int @ SV708 )
        | ( ( hAPP_int_int @ bit1 @ SV632 )
         != ( hAPP_int_int @ bit1 @ SV708 ) )
        | ( SV632 = SV708 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7690]) ).

thf(7839,plain,
    ! [SV709: $i,SV633: $i] :
      ( ( ~ ( is_int @ SV633 )
        | ~ ( is_int @ SV709 )
        | ( SV633 != SV709 )
        | ( ( hAPP_int_int @ bit1 @ SV633 )
          = ( hAPP_int_int @ bit1 @ SV709 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7691]) ).

thf(7840,plain,
    ! [SV710: $i,SV634: $i] :
      ( ( ( SV634 != zero_zero_nat )
        | ( SV710 != zero_zero_nat )
        | ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV634 ) )
          = ( hAPP_nat_int @ semiri1621563631at_int @ SV710 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7692]) ).

thf(7841,plain,
    ( ( ~ ! [SX0: $i] :
            ( ! [SX1: $i] :
                ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SX0 ) )
               != ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
            | ( SX0 = zero_zero_nat ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7693]) ).

thf(7842,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SX0 ) )
             != ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
            | ( SX1 = zero_zero_nat ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7693]) ).

thf(7843,plain,
    ! [SV711: $i,SV635: $i] :
      ( ( ~ ( is_int @ SV635 )
        | ~ ( is_int @ SV711 )
        | ( SV711 = zero_zero_int )
        | ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK7_C_3 @ SV711 @ SV635 ) )
                              | ~ ( is_int @ ( sK8_SY715 @ SV711 @ SV635 ) ) )
                        | ( SV711
                         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV711 ) @ SV635 ) ) @ ( sK7_C_3 @ SV711 @ SV635 ) ) ) )
                  | ( SV635
                   != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV711 ) @ SV635 ) ) @ ( sK8_SY715 @ SV711 @ SV635 ) ) ) )
            | ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK7_C_3 @ SV711 @ SV635 ) ) @ ( sK8_SY715 @ SV711 @ SV635 ) )
             != one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7694]) ).

thf(7844,plain,
    ! [SV712: $i,SV636: $i] :
      ( ( ~ ( is_int @ SV636 )
        | ~ ( is_int @ SV712 )
        | ( SV636 = zero_zero_int )
        | ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK5_C_3 @ SV712 @ SV636 ) )
                              | ~ ( is_int @ ( sK6_SY714 @ SV712 @ SV636 ) ) )
                        | ( SV712
                         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV712 ) @ SV636 ) ) @ ( sK5_C_3 @ SV712 @ SV636 ) ) ) )
                  | ( SV636
                   != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV712 ) @ SV636 ) ) @ ( sK6_SY714 @ SV712 @ SV636 ) ) ) )
            | ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK5_C_3 @ SV712 @ SV636 ) ) @ ( sK6_SY714 @ SV712 @ SV636 ) )
             != one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7695]) ).

thf(7845,plain,
    ! [SV637: $i,SV713: $i] :
      ( ( ~ ( is_int @ SV713 )
        | ( ( hAPP_int_int @ number_number_of_int @ SV637 )
         != SV713 )
        | ( SV713
          = ( hAPP_int_int @ number_number_of_int @ SV637 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7696]) ).

thf(7846,plain,
    ! [SV638: $i,SV714: $i] :
      ( ( ~ ( is_int @ SV714 )
        | ( SV714
         != ( hAPP_int_int @ number_number_of_int @ SV638 ) )
        | ( ( hAPP_int_int @ number_number_of_int @ SV638 )
          = SV714 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7697]) ).

thf(7847,plain,
    ! [SV715: $i,SV317: $i] :
      ( ( ! [SY1264: $i] :
            ( ~ ( is_int @ SV317 )
            | ~ ( is_int @ SY1264 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV317 ) @ SV715 )
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY1264 ) @ SV715 ) )
            | ( SV317 = SY1264 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7698]) ).

thf(7848,plain,
    ! [SV716: $i,SV317: $i] :
      ( ( ! [SY1265: $i] :
            ( ~ ( is_int @ SV317 )
            | ~ ( is_int @ SY1265 )
            | ( SV317 != SY1265 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV317 ) @ SV716 )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SY1265 ) @ SV716 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7699]) ).

thf(7849,plain,
    ! [SV717: $i,SV639: $i] :
      ( ( ~ ( is_int @ SV639 )
        | ~ ( is_int @ SV717 )
        | ( SV717 = zero_zero_int )
        | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV717 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV717 ) @ SV639 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV639 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV717 ) @ SV639 ) ) )
          = one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7700]) ).

thf(7850,plain,
    ! [SV718: $i,SV640: $i] :
      ( ( ~ ( is_int @ SV640 )
        | ~ ( is_int @ SV718 )
        | ( SV640 = zero_zero_int )
        | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV718 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV718 ) @ SV640 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV640 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV718 ) @ SV640 ) ) )
          = one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7701]) ).

thf(7851,plain,
    ! [SV488: $i,SV318: $i,SV569: $i] :
      ( ( ~ ( ~ ( is_int @ SV569 )
            | ! [SY1185: $i,SY1186: $i] :
                ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV318 ) @ SV488 ) ) @ SV569 )
                 != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1185 ) @ SV488 ) ) @ SY1186 ) )
                | ( SV569
                  = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1185 ) @ SV318 ) ) @ SV488 ) ) @ SY1186 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[7702]) ).

thf(7852,plain,
    ! [SV488: $i,SV318: $i,SV569: $i] :
      ( ( ~ ( ~ ( is_int @ SV569 )
            | ! [SY1187: $i,SY1188: $i] :
                ( ( SV569
                 != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1187 ) @ SV318 ) ) @ SV488 ) ) @ SY1188 ) )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV318 ) @ SV488 ) ) @ SV569 )
                  = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1187 ) @ SV488 ) ) @ SY1188 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[7702]) ).

thf(7853,plain,
    ! [SV489: $i,SV319: $i] :
      ( ( ! [SY1144: $i,SY1145: $i] :
            ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY1144 ) @ SY1145 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
             != one_one_int )
            | ( ( hAPP_int_int @ abs_abs_int @ SY1144 )
             != ( hAPP_int_int @ abs_abs_int @ SV319 ) )
            | ( ( hAPP_int_int @ abs_abs_int @ SV489 )
             != ( hAPP_int_int @ abs_abs_int @ SY1145 ) )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SY1144 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SY1145 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[7703]) ).

thf(7854,plain,
    ! [SV489: $i,SV319: $i] :
      ( ( ~ ( ~ ! [SY1146: $i,SY1147: $i] :
                  ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY1146 ) @ SY1147 )
                   != one_one_int )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
                   != one_one_int )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SY1146 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
                   != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SY1147 ) ) )
                  | ( ( hAPP_int_int @ abs_abs_int @ SY1146 )
                    = ( hAPP_int_int @ abs_abs_int @ SV319 ) ) )
            | ~ ! [SY1148: $i,SY1149: $i] :
                  ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY1148 ) @ SY1149 )
                   != one_one_int )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
                   != one_one_int )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SY1148 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
                   != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SY1149 ) ) )
                  | ( ( hAPP_int_int @ abs_abs_int @ SV489 )
                    = ( hAPP_int_int @ abs_abs_int @ SY1149 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[7704]) ).

thf(7855,plain,
    ! [SV490: $i,SV320: $i] :
      ( ( ! [SY1150: $i,SY1151: $i] :
            ( ~ ( is_int @ SV320 )
            | ~ ( is_int @ SV490 )
            | ~ ( is_int @ SY1150 )
            | ~ ( is_int @ SY1151 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1150 ) @ SY1151 ) )
            | ( SV320 != SV490 )
            | ( SY1150 = SY1151 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[7705]) ).

thf(7856,plain,
    ! [SV490: $i,SV320: $i] :
      ( ( ! [SY1152: $i,SY1153: $i] :
            ( ~ ( is_int @ SV320 )
            | ~ ( is_int @ SV490 )
            | ~ ( is_int @ SY1152 )
            | ~ ( is_int @ SY1153 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1152 ) @ SY1153 ) )
            | ( SY1152 != SY1153 )
            | ( SV320 = SV490 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[7706]) ).

thf(7857,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                   != one_one_int )
                  | ( SX0 = one_one_int )
                  | ( SX0
                    = ( hAPP_int_int @ number_number_of_int @ min ) ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                   != one_one_int )
                  | ( SX0 = one_one_int )
                  | ( SX1
                    = ( hAPP_int_int @ number_number_of_int @ min ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7707]) ).

thf(7858,plain,
    ( ( ~ ~ ( ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                   != one_one_int )
                  | ( SX1 = one_one_int )
                  | ( SX0
                    = ( hAPP_int_int @ number_number_of_int @ min ) ) )
            | ~ ! [SX0: $i,SX1: $i] :
                  ( ~ ( is_int @ SX0 )
                  | ~ ( is_int @ SX1 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                   != one_one_int )
                  | ( SX1 = one_one_int )
                  | ( SX1
                    = ( hAPP_int_int @ number_number_of_int @ min ) ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7707]) ).

thf(7859,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0 != one_one_int )
            | ( SX1 != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
              = one_one_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7708]) ).

thf(7860,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( SX0
             != ( hAPP_int_int @ number_number_of_int @ min ) )
            | ( SX1
             != ( hAPP_int_int @ number_number_of_int @ min ) )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
              = one_one_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7708]) ).

thf(7861,plain,
    ! [SV641: $i] :
      ( ( ( ~ ( is_int @ SV641 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ abs_abs_int @ SV641 )
           != one_one_int )
          | ( SV641 = one_one_int )
          | ( SV641
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7709]) ).

thf(7862,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( SX0 != one_one_int )
            | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
              = one_one_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7710]) ).

thf(7863,plain,
    ( ( ~ ! [SX0: $i] :
            ( ~ ( is_int @ SX0 )
            | ( SX0
             != ( hAPP_int_int @ number_number_of_int @ min ) )
            | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
              = one_one_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7710]) ).

thf(7864,plain,
    ! [SV642: $i] :
      ( ( ( ~ ( is_int @ SV642 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ bit0 @ SV642 )
           != pls )
          | ( SV642 = pls ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7711]) ).

thf(7865,plain,
    ! [SV643: $i] :
      ( ( ( ~ ( is_int @ SV643 ) )
        = $true )
      | ( ( ( SV643 != pls )
          | ( ( hAPP_int_int @ bit0 @ SV643 )
            = pls ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7712]) ).

thf(7866,plain,
    ! [SV491: $i,SV321: $i] :
      ( ( ~ ( ~ ! [SY1154: $i,SY1155: $i] :
                  ( ~ ( is_int @ SV321 )
                  | ~ ( is_int @ SV491 )
                  | ~ ( is_int @ SY1154 )
                  | ~ ( is_int @ SY1155 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1154 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1155 ) @ SV491 ) )
                    = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1154 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1155 ) @ SV321 ) ) )
                  | ( SY1154 != SY1155 ) )
            | ~ ! [SY1156: $i,SY1157: $i] :
                  ( ~ ( is_int @ SV321 )
                  | ~ ( is_int @ SV491 )
                  | ~ ( is_int @ SY1156 )
                  | ~ ( is_int @ SY1157 )
                  | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1156 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1157 ) @ SV491 ) )
                    = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1156 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1157 ) @ SV321 ) ) )
                  | ( SV321 != SV491 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[7713]) ).

thf(7867,plain,
    ! [SV491: $i,SV321: $i] :
      ( ( ! [SY1158: $i,SY1159: $i] :
            ( ~ ( is_int @ SV321 )
            | ~ ( is_int @ SV491 )
            | ~ ( is_int @ SY1158 )
            | ~ ( is_int @ SY1159 )
            | ( SY1158 = SY1159 )
            | ( SV321 = SV491 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1158 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1159 ) @ SV491 ) )
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1158 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1159 ) @ SV321 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[7714]) ).

thf(7868,plain,
    ! [SV719: $i,SV644: $i] :
      ( ( ~ ( is_int @ SV644 )
        | ~ ( is_int @ SV719 )
        | ( SV644 != zero_zero_int )
        | ( SV719 != zero_zero_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV644 ) @ SV719 )
          = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7715]) ).

thf(7869,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX0 ) @ SX1 )
             != zero_zero_int )
            | ( SX0 = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7716]) ).

thf(7870,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX0 ) @ SX1 )
             != zero_zero_int )
            | ( SX1 = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7716]) ).

thf(7871,plain,
    ! [SV645: $i,SV720: $i] :
      ( ( ~ ( is_int @ SV720 )
        | ( SV720 = zero_zero_int )
        | ( ( hAPP_int_int @ ( div_mod_int @ SV645 ) @ SV720 )
         != zero_zero_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV645 ) @ ( hAPP_int_int @ uminus_uminus_int @ SV720 ) )
          = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV645 ) @ SV720 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7717]) ).

thf(7872,plain,
    ! [SV646: $i,SV721: $i] :
      ( ( ~ ( is_int @ SV721 )
        | ( SV721 = zero_zero_int )
        | ( ( hAPP_int_int @ ( div_mod_int @ SV646 ) @ SV721 )
          = zero_zero_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV646 ) @ ( hAPP_int_int @ uminus_uminus_int @ SV721 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV646 ) @ SV721 ) ) ) @ one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7718]) ).

thf(7873,plain,
    ! [SV722: $i,SV647: $i] :
      ( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV647 )
         != ( hAPP_nat_int @ semiri1621563631at_int @ SV722 ) )
        | ( SV647 = SV722 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7719]) ).

thf(7874,plain,
    ! [SV723: $i,SV648: $i] :
      ( ( ( SV648 != SV723 )
        | ( ( hAPP_nat_int @ semiri1621563631at_int @ SV648 )
          = ( hAPP_nat_int @ semiri1621563631at_int @ SV723 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7720]) ).

thf(7875,plain,
    ! [SV724: $i,SV322: $i] :
      ( ( ! [SY1266: $i] :
            ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SV724 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SY1266 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV724 ) @ SY1266 ) )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7721]) ).

thf(7876,plain,
    ! [SV322: $i] :
      ( ( ~ ! [SY1027: $i] :
              ( ! [SY1028: $i] :
                  ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1027 ) @ SY1028 ) )
                 != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SY1027 )
                = one_one_int ) )
        | ~ ! [SY1029: $i,SY1030: $i] :
              ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1029 ) @ SY1030 ) )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SY1030 )
                = one_one_int ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[7722]) ).

thf(7877,plain,
    ! [SV649: $i] :
      ( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV649 )
         != zero_zero_int )
        = $true )
      | ( ( SV649 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7723]) ).

thf(7878,plain,
    ! [SV650: $i] :
      ( ( ( SV650 != zero_zero_nat )
        = $true )
      | ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV650 )
          = zero_zero_int )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7724]) ).

thf(7879,plain,
    ! [SV570: $i,SV492: $i,SV323: $i] :
      ( ( ~ ! [SY1189: $i,SY1190: $i] :
              ( ~ ( is_int @ SY1190 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV323 ) @ SV492 ) ) @ SV570 )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1189 ) @ SV492 ) ) @ SY1190 ) )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV323 ) @ SY1189 ) ) @ SV492 ) ) @ SV570 )
                = SY1190 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[7725]) ).

thf(7880,plain,
    ! [SV570: $i,SV492: $i,SV323: $i] :
      ( ( ~ ! [SY1191: $i,SY1192: $i] :
              ( ~ ( is_int @ SY1192 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV323 ) @ SY1191 ) ) @ SV492 ) ) @ SV570 )
               != SY1192 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV323 ) @ SV492 ) ) @ SV570 )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1191 ) @ SV492 ) ) @ SY1192 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[7725]) ).

thf(7881,plain,
    ! [SV651: $i] :
      ( ( ( ~ ( is_int @ SV651 ) )
        = $true )
      | ( ( ! [SY1239: $i] :
              ( ( ( hAPP_int_int @ ( div_mod_int @ SV651 ) @ SY1239 )
               != zero_zero_int )
              | ~ ( ( SV651
                   != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1239 ) @ ( sK12_Q_4 @ SY1239 @ SV651 ) ) )
                  | ~ ( is_int @ ( sK12_Q_4 @ SY1239 @ SV651 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7726]) ).

thf(7882,plain,
    ! [SV652: $i] :
      ( ( ( ~ ( is_int @ SV652 ) )
        = $true )
      | ( ( ! [SY1240: $i] :
              ( ! [SY1241: $i] :
                  ( ( SV652
                   != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1240 ) @ SY1241 ) )
                  | ~ ( is_int @ SY1241 ) )
              | ( ( hAPP_int_int @ ( div_mod_int @ SV652 ) @ SY1240 )
                = zero_zero_int ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7727]) ).

thf(7883,plain,
    ! [SV725: $i,SV653: $i] :
      ( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV653 )
         != ( hAPP_nat_int @ semiri1621563631at_int @ SV725 ) )
        | ( SV653 = SV725 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7728]) ).

thf(7884,plain,
    ! [SV726: $i,SV654: $i] :
      ( ( ( SV654 != SV726 )
        | ( ( hAPP_nat_int @ semiri1621563631at_int @ SV654 )
          = ( hAPP_nat_int @ semiri1621563631at_int @ SV726 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7729]) ).

thf(7885,plain,
    ! [SV727: $i,SV655: $i] :
      ( ( ~ ( is_int @ SV655 )
        | ~ ( is_int @ SV727 )
        | ( ( hAPP_int_int @ bit0 @ SV655 )
         != ( hAPP_int_int @ bit0 @ SV727 ) )
        | ( SV655 = SV727 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7730]) ).

thf(7886,plain,
    ! [SV728: $i,SV656: $i] :
      ( ( ~ ( is_int @ SV656 )
        | ~ ( is_int @ SV728 )
        | ( SV656 != SV728 )
        | ( ( hAPP_int_int @ bit0 @ SV656 )
          = ( hAPP_int_int @ bit0 @ SV728 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7731]) ).

thf(7887,plain,
    ! [SV657: $i] :
      ( ( ( ~ ( is_int @ SV657 ) )
        = $true )
      | ( ( ( min
           != ( hAPP_int_int @ bit1 @ SV657 ) )
          | ( min = SV657 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7732]) ).

thf(7888,plain,
    ! [SV658: $i] :
      ( ( ( ~ ( is_int @ SV658 ) )
        = $true )
      | ( ( ( min != SV658 )
          | ( min
            = ( hAPP_int_int @ bit1 @ SV658 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7733]) ).

thf(7889,plain,
    ! [SV729: $i,SV659: $i] :
      ( ( ( ( hAPP_nat_nat @ suc @ SV659 )
         != ( hAPP_nat_nat @ suc @ SV729 ) )
        | ( SV659 = SV729 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7734]) ).

thf(7890,plain,
    ! [SV730: $i,SV660: $i] :
      ( ( ( SV660 != SV730 )
        | ( ( hAPP_nat_nat @ suc @ SV660 )
          = ( hAPP_nat_nat @ suc @ SV730 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7735]) ).

thf(7891,plain,
    ! [SV661: $i] :
      ( ( ( ~ ( is_int @ SV661 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV661 ) @ SV661 )
           != zero_zero_int )
          | ( SV661 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7736]) ).

thf(7892,plain,
    ! [SV662: $i] :
      ( ( ( ~ ( is_int @ SV662 ) )
        = $true )
      | ( ( ( SV662 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV662 ) @ SV662 )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7737]) ).

thf(7893,plain,
    ! [SV731: $i,SV663: $i] :
      ( ( ~ ( is_int @ SV663 )
        | ~ ( is_int @ SV731 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV663 ) @ SV731 )
         != zero_zero_int )
        | ( SV663 = SV731 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7738]) ).

thf(7894,plain,
    ! [SV732: $i,SV664: $i] :
      ( ( ~ ( is_int @ SV664 )
        | ~ ( is_int @ SV732 )
        | ( SV664 != SV732 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV664 ) @ SV732 )
          = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7739]) ).

thf(7895,plain,
    ! [SV733: $i,SV665: $i] :
      ( ( ~ ( is_int @ SV665 )
        | ~ ( is_int @ SV733 )
        | ( SV665 != SV733 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV665 ) @ SV733 )
          = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7740]) ).

thf(7896,plain,
    ! [SV734: $i,SV666: $i] :
      ( ( ~ ( is_int @ SV666 )
        | ~ ( is_int @ SV734 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV666 ) @ SV734 )
         != zero_zero_int )
        | ( SV666 = SV734 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7741]) ).

thf(7897,plain,
    ! [SV667: $i] :
      ( ( ( ~ ( is_int @ SV667 ) )
        = $true )
      | ( ( ( zero_zero_int
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV667 ) @ SV667 ) )
          | ( SV667 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7742]) ).

thf(7898,plain,
    ! [SV668: $i] :
      ( ( ( ~ ( is_int @ SV668 ) )
        = $true )
      | ( ( ( SV668 != zero_zero_int )
          | ( zero_zero_int
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV668 ) @ SV668 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7743]) ).

thf(7899,plain,
    ! [SV669: $i] :
      ( ( ( ~ ( is_int @ SV669 ) )
        = $true )
      | ( ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV669 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
           != zero_zero_int )
          | ( SV669 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7744]) ).

thf(7900,plain,
    ! [SV670: $i] :
      ( ( ( ~ ( is_int @ SV670 ) )
        = $true )
      | ( ( ( SV670 != zero_zero_int )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV670 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7745]) ).

thf(7901,plain,
    ! [SV671: $i] :
      ( ( ( one_one_nat != SV671 )
        = $true )
      | ( ( SV671 = one_one_nat )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7746]) ).

thf(7902,plain,
    ! [SV672: $i] :
      ( ( ( SV672 != one_one_nat )
        = $true )
      | ( ( one_one_nat = SV672 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7747]) ).

thf(7903,plain,
    ! [SV735: $i,SV673: $i] :
      ( ( ( ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ SV673 ) @ SV735 ) )
         != SV735 )
        | ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ SV673 ) ) @ SV735 )
          = zero_zero_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7748]) ).

thf(7904,plain,
    ! [SV736: $i,SV674: $i] :
      ( ( ( ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ SV674 ) @ SV736 ) )
          = SV736 )
        | ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ SV674 ) ) @ SV736 )
          = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ SV674 ) @ SV736 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7749]) ).

thf(7905,plain,
    ! [SV675: $i] :
      ( ( ( ~ ( is_int @ SV675 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV675 ) @ zero_zero_int )
          = zero_zero_int )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7750]) ).

thf(7906,plain,
    ! [SV676: $i] :
      ( ( ( ~ ( is_int @ SV676 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ SV676 ) @ zero_zero_int )
          = SV676 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7751]) ).

thf(7907,plain,
    ! [SV737: $i,SV677: $i] :
      ( ( ~ ( is_int @ SV677 )
        | ~ ( is_int @ SV737 )
        | ( SV677 != zero_zero_int )
        | ( SV737 != zero_zero_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV677 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV737 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
          = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7752]) ).

thf(7908,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
             != zero_zero_int )
            | ( SX0 = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7753]) ).

thf(7909,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
             != zero_zero_int )
            | ( SX1 = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7753]) ).

thf(7910,plain,
    ! [SV738: $i,SV678: $i] :
      ( ( ~ ( is_int @ SV678 )
        | ~ ( is_int @ SV738 )
        | ( SV678 != zero_zero_int )
        | ( SV738 != zero_zero_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV678 ) @ SV678 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV738 ) @ SV738 ) )
          = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7754]) ).

thf(7911,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX0 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX1 ) @ SX1 ) )
             != zero_zero_int )
            | ( SX0 = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7755]) ).

thf(7912,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX0 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX1 ) @ SX1 ) )
             != zero_zero_int )
            | ( SX1 = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7755]) ).

thf(7913,plain,
    ! [SV739: $i,SV679: $i] :
      ( ( ~ ( is_int @ SV679 )
        | ~ ( is_int @ SV739 )
        | ( SV679 != zero_zero_int )
        | ( SV739 != zero_zero_int )
        | ( ( hAPP_int_int @ ( legacy_zgcd @ SV679 ) @ SV739 )
          = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7756]) ).

thf(7914,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ ( legacy_zgcd @ SX0 ) @ SX1 )
             != zero_zero_int )
            | ( SX0 = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7757]) ).

thf(7915,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ ( legacy_zgcd @ SX0 ) @ SX1 )
             != zero_zero_int )
            | ( SX1 = zero_zero_int ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[7757]) ).

thf(7916,plain,
    ! [SV35: $i,SV338: $i] :
      ( ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV338 ) @ SV35 )
          = zero_zero_int )
        = $false )
      | ( ( SV338 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV338 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[7758]) ).

thf(7917,plain,
    ! [SV339: $i,SV496: $i,SV41: $i] :
      ( ( ( is_int @ SV41 )
        = $false )
      | ( ( ~ ( is_int @ SV496 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV41 ) @ SV339 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV496 ) @ SV339 ) )
          | ( SV41 = SV496 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7759]) ).

thf(7918,plain,
    ! [SV42: $i,SV497: $i,SV340: $i] :
      ( ( ( is_int @ SV340 )
        = $false )
      | ( ( ~ ( is_int @ SV497 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV42 ) @ SV340 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV42 ) @ SV497 ) )
          | ( SV340 = SV497 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7760]) ).

thf(7919,plain,
    ! [SV43: $i,SV498: $i,SV341: $i] :
      ( ( ( is_int @ SV341 )
        = $false )
      | ( ( ~ ( is_int @ SV498 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV43 ) @ SV341 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV43 ) @ SV498 ) )
          | ( SV341 = SV498 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7761]) ).

thf(7920,plain,
    ! [SV79: $i,SV366: $i] :
      ( ( ( is_int @ SV366 )
        = $false )
      | ( ( is_int @ SV79 )
        = $false )
      | ( ( ( SV366 = zero_zero_int )
          | ( SV79 = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV366 ) @ SV79 )
           != zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7762]) ).

thf(7921,plain,
    ! [SV80: $i,SV367: $i] :
      ( ( ( is_int @ SV367 )
        = $false )
      | ( ( is_int @ SV80 )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV80 ) @ SV367 )
           != zero_zero_int )
          | ( SV80 = zero_zero_int )
          | ( SV367 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7763]) ).

thf(7922,plain,
    ! [SV576: $i,SV524: $i,SV680: $i,SV380: $i,SV104: $i] :
      ( ( ( ~ ( is_int @ SV104 )
          | ~ ( is_int @ SV380 )
          | ~ ( is_int @ SV680 ) )
        = $true )
      | ( ( ( SV680 = zero_zero_int )
          | ( SV104 = SV380 )
          | ( SV524 != SV576 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV524 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV680 ) @ SV104 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV576 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV680 ) @ SV380 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7764]) ).

thf(7923,plain,
    ! [SV681: $i,SV581: $i,SV144: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV144 ) @ SV581 )
         != SV681 )
        = $true )
      | ( ( SV144
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV681 ) @ SV581 ) )
        = $true )
      | ( ( is_int @ SV144 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[7765]) ).

thf(7924,plain,
    ! [SV740: $i,SV682: $i,SV582: $i,SV532: $i,SV397: $i,SV145: $i] :
      ( ( ! [SY1267: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV145 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV397 ) @ SV532 ) ) ) @ SV582 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV682 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV397 ) @ SV740 ) ) ) @ SY1267 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV145 ) @ SV582 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV682 ) @ SY1267 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV397 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV532 ) @ SV582 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV740 ) @ SY1267 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7766]) ).

thf(7925,plain,
    ! [SV425: $i,SV541: $i,SV203: $i] :
      ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV203 ) @ SV541 )
         != one_one_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV425 ) @ SV203 ) ) @ SV541 )
          = one_one_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV425 ) @ SV541 )
          = one_one_int )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[7768]) ).

thf(7926,plain,
    ! [SV437: $i,SV221: $i,SV583: $i,SV548: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV548 ) @ SV583 )
          = one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV548 ) @ SV221 ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV583 ) @ SV437 ) )
          = one_one_int )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7771]) ).

thf(7927,plain,
    ! [SV555: $i,SV244: $i,SV454: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV454 ) @ SV244 )
         != one_one_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV454 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV555 ) @ SV244 ) )
          = one_one_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV454 ) @ SV555 )
          = one_one_int )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[7774]) ).

thf(7928,plain,
    ! [SV247: $i,SV585: $i,SV457: $i,SV557: $i] :
      ( ( ( SV557
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV457 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV557 ) @ SV585 ) ) )
        = $true )
      | ( ( ( SV585
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV247 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV557 ) @ SV585 ) ) )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV457 ) @ SV247 )
            = one_one_int ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV557 ) @ SV585 )
          = zero_zero_int )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7777]) ).

thf(7929,plain,
    ! [SV683: $i,SV263: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV263 ) @ SV683 )
          = one_one_int )
        = $false )
      | ( ( ( SV263 = one_one_int )
          | ( SV263
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true )
      | ( ( is_int @ SV263 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[7778]) ).

thf(7930,plain,
    ! [SV564: $i,SV475: $i,SV287: $i,SV741: $i,SV684: $i,SV587: $i] :
      ( ( ! [SY1268: $i,SY1269: $i] :
            ( ( SV587
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV684 ) @ SV741 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1268 ) @ SY1269 ) ) )
            | ( SV287
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV475 ) @ SV741 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV564 ) @ SY1269 ) ) )
            | ( ( hAPP_int_int @ ( div_mod_int @ SV587 ) @ SV287 )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV684 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV587 ) @ SV287 ) ) @ SV475 ) ) ) @ SV741 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1268 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV587 ) @ SV287 ) ) @ SV564 ) ) ) @ SY1269 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7779]) ).

thf(7931,plain,
    ! [SV588: $i] :
      ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ zero_zero_int ) @ SV588 )
          = one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ abs_abs_int @ SV588 )
          = one_one_int )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7781]) ).

thf(7932,plain,
    ! [SV589: $i] :
      ( ( ( ( hAPP_int_int @ abs_abs_int @ SV589 )
          = one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( legacy_zgcd @ zero_zero_int ) @ SV589 )
          = one_one_int )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7782]) ).

thf(7933,plain,
    ! [SV590: $i] :
      ( ( ( is_int @ SV590 )
        = $false )
      | ( ( ( one_one_int != SV590 )
          | ( SV590 = one_one_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7783]) ).

thf(7934,plain,
    ! [SV591: $i] :
      ( ( ( is_int @ SV591 )
        = $false )
      | ( ( ( SV591 != one_one_int )
          | ( one_one_int = SV591 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7784]) ).

thf(7935,plain,
    ! [SV685: $i,SV592: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV592 ) @ SV685 )
         != zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ SV592 ) @ ( hAPP_int_int @ uminus_uminus_int @ SV685 ) )
          = zero_zero_int )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7785]) ).

thf(7936,plain,
    ! [SV686: $i,SV593: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV593 ) @ SV686 )
          = zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ SV593 ) @ ( hAPP_int_int @ uminus_uminus_int @ SV686 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( div_mod_int @ SV593 ) @ SV686 ) ) @ SV686 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7786]) ).

thf(7937,plain,
    ! [SV687: $i,SV594: $i] :
      ( ( ( SV594 != SV687 )
        = $true )
      | ( ( ( image_nat_int @ semiri1621563631at_int @ SV594 )
          = ( image_nat_int @ semiri1621563631at_int @ SV687 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7787]) ).

thf(7938,plain,
    ! [SV688: $i,SV595: $i] :
      ( ( ( ( image_nat_int @ semiri1621563631at_int @ SV595 )
         != ( image_nat_int @ semiri1621563631at_int @ SV688 ) )
        = $true )
      | ( ( SV595 = SV688 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7788]) ).

thf(7939,plain,
    ! [SV597: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV597 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ SV597 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
         != zero_zero_int )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7790]) ).

thf(7940,plain,
    ! [SV598: $i] :
      ( ( ( SV598 = zero_zero_nat )
        = $false )
      | ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ SV598 )
          = one_one_int )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7791]) ).

thf(7941,plain,
    ! [SV600: $i] :
      ( ( ( ( hAPP_int_nat @ number_number_of_nat @ SV600 )
          = zero_zero_nat )
        = $false )
      | ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ zero_zero_int ) @ ( hAPP_int_nat @ number_number_of_nat @ SV600 ) )
          = one_one_int )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7793]) ).

thf(7942,plain,
    ! [SV602: $i] :
      ( ( ( is_int @ SV602 )
        = $false )
      | ( ( ( pls
           != ( hAPP_int_int @ bit0 @ SV602 ) )
          | ( pls = SV602 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7795]) ).

thf(7943,plain,
    ! [SV603: $i] :
      ( ( ( is_int @ SV603 )
        = $false )
      | ( ( ( pls != SV603 )
          | ( pls
            = ( hAPP_int_int @ bit0 @ SV603 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7796]) ).

thf(7944,plain,
    ! [SV689: $i,SV604: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV604 ) @ SV689 )
         != zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ SV604 ) ) @ SV689 )
          = zero_zero_int )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7797]) ).

thf(7945,plain,
    ! [SV690: $i,SV605: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV605 ) @ SV690 )
          = zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ SV605 ) ) @ SV690 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV690 ) @ ( hAPP_int_int @ ( div_mod_int @ SV605 ) @ SV690 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7798]) ).

thf(7946,plain,
    ! [SV691: $i,SV606: $i] :
      ( ( ( ~ ( is_int @ SV606 )
          | ~ ( is_int @ SV691 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV606 ) @ SV691 )
           != zero_zero_int )
          | ( SV606 = zero_zero_int )
          | ( SV691 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7799]) ).

thf(7947,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( SX0 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
            = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7800]) ).

thf(7948,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( SX1 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
            = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7801]) ).

thf(7949,plain,
    ! [SV607: $i] :
      ( ( ( is_int @ SV607 )
        = $false )
      | ( ( ! [SY1209: $i] :
              ( ( ( hAPP_int_nat @ number_number_of_nat @ SY1209 )
                = zero_zero_nat )
              | ( SV607 != zero_zero_int )
              | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV607 ) @ ( hAPP_int_nat @ number_number_of_nat @ SY1209 ) )
                = zero_zero_int ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7802]) ).

thf(7950,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ! [SX1: $i] :
              ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ SX1 ) )
               != zero_zero_int )
              | ( ( hAPP_int_nat @ number_number_of_nat @ SX1 )
               != zero_zero_nat ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7803]) ).

thf(7951,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ! [SX1: $i] :
              ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ SX1 ) )
             != zero_zero_int )
          | ( SX0 = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7804]) ).

thf(7952,plain,
    ! [SV608: $i,SV313: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV313 ) @ SV608 )
          = zero_zero_int )
        = $false )
      | ( ( ~ ( ( SV313
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV608 ) @ ( sK11_Q_4 @ SV608 @ SV313 ) ) )
              | ~ ( is_int @ ( sK11_Q_4 @ SV608 @ SV313 ) ) ) )
        = $true )
      | ( ( is_int @ SV313 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[7805]) ).

thf(7953,plain,
    ! [SV692: $i,SV609: $i] :
      ( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV609 )
         != ( hAPP_nat_int @ semiri1621563631at_int @ SV692 ) )
        = $true )
      | ( ( SV609 = SV692 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7806]) ).

thf(7954,plain,
    ! [SV693: $i,SV610: $i] :
      ( ( ( SV610 != SV693 )
        = $true )
      | ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV610 )
          = ( hAPP_nat_int @ semiri1621563631at_int @ SV693 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7807]) ).

thf(7955,plain,
    ! [SV611: $i] :
      ( ( ( zero_zero_nat = SV611 )
        = $false )
      | ( ( SV611 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7808]) ).

thf(7956,plain,
    ! [SV612: $i] :
      ( ( ( SV612 = zero_zero_nat )
        = $false )
      | ( ( zero_zero_nat = SV612 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7809]) ).

thf(7957,plain,
    ( ( is_int @ sK13_X_1 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7810]) ).

thf(7958,plain,
    ( ( is_int @ sK14_SY716 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7811]) ).

thf(7959,plain,
    ! [SV613: $i,SV694: $i] :
      ( ( ( ~ ( is_int @ SV694 ) )
        = $true )
      | ( ( ( SV694 = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ SV613 ) @ SV694 )
           != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ SV613 ) ) @ SV694 )
            = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV613 ) @ SV694 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7812]) ).

thf(7960,plain,
    ! [SV614: $i,SV695: $i] :
      ( ( ( ~ ( is_int @ SV695 ) )
        = $true )
      | ( ( ( SV695 = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ SV614 ) @ SV695 )
            = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ SV614 ) ) @ SV695 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV614 ) @ SV695 ) ) ) @ one_one_int ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7813]) ).

thf(7961,plain,
    ! [SV615: $i] :
      ( ( ( is_int @ SV615 )
        = $false )
      | ( ( ( ( hAPP_int_int @ abs_abs_int @ SV615 )
           != zero_zero_int )
          | ( SV615 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7814]) ).

thf(7962,plain,
    ! [SV616: $i] :
      ( ( ( is_int @ SV616 )
        = $false )
      | ( ( ( SV616 != zero_zero_int )
          | ( ( hAPP_int_int @ abs_abs_int @ SV616 )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7815]) ).

thf(7963,plain,
    ! [SV617: $i] :
      ( ( ( is_int @ SV617 )
        = $false )
      | ( ( ( ( hAPP_int_int @ bit1 @ SV617 )
           != min )
          | ( SV617 = min ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7816]) ).

thf(7964,plain,
    ! [SV618: $i] :
      ( ( ( is_int @ SV618 )
        = $false )
      | ( ( ( SV618 != min )
          | ( ( hAPP_int_int @ bit1 @ SV618 )
            = min ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7817]) ).

thf(7965,plain,
    ! [SV314: $i,SV486: $i] :
      ( ( ( is_int @ SV486 )
        = $false )
      | ( ( is_int @ SV314 )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 )
            = zero_zero_int )
          | ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK1_A_4 @ SV486 @ SV314 ) )
                                | ~ ( is_int @ ( sK2_SY713 @ SV486 @ SV314 ) ) )
                          | ( SV314
                           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK1_A_4 @ SV486 @ SV314 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 ) ) ) )
                    | ( SV486
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK2_SY713 @ SV486 @ SV314 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 ) ) ) )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( sK1_A_4 @ SV486 @ SV314 ) ) @ ( sK2_SY713 @ SV486 @ SV314 ) )
               != one_one_int ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7818]) ).

thf(7966,plain,
    ! [SV696: $i,SV619: $i] :
      ( ( ( ~ ( is_int @ SV619 )
          | ~ ( is_int @ SV696 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ number_number_of_int @ SV619 )
           != ( hAPP_int_int @ number_number_of_int @ SV696 ) )
          | ( SV619 = SV696 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7819]) ).

thf(7967,plain,
    ! [SV697: $i,SV620: $i] :
      ( ( ( ~ ( is_int @ SV620 )
          | ~ ( is_int @ SV697 ) )
        = $true )
      | ( ( ( SV620 != SV697 )
          | ( ( hAPP_int_int @ number_number_of_int @ SV620 )
            = ( hAPP_int_int @ number_number_of_int @ SV697 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7820]) ).

thf(7968,plain,
    ! [SV698: $i,SV621: $i] :
      ( ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV621 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
         != ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV698 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
        = $true )
      | ( ( ( hAPP_int_int @ abs_abs_int @ SV621 )
          = ( hAPP_int_int @ abs_abs_int @ SV698 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7821]) ).

thf(7969,plain,
    ! [SV699: $i,SV622: $i] :
      ( ( ( ( hAPP_int_int @ abs_abs_int @ SV622 )
         != ( hAPP_int_int @ abs_abs_int @ SV699 ) )
        = $true )
      | ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV622 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV699 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7822]) ).

thf(7970,plain,
    ! [SV623: $i] :
      ( ( ( is_int @ SV623 )
        = $false )
      | ( ( ! [SY1218: $i] :
              ( ( SY1218 = zero_zero_nat )
              | ( SV623 != zero_zero_int )
              | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV623 ) @ SY1218 )
                = zero_zero_int ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7823]) ).

thf(7971,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ! [SX1: $i] :
              ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ SX1 )
               != zero_zero_int )
              | ( SX1 != zero_zero_nat ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7824]) ).

thf(7972,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ! [SX1: $i] :
              ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ SX1 )
             != zero_zero_int )
          | ( SX0 = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7825]) ).

thf(7973,plain,
    ! [SV742: $i,SV487: $i,SV315: $i] :
      ( ( ! [SY1270: $i] :
            ( ~ ( is_int @ SV315 )
            | ~ ( is_int @ SV487 )
            | ~ ( is_int @ SV742 )
            | ~ ( is_int @ SY1270 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV742 ) @ SY1270 ) )
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SY1270 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV742 ) @ SV487 ) ) )
            | ( SV315 = SV742 )
            | ( SV487 = SY1270 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7826]) ).

thf(7974,plain,
    ! [SV487: $i,SV315: $i] :
      ( ( ~ ! [SY1135: $i,SY1136: $i] :
              ( ~ ( is_int @ SV315 )
              | ~ ( is_int @ SV487 )
              | ~ ( is_int @ SY1135 )
              | ~ ( is_int @ SY1136 )
              | ( SV315 != SY1135 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1135 ) @ SY1136 ) )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SY1136 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1135 ) @ SV487 ) ) ) )
        | ~ ! [SY1137: $i,SY1138: $i] :
              ( ~ ( is_int @ SV315 )
              | ~ ( is_int @ SV487 )
              | ~ ( is_int @ SY1137 )
              | ~ ( is_int @ SY1138 )
              | ( SV487 != SY1138 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1137 ) @ SY1138 ) )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SY1138 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1137 ) @ SV487 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[7827]) ).

thf(7975,plain,
    ! [SV700: $i,SV624: $i] :
      ( ( ( ~ ( is_int @ SV624 )
          | ~ ( is_int @ SV700 ) )
        = $true )
      | ( ( ( SV624
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV624 ) @ SV700 ) )
          | ( SV700 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7828]) ).

thf(7976,plain,
    ! [SV701: $i,SV625: $i] :
      ( ( ( ~ ( is_int @ SV625 )
          | ~ ( is_int @ SV701 ) )
        = $true )
      | ( ( ( SV701 != zero_zero_int )
          | ( SV625
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV625 ) @ SV701 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7829]) ).

thf(7977,plain,
    ! [SV702: $i,SV626: $i] :
      ( ( ( ( hAPP_int_nat @ number_number_of_nat @ SV626 )
         != SV702 )
        = $true )
      | ( ( SV702
          = ( hAPP_int_nat @ number_number_of_nat @ SV626 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7830]) ).

thf(7978,plain,
    ! [SV627: $i,SV703: $i] :
      ( ( ( SV703
         != ( hAPP_int_nat @ number_number_of_nat @ SV627 ) )
        = $true )
      | ( ( ( hAPP_int_nat @ number_number_of_nat @ SV627 )
          = SV703 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7831]) ).

thf(7979,plain,
    ! [SV628: $i] :
      ( ( ( is_int @ SV628 )
        = $false )
      | ( ( ( zero_zero_int != SV628 )
          | ( SV628 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7832]) ).

thf(7980,plain,
    ! [SV629: $i] :
      ( ( ( is_int @ SV629 )
        = $false )
      | ( ( ( SV629 != zero_zero_int )
          | ( zero_zero_int = SV629 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7833]) ).

thf(7981,plain,
    ! [SV316: $i,SV743: $i,SV704: $i] :
      ( ( ~ ( is_int @ SV704 )
        | ~ ( is_int @ SV743 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SV704 )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SV743 ) )
        | ( SV704 = SV743 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7834]) ).

thf(7982,plain,
    ! [SV316: $i,SV744: $i,SV705: $i] :
      ( ( ~ ( is_int @ SV705 )
        | ~ ( is_int @ SV744 )
        | ( SV705 != SV744 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SV705 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SV744 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7835]) ).

thf(7983,plain,
    ! [SV706: $i,SV630: $i] :
      ( ( ( ~ ( is_int @ SV630 )
          | ~ ( is_int @ SV706 ) )
        = $true )
      | ( ( ( SV706 = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV706 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV706 ) @ SV630 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV630 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV706 ) @ SV630 ) ) )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7836]) ).

thf(7984,plain,
    ! [SV707: $i,SV631: $i] :
      ( ( ( ~ ( is_int @ SV631 )
          | ~ ( is_int @ SV707 ) )
        = $true )
      | ( ( ( SV631 = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV707 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV707 ) @ SV631 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV631 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV707 ) @ SV631 ) ) )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7837]) ).

thf(7985,plain,
    ! [SV708: $i,SV632: $i] :
      ( ( ( ~ ( is_int @ SV632 )
          | ~ ( is_int @ SV708 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ bit1 @ SV632 )
           != ( hAPP_int_int @ bit1 @ SV708 ) )
          | ( SV632 = SV708 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7838]) ).

thf(7986,plain,
    ! [SV709: $i,SV633: $i] :
      ( ( ( ~ ( is_int @ SV633 )
          | ~ ( is_int @ SV709 ) )
        = $true )
      | ( ( ( SV633 != SV709 )
          | ( ( hAPP_int_int @ bit1 @ SV633 )
            = ( hAPP_int_int @ bit1 @ SV709 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7839]) ).

thf(7987,plain,
    ! [SV710: $i,SV634: $i] :
      ( ( ( ( SV634 != zero_zero_nat )
          | ( SV710 != zero_zero_nat ) )
        = $true )
      | ( ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV634 ) )
          = ( hAPP_nat_int @ semiri1621563631at_int @ SV710 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7840]) ).

thf(7988,plain,
    ( ( ! [SX0: $i] :
          ( ! [SX1: $i] :
              ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SX0 ) )
             != ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
          | ( SX0 = zero_zero_nat ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7841]) ).

thf(7989,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SX0 ) )
           != ( hAPP_nat_int @ semiri1621563631at_int @ SX1 ) )
          | ( SX1 = zero_zero_nat ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7842]) ).

thf(7990,plain,
    ! [SV711: $i,SV635: $i] :
      ( ( ( ~ ( is_int @ SV635 )
          | ~ ( is_int @ SV711 ) )
        = $true )
      | ( ( ( SV711 = zero_zero_int )
          | ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK7_C_3 @ SV711 @ SV635 ) )
                                | ~ ( is_int @ ( sK8_SY715 @ SV711 @ SV635 ) ) )
                          | ( SV711
                           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV711 ) @ SV635 ) ) @ ( sK7_C_3 @ SV711 @ SV635 ) ) ) )
                    | ( SV635
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV711 ) @ SV635 ) ) @ ( sK8_SY715 @ SV711 @ SV635 ) ) ) )
              | ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK7_C_3 @ SV711 @ SV635 ) ) @ ( sK8_SY715 @ SV711 @ SV635 ) )
               != one_one_int ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7843]) ).

thf(7991,plain,
    ! [SV712: $i,SV636: $i] :
      ( ( ( ~ ( is_int @ SV636 )
          | ~ ( is_int @ SV712 ) )
        = $true )
      | ( ( ( SV636 = zero_zero_int )
          | ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK5_C_3 @ SV712 @ SV636 ) )
                                | ~ ( is_int @ ( sK6_SY714 @ SV712 @ SV636 ) ) )
                          | ( SV712
                           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV712 ) @ SV636 ) ) @ ( sK5_C_3 @ SV712 @ SV636 ) ) ) )
                    | ( SV636
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV712 ) @ SV636 ) ) @ ( sK6_SY714 @ SV712 @ SV636 ) ) ) )
              | ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK5_C_3 @ SV712 @ SV636 ) ) @ ( sK6_SY714 @ SV712 @ SV636 ) )
               != one_one_int ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7844]) ).

thf(7992,plain,
    ! [SV637: $i,SV713: $i] :
      ( ( ( ~ ( is_int @ SV713 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ number_number_of_int @ SV637 )
           != SV713 )
          | ( SV713
            = ( hAPP_int_int @ number_number_of_int @ SV637 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7845]) ).

thf(7993,plain,
    ! [SV638: $i,SV714: $i] :
      ( ( ( ~ ( is_int @ SV714 ) )
        = $true )
      | ( ( ( SV714
           != ( hAPP_int_int @ number_number_of_int @ SV638 ) )
          | ( ( hAPP_int_int @ number_number_of_int @ SV638 )
            = SV714 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7846]) ).

thf(7994,plain,
    ! [SV715: $i,SV745: $i,SV317: $i] :
      ( ( ~ ( is_int @ SV317 )
        | ~ ( is_int @ SV745 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV317 ) @ SV715 )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV745 ) @ SV715 ) )
        | ( SV317 = SV745 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7847]) ).

thf(7995,plain,
    ! [SV716: $i,SV746: $i,SV317: $i] :
      ( ( ~ ( is_int @ SV317 )
        | ~ ( is_int @ SV746 )
        | ( SV317 != SV746 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV317 ) @ SV716 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV746 ) @ SV716 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7848]) ).

thf(7996,plain,
    ! [SV717: $i,SV639: $i] :
      ( ( ( ~ ( is_int @ SV639 )
          | ~ ( is_int @ SV717 ) )
        = $true )
      | ( ( ( SV717 = zero_zero_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV717 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV717 ) @ SV639 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV639 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV717 ) @ SV639 ) ) )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7849]) ).

thf(7997,plain,
    ! [SV718: $i,SV640: $i] :
      ( ( ( ~ ( is_int @ SV640 )
          | ~ ( is_int @ SV718 ) )
        = $true )
      | ( ( ( SV640 = zero_zero_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV718 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV718 ) @ SV640 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV640 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV718 ) @ SV640 ) ) )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7850]) ).

thf(7998,plain,
    ! [SV488: $i,SV318: $i,SV569: $i] :
      ( ( ~ ( is_int @ SV569 )
        | ! [SY1185: $i,SY1186: $i] :
            ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV318 ) @ SV488 ) ) @ SV569 )
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1185 ) @ SV488 ) ) @ SY1186 ) )
            | ( SV569
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1185 ) @ SV318 ) ) @ SV488 ) ) @ SY1186 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[7851]) ).

thf(7999,plain,
    ! [SV488: $i,SV318: $i,SV569: $i] :
      ( ( ~ ( is_int @ SV569 )
        | ! [SY1187: $i,SY1188: $i] :
            ( ( SV569
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1187 ) @ SV318 ) ) @ SV488 ) ) @ SY1188 ) )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV318 ) @ SV488 ) ) @ SV569 )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1187 ) @ SV488 ) ) @ SY1188 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[7852]) ).

thf(8000,plain,
    ! [SV489: $i,SV319: $i,SV747: $i] :
      ( ( ! [SY1271: $i] :
            ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV747 ) @ SY1271 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
             != one_one_int )
            | ( ( hAPP_int_int @ abs_abs_int @ SV747 )
             != ( hAPP_int_int @ abs_abs_int @ SV319 ) )
            | ( ( hAPP_int_int @ abs_abs_int @ SV489 )
             != ( hAPP_int_int @ abs_abs_int @ SY1271 ) )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV747 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SY1271 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7853]) ).

thf(8001,plain,
    ! [SV489: $i,SV319: $i] :
      ( ( ~ ! [SY1146: $i,SY1147: $i] :
              ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY1146 ) @ SY1147 )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SY1146 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SY1147 ) ) )
              | ( ( hAPP_int_int @ abs_abs_int @ SY1146 )
                = ( hAPP_int_int @ abs_abs_int @ SV319 ) ) )
        | ~ ! [SY1148: $i,SY1149: $i] :
              ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY1148 ) @ SY1149 )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SY1148 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SY1149 ) ) )
              | ( ( hAPP_int_int @ abs_abs_int @ SV489 )
                = ( hAPP_int_int @ abs_abs_int @ SY1149 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[7854]) ).

thf(8002,plain,
    ! [SV748: $i,SV490: $i,SV320: $i] :
      ( ( ! [SY1272: $i] :
            ( ~ ( is_int @ SV320 )
            | ~ ( is_int @ SV490 )
            | ~ ( is_int @ SV748 )
            | ~ ( is_int @ SY1272 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV748 ) @ SY1272 ) )
            | ( SV320 != SV490 )
            | ( SV748 = SY1272 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7855]) ).

thf(8003,plain,
    ! [SV749: $i,SV490: $i,SV320: $i] :
      ( ( ! [SY1273: $i] :
            ( ~ ( is_int @ SV320 )
            | ~ ( is_int @ SV490 )
            | ~ ( is_int @ SV749 )
            | ~ ( is_int @ SY1273 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV749 ) @ SY1273 ) )
            | ( SV749 != SY1273 )
            | ( SV320 = SV490 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7856]) ).

thf(8004,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                 != one_one_int )
                | ( SX0 = one_one_int )
                | ( SX0
                  = ( hAPP_int_int @ number_number_of_int @ min ) ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                 != one_one_int )
                | ( SX0 = one_one_int )
                | ( SX1
                  = ( hAPP_int_int @ number_number_of_int @ min ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7857]) ).

thf(8005,plain,
    ( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                 != one_one_int )
                | ( SX1 = one_one_int )
                | ( SX0
                  = ( hAPP_int_int @ number_number_of_int @ min ) ) )
          | ~ ! [SX0: $i,SX1: $i] :
                ( ~ ( is_int @ SX0 )
                | ~ ( is_int @ SX1 )
                | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
                 != one_one_int )
                | ( SX1 = one_one_int )
                | ( SX1
                  = ( hAPP_int_int @ number_number_of_int @ min ) ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7858]) ).

thf(8006,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( SX0 != one_one_int )
          | ( SX1 != one_one_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
            = one_one_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7859]) ).

thf(8007,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( SX0
           != ( hAPP_int_int @ number_number_of_int @ min ) )
          | ( SX1
           != ( hAPP_int_int @ number_number_of_int @ min ) )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
            = one_one_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7860]) ).

thf(8008,plain,
    ! [SV641: $i] :
      ( ( ( is_int @ SV641 )
        = $false )
      | ( ( ( ( hAPP_int_int @ abs_abs_int @ SV641 )
           != one_one_int )
          | ( SV641 = one_one_int )
          | ( SV641
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7861]) ).

thf(8009,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ( SX0 != one_one_int )
          | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
            = one_one_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7862]) ).

thf(8010,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_int @ SX0 )
          | ( SX0
           != ( hAPP_int_int @ number_number_of_int @ min ) )
          | ( ( hAPP_int_int @ abs_abs_int @ SX0 )
            = one_one_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7863]) ).

thf(8011,plain,
    ! [SV642: $i] :
      ( ( ( is_int @ SV642 )
        = $false )
      | ( ( ( ( hAPP_int_int @ bit0 @ SV642 )
           != pls )
          | ( SV642 = pls ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7864]) ).

thf(8012,plain,
    ! [SV643: $i] :
      ( ( ( is_int @ SV643 )
        = $false )
      | ( ( ( SV643 != pls )
          | ( ( hAPP_int_int @ bit0 @ SV643 )
            = pls ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7865]) ).

thf(8013,plain,
    ! [SV491: $i,SV321: $i] :
      ( ( ~ ! [SY1154: $i,SY1155: $i] :
              ( ~ ( is_int @ SV321 )
              | ~ ( is_int @ SV491 )
              | ~ ( is_int @ SY1154 )
              | ~ ( is_int @ SY1155 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1154 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1155 ) @ SV491 ) )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1154 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1155 ) @ SV321 ) ) )
              | ( SY1154 != SY1155 ) )
        | ~ ! [SY1156: $i,SY1157: $i] :
              ( ~ ( is_int @ SV321 )
              | ~ ( is_int @ SV491 )
              | ~ ( is_int @ SY1156 )
              | ~ ( is_int @ SY1157 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1156 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1157 ) @ SV491 ) )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1156 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1157 ) @ SV321 ) ) )
              | ( SV321 != SV491 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[7866]) ).

thf(8014,plain,
    ! [SV750: $i,SV491: $i,SV321: $i] :
      ( ( ! [SY1274: $i] :
            ( ~ ( is_int @ SV321 )
            | ~ ( is_int @ SV491 )
            | ~ ( is_int @ SV750 )
            | ~ ( is_int @ SY1274 )
            | ( SV750 = SY1274 )
            | ( SV321 = SV491 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV750 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1274 ) @ SV491 ) )
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV750 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1274 ) @ SV321 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7867]) ).

thf(8015,plain,
    ! [SV719: $i,SV644: $i] :
      ( ( ( ~ ( is_int @ SV644 )
          | ~ ( is_int @ SV719 ) )
        = $true )
      | ( ( ( SV644 != zero_zero_int )
          | ( SV719 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV644 ) @ SV719 )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7868]) ).

thf(8016,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX0 ) @ SX1 )
           != zero_zero_int )
          | ( SX0 = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7869]) ).

thf(8017,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SX0 ) @ SX1 )
           != zero_zero_int )
          | ( SX1 = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7870]) ).

thf(8018,plain,
    ! [SV645: $i,SV720: $i] :
      ( ( ( ~ ( is_int @ SV720 ) )
        = $true )
      | ( ( ( SV720 = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ SV645 ) @ SV720 )
           != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV645 ) @ ( hAPP_int_int @ uminus_uminus_int @ SV720 ) )
            = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV645 ) @ SV720 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7871]) ).

thf(8019,plain,
    ! [SV646: $i,SV721: $i] :
      ( ( ( ~ ( is_int @ SV721 ) )
        = $true )
      | ( ( ( SV721 = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ SV646 ) @ SV721 )
            = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV646 ) @ ( hAPP_int_int @ uminus_uminus_int @ SV721 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV646 ) @ SV721 ) ) ) @ one_one_int ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7872]) ).

thf(8020,plain,
    ! [SV722: $i,SV647: $i] :
      ( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV647 )
         != ( hAPP_nat_int @ semiri1621563631at_int @ SV722 ) )
        = $true )
      | ( ( SV647 = SV722 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7873]) ).

thf(8021,plain,
    ! [SV723: $i,SV648: $i] :
      ( ( ( SV648 != SV723 )
        = $true )
      | ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV648 )
          = ( hAPP_nat_int @ semiri1621563631at_int @ SV723 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7874]) ).

thf(8022,plain,
    ! [SV751: $i,SV724: $i,SV322: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SV724 )
         != one_one_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SV751 )
         != one_one_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV724 ) @ SV751 ) )
          = one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7875]) ).

thf(8023,plain,
    ! [SV322: $i] :
      ( ( ~ ! [SY1027: $i] :
              ( ! [SY1028: $i] :
                  ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1027 ) @ SY1028 ) )
                 != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SY1027 )
                = one_one_int ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[7876]) ).

thf(8024,plain,
    ! [SV322: $i] :
      ( ( ~ ! [SY1029: $i,SY1030: $i] :
              ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1029 ) @ SY1030 ) )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SY1030 )
                = one_one_int ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[7876]) ).

thf(8025,plain,
    ! [SV649: $i] :
      ( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV649 )
          = zero_zero_int )
        = $false )
      | ( ( SV649 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7877]) ).

thf(8026,plain,
    ! [SV650: $i] :
      ( ( ( SV650 = zero_zero_nat )
        = $false )
      | ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV650 )
          = zero_zero_int )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7878]) ).

thf(8027,plain,
    ! [SV570: $i,SV492: $i,SV323: $i] :
      ( ( ! [SY1189: $i,SY1190: $i] :
            ( ~ ( is_int @ SY1190 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV323 ) @ SV492 ) ) @ SV570 )
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1189 ) @ SV492 ) ) @ SY1190 ) )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV323 ) @ SY1189 ) ) @ SV492 ) ) @ SV570 )
              = SY1190 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[7879]) ).

thf(8028,plain,
    ! [SV570: $i,SV492: $i,SV323: $i] :
      ( ( ! [SY1191: $i,SY1192: $i] :
            ( ~ ( is_int @ SY1192 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV323 ) @ SY1191 ) ) @ SV492 ) ) @ SV570 )
             != SY1192 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV323 ) @ SV492 ) ) @ SV570 )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1191 ) @ SV492 ) ) @ SY1192 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[7880]) ).

thf(8029,plain,
    ! [SV651: $i] :
      ( ( ( is_int @ SV651 )
        = $false )
      | ( ( ! [SY1239: $i] :
              ( ( ( hAPP_int_int @ ( div_mod_int @ SV651 ) @ SY1239 )
               != zero_zero_int )
              | ~ ( ( SV651
                   != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1239 ) @ ( sK12_Q_4 @ SY1239 @ SV651 ) ) )
                  | ~ ( is_int @ ( sK12_Q_4 @ SY1239 @ SV651 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7881]) ).

thf(8030,plain,
    ! [SV652: $i] :
      ( ( ( is_int @ SV652 )
        = $false )
      | ( ( ! [SY1240: $i] :
              ( ! [SY1241: $i] :
                  ( ( SV652
                   != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1240 ) @ SY1241 ) )
                  | ~ ( is_int @ SY1241 ) )
              | ( ( hAPP_int_int @ ( div_mod_int @ SV652 ) @ SY1240 )
                = zero_zero_int ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7882]) ).

thf(8031,plain,
    ! [SV725: $i,SV653: $i] :
      ( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV653 )
         != ( hAPP_nat_int @ semiri1621563631at_int @ SV725 ) )
        = $true )
      | ( ( SV653 = SV725 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7883]) ).

thf(8032,plain,
    ! [SV726: $i,SV654: $i] :
      ( ( ( SV654 != SV726 )
        = $true )
      | ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV654 )
          = ( hAPP_nat_int @ semiri1621563631at_int @ SV726 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7884]) ).

thf(8033,plain,
    ! [SV727: $i,SV655: $i] :
      ( ( ( ~ ( is_int @ SV655 )
          | ~ ( is_int @ SV727 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ bit0 @ SV655 )
           != ( hAPP_int_int @ bit0 @ SV727 ) )
          | ( SV655 = SV727 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7885]) ).

thf(8034,plain,
    ! [SV728: $i,SV656: $i] :
      ( ( ( ~ ( is_int @ SV656 )
          | ~ ( is_int @ SV728 ) )
        = $true )
      | ( ( ( SV656 != SV728 )
          | ( ( hAPP_int_int @ bit0 @ SV656 )
            = ( hAPP_int_int @ bit0 @ SV728 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7886]) ).

thf(8035,plain,
    ! [SV657: $i] :
      ( ( ( is_int @ SV657 )
        = $false )
      | ( ( ( min
           != ( hAPP_int_int @ bit1 @ SV657 ) )
          | ( min = SV657 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7887]) ).

thf(8036,plain,
    ! [SV658: $i] :
      ( ( ( is_int @ SV658 )
        = $false )
      | ( ( ( min != SV658 )
          | ( min
            = ( hAPP_int_int @ bit1 @ SV658 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7888]) ).

thf(8037,plain,
    ! [SV729: $i,SV659: $i] :
      ( ( ( ( hAPP_nat_nat @ suc @ SV659 )
         != ( hAPP_nat_nat @ suc @ SV729 ) )
        = $true )
      | ( ( SV659 = SV729 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7889]) ).

thf(8038,plain,
    ! [SV730: $i,SV660: $i] :
      ( ( ( SV660 != SV730 )
        = $true )
      | ( ( ( hAPP_nat_nat @ suc @ SV660 )
          = ( hAPP_nat_nat @ suc @ SV730 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7890]) ).

thf(8039,plain,
    ! [SV661: $i] :
      ( ( ( is_int @ SV661 )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV661 ) @ SV661 )
           != zero_zero_int )
          | ( SV661 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7891]) ).

thf(8040,plain,
    ! [SV662: $i] :
      ( ( ( is_int @ SV662 )
        = $false )
      | ( ( ( SV662 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV662 ) @ SV662 )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7892]) ).

thf(8041,plain,
    ! [SV731: $i,SV663: $i] :
      ( ( ( ~ ( is_int @ SV663 )
          | ~ ( is_int @ SV731 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV663 ) @ SV731 )
           != zero_zero_int )
          | ( SV663 = SV731 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7893]) ).

thf(8042,plain,
    ! [SV732: $i,SV664: $i] :
      ( ( ( ~ ( is_int @ SV664 )
          | ~ ( is_int @ SV732 ) )
        = $true )
      | ( ( ( SV664 != SV732 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV664 ) @ SV732 )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7894]) ).

thf(8043,plain,
    ! [SV733: $i,SV665: $i] :
      ( ( ( ~ ( is_int @ SV665 )
          | ~ ( is_int @ SV733 ) )
        = $true )
      | ( ( ( SV665 != SV733 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV665 ) @ SV733 )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7895]) ).

thf(8044,plain,
    ! [SV734: $i,SV666: $i] :
      ( ( ( ~ ( is_int @ SV666 )
          | ~ ( is_int @ SV734 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV666 ) @ SV734 )
           != zero_zero_int )
          | ( SV666 = SV734 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7896]) ).

thf(8045,plain,
    ! [SV667: $i] :
      ( ( ( is_int @ SV667 )
        = $false )
      | ( ( ( zero_zero_int
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV667 ) @ SV667 ) )
          | ( SV667 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7897]) ).

thf(8046,plain,
    ! [SV668: $i] :
      ( ( ( is_int @ SV668 )
        = $false )
      | ( ( ( SV668 != zero_zero_int )
          | ( zero_zero_int
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV668 ) @ SV668 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7898]) ).

thf(8047,plain,
    ! [SV669: $i] :
      ( ( ( is_int @ SV669 )
        = $false )
      | ( ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV669 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
           != zero_zero_int )
          | ( SV669 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7899]) ).

thf(8048,plain,
    ! [SV670: $i] :
      ( ( ( is_int @ SV670 )
        = $false )
      | ( ( ( SV670 != zero_zero_int )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV670 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7900]) ).

thf(8049,plain,
    ! [SV671: $i] :
      ( ( ( one_one_nat = SV671 )
        = $false )
      | ( ( SV671 = one_one_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7901]) ).

thf(8050,plain,
    ! [SV672: $i] :
      ( ( ( SV672 = one_one_nat )
        = $false )
      | ( ( one_one_nat = SV672 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7902]) ).

thf(8051,plain,
    ! [SV735: $i,SV673: $i] :
      ( ( ( ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ SV673 ) @ SV735 ) )
         != SV735 )
        = $true )
      | ( ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ SV673 ) ) @ SV735 )
          = zero_zero_nat )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7903]) ).

thf(8052,plain,
    ! [SV736: $i,SV674: $i] :
      ( ( ( ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ SV674 ) @ SV736 ) )
          = SV736 )
        = $true )
      | ( ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ SV674 ) ) @ SV736 )
          = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ SV674 ) @ SV736 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7904]) ).

thf(8053,plain,
    ! [SV675: $i] :
      ( ( ( is_int @ SV675 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV675 ) @ zero_zero_int )
          = zero_zero_int )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7905]) ).

thf(8054,plain,
    ! [SV676: $i] :
      ( ( ( is_int @ SV676 )
        = $false )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ SV676 ) @ zero_zero_int )
          = SV676 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7906]) ).

thf(8055,plain,
    ! [SV737: $i,SV677: $i] :
      ( ( ( ~ ( is_int @ SV677 )
          | ~ ( is_int @ SV737 ) )
        = $true )
      | ( ( ( SV677 != zero_zero_int )
          | ( SV737 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV677 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV737 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7907]) ).

thf(8056,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
           != zero_zero_int )
          | ( SX0 = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7908]) ).

thf(8057,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX0 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SX1 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
           != zero_zero_int )
          | ( SX1 = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7909]) ).

thf(8058,plain,
    ! [SV738: $i,SV678: $i] :
      ( ( ( ~ ( is_int @ SV678 )
          | ~ ( is_int @ SV738 ) )
        = $true )
      | ( ( ( SV678 != zero_zero_int )
          | ( SV738 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV678 ) @ SV678 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV738 ) @ SV738 ) )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7910]) ).

thf(8059,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX0 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX1 ) @ SX1 ) )
           != zero_zero_int )
          | ( SX0 = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7911]) ).

thf(8060,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX0 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX1 ) @ SX1 ) )
           != zero_zero_int )
          | ( SX1 = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7912]) ).

thf(8061,plain,
    ! [SV739: $i,SV679: $i] :
      ( ( ( ~ ( is_int @ SV679 )
          | ~ ( is_int @ SV739 ) )
        = $true )
      | ( ( ( SV679 != zero_zero_int )
          | ( SV739 != zero_zero_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ SV679 ) @ SV739 )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7913]) ).

thf(8062,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ SX0 ) @ SX1 )
           != zero_zero_int )
          | ( SX0 = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7914]) ).

thf(8063,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ SX0 ) @ SX1 )
           != zero_zero_int )
          | ( SX1 = zero_zero_int ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[7915]) ).

thf(8064,plain,
    ! [SV339: $i,SV41: $i,SV496: $i] :
      ( ( ( is_int @ SV496 )
        = $false )
      | ( ( is_int @ SV41 )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV41 ) @ SV339 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV496 ) @ SV339 ) )
          | ( SV41 = SV496 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7917]) ).

thf(8065,plain,
    ! [SV42: $i,SV340: $i,SV497: $i] :
      ( ( ( is_int @ SV497 )
        = $false )
      | ( ( is_int @ SV340 )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV42 ) @ SV340 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV42 ) @ SV497 ) )
          | ( SV340 = SV497 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7918]) ).

thf(8066,plain,
    ! [SV43: $i,SV341: $i,SV498: $i] :
      ( ( ( is_int @ SV498 )
        = $false )
      | ( ( is_int @ SV341 )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV43 ) @ SV341 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV43 ) @ SV498 ) )
          | ( SV341 = SV498 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7919]) ).

thf(8067,plain,
    ! [SV79: $i,SV366: $i] :
      ( ( ( SV366 = zero_zero_int )
        = $true )
      | ( ( ( SV79 = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV366 ) @ SV79 )
           != zero_zero_int ) )
        = $true )
      | ( ( is_int @ SV79 )
        = $false )
      | ( ( is_int @ SV366 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[7920]) ).

thf(8068,plain,
    ! [SV367: $i,SV80: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV80 ) @ SV367 )
         != zero_zero_int )
        = $true )
      | ( ( ( SV80 = zero_zero_int )
          | ( SV367 = zero_zero_int ) )
        = $true )
      | ( ( is_int @ SV80 )
        = $false )
      | ( ( is_int @ SV367 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[7921]) ).

thf(8069,plain,
    ! [SV576: $i,SV524: $i,SV680: $i,SV380: $i,SV104: $i] :
      ( ( ( ~ ( is_int @ SV104 )
          | ~ ( is_int @ SV380 ) )
        = $true )
      | ( ( ~ ( is_int @ SV680 ) )
        = $true )
      | ( ( ( SV680 = zero_zero_int )
          | ( SV104 = SV380 )
          | ( SV524 != SV576 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV524 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV680 ) @ SV104 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV576 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV680 ) @ SV380 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7922]) ).

thf(8070,plain,
    ! [SV681: $i,SV581: $i,SV144: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV144 ) @ SV581 )
          = SV681 )
        = $false )
      | ( ( SV144
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV681 ) @ SV581 ) )
        = $true )
      | ( ( is_int @ SV144 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[7923]) ).

thf(8071,plain,
    ! [SV752: $i,SV740: $i,SV682: $i,SV582: $i,SV532: $i,SV397: $i,SV145: $i] :
      ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV145 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV397 ) @ SV532 ) ) ) @ SV582 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV682 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV397 ) @ SV740 ) ) ) @ SV752 ) )
        = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV145 ) @ SV582 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV682 ) @ SV752 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV397 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV532 ) @ SV582 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV740 ) @ SV752 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7924]) ).

thf(8072,plain,
    ! [SV425: $i,SV541: $i,SV203: $i] :
      ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV203 ) @ SV541 )
          = one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV425 ) @ SV203 ) ) @ SV541 )
          = one_one_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV425 ) @ SV541 )
          = one_one_int )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[7925]) ).

thf(8073,plain,
    ! [SV555: $i,SV244: $i,SV454: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV454 ) @ SV244 )
          = one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV454 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV555 ) @ SV244 ) )
          = one_one_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV454 ) @ SV555 )
          = one_one_int )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[7927]) ).

thf(8074,plain,
    ! [SV247: $i,SV585: $i,SV457: $i,SV557: $i] :
      ( ( ( SV557
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV457 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV557 ) @ SV585 ) ) )
        = $false )
      | ( ( ( SV585
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV247 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV557 ) @ SV585 ) ) )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV457 ) @ SV247 )
            = one_one_int ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV557 ) @ SV585 )
          = zero_zero_int )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7928]) ).

thf(8075,plain,
    ! [SV683: $i,SV263: $i] :
      ( ( ( SV263 = one_one_int )
        = $true )
      | ( ( SV263
          = ( hAPP_int_int @ number_number_of_int @ min ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV263 ) @ SV683 )
          = one_one_int )
        = $false )
      | ( ( is_int @ SV263 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[7929]) ).

thf(8076,plain,
    ! [SV564: $i,SV475: $i,SV287: $i,SV753: $i,SV741: $i,SV684: $i,SV587: $i] :
      ( ( ! [SY1275: $i] :
            ( ( SV587
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV684 ) @ SV741 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV753 ) @ SY1275 ) ) )
            | ( SV287
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV475 ) @ SV741 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV564 ) @ SY1275 ) ) )
            | ( ( hAPP_int_int @ ( div_mod_int @ SV587 ) @ SV287 )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV684 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV587 ) @ SV287 ) ) @ SV475 ) ) ) @ SV741 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV753 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV587 ) @ SV287 ) ) @ SV564 ) ) ) @ SY1275 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7930]) ).

thf(8077,plain,
    ! [SV590: $i] :
      ( ( ( one_one_int != SV590 )
        = $true )
      | ( ( SV590 = one_one_int )
        = $true )
      | ( ( is_int @ SV590 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[7933]) ).

thf(8078,plain,
    ! [SV591: $i] :
      ( ( ( SV591 != one_one_int )
        = $true )
      | ( ( one_one_int = SV591 )
        = $true )
      | ( ( is_int @ SV591 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[7934]) ).

thf(8079,plain,
    ! [SV685: $i,SV592: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV592 ) @ SV685 )
          = zero_zero_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ SV592 ) @ ( hAPP_int_int @ uminus_uminus_int @ SV685 ) )
          = zero_zero_int )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7935]) ).

thf(8080,plain,
    ! [SV687: $i,SV594: $i] :
      ( ( ( SV594 = SV687 )
        = $false )
      | ( ( ( image_nat_int @ semiri1621563631at_int @ SV594 )
          = ( image_nat_int @ semiri1621563631at_int @ SV687 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7937]) ).

thf(8081,plain,
    ! [SV688: $i,SV595: $i] :
      ( ( ( ( image_nat_int @ semiri1621563631at_int @ SV595 )
          = ( image_nat_int @ semiri1621563631at_int @ SV688 ) )
        = $false )
      | ( ( SV595 = SV688 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7938]) ).

thf(8082,plain,
    ! [SV597: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV597 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = zero_zero_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ SV597 ) @ ( hAPP_int_int @ number_number_of_int @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = one_one_int )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[7939]) ).

thf(8083,plain,
    ! [SV602: $i] :
      ( ( ( pls
         != ( hAPP_int_int @ bit0 @ SV602 ) )
        = $true )
      | ( ( pls = SV602 )
        = $true )
      | ( ( is_int @ SV602 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[7942]) ).

thf(8084,plain,
    ! [SV603: $i] :
      ( ( ( pls != SV603 )
        = $true )
      | ( ( pls
          = ( hAPP_int_int @ bit0 @ SV603 ) )
        = $true )
      | ( ( is_int @ SV603 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[7943]) ).

thf(8085,plain,
    ! [SV689: $i,SV604: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV604 ) @ SV689 )
          = zero_zero_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ ( hAPP_int_int @ uminus_uminus_int @ SV604 ) ) @ SV689 )
          = zero_zero_int )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7944]) ).

thf(8086,plain,
    ! [SV691: $i,SV606: $i] :
      ( ( ( ~ ( is_int @ SV606 ) )
        = $true )
      | ( ( ~ ( is_int @ SV691 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV606 ) @ SV691 )
           != zero_zero_int )
          | ( SV606 = zero_zero_int )
          | ( SV691 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7946]) ).

thf(8087,plain,
    ! [SV754: $i] :
      ( ( ! [SY1276: $i] :
            ( ~ ( is_int @ SV754 )
            | ~ ( is_int @ SY1276 )
            | ( SV754 != zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV754 ) @ SY1276 )
              = zero_zero_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7947]) ).

thf(8088,plain,
    ! [SV755: $i] :
      ( ( ! [SY1277: $i] :
            ( ~ ( is_int @ SV755 )
            | ~ ( is_int @ SY1277 )
            | ( SY1277 != zero_zero_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV755 ) @ SY1277 )
              = zero_zero_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7948]) ).

thf(8089,plain,
    ! [SV607: $i,SV756: $i] :
      ( ( ( ( ( hAPP_int_nat @ number_number_of_nat @ SV756 )
            = zero_zero_nat )
          | ( SV607 != zero_zero_int )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV607 ) @ ( hAPP_int_nat @ number_number_of_nat @ SV756 ) )
            = zero_zero_int ) )
        = $true )
      | ( ( is_int @ SV607 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[7949]) ).

thf(8090,plain,
    ! [SV757: $i] :
      ( ( ~ ( is_int @ SV757 )
        | ! [SY1278: $i] :
            ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV757 ) @ ( hAPP_int_nat @ number_number_of_nat @ SY1278 ) )
             != zero_zero_int )
            | ( ( hAPP_int_nat @ number_number_of_nat @ SY1278 )
             != zero_zero_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7950]) ).

thf(8091,plain,
    ! [SV758: $i] :
      ( ( ~ ( is_int @ SV758 )
        | ! [SY1279: $i] :
            ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV758 ) @ ( hAPP_int_nat @ number_number_of_nat @ SY1279 ) )
           != zero_zero_int )
        | ( SV758 = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7951]) ).

thf(8092,plain,
    ! [SV608: $i,SV313: $i] :
      ( ( ( ( SV313
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV608 ) @ ( sK11_Q_4 @ SV608 @ SV313 ) ) )
          | ~ ( is_int @ ( sK11_Q_4 @ SV608 @ SV313 ) ) )
        = $false )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ SV313 ) @ SV608 )
          = zero_zero_int )
        = $false )
      | ( ( is_int @ SV313 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[7952]) ).

thf(8093,plain,
    ! [SV692: $i,SV609: $i] :
      ( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV609 )
          = ( hAPP_nat_int @ semiri1621563631at_int @ SV692 ) )
        = $false )
      | ( ( SV609 = SV692 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7953]) ).

thf(8094,plain,
    ! [SV693: $i,SV610: $i] :
      ( ( ( SV610 = SV693 )
        = $false )
      | ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV610 )
          = ( hAPP_nat_int @ semiri1621563631at_int @ SV693 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7954]) ).

thf(8095,plain,
    ! [SV613: $i,SV694: $i] :
      ( ( ( is_int @ SV694 )
        = $false )
      | ( ( ( SV694 = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ SV613 ) @ SV694 )
           != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ SV613 ) ) @ SV694 )
            = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV613 ) @ SV694 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7959]) ).

thf(8096,plain,
    ! [SV614: $i,SV695: $i] :
      ( ( ( is_int @ SV695 )
        = $false )
      | ( ( ( SV695 = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ SV614 ) @ SV695 )
            = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ SV614 ) ) @ SV695 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV614 ) @ SV695 ) ) ) @ one_one_int ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7960]) ).

thf(8097,plain,
    ! [SV615: $i] :
      ( ( ( ( hAPP_int_int @ abs_abs_int @ SV615 )
         != zero_zero_int )
        = $true )
      | ( ( SV615 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV615 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[7961]) ).

thf(8098,plain,
    ! [SV616: $i] :
      ( ( ( SV616 != zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_int @ abs_abs_int @ SV616 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV616 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[7962]) ).

thf(8099,plain,
    ! [SV617: $i] :
      ( ( ( ( hAPP_int_int @ bit1 @ SV617 )
         != min )
        = $true )
      | ( ( SV617 = min )
        = $true )
      | ( ( is_int @ SV617 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[7963]) ).

thf(8100,plain,
    ! [SV618: $i] :
      ( ( ( SV618 != min )
        = $true )
      | ( ( ( hAPP_int_int @ bit1 @ SV618 )
          = min )
        = $true )
      | ( ( is_int @ SV618 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[7964]) ).

thf(8101,plain,
    ! [SV486: $i,SV314: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 )
          = zero_zero_int )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK1_A_4 @ SV486 @ SV314 ) )
                                | ~ ( is_int @ ( sK2_SY713 @ SV486 @ SV314 ) ) )
                          | ( SV314
                           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK1_A_4 @ SV486 @ SV314 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 ) ) ) )
                    | ( SV486
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK2_SY713 @ SV486 @ SV314 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 ) ) ) )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( sK1_A_4 @ SV486 @ SV314 ) ) @ ( sK2_SY713 @ SV486 @ SV314 ) )
               != one_one_int ) ) )
        = $true )
      | ( ( is_int @ SV314 )
        = $false )
      | ( ( is_int @ SV486 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[7965]) ).

thf(8102,plain,
    ! [SV696: $i,SV619: $i] :
      ( ( ( ~ ( is_int @ SV619 ) )
        = $true )
      | ( ( ~ ( is_int @ SV696 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ number_number_of_int @ SV619 )
           != ( hAPP_int_int @ number_number_of_int @ SV696 ) )
          | ( SV619 = SV696 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7966]) ).

thf(8103,plain,
    ! [SV697: $i,SV620: $i] :
      ( ( ( ~ ( is_int @ SV620 ) )
        = $true )
      | ( ( ~ ( is_int @ SV697 ) )
        = $true )
      | ( ( ( SV620 != SV697 )
          | ( ( hAPP_int_int @ number_number_of_int @ SV620 )
            = ( hAPP_int_int @ number_number_of_int @ SV697 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7967]) ).

thf(8104,plain,
    ! [SV698: $i,SV621: $i] :
      ( ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV621 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV698 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
        = $false )
      | ( ( ( hAPP_int_int @ abs_abs_int @ SV621 )
          = ( hAPP_int_int @ abs_abs_int @ SV698 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7968]) ).

thf(8105,plain,
    ! [SV699: $i,SV622: $i] :
      ( ( ( ( hAPP_int_int @ abs_abs_int @ SV622 )
          = ( hAPP_int_int @ abs_abs_int @ SV699 ) )
        = $false )
      | ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV622 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV699 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7969]) ).

thf(8106,plain,
    ! [SV623: $i,SV759: $i] :
      ( ( ( ( SV759 = zero_zero_nat )
          | ( SV623 != zero_zero_int )
          | ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV623 ) @ SV759 )
            = zero_zero_int ) )
        = $true )
      | ( ( is_int @ SV623 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[7970]) ).

thf(8107,plain,
    ! [SV760: $i] :
      ( ( ~ ( is_int @ SV760 )
        | ! [SY1280: $i] :
            ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV760 ) @ SY1280 )
             != zero_zero_int )
            | ( SY1280 != zero_zero_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7971]) ).

thf(8108,plain,
    ! [SV761: $i] :
      ( ( ~ ( is_int @ SV761 )
        | ! [SY1281: $i] :
            ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV761 ) @ SY1281 )
           != zero_zero_int )
        | ( SV761 = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7972]) ).

thf(8109,plain,
    ! [SV762: $i,SV742: $i,SV487: $i,SV315: $i] :
      ( ( ~ ( is_int @ SV315 )
        | ~ ( is_int @ SV487 )
        | ~ ( is_int @ SV742 )
        | ~ ( is_int @ SV762 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV742 ) @ SV762 ) )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV762 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV742 ) @ SV487 ) ) )
        | ( SV315 = SV742 )
        | ( SV487 = SV762 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7973]) ).

thf(8110,plain,
    ! [SV487: $i,SV315: $i] :
      ( ( ~ ! [SY1135: $i,SY1136: $i] :
              ( ~ ( is_int @ SV315 )
              | ~ ( is_int @ SV487 )
              | ~ ( is_int @ SY1135 )
              | ~ ( is_int @ SY1136 )
              | ( SV315 != SY1135 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1135 ) @ SY1136 ) )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SY1136 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1135 ) @ SV487 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[7974]) ).

thf(8111,plain,
    ! [SV487: $i,SV315: $i] :
      ( ( ~ ! [SY1137: $i,SY1138: $i] :
              ( ~ ( is_int @ SV315 )
              | ~ ( is_int @ SV487 )
              | ~ ( is_int @ SY1137 )
              | ~ ( is_int @ SY1138 )
              | ( SV487 != SY1138 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1137 ) @ SY1138 ) )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SY1138 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1137 ) @ SV487 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[7974]) ).

thf(8112,plain,
    ! [SV700: $i,SV624: $i] :
      ( ( ( ~ ( is_int @ SV624 ) )
        = $true )
      | ( ( ~ ( is_int @ SV700 ) )
        = $true )
      | ( ( ( SV624
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV624 ) @ SV700 ) )
          | ( SV700 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7975]) ).

thf(8113,plain,
    ! [SV701: $i,SV625: $i] :
      ( ( ( ~ ( is_int @ SV625 ) )
        = $true )
      | ( ( ~ ( is_int @ SV701 ) )
        = $true )
      | ( ( ( SV701 != zero_zero_int )
          | ( SV625
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV625 ) @ SV701 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7976]) ).

thf(8114,plain,
    ! [SV702: $i,SV626: $i] :
      ( ( ( ( hAPP_int_nat @ number_number_of_nat @ SV626 )
          = SV702 )
        = $false )
      | ( ( SV702
          = ( hAPP_int_nat @ number_number_of_nat @ SV626 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7977]) ).

thf(8115,plain,
    ! [SV627: $i,SV703: $i] :
      ( ( ( SV703
          = ( hAPP_int_nat @ number_number_of_nat @ SV627 ) )
        = $false )
      | ( ( ( hAPP_int_nat @ number_number_of_nat @ SV627 )
          = SV703 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7978]) ).

thf(8116,plain,
    ! [SV628: $i] :
      ( ( ( zero_zero_int != SV628 )
        = $true )
      | ( ( SV628 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV628 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[7979]) ).

thf(8117,plain,
    ! [SV629: $i] :
      ( ( ( SV629 != zero_zero_int )
        = $true )
      | ( ( zero_zero_int = SV629 )
        = $true )
      | ( ( is_int @ SV629 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[7980]) ).

thf(8118,plain,
    ! [SV316: $i,SV743: $i,SV704: $i] :
      ( ( ( ~ ( is_int @ SV704 )
          | ~ ( is_int @ SV743 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SV704 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SV743 ) )
          | ( SV704 = SV743 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7981]) ).

thf(8119,plain,
    ! [SV316: $i,SV744: $i,SV705: $i] :
      ( ( ( ~ ( is_int @ SV705 )
          | ~ ( is_int @ SV744 ) )
        = $true )
      | ( ( ( SV705 != SV744 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SV705 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SV744 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7982]) ).

thf(8120,plain,
    ! [SV706: $i,SV630: $i] :
      ( ( ( ~ ( is_int @ SV630 ) )
        = $true )
      | ( ( ~ ( is_int @ SV706 ) )
        = $true )
      | ( ( ( SV706 = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV706 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV706 ) @ SV630 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV630 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV706 ) @ SV630 ) ) )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7983]) ).

thf(8121,plain,
    ! [SV707: $i,SV631: $i] :
      ( ( ( ~ ( is_int @ SV631 ) )
        = $true )
      | ( ( ~ ( is_int @ SV707 ) )
        = $true )
      | ( ( ( SV631 = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV707 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV707 ) @ SV631 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV631 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV707 ) @ SV631 ) ) )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7984]) ).

thf(8122,plain,
    ! [SV708: $i,SV632: $i] :
      ( ( ( ~ ( is_int @ SV632 ) )
        = $true )
      | ( ( ~ ( is_int @ SV708 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ bit1 @ SV632 )
           != ( hAPP_int_int @ bit1 @ SV708 ) )
          | ( SV632 = SV708 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7985]) ).

thf(8123,plain,
    ! [SV709: $i,SV633: $i] :
      ( ( ( ~ ( is_int @ SV633 ) )
        = $true )
      | ( ( ~ ( is_int @ SV709 ) )
        = $true )
      | ( ( ( SV633 != SV709 )
          | ( ( hAPP_int_int @ bit1 @ SV633 )
            = ( hAPP_int_int @ bit1 @ SV709 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7986]) ).

thf(8124,plain,
    ! [SV710: $i,SV634: $i] :
      ( ( ( SV634 != zero_zero_nat )
        = $true )
      | ( ( SV710 != zero_zero_nat )
        = $true )
      | ( ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV634 ) )
          = ( hAPP_nat_int @ semiri1621563631at_int @ SV710 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7987]) ).

thf(8125,plain,
    ! [SV763: $i] :
      ( ( ! [SY1282: $i] :
            ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV763 ) )
           != ( hAPP_nat_int @ semiri1621563631at_int @ SY1282 ) )
        | ( SV763 = zero_zero_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7988]) ).

thf(8126,plain,
    ! [SV764: $i] :
      ( ( ! [SY1283: $i] :
            ( ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV764 ) )
             != ( hAPP_nat_int @ semiri1621563631at_int @ SY1283 ) )
            | ( SY1283 = zero_zero_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[7989]) ).

thf(8127,plain,
    ! [SV711: $i,SV635: $i] :
      ( ( ( ~ ( is_int @ SV635 ) )
        = $true )
      | ( ( ~ ( is_int @ SV711 ) )
        = $true )
      | ( ( ( SV711 = zero_zero_int )
          | ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK7_C_3 @ SV711 @ SV635 ) )
                                | ~ ( is_int @ ( sK8_SY715 @ SV711 @ SV635 ) ) )
                          | ( SV711
                           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV711 ) @ SV635 ) ) @ ( sK7_C_3 @ SV711 @ SV635 ) ) ) )
                    | ( SV635
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV711 ) @ SV635 ) ) @ ( sK8_SY715 @ SV711 @ SV635 ) ) ) )
              | ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK7_C_3 @ SV711 @ SV635 ) ) @ ( sK8_SY715 @ SV711 @ SV635 ) )
               != one_one_int ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7990]) ).

thf(8128,plain,
    ! [SV712: $i,SV636: $i] :
      ( ( ( ~ ( is_int @ SV636 ) )
        = $true )
      | ( ( ~ ( is_int @ SV712 ) )
        = $true )
      | ( ( ( SV636 = zero_zero_int )
          | ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK5_C_3 @ SV712 @ SV636 ) )
                                | ~ ( is_int @ ( sK6_SY714 @ SV712 @ SV636 ) ) )
                          | ( SV712
                           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV712 ) @ SV636 ) ) @ ( sK5_C_3 @ SV712 @ SV636 ) ) ) )
                    | ( SV636
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV712 ) @ SV636 ) ) @ ( sK6_SY714 @ SV712 @ SV636 ) ) ) )
              | ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK5_C_3 @ SV712 @ SV636 ) ) @ ( sK6_SY714 @ SV712 @ SV636 ) )
               != one_one_int ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7991]) ).

thf(8129,plain,
    ! [SV637: $i,SV713: $i] :
      ( ( ( is_int @ SV713 )
        = $false )
      | ( ( ( ( hAPP_int_int @ number_number_of_int @ SV637 )
           != SV713 )
          | ( SV713
            = ( hAPP_int_int @ number_number_of_int @ SV637 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7992]) ).

thf(8130,plain,
    ! [SV638: $i,SV714: $i] :
      ( ( ( is_int @ SV714 )
        = $false )
      | ( ( ( SV714
           != ( hAPP_int_int @ number_number_of_int @ SV638 ) )
          | ( ( hAPP_int_int @ number_number_of_int @ SV638 )
            = SV714 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[7993]) ).

thf(8131,plain,
    ! [SV715: $i,SV745: $i,SV317: $i] :
      ( ( ( ~ ( is_int @ SV317 )
          | ~ ( is_int @ SV745 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV317 ) @ SV715 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV745 ) @ SV715 ) )
          | ( SV317 = SV745 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7994]) ).

thf(8132,plain,
    ! [SV716: $i,SV746: $i,SV317: $i] :
      ( ( ( ~ ( is_int @ SV317 )
          | ~ ( is_int @ SV746 ) )
        = $true )
      | ( ( ( SV317 != SV746 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV317 ) @ SV716 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV746 ) @ SV716 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7995]) ).

thf(8133,plain,
    ! [SV717: $i,SV639: $i] :
      ( ( ( ~ ( is_int @ SV639 ) )
        = $true )
      | ( ( ~ ( is_int @ SV717 ) )
        = $true )
      | ( ( ( SV717 = zero_zero_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV717 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV717 ) @ SV639 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV639 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV717 ) @ SV639 ) ) )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7996]) ).

thf(8134,plain,
    ! [SV718: $i,SV640: $i] :
      ( ( ( ~ ( is_int @ SV640 ) )
        = $true )
      | ( ( ~ ( is_int @ SV718 ) )
        = $true )
      | ( ( ( SV640 = zero_zero_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV718 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV718 ) @ SV640 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV640 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV718 ) @ SV640 ) ) )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7997]) ).

thf(8135,plain,
    ! [SV488: $i,SV318: $i,SV569: $i] :
      ( ( ( ~ ( is_int @ SV569 ) )
        = $true )
      | ( ( ! [SY1185: $i,SY1186: $i] :
              ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV318 ) @ SV488 ) ) @ SV569 )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1185 ) @ SV488 ) ) @ SY1186 ) )
              | ( SV569
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1185 ) @ SV318 ) ) @ SV488 ) ) @ SY1186 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7998]) ).

thf(8136,plain,
    ! [SV488: $i,SV318: $i,SV569: $i] :
      ( ( ( ~ ( is_int @ SV569 ) )
        = $true )
      | ( ( ! [SY1187: $i,SY1188: $i] :
              ( ( SV569
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1187 ) @ SV318 ) ) @ SV488 ) ) @ SY1188 ) )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV318 ) @ SV488 ) ) @ SV569 )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1187 ) @ SV488 ) ) @ SY1188 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[7999]) ).

thf(8137,plain,
    ! [SV489: $i,SV319: $i,SV765: $i,SV747: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV747 ) @ SV765 )
         != one_one_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
         != one_one_int )
        | ( ( hAPP_int_int @ abs_abs_int @ SV747 )
         != ( hAPP_int_int @ abs_abs_int @ SV319 ) )
        | ( ( hAPP_int_int @ abs_abs_int @ SV489 )
         != ( hAPP_int_int @ abs_abs_int @ SV765 ) )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV747 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV765 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8000]) ).

thf(8138,plain,
    ! [SV489: $i,SV319: $i] :
      ( ( ~ ! [SY1146: $i,SY1147: $i] :
              ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY1146 ) @ SY1147 )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SY1146 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SY1147 ) ) )
              | ( ( hAPP_int_int @ abs_abs_int @ SY1146 )
                = ( hAPP_int_int @ abs_abs_int @ SV319 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[8001]) ).

thf(8139,plain,
    ! [SV489: $i,SV319: $i] :
      ( ( ~ ! [SY1148: $i,SY1149: $i] :
              ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY1148 ) @ SY1149 )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
               != one_one_int )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SY1148 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SY1149 ) ) )
              | ( ( hAPP_int_int @ abs_abs_int @ SV489 )
                = ( hAPP_int_int @ abs_abs_int @ SY1149 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[8001]) ).

thf(8140,plain,
    ! [SV766: $i,SV748: $i,SV490: $i,SV320: $i] :
      ( ( ~ ( is_int @ SV320 )
        | ~ ( is_int @ SV490 )
        | ~ ( is_int @ SV748 )
        | ~ ( is_int @ SV766 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV748 ) @ SV766 ) )
        | ( SV320 != SV490 )
        | ( SV748 = SV766 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8002]) ).

thf(8141,plain,
    ! [SV767: $i,SV749: $i,SV490: $i,SV320: $i] :
      ( ( ~ ( is_int @ SV320 )
        | ~ ( is_int @ SV490 )
        | ~ ( is_int @ SV749 )
        | ~ ( is_int @ SV767 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV749 ) @ SV767 ) )
        | ( SV749 != SV767 )
        | ( SV320 = SV490 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8003]) ).

thf(8142,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
             != one_one_int )
            | ( SX0 = one_one_int )
            | ( SX0
              = ( hAPP_int_int @ number_number_of_int @ min ) ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
             != one_one_int )
            | ( SX0 = one_one_int )
            | ( SX1
              = ( hAPP_int_int @ number_number_of_int @ min ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[8004]) ).

thf(8143,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
             != one_one_int )
            | ( SX1 = one_one_int )
            | ( SX0
              = ( hAPP_int_int @ number_number_of_int @ min ) ) )
      | ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
             != one_one_int )
            | ( SX1 = one_one_int )
            | ( SX1
              = ( hAPP_int_int @ number_number_of_int @ min ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[8005]) ).

thf(8144,plain,
    ! [SV768: $i] :
      ( ( ! [SY1284: $i] :
            ( ~ ( is_int @ SV768 )
            | ~ ( is_int @ SY1284 )
            | ( SV768 != one_one_int )
            | ( SY1284 != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV768 ) @ SY1284 )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8006]) ).

thf(8145,plain,
    ! [SV769: $i] :
      ( ( ! [SY1285: $i] :
            ( ~ ( is_int @ SV769 )
            | ~ ( is_int @ SY1285 )
            | ( SV769
             != ( hAPP_int_int @ number_number_of_int @ min ) )
            | ( SY1285
             != ( hAPP_int_int @ number_number_of_int @ min ) )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV769 ) @ SY1285 )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8007]) ).

thf(8146,plain,
    ! [SV641: $i] :
      ( ( ( ( hAPP_int_int @ abs_abs_int @ SV641 )
         != one_one_int )
        = $true )
      | ( ( ( SV641 = one_one_int )
          | ( SV641
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true )
      | ( ( is_int @ SV641 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8008]) ).

thf(8147,plain,
    ! [SV770: $i] :
      ( ( ~ ( is_int @ SV770 )
        | ( SV770 != one_one_int )
        | ( ( hAPP_int_int @ abs_abs_int @ SV770 )
          = one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8009]) ).

thf(8148,plain,
    ! [SV771: $i] :
      ( ( ~ ( is_int @ SV771 )
        | ( SV771
         != ( hAPP_int_int @ number_number_of_int @ min ) )
        | ( ( hAPP_int_int @ abs_abs_int @ SV771 )
          = one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8010]) ).

thf(8149,plain,
    ! [SV642: $i] :
      ( ( ( ( hAPP_int_int @ bit0 @ SV642 )
         != pls )
        = $true )
      | ( ( SV642 = pls )
        = $true )
      | ( ( is_int @ SV642 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8011]) ).

thf(8150,plain,
    ! [SV643: $i] :
      ( ( ( SV643 != pls )
        = $true )
      | ( ( ( hAPP_int_int @ bit0 @ SV643 )
          = pls )
        = $true )
      | ( ( is_int @ SV643 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8012]) ).

thf(8151,plain,
    ! [SV491: $i,SV321: $i] :
      ( ( ~ ! [SY1154: $i,SY1155: $i] :
              ( ~ ( is_int @ SV321 )
              | ~ ( is_int @ SV491 )
              | ~ ( is_int @ SY1154 )
              | ~ ( is_int @ SY1155 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1154 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1155 ) @ SV491 ) )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1154 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1155 ) @ SV321 ) ) )
              | ( SY1154 != SY1155 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[8013]) ).

thf(8152,plain,
    ! [SV491: $i,SV321: $i] :
      ( ( ~ ! [SY1156: $i,SY1157: $i] :
              ( ~ ( is_int @ SV321 )
              | ~ ( is_int @ SV491 )
              | ~ ( is_int @ SY1156 )
              | ~ ( is_int @ SY1157 )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1156 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1157 ) @ SV491 ) )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1156 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1157 ) @ SV321 ) ) )
              | ( SV321 != SV491 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[8013]) ).

thf(8153,plain,
    ! [SV772: $i,SV750: $i,SV491: $i,SV321: $i] :
      ( ( ~ ( is_int @ SV321 )
        | ~ ( is_int @ SV491 )
        | ~ ( is_int @ SV750 )
        | ~ ( is_int @ SV772 )
        | ( SV750 = SV772 )
        | ( SV321 = SV491 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV750 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV772 ) @ SV491 ) )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV750 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV772 ) @ SV321 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8014]) ).

thf(8154,plain,
    ! [SV719: $i,SV644: $i] :
      ( ( ( ~ ( is_int @ SV644 ) )
        = $true )
      | ( ( ~ ( is_int @ SV719 ) )
        = $true )
      | ( ( ( SV644 != zero_zero_int )
          | ( SV719 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV644 ) @ SV719 )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8015]) ).

thf(8155,plain,
    ! [SV773: $i] :
      ( ( ! [SY1286: $i] :
            ( ~ ( is_int @ SV773 )
            | ~ ( is_int @ SY1286 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV773 ) @ SY1286 )
             != zero_zero_int )
            | ( SV773 = zero_zero_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8016]) ).

thf(8156,plain,
    ! [SV774: $i] :
      ( ( ! [SY1287: $i] :
            ( ~ ( is_int @ SV774 )
            | ~ ( is_int @ SY1287 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV774 ) @ SY1287 )
             != zero_zero_int )
            | ( SY1287 = zero_zero_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8017]) ).

thf(8157,plain,
    ! [SV645: $i,SV720: $i] :
      ( ( ( is_int @ SV720 )
        = $false )
      | ( ( ( SV720 = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ SV645 ) @ SV720 )
           != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV645 ) @ ( hAPP_int_int @ uminus_uminus_int @ SV720 ) )
            = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV645 ) @ SV720 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8018]) ).

thf(8158,plain,
    ! [SV646: $i,SV721: $i] :
      ( ( ( is_int @ SV721 )
        = $false )
      | ( ( ( SV721 = zero_zero_int )
          | ( ( hAPP_int_int @ ( div_mod_int @ SV646 ) @ SV721 )
            = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV646 ) @ ( hAPP_int_int @ uminus_uminus_int @ SV721 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV646 ) @ SV721 ) ) ) @ one_one_int ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8019]) ).

thf(8159,plain,
    ! [SV722: $i,SV647: $i] :
      ( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV647 )
          = ( hAPP_nat_int @ semiri1621563631at_int @ SV722 ) )
        = $false )
      | ( ( SV647 = SV722 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8020]) ).

thf(8160,plain,
    ! [SV723: $i,SV648: $i] :
      ( ( ( SV648 = SV723 )
        = $false )
      | ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV648 )
          = ( hAPP_nat_int @ semiri1621563631at_int @ SV723 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8021]) ).

thf(8161,plain,
    ! [SV751: $i,SV724: $i,SV322: $i] :
      ( ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SV724 )
           != one_one_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SV751 )
           != one_one_int ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV724 ) @ SV751 ) )
          = one_one_int )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8022]) ).

thf(8162,plain,
    ! [SV322: $i] :
      ( ( ! [SY1027: $i] :
            ( ! [SY1028: $i] :
                ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1027 ) @ SY1028 ) )
               != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SY1027 )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[8023]) ).

thf(8163,plain,
    ! [SV322: $i] :
      ( ( ! [SY1029: $i,SY1030: $i] :
            ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1029 ) @ SY1030 ) )
             != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SY1030 )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[8024]) ).

thf(8164,plain,
    ! [SV775: $i,SV570: $i,SV492: $i,SV323: $i] :
      ( ( ! [SY1288: $i] :
            ( ~ ( is_int @ SY1288 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV323 ) @ SV492 ) ) @ SV570 )
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV775 ) @ SV492 ) ) @ SY1288 ) )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV323 ) @ SV775 ) ) @ SV492 ) ) @ SV570 )
              = SY1288 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8027]) ).

thf(8165,plain,
    ! [SV570: $i,SV492: $i,SV776: $i,SV323: $i] :
      ( ( ! [SY1289: $i] :
            ( ~ ( is_int @ SY1289 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV323 ) @ SV776 ) ) @ SV492 ) ) @ SV570 )
             != SY1289 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV323 ) @ SV492 ) ) @ SV570 )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV776 ) @ SV492 ) ) @ SY1289 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8028]) ).

thf(8166,plain,
    ! [SV777: $i,SV651: $i] :
      ( ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV651 ) @ SV777 )
           != zero_zero_int )
          | ~ ( ( SV651
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV777 ) @ ( sK12_Q_4 @ SV777 @ SV651 ) ) )
              | ~ ( is_int @ ( sK12_Q_4 @ SV777 @ SV651 ) ) ) )
        = $true )
      | ( ( is_int @ SV651 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8029]) ).

thf(8167,plain,
    ! [SV778: $i,SV652: $i] :
      ( ( ( ! [SY1290: $i] :
              ( ( SV652
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV778 ) @ SY1290 ) )
              | ~ ( is_int @ SY1290 ) )
          | ( ( hAPP_int_int @ ( div_mod_int @ SV652 ) @ SV778 )
            = zero_zero_int ) )
        = $true )
      | ( ( is_int @ SV652 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8030]) ).

thf(8168,plain,
    ! [SV725: $i,SV653: $i] :
      ( ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV653 )
          = ( hAPP_nat_int @ semiri1621563631at_int @ SV725 ) )
        = $false )
      | ( ( SV653 = SV725 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8031]) ).

thf(8169,plain,
    ! [SV726: $i,SV654: $i] :
      ( ( ( SV654 = SV726 )
        = $false )
      | ( ( ( hAPP_nat_int @ semiri1621563631at_int @ SV654 )
          = ( hAPP_nat_int @ semiri1621563631at_int @ SV726 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8032]) ).

thf(8170,plain,
    ! [SV727: $i,SV655: $i] :
      ( ( ( ~ ( is_int @ SV655 ) )
        = $true )
      | ( ( ~ ( is_int @ SV727 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ bit0 @ SV655 )
           != ( hAPP_int_int @ bit0 @ SV727 ) )
          | ( SV655 = SV727 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8033]) ).

thf(8171,plain,
    ! [SV728: $i,SV656: $i] :
      ( ( ( ~ ( is_int @ SV656 ) )
        = $true )
      | ( ( ~ ( is_int @ SV728 ) )
        = $true )
      | ( ( ( SV656 != SV728 )
          | ( ( hAPP_int_int @ bit0 @ SV656 )
            = ( hAPP_int_int @ bit0 @ SV728 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8034]) ).

thf(8172,plain,
    ! [SV657: $i] :
      ( ( ( min
         != ( hAPP_int_int @ bit1 @ SV657 ) )
        = $true )
      | ( ( min = SV657 )
        = $true )
      | ( ( is_int @ SV657 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8035]) ).

thf(8173,plain,
    ! [SV658: $i] :
      ( ( ( min != SV658 )
        = $true )
      | ( ( min
          = ( hAPP_int_int @ bit1 @ SV658 ) )
        = $true )
      | ( ( is_int @ SV658 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8036]) ).

thf(8174,plain,
    ! [SV729: $i,SV659: $i] :
      ( ( ( ( hAPP_nat_nat @ suc @ SV659 )
          = ( hAPP_nat_nat @ suc @ SV729 ) )
        = $false )
      | ( ( SV659 = SV729 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8037]) ).

thf(8175,plain,
    ! [SV730: $i,SV660: $i] :
      ( ( ( SV660 = SV730 )
        = $false )
      | ( ( ( hAPP_nat_nat @ suc @ SV660 )
          = ( hAPP_nat_nat @ suc @ SV730 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8038]) ).

thf(8176,plain,
    ! [SV661: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV661 ) @ SV661 )
         != zero_zero_int )
        = $true )
      | ( ( SV661 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV661 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8039]) ).

thf(8177,plain,
    ! [SV662: $i] :
      ( ( ( SV662 != zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV662 ) @ SV662 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV662 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8040]) ).

thf(8178,plain,
    ! [SV731: $i,SV663: $i] :
      ( ( ( ~ ( is_int @ SV663 ) )
        = $true )
      | ( ( ~ ( is_int @ SV731 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV663 ) @ SV731 )
           != zero_zero_int )
          | ( SV663 = SV731 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8041]) ).

thf(8179,plain,
    ! [SV732: $i,SV664: $i] :
      ( ( ( ~ ( is_int @ SV664 ) )
        = $true )
      | ( ( ~ ( is_int @ SV732 ) )
        = $true )
      | ( ( ( SV664 != SV732 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV664 ) @ SV732 )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8042]) ).

thf(8180,plain,
    ! [SV733: $i,SV665: $i] :
      ( ( ( ~ ( is_int @ SV665 ) )
        = $true )
      | ( ( ~ ( is_int @ SV733 ) )
        = $true )
      | ( ( ( SV665 != SV733 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV665 ) @ SV733 )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8043]) ).

thf(8181,plain,
    ! [SV734: $i,SV666: $i] :
      ( ( ( ~ ( is_int @ SV666 ) )
        = $true )
      | ( ( ~ ( is_int @ SV734 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV666 ) @ SV734 )
           != zero_zero_int )
          | ( SV666 = SV734 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8044]) ).

thf(8182,plain,
    ! [SV667: $i] :
      ( ( ( zero_zero_int
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV667 ) @ SV667 ) )
        = $true )
      | ( ( SV667 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV667 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8045]) ).

thf(8183,plain,
    ! [SV668: $i] :
      ( ( ( SV668 != zero_zero_int )
        = $true )
      | ( ( zero_zero_int
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV668 ) @ SV668 ) )
        = $true )
      | ( ( is_int @ SV668 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8046]) ).

thf(8184,plain,
    ! [SV669: $i] :
      ( ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV669 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
         != zero_zero_int )
        = $true )
      | ( ( SV669 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV669 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8047]) ).

thf(8185,plain,
    ! [SV670: $i] :
      ( ( ( SV670 != zero_zero_int )
        = $true )
      | ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV670 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV670 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8048]) ).

thf(8186,plain,
    ! [SV735: $i,SV673: $i] :
      ( ( ( ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( div_mod_nat @ SV673 ) @ SV735 ) )
          = SV735 )
        = $false )
      | ( ( ( hAPP_nat_nat @ ( div_mod_nat @ ( hAPP_nat_nat @ suc @ SV673 ) ) @ SV735 )
          = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8051]) ).

thf(8187,plain,
    ! [SV737: $i,SV677: $i] :
      ( ( ( ~ ( is_int @ SV677 ) )
        = $true )
      | ( ( ~ ( is_int @ SV737 ) )
        = $true )
      | ( ( ( SV677 != zero_zero_int )
          | ( SV737 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV677 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV737 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8055]) ).

thf(8188,plain,
    ! [SV779: $i] :
      ( ( ! [SY1291: $i] :
            ( ~ ( is_int @ SV779 )
            | ~ ( is_int @ SY1291 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV779 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY1291 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
             != zero_zero_int )
            | ( SV779 = zero_zero_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8056]) ).

thf(8189,plain,
    ! [SV780: $i] :
      ( ( ! [SY1292: $i] :
            ( ~ ( is_int @ SV780 )
            | ~ ( is_int @ SY1292 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV780 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SY1292 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
             != zero_zero_int )
            | ( SY1292 = zero_zero_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8057]) ).

thf(8190,plain,
    ! [SV738: $i,SV678: $i] :
      ( ( ( ~ ( is_int @ SV678 ) )
        = $true )
      | ( ( ~ ( is_int @ SV738 ) )
        = $true )
      | ( ( ( SV678 != zero_zero_int )
          | ( SV738 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV678 ) @ SV678 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV738 ) @ SV738 ) )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8058]) ).

thf(8191,plain,
    ! [SV781: $i] :
      ( ( ! [SY1293: $i] :
            ( ~ ( is_int @ SV781 )
            | ~ ( is_int @ SY1293 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV781 ) @ SV781 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1293 ) @ SY1293 ) )
             != zero_zero_int )
            | ( SV781 = zero_zero_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8059]) ).

thf(8192,plain,
    ! [SV782: $i] :
      ( ( ! [SY1294: $i] :
            ( ~ ( is_int @ SV782 )
            | ~ ( is_int @ SY1294 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV782 ) @ SV782 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1294 ) @ SY1294 ) )
             != zero_zero_int )
            | ( SY1294 = zero_zero_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8060]) ).

thf(8193,plain,
    ! [SV739: $i,SV679: $i] :
      ( ( ( ~ ( is_int @ SV679 ) )
        = $true )
      | ( ( ~ ( is_int @ SV739 ) )
        = $true )
      | ( ( ( SV679 != zero_zero_int )
          | ( SV739 != zero_zero_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ SV679 ) @ SV739 )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8061]) ).

thf(8194,plain,
    ! [SV783: $i] :
      ( ( ! [SY1295: $i] :
            ( ~ ( is_int @ SV783 )
            | ~ ( is_int @ SY1295 )
            | ( ( hAPP_int_int @ ( legacy_zgcd @ SV783 ) @ SY1295 )
             != zero_zero_int )
            | ( SV783 = zero_zero_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8062]) ).

thf(8195,plain,
    ! [SV784: $i] :
      ( ( ! [SY1296: $i] :
            ( ~ ( is_int @ SV784 )
            | ~ ( is_int @ SY1296 )
            | ( ( hAPP_int_int @ ( legacy_zgcd @ SV784 ) @ SY1296 )
             != zero_zero_int )
            | ( SY1296 = zero_zero_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8063]) ).

thf(8196,plain,
    ! [SV496: $i,SV339: $i,SV41: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV41 ) @ SV339 )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV496 ) @ SV339 ) )
        = $true )
      | ( ( SV41 = SV496 )
        = $true )
      | ( ( is_int @ SV41 )
        = $false )
      | ( ( is_int @ SV496 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8064]) ).

thf(8197,plain,
    ! [SV497: $i,SV340: $i,SV42: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV42 ) @ SV340 )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV42 ) @ SV497 ) )
        = $true )
      | ( ( SV340 = SV497 )
        = $true )
      | ( ( is_int @ SV340 )
        = $false )
      | ( ( is_int @ SV497 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8065]) ).

thf(8198,plain,
    ! [SV498: $i,SV341: $i,SV43: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV43 ) @ SV341 )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV43 ) @ SV498 ) )
        = $true )
      | ( ( SV341 = SV498 )
        = $true )
      | ( ( is_int @ SV341 )
        = $false )
      | ( ( is_int @ SV498 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8066]) ).

thf(8199,plain,
    ! [SV366: $i,SV79: $i] :
      ( ( ( SV79 = zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV366 ) @ SV79 )
         != zero_zero_int )
        = $true )
      | ( ( SV366 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV79 )
        = $false )
      | ( ( is_int @ SV366 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8067]) ).

thf(8200,plain,
    ! [SV367: $i,SV80: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV80 ) @ SV367 )
          = zero_zero_int )
        = $false )
      | ( ( ( SV80 = zero_zero_int )
          | ( SV367 = zero_zero_int ) )
        = $true )
      | ( ( is_int @ SV80 )
        = $false )
      | ( ( is_int @ SV367 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8068]) ).

thf(8201,plain,
    ! [SV576: $i,SV524: $i,SV680: $i,SV380: $i,SV104: $i] :
      ( ( ( ~ ( is_int @ SV104 ) )
        = $true )
      | ( ( ~ ( is_int @ SV380 ) )
        = $true )
      | ( ( ~ ( is_int @ SV680 ) )
        = $true )
      | ( ( ( SV680 = zero_zero_int )
          | ( SV104 = SV380 )
          | ( SV524 != SV576 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV524 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV680 ) @ SV104 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV576 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV680 ) @ SV380 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8069]) ).

thf(8202,plain,
    ! [SV457: $i,SV557: $i,SV247: $i,SV585: $i] :
      ( ( ( SV585
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV247 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV557 ) @ SV585 ) ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV457 ) @ SV247 )
          = one_one_int )
        = $true )
      | ( ( SV557
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV457 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV557 ) @ SV585 ) ) )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV557 ) @ SV585 )
          = zero_zero_int )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8074]) ).

thf(8203,plain,
    ! [SV564: $i,SV475: $i,SV287: $i,SV785: $i,SV753: $i,SV741: $i,SV684: $i,SV587: $i] :
      ( ( ( SV587
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV684 ) @ SV741 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV753 ) @ SV785 ) ) )
        | ( SV287
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV475 ) @ SV741 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV564 ) @ SV785 ) ) )
        | ( ( hAPP_int_int @ ( div_mod_int @ SV587 ) @ SV287 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV684 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV587 ) @ SV287 ) ) @ SV475 ) ) ) @ SV741 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV753 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV587 ) @ SV287 ) ) @ SV564 ) ) ) @ SV785 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8076]) ).

thf(8204,plain,
    ! [SV590: $i] :
      ( ( ( one_one_int = SV590 )
        = $false )
      | ( ( SV590 = one_one_int )
        = $true )
      | ( ( is_int @ SV590 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8077]) ).

thf(8205,plain,
    ! [SV591: $i] :
      ( ( ( SV591 = one_one_int )
        = $false )
      | ( ( one_one_int = SV591 )
        = $true )
      | ( ( is_int @ SV591 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8078]) ).

thf(8206,plain,
    ! [SV602: $i] :
      ( ( ( pls
          = ( hAPP_int_int @ bit0 @ SV602 ) )
        = $false )
      | ( ( pls = SV602 )
        = $true )
      | ( ( is_int @ SV602 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8083]) ).

thf(8207,plain,
    ! [SV603: $i] :
      ( ( ( pls = SV603 )
        = $false )
      | ( ( pls
          = ( hAPP_int_int @ bit0 @ SV603 ) )
        = $true )
      | ( ( is_int @ SV603 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8084]) ).

thf(8208,plain,
    ! [SV691: $i,SV606: $i] :
      ( ( ( is_int @ SV606 )
        = $false )
      | ( ( ~ ( is_int @ SV691 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV606 ) @ SV691 )
           != zero_zero_int )
          | ( SV606 = zero_zero_int )
          | ( SV691 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8086]) ).

thf(8209,plain,
    ! [SV786: $i,SV754: $i] :
      ( ( ~ ( is_int @ SV754 )
        | ~ ( is_int @ SV786 )
        | ( SV754 != zero_zero_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV754 ) @ SV786 )
          = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8087]) ).

thf(8210,plain,
    ! [SV787: $i,SV755: $i] :
      ( ( ~ ( is_int @ SV755 )
        | ~ ( is_int @ SV787 )
        | ( SV787 != zero_zero_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV755 ) @ SV787 )
          = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8088]) ).

thf(8211,plain,
    ! [SV607: $i,SV756: $i] :
      ( ( ( ( ( hAPP_int_nat @ number_number_of_nat @ SV756 )
            = zero_zero_nat )
          | ( SV607 != zero_zero_int ) )
        = $true )
      | ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV607 ) @ ( hAPP_int_nat @ number_number_of_nat @ SV756 ) )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV607 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8089]) ).

thf(8212,plain,
    ! [SV757: $i] :
      ( ( ( ~ ( is_int @ SV757 ) )
        = $true )
      | ( ( ! [SY1278: $i] :
              ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV757 ) @ ( hAPP_int_nat @ number_number_of_nat @ SY1278 ) )
               != zero_zero_int )
              | ( ( hAPP_int_nat @ number_number_of_nat @ SY1278 )
               != zero_zero_nat ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8090]) ).

thf(8213,plain,
    ! [SV758: $i] :
      ( ( ( ~ ( is_int @ SV758 ) )
        = $true )
      | ( ( ! [SY1279: $i] :
              ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV758 ) @ ( hAPP_int_nat @ number_number_of_nat @ SY1279 ) )
             != zero_zero_int )
          | ( SV758 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8091]) ).

thf(8214,plain,
    ! [SV608: $i,SV313: $i] :
      ( ( ( SV313
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV608 ) @ ( sK11_Q_4 @ SV608 @ SV313 ) ) )
        = $false )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ SV313 ) @ SV608 )
          = zero_zero_int )
        = $false )
      | ( ( is_int @ SV313 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[8092]) ).

thf(8215,plain,
    ! [SV313: $i,SV608: $i] :
      ( ( ( ~ ( is_int @ ( sK11_Q_4 @ SV608 @ SV313 ) ) )
        = $false )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ SV313 ) @ SV608 )
          = zero_zero_int )
        = $false )
      | ( ( is_int @ SV313 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[8092]) ).

thf(8216,plain,
    ! [SV613: $i,SV694: $i] :
      ( ( ( SV694 = zero_zero_int )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV613 ) @ SV694 )
           != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ SV613 ) ) @ SV694 )
            = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV613 ) @ SV694 ) ) ) )
        = $true )
      | ( ( is_int @ SV694 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8095]) ).

thf(8217,plain,
    ! [SV614: $i,SV695: $i] :
      ( ( ( SV695 = zero_zero_int )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV614 ) @ SV695 )
            = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ SV614 ) ) @ SV695 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV614 ) @ SV695 ) ) ) @ one_one_int ) ) )
        = $true )
      | ( ( is_int @ SV695 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8096]) ).

thf(8218,plain,
    ! [SV615: $i] :
      ( ( ( ( hAPP_int_int @ abs_abs_int @ SV615 )
          = zero_zero_int )
        = $false )
      | ( ( SV615 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV615 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8097]) ).

thf(8219,plain,
    ! [SV616: $i] :
      ( ( ( SV616 = zero_zero_int )
        = $false )
      | ( ( ( hAPP_int_int @ abs_abs_int @ SV616 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV616 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8098]) ).

thf(8220,plain,
    ! [SV617: $i] :
      ( ( ( ( hAPP_int_int @ bit1 @ SV617 )
          = min )
        = $false )
      | ( ( SV617 = min )
        = $true )
      | ( ( is_int @ SV617 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8099]) ).

thf(8221,plain,
    ! [SV618: $i] :
      ( ( ( SV618 = min )
        = $false )
      | ( ( ( hAPP_int_int @ bit1 @ SV618 )
          = min )
        = $true )
      | ( ( is_int @ SV618 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8100]) ).

thf(8222,plain,
    ! [SV314: $i,SV486: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK1_A_4 @ SV486 @ SV314 ) )
                            | ~ ( is_int @ ( sK2_SY713 @ SV486 @ SV314 ) ) )
                      | ( SV314
                       != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK1_A_4 @ SV486 @ SV314 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 ) ) ) )
                | ( SV486
                 != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK2_SY713 @ SV486 @ SV314 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 ) ) ) )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( sK1_A_4 @ SV486 @ SV314 ) ) @ ( sK2_SY713 @ SV486 @ SV314 ) )
           != one_one_int ) )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV314 )
        = $false )
      | ( ( is_int @ SV486 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8101]) ).

thf(8223,plain,
    ! [SV696: $i,SV619: $i] :
      ( ( ( is_int @ SV619 )
        = $false )
      | ( ( ~ ( is_int @ SV696 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ number_number_of_int @ SV619 )
           != ( hAPP_int_int @ number_number_of_int @ SV696 ) )
          | ( SV619 = SV696 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8102]) ).

thf(8224,plain,
    ! [SV697: $i,SV620: $i] :
      ( ( ( is_int @ SV620 )
        = $false )
      | ( ( ~ ( is_int @ SV697 ) )
        = $true )
      | ( ( ( SV620 != SV697 )
          | ( ( hAPP_int_int @ number_number_of_int @ SV620 )
            = ( hAPP_int_int @ number_number_of_int @ SV697 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8103]) ).

thf(8225,plain,
    ! [SV623: $i,SV759: $i] :
      ( ( ( ( SV759 = zero_zero_nat )
          | ( SV623 != zero_zero_int ) )
        = $true )
      | ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV623 ) @ SV759 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV623 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8106]) ).

thf(8226,plain,
    ! [SV760: $i] :
      ( ( ( ~ ( is_int @ SV760 ) )
        = $true )
      | ( ( ! [SY1280: $i] :
              ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV760 ) @ SY1280 )
               != zero_zero_int )
              | ( SY1280 != zero_zero_nat ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8107]) ).

thf(8227,plain,
    ! [SV761: $i] :
      ( ( ( ~ ( is_int @ SV761 ) )
        = $true )
      | ( ( ! [SY1281: $i] :
              ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV761 ) @ SY1281 )
             != zero_zero_int )
          | ( SV761 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8108]) ).

thf(8228,plain,
    ! [SV762: $i,SV742: $i,SV487: $i,SV315: $i] :
      ( ( ( ~ ( is_int @ SV315 )
          | ~ ( is_int @ SV487 )
          | ~ ( is_int @ SV742 )
          | ~ ( is_int @ SV762 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV742 ) @ SV762 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV762 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV742 ) @ SV487 ) ) )
          | ( SV315 = SV742 )
          | ( SV487 = SV762 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8109]) ).

thf(8229,plain,
    ! [SV487: $i,SV315: $i] :
      ( ( ! [SY1135: $i,SY1136: $i] :
            ( ~ ( is_int @ SV315 )
            | ~ ( is_int @ SV487 )
            | ~ ( is_int @ SY1135 )
            | ~ ( is_int @ SY1136 )
            | ( SV315 != SY1135 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1135 ) @ SY1136 ) )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SY1136 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1135 ) @ SV487 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[8110]) ).

thf(8230,plain,
    ! [SV487: $i,SV315: $i] :
      ( ( ! [SY1137: $i,SY1138: $i] :
            ( ~ ( is_int @ SV315 )
            | ~ ( is_int @ SV487 )
            | ~ ( is_int @ SY1137 )
            | ~ ( is_int @ SY1138 )
            | ( SV487 != SY1138 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1137 ) @ SY1138 ) )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SY1138 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1137 ) @ SV487 ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[8111]) ).

thf(8231,plain,
    ! [SV700: $i,SV624: $i] :
      ( ( ( is_int @ SV624 )
        = $false )
      | ( ( ~ ( is_int @ SV700 ) )
        = $true )
      | ( ( ( SV624
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV624 ) @ SV700 ) )
          | ( SV700 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8112]) ).

thf(8232,plain,
    ! [SV701: $i,SV625: $i] :
      ( ( ( is_int @ SV625 )
        = $false )
      | ( ( ~ ( is_int @ SV701 ) )
        = $true )
      | ( ( ( SV701 != zero_zero_int )
          | ( SV625
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV625 ) @ SV701 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8113]) ).

thf(8233,plain,
    ! [SV628: $i] :
      ( ( ( zero_zero_int = SV628 )
        = $false )
      | ( ( SV628 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV628 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8116]) ).

thf(8234,plain,
    ! [SV629: $i] :
      ( ( ( SV629 = zero_zero_int )
        = $false )
      | ( ( zero_zero_int = SV629 )
        = $true )
      | ( ( is_int @ SV629 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8117]) ).

thf(8235,plain,
    ! [SV316: $i,SV743: $i,SV704: $i] :
      ( ( ( ~ ( is_int @ SV704 ) )
        = $true )
      | ( ( ~ ( is_int @ SV743 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SV704 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SV743 ) )
          | ( SV704 = SV743 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8118]) ).

thf(8236,plain,
    ! [SV316: $i,SV744: $i,SV705: $i] :
      ( ( ( ~ ( is_int @ SV705 ) )
        = $true )
      | ( ( ~ ( is_int @ SV744 ) )
        = $true )
      | ( ( ( SV705 != SV744 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SV705 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SV744 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8119]) ).

thf(8237,plain,
    ! [SV706: $i,SV630: $i] :
      ( ( ( is_int @ SV630 )
        = $false )
      | ( ( ~ ( is_int @ SV706 ) )
        = $true )
      | ( ( ( SV706 = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV706 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV706 ) @ SV630 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV630 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV706 ) @ SV630 ) ) )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8120]) ).

thf(8238,plain,
    ! [SV707: $i,SV631: $i] :
      ( ( ( is_int @ SV631 )
        = $false )
      | ( ( ~ ( is_int @ SV707 ) )
        = $true )
      | ( ( ( SV631 = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV707 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV707 ) @ SV631 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV631 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV707 ) @ SV631 ) ) )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8121]) ).

thf(8239,plain,
    ! [SV708: $i,SV632: $i] :
      ( ( ( is_int @ SV632 )
        = $false )
      | ( ( ~ ( is_int @ SV708 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ bit1 @ SV632 )
           != ( hAPP_int_int @ bit1 @ SV708 ) )
          | ( SV632 = SV708 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8122]) ).

thf(8240,plain,
    ! [SV709: $i,SV633: $i] :
      ( ( ( is_int @ SV633 )
        = $false )
      | ( ( ~ ( is_int @ SV709 ) )
        = $true )
      | ( ( ( SV633 != SV709 )
          | ( ( hAPP_int_int @ bit1 @ SV633 )
            = ( hAPP_int_int @ bit1 @ SV709 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8123]) ).

thf(8241,plain,
    ! [SV710: $i,SV634: $i] :
      ( ( ( SV634 = zero_zero_nat )
        = $false )
      | ( ( SV710 != zero_zero_nat )
        = $true )
      | ( ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV634 ) )
          = ( hAPP_nat_int @ semiri1621563631at_int @ SV710 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8124]) ).

thf(8242,plain,
    ! [SV763: $i] :
      ( ( ( ! [SY1282: $i] :
              ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV763 ) )
             != ( hAPP_nat_int @ semiri1621563631at_int @ SY1282 ) ) )
        = $true )
      | ( ( SV763 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8125]) ).

thf(8243,plain,
    ! [SV788: $i,SV764: $i] :
      ( ( ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV764 ) )
         != ( hAPP_nat_int @ semiri1621563631at_int @ SV788 ) )
        | ( SV788 = zero_zero_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8126]) ).

thf(8244,plain,
    ! [SV711: $i,SV635: $i] :
      ( ( ( is_int @ SV635 )
        = $false )
      | ( ( ~ ( is_int @ SV711 ) )
        = $true )
      | ( ( ( SV711 = zero_zero_int )
          | ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK7_C_3 @ SV711 @ SV635 ) )
                                | ~ ( is_int @ ( sK8_SY715 @ SV711 @ SV635 ) ) )
                          | ( SV711
                           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV711 ) @ SV635 ) ) @ ( sK7_C_3 @ SV711 @ SV635 ) ) ) )
                    | ( SV635
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV711 ) @ SV635 ) ) @ ( sK8_SY715 @ SV711 @ SV635 ) ) ) )
              | ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK7_C_3 @ SV711 @ SV635 ) ) @ ( sK8_SY715 @ SV711 @ SV635 ) )
               != one_one_int ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8127]) ).

thf(8245,plain,
    ! [SV712: $i,SV636: $i] :
      ( ( ( is_int @ SV636 )
        = $false )
      | ( ( ~ ( is_int @ SV712 ) )
        = $true )
      | ( ( ( SV636 = zero_zero_int )
          | ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK5_C_3 @ SV712 @ SV636 ) )
                                | ~ ( is_int @ ( sK6_SY714 @ SV712 @ SV636 ) ) )
                          | ( SV712
                           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV712 ) @ SV636 ) ) @ ( sK5_C_3 @ SV712 @ SV636 ) ) ) )
                    | ( SV636
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV712 ) @ SV636 ) ) @ ( sK6_SY714 @ SV712 @ SV636 ) ) ) )
              | ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK5_C_3 @ SV712 @ SV636 ) ) @ ( sK6_SY714 @ SV712 @ SV636 ) )
               != one_one_int ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8128]) ).

thf(8246,plain,
    ! [SV713: $i,SV637: $i] :
      ( ( ( ( hAPP_int_int @ number_number_of_int @ SV637 )
         != SV713 )
        = $true )
      | ( ( SV713
          = ( hAPP_int_int @ number_number_of_int @ SV637 ) )
        = $true )
      | ( ( is_int @ SV713 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8129]) ).

thf(8247,plain,
    ! [SV638: $i,SV714: $i] :
      ( ( ( SV714
         != ( hAPP_int_int @ number_number_of_int @ SV638 ) )
        = $true )
      | ( ( ( hAPP_int_int @ number_number_of_int @ SV638 )
          = SV714 )
        = $true )
      | ( ( is_int @ SV714 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8130]) ).

thf(8248,plain,
    ! [SV715: $i,SV745: $i,SV317: $i] :
      ( ( ( ~ ( is_int @ SV317 ) )
        = $true )
      | ( ( ~ ( is_int @ SV745 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV317 ) @ SV715 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV745 ) @ SV715 ) )
          | ( SV317 = SV745 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8131]) ).

thf(8249,plain,
    ! [SV716: $i,SV746: $i,SV317: $i] :
      ( ( ( ~ ( is_int @ SV317 ) )
        = $true )
      | ( ( ~ ( is_int @ SV746 ) )
        = $true )
      | ( ( ( SV317 != SV746 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV317 ) @ SV716 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV746 ) @ SV716 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8132]) ).

thf(8250,plain,
    ! [SV717: $i,SV639: $i] :
      ( ( ( is_int @ SV639 )
        = $false )
      | ( ( ~ ( is_int @ SV717 ) )
        = $true )
      | ( ( ( SV717 = zero_zero_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV717 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV717 ) @ SV639 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV639 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV717 ) @ SV639 ) ) )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8133]) ).

thf(8251,plain,
    ! [SV718: $i,SV640: $i] :
      ( ( ( is_int @ SV640 )
        = $false )
      | ( ( ~ ( is_int @ SV718 ) )
        = $true )
      | ( ( ( SV640 = zero_zero_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV718 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV718 ) @ SV640 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV640 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV718 ) @ SV640 ) ) )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8134]) ).

thf(8252,plain,
    ! [SV488: $i,SV318: $i,SV569: $i] :
      ( ( ( is_int @ SV569 )
        = $false )
      | ( ( ! [SY1185: $i,SY1186: $i] :
              ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV318 ) @ SV488 ) ) @ SV569 )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1185 ) @ SV488 ) ) @ SY1186 ) )
              | ( SV569
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1185 ) @ SV318 ) ) @ SV488 ) ) @ SY1186 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8135]) ).

thf(8253,plain,
    ! [SV488: $i,SV318: $i,SV569: $i] :
      ( ( ( is_int @ SV569 )
        = $false )
      | ( ( ! [SY1187: $i,SY1188: $i] :
              ( ( SV569
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SY1187 ) @ SV318 ) ) @ SV488 ) ) @ SY1188 ) )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV318 ) @ SV488 ) ) @ SV569 )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1187 ) @ SV488 ) ) @ SY1188 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8136]) ).

thf(8254,plain,
    ! [SV489: $i,SV319: $i,SV765: $i,SV747: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV747 ) @ SV765 )
         != one_one_int )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
           != one_one_int )
          | ( ( hAPP_int_int @ abs_abs_int @ SV747 )
           != ( hAPP_int_int @ abs_abs_int @ SV319 ) )
          | ( ( hAPP_int_int @ abs_abs_int @ SV489 )
           != ( hAPP_int_int @ abs_abs_int @ SV765 ) )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV747 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV765 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8137]) ).

thf(8255,plain,
    ! [SV489: $i,SV319: $i] :
      ( ( ! [SY1146: $i,SY1147: $i] :
            ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY1146 ) @ SY1147 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SY1146 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SY1147 ) ) )
            | ( ( hAPP_int_int @ abs_abs_int @ SY1146 )
              = ( hAPP_int_int @ abs_abs_int @ SV319 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[8138]) ).

thf(8256,plain,
    ! [SV489: $i,SV319: $i] :
      ( ( ! [SY1148: $i,SY1149: $i] :
            ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SY1148 ) @ SY1149 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SY1148 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SY1149 ) ) )
            | ( ( hAPP_int_int @ abs_abs_int @ SV489 )
              = ( hAPP_int_int @ abs_abs_int @ SY1149 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[8139]) ).

thf(8257,plain,
    ! [SV766: $i,SV748: $i,SV490: $i,SV320: $i] :
      ( ( ( ~ ( is_int @ SV320 )
          | ~ ( is_int @ SV490 )
          | ~ ( is_int @ SV748 )
          | ~ ( is_int @ SV766 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV748 ) @ SV766 ) )
          | ( SV320 != SV490 )
          | ( SV748 = SV766 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8140]) ).

thf(8258,plain,
    ! [SV767: $i,SV749: $i,SV490: $i,SV320: $i] :
      ( ( ( ~ ( is_int @ SV320 )
          | ~ ( is_int @ SV490 )
          | ~ ( is_int @ SV749 )
          | ~ ( is_int @ SV767 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV749 ) @ SV767 ) )
          | ( SV749 != SV767 )
          | ( SV320 = SV490 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8141]) ).

thf(8259,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
             != one_one_int )
            | ( SX0 = one_one_int )
            | ( SX0
              = ( hAPP_int_int @ number_number_of_int @ min ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[8142]) ).

thf(8260,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
             != one_one_int )
            | ( SX0 = one_one_int )
            | ( SX1
              = ( hAPP_int_int @ number_number_of_int @ min ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[8142]) ).

thf(8261,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
             != one_one_int )
            | ( SX1 = one_one_int )
            | ( SX0
              = ( hAPP_int_int @ number_number_of_int @ min ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[8143]) ).

thf(8262,plain,
    ( ( ~ ! [SX0: $i,SX1: $i] :
            ( ~ ( is_int @ SX0 )
            | ~ ( is_int @ SX1 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
             != one_one_int )
            | ( SX1 = one_one_int )
            | ( SX1
              = ( hAPP_int_int @ number_number_of_int @ min ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[8143]) ).

thf(8263,plain,
    ! [SV789: $i,SV768: $i] :
      ( ( ~ ( is_int @ SV768 )
        | ~ ( is_int @ SV789 )
        | ( SV768 != one_one_int )
        | ( SV789 != one_one_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV768 ) @ SV789 )
          = one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8144]) ).

thf(8264,plain,
    ! [SV790: $i,SV769: $i] :
      ( ( ~ ( is_int @ SV769 )
        | ~ ( is_int @ SV790 )
        | ( SV769
         != ( hAPP_int_int @ number_number_of_int @ min ) )
        | ( SV790
         != ( hAPP_int_int @ number_number_of_int @ min ) )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV769 ) @ SV790 )
          = one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8145]) ).

thf(8265,plain,
    ! [SV641: $i] :
      ( ( ( ( hAPP_int_int @ abs_abs_int @ SV641 )
          = one_one_int )
        = $false )
      | ( ( ( SV641 = one_one_int )
          | ( SV641
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true )
      | ( ( is_int @ SV641 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8146]) ).

thf(8266,plain,
    ! [SV770: $i] :
      ( ( ( ~ ( is_int @ SV770 ) )
        = $true )
      | ( ( ( SV770 != one_one_int )
          | ( ( hAPP_int_int @ abs_abs_int @ SV770 )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8147]) ).

thf(8267,plain,
    ! [SV771: $i] :
      ( ( ( ~ ( is_int @ SV771 ) )
        = $true )
      | ( ( ( SV771
           != ( hAPP_int_int @ number_number_of_int @ min ) )
          | ( ( hAPP_int_int @ abs_abs_int @ SV771 )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8148]) ).

thf(8268,plain,
    ! [SV642: $i] :
      ( ( ( ( hAPP_int_int @ bit0 @ SV642 )
          = pls )
        = $false )
      | ( ( SV642 = pls )
        = $true )
      | ( ( is_int @ SV642 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8149]) ).

thf(8269,plain,
    ! [SV643: $i] :
      ( ( ( SV643 = pls )
        = $false )
      | ( ( ( hAPP_int_int @ bit0 @ SV643 )
          = pls )
        = $true )
      | ( ( is_int @ SV643 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8150]) ).

thf(8270,plain,
    ! [SV491: $i,SV321: $i] :
      ( ( ! [SY1154: $i,SY1155: $i] :
            ( ~ ( is_int @ SV321 )
            | ~ ( is_int @ SV491 )
            | ~ ( is_int @ SY1154 )
            | ~ ( is_int @ SY1155 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1154 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1155 ) @ SV491 ) )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1154 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1155 ) @ SV321 ) ) )
            | ( SY1154 != SY1155 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[8151]) ).

thf(8271,plain,
    ! [SV491: $i,SV321: $i] :
      ( ( ! [SY1156: $i,SY1157: $i] :
            ( ~ ( is_int @ SV321 )
            | ~ ( is_int @ SV491 )
            | ~ ( is_int @ SY1156 )
            | ~ ( is_int @ SY1157 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1156 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1157 ) @ SV491 ) )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1156 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1157 ) @ SV321 ) ) )
            | ( SV321 != SV491 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[8152]) ).

thf(8272,plain,
    ! [SV772: $i,SV750: $i,SV491: $i,SV321: $i] :
      ( ( ( ~ ( is_int @ SV321 )
          | ~ ( is_int @ SV491 )
          | ~ ( is_int @ SV750 )
          | ~ ( is_int @ SV772 ) )
        = $true )
      | ( ( ( SV750 = SV772 )
          | ( SV321 = SV491 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV750 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV772 ) @ SV491 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV750 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV772 ) @ SV321 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8153]) ).

thf(8273,plain,
    ! [SV719: $i,SV644: $i] :
      ( ( ( is_int @ SV644 )
        = $false )
      | ( ( ~ ( is_int @ SV719 ) )
        = $true )
      | ( ( ( SV644 != zero_zero_int )
          | ( SV719 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV644 ) @ SV719 )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8154]) ).

thf(8274,plain,
    ! [SV791: $i,SV773: $i] :
      ( ( ~ ( is_int @ SV773 )
        | ~ ( is_int @ SV791 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV773 ) @ SV791 )
         != zero_zero_int )
        | ( SV773 = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8155]) ).

thf(8275,plain,
    ! [SV792: $i,SV774: $i] :
      ( ( ~ ( is_int @ SV774 )
        | ~ ( is_int @ SV792 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV774 ) @ SV792 )
         != zero_zero_int )
        | ( SV792 = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8156]) ).

thf(8276,plain,
    ! [SV645: $i,SV720: $i] :
      ( ( ( SV720 = zero_zero_int )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV645 ) @ SV720 )
           != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV645 ) @ ( hAPP_int_int @ uminus_uminus_int @ SV720 ) )
            = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV645 ) @ SV720 ) ) ) )
        = $true )
      | ( ( is_int @ SV720 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8157]) ).

thf(8277,plain,
    ! [SV646: $i,SV721: $i] :
      ( ( ( SV721 = zero_zero_int )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV646 ) @ SV721 )
            = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV646 ) @ ( hAPP_int_int @ uminus_uminus_int @ SV721 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV646 ) @ SV721 ) ) ) @ one_one_int ) ) )
        = $true )
      | ( ( is_int @ SV721 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8158]) ).

thf(8278,plain,
    ! [SV751: $i,SV724: $i,SV322: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SV724 )
         != one_one_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SV751 )
         != one_one_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV724 ) @ SV751 ) )
          = one_one_int )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8161]) ).

thf(8279,plain,
    ! [SV793: $i,SV322: $i] :
      ( ( ! [SY1297: $i] :
            ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV793 ) @ SY1297 ) )
           != one_one_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SV793 )
          = one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8162]) ).

thf(8280,plain,
    ! [SV794: $i,SV322: $i] :
      ( ( ! [SY1298: $i] :
            ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV794 ) @ SY1298 ) )
             != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SY1298 )
              = one_one_int ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8163]) ).

thf(8281,plain,
    ! [SV775: $i,SV570: $i,SV492: $i,SV323: $i,SV795: $i] :
      ( ( ~ ( is_int @ SV795 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV323 ) @ SV492 ) ) @ SV570 )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV775 ) @ SV492 ) ) @ SV795 ) )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV323 ) @ SV775 ) ) @ SV492 ) ) @ SV570 )
          = SV795 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8164]) ).

thf(8282,plain,
    ! [SV570: $i,SV492: $i,SV776: $i,SV323: $i,SV796: $i] :
      ( ( ~ ( is_int @ SV796 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV323 ) @ SV776 ) ) @ SV492 ) ) @ SV570 )
         != SV796 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV323 ) @ SV492 ) ) @ SV570 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV776 ) @ SV492 ) ) @ SV796 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8165]) ).

thf(8283,plain,
    ! [SV777: $i,SV651: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV651 ) @ SV777 )
         != zero_zero_int )
        = $true )
      | ( ( ~ ( ( SV651
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV777 ) @ ( sK12_Q_4 @ SV777 @ SV651 ) ) )
              | ~ ( is_int @ ( sK12_Q_4 @ SV777 @ SV651 ) ) ) )
        = $true )
      | ( ( is_int @ SV651 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8166]) ).

thf(8284,plain,
    ! [SV778: $i,SV652: $i] :
      ( ( ( ! [SY1290: $i] :
              ( ( SV652
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV778 ) @ SY1290 ) )
              | ~ ( is_int @ SY1290 ) ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ SV652 ) @ SV778 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV652 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8167]) ).

thf(8285,plain,
    ! [SV727: $i,SV655: $i] :
      ( ( ( is_int @ SV655 )
        = $false )
      | ( ( ~ ( is_int @ SV727 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ bit0 @ SV655 )
           != ( hAPP_int_int @ bit0 @ SV727 ) )
          | ( SV655 = SV727 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8170]) ).

thf(8286,plain,
    ! [SV728: $i,SV656: $i] :
      ( ( ( is_int @ SV656 )
        = $false )
      | ( ( ~ ( is_int @ SV728 ) )
        = $true )
      | ( ( ( SV656 != SV728 )
          | ( ( hAPP_int_int @ bit0 @ SV656 )
            = ( hAPP_int_int @ bit0 @ SV728 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8171]) ).

thf(8287,plain,
    ! [SV657: $i] :
      ( ( ( min
          = ( hAPP_int_int @ bit1 @ SV657 ) )
        = $false )
      | ( ( min = SV657 )
        = $true )
      | ( ( is_int @ SV657 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8172]) ).

thf(8288,plain,
    ! [SV658: $i] :
      ( ( ( min = SV658 )
        = $false )
      | ( ( min
          = ( hAPP_int_int @ bit1 @ SV658 ) )
        = $true )
      | ( ( is_int @ SV658 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8173]) ).

thf(8289,plain,
    ! [SV661: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV661 ) @ SV661 )
          = zero_zero_int )
        = $false )
      | ( ( SV661 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV661 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8176]) ).

thf(8290,plain,
    ! [SV662: $i] :
      ( ( ( SV662 = zero_zero_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV662 ) @ SV662 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV662 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8177]) ).

thf(8291,plain,
    ! [SV731: $i,SV663: $i] :
      ( ( ( is_int @ SV663 )
        = $false )
      | ( ( ~ ( is_int @ SV731 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV663 ) @ SV731 )
           != zero_zero_int )
          | ( SV663 = SV731 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8178]) ).

thf(8292,plain,
    ! [SV732: $i,SV664: $i] :
      ( ( ( is_int @ SV664 )
        = $false )
      | ( ( ~ ( is_int @ SV732 ) )
        = $true )
      | ( ( ( SV664 != SV732 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV664 ) @ SV732 )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8179]) ).

thf(8293,plain,
    ! [SV733: $i,SV665: $i] :
      ( ( ( is_int @ SV665 )
        = $false )
      | ( ( ~ ( is_int @ SV733 ) )
        = $true )
      | ( ( ( SV665 != SV733 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV665 ) @ SV733 )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8180]) ).

thf(8294,plain,
    ! [SV734: $i,SV666: $i] :
      ( ( ( is_int @ SV666 )
        = $false )
      | ( ( ~ ( is_int @ SV734 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV666 ) @ SV734 )
           != zero_zero_int )
          | ( SV666 = SV734 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8181]) ).

thf(8295,plain,
    ! [SV667: $i] :
      ( ( ( zero_zero_int
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV667 ) @ SV667 ) )
        = $false )
      | ( ( SV667 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV667 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8182]) ).

thf(8296,plain,
    ! [SV668: $i] :
      ( ( ( SV668 = zero_zero_int )
        = $false )
      | ( ( zero_zero_int
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV668 ) @ SV668 ) )
        = $true )
      | ( ( is_int @ SV668 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8183]) ).

thf(8297,plain,
    ! [SV669: $i] :
      ( ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV669 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = zero_zero_int )
        = $false )
      | ( ( SV669 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV669 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8184]) ).

thf(8298,plain,
    ! [SV670: $i] :
      ( ( ( SV670 = zero_zero_int )
        = $false )
      | ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV670 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV670 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8185]) ).

thf(8299,plain,
    ! [SV737: $i,SV677: $i] :
      ( ( ( is_int @ SV677 )
        = $false )
      | ( ( ~ ( is_int @ SV737 ) )
        = $true )
      | ( ( ( SV677 != zero_zero_int )
          | ( SV737 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV677 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV737 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8187]) ).

thf(8300,plain,
    ! [SV797: $i,SV779: $i] :
      ( ( ~ ( is_int @ SV779 )
        | ~ ( is_int @ SV797 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV779 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV797 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
         != zero_zero_int )
        | ( SV779 = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8188]) ).

thf(8301,plain,
    ! [SV798: $i,SV780: $i] :
      ( ( ~ ( is_int @ SV780 )
        | ~ ( is_int @ SV798 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV780 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV798 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
         != zero_zero_int )
        | ( SV798 = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8189]) ).

thf(8302,plain,
    ! [SV738: $i,SV678: $i] :
      ( ( ( is_int @ SV678 )
        = $false )
      | ( ( ~ ( is_int @ SV738 ) )
        = $true )
      | ( ( ( SV678 != zero_zero_int )
          | ( SV738 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV678 ) @ SV678 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV738 ) @ SV738 ) )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8190]) ).

thf(8303,plain,
    ! [SV799: $i,SV781: $i] :
      ( ( ~ ( is_int @ SV781 )
        | ~ ( is_int @ SV799 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV781 ) @ SV781 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV799 ) @ SV799 ) )
         != zero_zero_int )
        | ( SV781 = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8191]) ).

thf(8304,plain,
    ! [SV800: $i,SV782: $i] :
      ( ( ~ ( is_int @ SV782 )
        | ~ ( is_int @ SV800 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV782 ) @ SV782 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV800 ) @ SV800 ) )
         != zero_zero_int )
        | ( SV800 = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8192]) ).

thf(8305,plain,
    ! [SV739: $i,SV679: $i] :
      ( ( ( is_int @ SV679 )
        = $false )
      | ( ( ~ ( is_int @ SV739 ) )
        = $true )
      | ( ( ( SV679 != zero_zero_int )
          | ( SV739 != zero_zero_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ SV679 ) @ SV739 )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8193]) ).

thf(8306,plain,
    ! [SV801: $i,SV783: $i] :
      ( ( ~ ( is_int @ SV783 )
        | ~ ( is_int @ SV801 )
        | ( ( hAPP_int_int @ ( legacy_zgcd @ SV783 ) @ SV801 )
         != zero_zero_int )
        | ( SV783 = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8194]) ).

thf(8307,plain,
    ! [SV802: $i,SV784: $i] :
      ( ( ~ ( is_int @ SV784 )
        | ~ ( is_int @ SV802 )
        | ( ( hAPP_int_int @ ( legacy_zgcd @ SV784 ) @ SV802 )
         != zero_zero_int )
        | ( SV802 = zero_zero_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8195]) ).

thf(8308,plain,
    ! [SV496: $i,SV339: $i,SV41: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV41 ) @ SV339 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV496 ) @ SV339 ) )
        = $false )
      | ( ( SV41 = SV496 )
        = $true )
      | ( ( is_int @ SV41 )
        = $false )
      | ( ( is_int @ SV496 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8196]) ).

thf(8309,plain,
    ! [SV497: $i,SV340: $i,SV42: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV42 ) @ SV340 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV42 ) @ SV497 ) )
        = $false )
      | ( ( SV340 = SV497 )
        = $true )
      | ( ( is_int @ SV340 )
        = $false )
      | ( ( is_int @ SV497 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8197]) ).

thf(8310,plain,
    ! [SV498: $i,SV341: $i,SV43: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV43 ) @ SV341 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV43 ) @ SV498 ) )
        = $false )
      | ( ( SV341 = SV498 )
        = $true )
      | ( ( is_int @ SV341 )
        = $false )
      | ( ( is_int @ SV498 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8198]) ).

thf(8311,plain,
    ! [SV79: $i,SV366: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV366 ) @ SV79 )
          = zero_zero_int )
        = $false )
      | ( ( SV79 = zero_zero_int )
        = $true )
      | ( ( SV366 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV79 )
        = $false )
      | ( ( is_int @ SV366 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8199]) ).

thf(8312,plain,
    ! [SV367: $i,SV80: $i] :
      ( ( ( SV80 = zero_zero_int )
        = $true )
      | ( ( SV367 = zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV80 ) @ SV367 )
          = zero_zero_int )
        = $false )
      | ( ( is_int @ SV80 )
        = $false )
      | ( ( is_int @ SV367 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8200]) ).

thf(8313,plain,
    ! [SV576: $i,SV524: $i,SV680: $i,SV380: $i,SV104: $i] :
      ( ( ( is_int @ SV104 )
        = $false )
      | ( ( ~ ( is_int @ SV380 ) )
        = $true )
      | ( ( ~ ( is_int @ SV680 ) )
        = $true )
      | ( ( ( SV680 = zero_zero_int )
          | ( SV104 = SV380 )
          | ( SV524 != SV576 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV524 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV680 ) @ SV104 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV576 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV680 ) @ SV380 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8201]) ).

thf(8314,plain,
    ! [SV457: $i,SV557: $i,SV247: $i,SV585: $i] :
      ( ( ( SV585
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV247 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV557 ) @ SV585 ) ) )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV457 ) @ SV247 )
          = one_one_int )
        = $true )
      | ( ( SV557
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV457 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV557 ) @ SV585 ) ) )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV557 ) @ SV585 )
          = zero_zero_int )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8202]) ).

thf(8315,plain,
    ! [SV564: $i,SV475: $i,SV287: $i,SV785: $i,SV753: $i,SV741: $i,SV684: $i,SV587: $i] :
      ( ( ( SV587
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV684 ) @ SV741 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV753 ) @ SV785 ) ) )
        = $true )
      | ( ( ( SV287
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV475 ) @ SV741 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV564 ) @ SV785 ) ) )
          | ( ( hAPP_int_int @ ( div_mod_int @ SV587 ) @ SV287 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV684 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV587 ) @ SV287 ) ) @ SV475 ) ) ) @ SV741 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV753 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV587 ) @ SV287 ) ) @ SV564 ) ) ) @ SV785 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8203]) ).

thf(8316,plain,
    ! [SV606: $i,SV691: $i] :
      ( ( ( is_int @ SV691 )
        = $false )
      | ( ( is_int @ SV606 )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV606 ) @ SV691 )
           != zero_zero_int )
          | ( SV606 = zero_zero_int )
          | ( SV691 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8208]) ).

thf(8317,plain,
    ! [SV786: $i,SV754: $i] :
      ( ( ( ~ ( is_int @ SV754 )
          | ~ ( is_int @ SV786 ) )
        = $true )
      | ( ( ( SV754 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV754 ) @ SV786 )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8209]) ).

thf(8318,plain,
    ! [SV787: $i,SV755: $i] :
      ( ( ( ~ ( is_int @ SV755 )
          | ~ ( is_int @ SV787 ) )
        = $true )
      | ( ( ( SV787 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV755 ) @ SV787 )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8210]) ).

thf(8319,plain,
    ! [SV607: $i,SV756: $i] :
      ( ( ( ( hAPP_int_nat @ number_number_of_nat @ SV756 )
          = zero_zero_nat )
        = $true )
      | ( ( SV607 != zero_zero_int )
        = $true )
      | ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV607 ) @ ( hAPP_int_nat @ number_number_of_nat @ SV756 ) )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV607 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8211]) ).

thf(8320,plain,
    ! [SV757: $i] :
      ( ( ( is_int @ SV757 )
        = $false )
      | ( ( ! [SY1278: $i] :
              ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV757 ) @ ( hAPP_int_nat @ number_number_of_nat @ SY1278 ) )
               != zero_zero_int )
              | ( ( hAPP_int_nat @ number_number_of_nat @ SY1278 )
               != zero_zero_nat ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8212]) ).

thf(8321,plain,
    ! [SV758: $i] :
      ( ( ( is_int @ SV758 )
        = $false )
      | ( ( ! [SY1279: $i] :
              ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV758 ) @ ( hAPP_int_nat @ number_number_of_nat @ SY1279 ) )
             != zero_zero_int )
          | ( SV758 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8213]) ).

thf(8322,plain,
    ! [SV608: $i,SV313: $i] :
      ( ( ( SV313
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV608 ) @ ( sK11_Q_4 @ SV608 @ SV313 ) ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ SV313 ) @ SV608 )
          = zero_zero_int )
        = $false )
      | ( ( is_int @ SV313 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[8214]) ).

thf(8323,plain,
    ! [SV313: $i,SV608: $i] :
      ( ( ( is_int @ ( sK11_Q_4 @ SV608 @ SV313 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ SV313 ) @ SV608 )
          = zero_zero_int )
        = $false )
      | ( ( is_int @ SV313 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[8215]) ).

thf(8324,plain,
    ! [SV694: $i,SV613: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV613 ) @ SV694 )
         != zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ SV613 ) ) @ SV694 )
          = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV613 ) @ SV694 ) ) )
        = $true )
      | ( ( SV694 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV694 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8216]) ).

thf(8325,plain,
    ! [SV695: $i,SV614: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV614 ) @ SV695 )
          = zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ SV614 ) ) @ SV695 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV614 ) @ SV695 ) ) ) @ one_one_int ) )
        = $true )
      | ( ( SV695 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV695 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8217]) ).

thf(8326,plain,
    ! [SV314: $i,SV486: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK1_A_4 @ SV486 @ SV314 ) )
                            | ~ ( is_int @ ( sK2_SY713 @ SV486 @ SV314 ) ) )
                      | ( SV314
                       != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK1_A_4 @ SV486 @ SV314 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 ) ) ) )
                | ( SV486
                 != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK2_SY713 @ SV486 @ SV314 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 ) ) ) ) )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV314 )
        = $false )
      | ( ( is_int @ SV486 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[8222]) ).

thf(8327,plain,
    ! [SV314: $i,SV486: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( sK1_A_4 @ SV486 @ SV314 ) ) @ ( sK2_SY713 @ SV486 @ SV314 ) )
         != one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV314 )
        = $false )
      | ( ( is_int @ SV486 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[8222]) ).

thf(8328,plain,
    ! [SV619: $i,SV696: $i] :
      ( ( ( is_int @ SV696 )
        = $false )
      | ( ( is_int @ SV619 )
        = $false )
      | ( ( ( ( hAPP_int_int @ number_number_of_int @ SV619 )
           != ( hAPP_int_int @ number_number_of_int @ SV696 ) )
          | ( SV619 = SV696 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8223]) ).

thf(8329,plain,
    ! [SV620: $i,SV697: $i] :
      ( ( ( is_int @ SV697 )
        = $false )
      | ( ( is_int @ SV620 )
        = $false )
      | ( ( ( SV620 != SV697 )
          | ( ( hAPP_int_int @ number_number_of_int @ SV620 )
            = ( hAPP_int_int @ number_number_of_int @ SV697 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8224]) ).

thf(8330,plain,
    ! [SV623: $i,SV759: $i] :
      ( ( ( SV759 = zero_zero_nat )
        = $true )
      | ( ( SV623 != zero_zero_int )
        = $true )
      | ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV623 ) @ SV759 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV623 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8225]) ).

thf(8331,plain,
    ! [SV760: $i] :
      ( ( ( is_int @ SV760 )
        = $false )
      | ( ( ! [SY1280: $i] :
              ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV760 ) @ SY1280 )
               != zero_zero_int )
              | ( SY1280 != zero_zero_nat ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8226]) ).

thf(8332,plain,
    ! [SV761: $i] :
      ( ( ( is_int @ SV761 )
        = $false )
      | ( ( ! [SY1281: $i] :
              ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV761 ) @ SY1281 )
             != zero_zero_int )
          | ( SV761 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8227]) ).

thf(8333,plain,
    ! [SV762: $i,SV742: $i,SV487: $i,SV315: $i] :
      ( ( ( ~ ( is_int @ SV315 )
          | ~ ( is_int @ SV487 )
          | ~ ( is_int @ SV742 ) )
        = $true )
      | ( ( ~ ( is_int @ SV762 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV742 ) @ SV762 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV762 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV742 ) @ SV487 ) ) )
          | ( SV315 = SV742 )
          | ( SV487 = SV762 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8228]) ).

thf(8334,plain,
    ! [SV803: $i,SV487: $i,SV315: $i] :
      ( ( ! [SY1299: $i] :
            ( ~ ( is_int @ SV315 )
            | ~ ( is_int @ SV487 )
            | ~ ( is_int @ SV803 )
            | ~ ( is_int @ SY1299 )
            | ( SV315 != SV803 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV803 ) @ SY1299 ) )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SY1299 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV803 ) @ SV487 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8229]) ).

thf(8335,plain,
    ! [SV804: $i,SV487: $i,SV315: $i] :
      ( ( ! [SY1300: $i] :
            ( ~ ( is_int @ SV315 )
            | ~ ( is_int @ SV487 )
            | ~ ( is_int @ SV804 )
            | ~ ( is_int @ SY1300 )
            | ( SV487 != SY1300 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV804 ) @ SY1300 ) )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SY1300 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV804 ) @ SV487 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8230]) ).

thf(8336,plain,
    ! [SV624: $i,SV700: $i] :
      ( ( ( is_int @ SV700 )
        = $false )
      | ( ( is_int @ SV624 )
        = $false )
      | ( ( ( SV624
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV624 ) @ SV700 ) )
          | ( SV700 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8231]) ).

thf(8337,plain,
    ! [SV625: $i,SV701: $i] :
      ( ( ( is_int @ SV701 )
        = $false )
      | ( ( is_int @ SV625 )
        = $false )
      | ( ( ( SV701 != zero_zero_int )
          | ( SV625
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV625 ) @ SV701 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8232]) ).

thf(8338,plain,
    ! [SV316: $i,SV743: $i,SV704: $i] :
      ( ( ( is_int @ SV704 )
        = $false )
      | ( ( ~ ( is_int @ SV743 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SV704 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SV743 ) )
          | ( SV704 = SV743 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8235]) ).

thf(8339,plain,
    ! [SV316: $i,SV744: $i,SV705: $i] :
      ( ( ( is_int @ SV705 )
        = $false )
      | ( ( ~ ( is_int @ SV744 ) )
        = $true )
      | ( ( ( SV705 != SV744 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SV705 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SV744 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8236]) ).

thf(8340,plain,
    ! [SV630: $i,SV706: $i] :
      ( ( ( is_int @ SV706 )
        = $false )
      | ( ( is_int @ SV630 )
        = $false )
      | ( ( ( SV706 = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV706 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV706 ) @ SV630 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV630 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV706 ) @ SV630 ) ) )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8237]) ).

thf(8341,plain,
    ! [SV631: $i,SV707: $i] :
      ( ( ( is_int @ SV707 )
        = $false )
      | ( ( is_int @ SV631 )
        = $false )
      | ( ( ( SV631 = zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV707 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV707 ) @ SV631 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV631 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV707 ) @ SV631 ) ) )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8238]) ).

thf(8342,plain,
    ! [SV632: $i,SV708: $i] :
      ( ( ( is_int @ SV708 )
        = $false )
      | ( ( is_int @ SV632 )
        = $false )
      | ( ( ( ( hAPP_int_int @ bit1 @ SV632 )
           != ( hAPP_int_int @ bit1 @ SV708 ) )
          | ( SV632 = SV708 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8239]) ).

thf(8343,plain,
    ! [SV633: $i,SV709: $i] :
      ( ( ( is_int @ SV709 )
        = $false )
      | ( ( is_int @ SV633 )
        = $false )
      | ( ( ( SV633 != SV709 )
          | ( ( hAPP_int_int @ bit1 @ SV633 )
            = ( hAPP_int_int @ bit1 @ SV709 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8240]) ).

thf(8344,plain,
    ! [SV634: $i,SV710: $i] :
      ( ( ( SV710 = zero_zero_nat )
        = $false )
      | ( ( SV634 = zero_zero_nat )
        = $false )
      | ( ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV634 ) )
          = ( hAPP_nat_int @ semiri1621563631at_int @ SV710 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8241]) ).

thf(8345,plain,
    ! [SV805: $i,SV763: $i] :
      ( ( ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV763 ) )
         != ( hAPP_nat_int @ semiri1621563631at_int @ SV805 ) )
        = $true )
      | ( ( SV763 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[8242]) ).

thf(8346,plain,
    ! [SV788: $i,SV764: $i] :
      ( ( ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV764 ) )
         != ( hAPP_nat_int @ semiri1621563631at_int @ SV788 ) )
        = $true )
      | ( ( SV788 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8243]) ).

thf(8347,plain,
    ! [SV635: $i,SV711: $i] :
      ( ( ( is_int @ SV711 )
        = $false )
      | ( ( is_int @ SV635 )
        = $false )
      | ( ( ( SV711 = zero_zero_int )
          | ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK7_C_3 @ SV711 @ SV635 ) )
                                | ~ ( is_int @ ( sK8_SY715 @ SV711 @ SV635 ) ) )
                          | ( SV711
                           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV711 ) @ SV635 ) ) @ ( sK7_C_3 @ SV711 @ SV635 ) ) ) )
                    | ( SV635
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV711 ) @ SV635 ) ) @ ( sK8_SY715 @ SV711 @ SV635 ) ) ) )
              | ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK7_C_3 @ SV711 @ SV635 ) ) @ ( sK8_SY715 @ SV711 @ SV635 ) )
               != one_one_int ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8244]) ).

thf(8348,plain,
    ! [SV636: $i,SV712: $i] :
      ( ( ( is_int @ SV712 )
        = $false )
      | ( ( is_int @ SV636 )
        = $false )
      | ( ( ( SV636 = zero_zero_int )
          | ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK5_C_3 @ SV712 @ SV636 ) )
                                | ~ ( is_int @ ( sK6_SY714 @ SV712 @ SV636 ) ) )
                          | ( SV712
                           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV712 ) @ SV636 ) ) @ ( sK5_C_3 @ SV712 @ SV636 ) ) ) )
                    | ( SV636
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV712 ) @ SV636 ) ) @ ( sK6_SY714 @ SV712 @ SV636 ) ) ) )
              | ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK5_C_3 @ SV712 @ SV636 ) ) @ ( sK6_SY714 @ SV712 @ SV636 ) )
               != one_one_int ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8245]) ).

thf(8349,plain,
    ! [SV713: $i,SV637: $i] :
      ( ( ( ( hAPP_int_int @ number_number_of_int @ SV637 )
          = SV713 )
        = $false )
      | ( ( SV713
          = ( hAPP_int_int @ number_number_of_int @ SV637 ) )
        = $true )
      | ( ( is_int @ SV713 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8246]) ).

thf(8350,plain,
    ! [SV638: $i,SV714: $i] :
      ( ( ( SV714
          = ( hAPP_int_int @ number_number_of_int @ SV638 ) )
        = $false )
      | ( ( ( hAPP_int_int @ number_number_of_int @ SV638 )
          = SV714 )
        = $true )
      | ( ( is_int @ SV714 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8247]) ).

thf(8351,plain,
    ! [SV715: $i,SV745: $i,SV317: $i] :
      ( ( ( is_int @ SV317 )
        = $false )
      | ( ( ~ ( is_int @ SV745 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV317 ) @ SV715 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV745 ) @ SV715 ) )
          | ( SV317 = SV745 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8248]) ).

thf(8352,plain,
    ! [SV716: $i,SV746: $i,SV317: $i] :
      ( ( ( is_int @ SV317 )
        = $false )
      | ( ( ~ ( is_int @ SV746 ) )
        = $true )
      | ( ( ( SV317 != SV746 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV317 ) @ SV716 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV746 ) @ SV716 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8249]) ).

thf(8353,plain,
    ! [SV639: $i,SV717: $i] :
      ( ( ( is_int @ SV717 )
        = $false )
      | ( ( is_int @ SV639 )
        = $false )
      | ( ( ( SV717 = zero_zero_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV717 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV717 ) @ SV639 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV639 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV717 ) @ SV639 ) ) )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8250]) ).

thf(8354,plain,
    ! [SV640: $i,SV718: $i] :
      ( ( ( is_int @ SV718 )
        = $false )
      | ( ( is_int @ SV640 )
        = $false )
      | ( ( ( SV640 = zero_zero_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV718 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV718 ) @ SV640 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV640 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV718 ) @ SV640 ) ) )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8251]) ).

thf(8355,plain,
    ! [SV806: $i,SV569: $i,SV488: $i,SV318: $i] :
      ( ( ( ! [SY1301: $i] :
              ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV318 ) @ SV488 ) ) @ SV569 )
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV806 ) @ SV488 ) ) @ SY1301 ) )
              | ( SV569
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV806 ) @ SV318 ) ) @ SV488 ) ) @ SY1301 ) ) ) )
        = $true )
      | ( ( is_int @ SV569 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8252]) ).

thf(8356,plain,
    ! [SV488: $i,SV318: $i,SV807: $i,SV569: $i] :
      ( ( ( ! [SY1302: $i] :
              ( ( SV569
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV807 ) @ SV318 ) ) @ SV488 ) ) @ SY1302 ) )
              | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV318 ) @ SV488 ) ) @ SV569 )
                = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV807 ) @ SV488 ) ) @ SY1302 ) ) ) )
        = $true )
      | ( ( is_int @ SV569 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8253]) ).

thf(8357,plain,
    ! [SV489: $i,SV319: $i,SV765: $i,SV747: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV747 ) @ SV765 )
          = one_one_int )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
           != one_one_int )
          | ( ( hAPP_int_int @ abs_abs_int @ SV747 )
           != ( hAPP_int_int @ abs_abs_int @ SV319 ) )
          | ( ( hAPP_int_int @ abs_abs_int @ SV489 )
           != ( hAPP_int_int @ abs_abs_int @ SV765 ) )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV747 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV765 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8254]) ).

thf(8358,plain,
    ! [SV489: $i,SV319: $i,SV808: $i] :
      ( ( ! [SY1303: $i] :
            ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV808 ) @ SY1303 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV808 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SY1303 ) ) )
            | ( ( hAPP_int_int @ abs_abs_int @ SV808 )
              = ( hAPP_int_int @ abs_abs_int @ SV319 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8255]) ).

thf(8359,plain,
    ! [SV489: $i,SV319: $i,SV809: $i] :
      ( ( ! [SY1304: $i] :
            ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV809 ) @ SY1304 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
             != one_one_int )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV809 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
             != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SY1304 ) ) )
            | ( ( hAPP_int_int @ abs_abs_int @ SV489 )
              = ( hAPP_int_int @ abs_abs_int @ SY1304 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8256]) ).

thf(8360,plain,
    ! [SV766: $i,SV748: $i,SV490: $i,SV320: $i] :
      ( ( ( ~ ( is_int @ SV320 )
          | ~ ( is_int @ SV490 )
          | ~ ( is_int @ SV748 ) )
        = $true )
      | ( ( ~ ( is_int @ SV766 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV748 ) @ SV766 ) )
          | ( SV320 != SV490 )
          | ( SV748 = SV766 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8257]) ).

thf(8361,plain,
    ! [SV767: $i,SV749: $i,SV490: $i,SV320: $i] :
      ( ( ( ~ ( is_int @ SV320 )
          | ~ ( is_int @ SV490 )
          | ~ ( is_int @ SV749 ) )
        = $true )
      | ( ( ~ ( is_int @ SV767 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV749 ) @ SV767 ) )
          | ( SV749 != SV767 )
          | ( SV320 = SV490 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8258]) ).

thf(8362,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
           != one_one_int )
          | ( SX0 = one_one_int )
          | ( SX0
            = ( hAPP_int_int @ number_number_of_int @ min ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[8259]) ).

thf(8363,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
           != one_one_int )
          | ( SX0 = one_one_int )
          | ( SX1
            = ( hAPP_int_int @ number_number_of_int @ min ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[8260]) ).

thf(8364,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
           != one_one_int )
          | ( SX1 = one_one_int )
          | ( SX0
            = ( hAPP_int_int @ number_number_of_int @ min ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[8261]) ).

thf(8365,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_int @ SX0 )
          | ~ ( is_int @ SX1 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SX0 ) @ SX1 )
           != one_one_int )
          | ( SX1 = one_one_int )
          | ( SX1
            = ( hAPP_int_int @ number_number_of_int @ min ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[8262]) ).

thf(8366,plain,
    ! [SV789: $i,SV768: $i] :
      ( ( ( ~ ( is_int @ SV768 )
          | ~ ( is_int @ SV789 ) )
        = $true )
      | ( ( ( SV768 != one_one_int )
          | ( SV789 != one_one_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV768 ) @ SV789 )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8263]) ).

thf(8367,plain,
    ! [SV790: $i,SV769: $i] :
      ( ( ( ~ ( is_int @ SV769 )
          | ~ ( is_int @ SV790 ) )
        = $true )
      | ( ( ( SV769
           != ( hAPP_int_int @ number_number_of_int @ min ) )
          | ( SV790
           != ( hAPP_int_int @ number_number_of_int @ min ) )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV769 ) @ SV790 )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8264]) ).

thf(8368,plain,
    ! [SV641: $i] :
      ( ( ( SV641 = one_one_int )
        = $true )
      | ( ( SV641
          = ( hAPP_int_int @ number_number_of_int @ min ) )
        = $true )
      | ( ( ( hAPP_int_int @ abs_abs_int @ SV641 )
          = one_one_int )
        = $false )
      | ( ( is_int @ SV641 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8265]) ).

thf(8369,plain,
    ! [SV770: $i] :
      ( ( ( is_int @ SV770 )
        = $false )
      | ( ( ( SV770 != one_one_int )
          | ( ( hAPP_int_int @ abs_abs_int @ SV770 )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8266]) ).

thf(8370,plain,
    ! [SV771: $i] :
      ( ( ( is_int @ SV771 )
        = $false )
      | ( ( ( SV771
           != ( hAPP_int_int @ number_number_of_int @ min ) )
          | ( ( hAPP_int_int @ abs_abs_int @ SV771 )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8267]) ).

thf(8371,plain,
    ! [SV810: $i,SV491: $i,SV321: $i] :
      ( ( ! [SY1305: $i] :
            ( ~ ( is_int @ SV321 )
            | ~ ( is_int @ SV491 )
            | ~ ( is_int @ SV810 )
            | ~ ( is_int @ SY1305 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV810 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1305 ) @ SV491 ) )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV810 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1305 ) @ SV321 ) ) )
            | ( SV810 != SY1305 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8270]) ).

thf(8372,plain,
    ! [SV811: $i,SV491: $i,SV321: $i] :
      ( ( ! [SY1306: $i] :
            ( ~ ( is_int @ SV321 )
            | ~ ( is_int @ SV491 )
            | ~ ( is_int @ SV811 )
            | ~ ( is_int @ SY1306 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV811 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1306 ) @ SV491 ) )
              = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV811 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SY1306 ) @ SV321 ) ) )
            | ( SV321 != SV491 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8271]) ).

thf(8373,plain,
    ! [SV772: $i,SV750: $i,SV491: $i,SV321: $i] :
      ( ( ( ~ ( is_int @ SV321 )
          | ~ ( is_int @ SV491 )
          | ~ ( is_int @ SV750 ) )
        = $true )
      | ( ( ~ ( is_int @ SV772 ) )
        = $true )
      | ( ( ( SV750 = SV772 )
          | ( SV321 = SV491 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV750 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV772 ) @ SV491 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV750 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV772 ) @ SV321 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8272]) ).

thf(8374,plain,
    ! [SV644: $i,SV719: $i] :
      ( ( ( is_int @ SV719 )
        = $false )
      | ( ( is_int @ SV644 )
        = $false )
      | ( ( ( SV644 != zero_zero_int )
          | ( SV719 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV644 ) @ SV719 )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8273]) ).

thf(8375,plain,
    ! [SV791: $i,SV773: $i] :
      ( ( ( ~ ( is_int @ SV773 )
          | ~ ( is_int @ SV791 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV773 ) @ SV791 )
           != zero_zero_int )
          | ( SV773 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8274]) ).

thf(8376,plain,
    ! [SV792: $i,SV774: $i] :
      ( ( ( ~ ( is_int @ SV774 )
          | ~ ( is_int @ SV792 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV774 ) @ SV792 )
           != zero_zero_int )
          | ( SV792 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8275]) ).

thf(8377,plain,
    ! [SV720: $i,SV645: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV645 ) @ SV720 )
         != zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV645 ) @ ( hAPP_int_int @ uminus_uminus_int @ SV720 ) )
          = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV645 ) @ SV720 ) ) )
        = $true )
      | ( ( SV720 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV720 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8276]) ).

thf(8378,plain,
    ! [SV721: $i,SV646: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV646 ) @ SV721 )
          = zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV646 ) @ ( hAPP_int_int @ uminus_uminus_int @ SV721 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV646 ) @ SV721 ) ) ) @ one_one_int ) )
        = $true )
      | ( ( SV721 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV721 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8277]) ).

thf(8379,plain,
    ! [SV751: $i,SV724: $i,SV322: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SV724 )
          = one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SV751 )
         != one_one_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV724 ) @ SV751 ) )
          = one_one_int )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8278]) ).

thf(8380,plain,
    ! [SV793: $i,SV322: $i] :
      ( ( ( ! [SY1297: $i] :
              ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV793 ) @ SY1297 ) )
             != one_one_int ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SV793 )
          = one_one_int )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8279]) ).

thf(8381,plain,
    ! [SV812: $i,SV794: $i,SV322: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV794 ) @ SV812 ) )
         != one_one_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SV812 )
          = one_one_int ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8280]) ).

thf(8382,plain,
    ! [SV775: $i,SV570: $i,SV492: $i,SV323: $i,SV795: $i] :
      ( ( ( ~ ( is_int @ SV795 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV323 ) @ SV492 ) ) @ SV570 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV775 ) @ SV492 ) ) @ SV795 ) )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV323 ) @ SV775 ) ) @ SV492 ) ) @ SV570 )
            = SV795 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8281]) ).

thf(8383,plain,
    ! [SV570: $i,SV492: $i,SV776: $i,SV323: $i,SV796: $i] :
      ( ( ( ~ ( is_int @ SV796 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV323 ) @ SV776 ) ) @ SV492 ) ) @ SV570 )
           != SV796 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV323 ) @ SV492 ) ) @ SV570 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV776 ) @ SV492 ) ) @ SV796 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8282]) ).

thf(8384,plain,
    ! [SV777: $i,SV651: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV651 ) @ SV777 )
          = zero_zero_int )
        = $false )
      | ( ( ~ ( ( SV651
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV777 ) @ ( sK12_Q_4 @ SV777 @ SV651 ) ) )
              | ~ ( is_int @ ( sK12_Q_4 @ SV777 @ SV651 ) ) ) )
        = $true )
      | ( ( is_int @ SV651 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8283]) ).

thf(8385,plain,
    ! [SV813: $i,SV778: $i,SV652: $i] :
      ( ( ( ( SV652
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV778 ) @ SV813 ) )
          | ~ ( is_int @ SV813 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ SV652 ) @ SV778 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV652 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8284]) ).

thf(8386,plain,
    ! [SV655: $i,SV727: $i] :
      ( ( ( is_int @ SV727 )
        = $false )
      | ( ( is_int @ SV655 )
        = $false )
      | ( ( ( ( hAPP_int_int @ bit0 @ SV655 )
           != ( hAPP_int_int @ bit0 @ SV727 ) )
          | ( SV655 = SV727 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8285]) ).

thf(8387,plain,
    ! [SV656: $i,SV728: $i] :
      ( ( ( is_int @ SV728 )
        = $false )
      | ( ( is_int @ SV656 )
        = $false )
      | ( ( ( SV656 != SV728 )
          | ( ( hAPP_int_int @ bit0 @ SV656 )
            = ( hAPP_int_int @ bit0 @ SV728 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8286]) ).

thf(8388,plain,
    ! [SV663: $i,SV731: $i] :
      ( ( ( is_int @ SV731 )
        = $false )
      | ( ( is_int @ SV663 )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV663 ) @ SV731 )
           != zero_zero_int )
          | ( SV663 = SV731 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8291]) ).

thf(8389,plain,
    ! [SV664: $i,SV732: $i] :
      ( ( ( is_int @ SV732 )
        = $false )
      | ( ( is_int @ SV664 )
        = $false )
      | ( ( ( SV664 != SV732 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV664 ) @ SV732 )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8292]) ).

thf(8390,plain,
    ! [SV665: $i,SV733: $i] :
      ( ( ( is_int @ SV733 )
        = $false )
      | ( ( is_int @ SV665 )
        = $false )
      | ( ( ( SV665 != SV733 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV665 ) @ SV733 )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8293]) ).

thf(8391,plain,
    ! [SV666: $i,SV734: $i] :
      ( ( ( is_int @ SV734 )
        = $false )
      | ( ( is_int @ SV666 )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV666 ) @ SV734 )
           != zero_zero_int )
          | ( SV666 = SV734 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8294]) ).

thf(8392,plain,
    ! [SV677: $i,SV737: $i] :
      ( ( ( is_int @ SV737 )
        = $false )
      | ( ( is_int @ SV677 )
        = $false )
      | ( ( ( SV677 != zero_zero_int )
          | ( SV737 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV677 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV737 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8299]) ).

thf(8393,plain,
    ! [SV797: $i,SV779: $i] :
      ( ( ( ~ ( is_int @ SV779 )
          | ~ ( is_int @ SV797 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV779 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV797 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
           != zero_zero_int )
          | ( SV779 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8300]) ).

thf(8394,plain,
    ! [SV798: $i,SV780: $i] :
      ( ( ( ~ ( is_int @ SV780 )
          | ~ ( is_int @ SV798 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV780 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV798 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
           != zero_zero_int )
          | ( SV798 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8301]) ).

thf(8395,plain,
    ! [SV678: $i,SV738: $i] :
      ( ( ( is_int @ SV738 )
        = $false )
      | ( ( is_int @ SV678 )
        = $false )
      | ( ( ( SV678 != zero_zero_int )
          | ( SV738 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV678 ) @ SV678 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV738 ) @ SV738 ) )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8302]) ).

thf(8396,plain,
    ! [SV799: $i,SV781: $i] :
      ( ( ( ~ ( is_int @ SV781 )
          | ~ ( is_int @ SV799 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV781 ) @ SV781 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV799 ) @ SV799 ) )
           != zero_zero_int )
          | ( SV781 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8303]) ).

thf(8397,plain,
    ! [SV800: $i,SV782: $i] :
      ( ( ( ~ ( is_int @ SV782 )
          | ~ ( is_int @ SV800 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV782 ) @ SV782 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV800 ) @ SV800 ) )
           != zero_zero_int )
          | ( SV800 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8304]) ).

thf(8398,plain,
    ! [SV679: $i,SV739: $i] :
      ( ( ( is_int @ SV739 )
        = $false )
      | ( ( is_int @ SV679 )
        = $false )
      | ( ( ( SV679 != zero_zero_int )
          | ( SV739 != zero_zero_int )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ SV679 ) @ SV739 )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8305]) ).

thf(8399,plain,
    ! [SV801: $i,SV783: $i] :
      ( ( ( ~ ( is_int @ SV783 )
          | ~ ( is_int @ SV801 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV783 ) @ SV801 )
           != zero_zero_int )
          | ( SV783 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8306]) ).

thf(8400,plain,
    ! [SV802: $i,SV784: $i] :
      ( ( ( ~ ( is_int @ SV784 )
          | ~ ( is_int @ SV802 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV784 ) @ SV802 )
           != zero_zero_int )
          | ( SV802 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8307]) ).

thf(8401,plain,
    ! [SV576: $i,SV524: $i,SV680: $i,SV104: $i,SV380: $i] :
      ( ( ( is_int @ SV380 )
        = $false )
      | ( ( is_int @ SV104 )
        = $false )
      | ( ( ~ ( is_int @ SV680 ) )
        = $true )
      | ( ( ( SV680 = zero_zero_int )
          | ( SV104 = SV380 )
          | ( SV524 != SV576 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV524 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV680 ) @ SV104 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV576 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV680 ) @ SV380 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8313]) ).

thf(8402,plain,
    ! [SV564: $i,SV475: $i,SV287: $i,SV785: $i,SV753: $i,SV741: $i,SV684: $i,SV587: $i] :
      ( ( ( SV587
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV684 ) @ SV741 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV753 ) @ SV785 ) ) )
        = $false )
      | ( ( ( SV287
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV475 ) @ SV741 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV564 ) @ SV785 ) ) )
          | ( ( hAPP_int_int @ ( div_mod_int @ SV587 ) @ SV287 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV684 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV587 ) @ SV287 ) ) @ SV475 ) ) ) @ SV741 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV753 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV587 ) @ SV287 ) ) @ SV564 ) ) ) @ SV785 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8315]) ).

thf(8403,plain,
    ! [SV691: $i,SV606: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV606 ) @ SV691 )
         != zero_zero_int )
        = $true )
      | ( ( ( SV606 = zero_zero_int )
          | ( SV691 = zero_zero_int ) )
        = $true )
      | ( ( is_int @ SV606 )
        = $false )
      | ( ( is_int @ SV691 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8316]) ).

thf(8404,plain,
    ! [SV786: $i,SV754: $i] :
      ( ( ( ~ ( is_int @ SV754 ) )
        = $true )
      | ( ( ~ ( is_int @ SV786 ) )
        = $true )
      | ( ( ( SV754 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV754 ) @ SV786 )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8317]) ).

thf(8405,plain,
    ! [SV787: $i,SV755: $i] :
      ( ( ( ~ ( is_int @ SV755 ) )
        = $true )
      | ( ( ~ ( is_int @ SV787 ) )
        = $true )
      | ( ( ( SV787 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV755 ) @ SV787 )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8318]) ).

thf(8406,plain,
    ! [SV756: $i,SV607: $i] :
      ( ( ( SV607 = zero_zero_int )
        = $false )
      | ( ( ( hAPP_int_nat @ number_number_of_nat @ SV756 )
          = zero_zero_nat )
        = $true )
      | ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV607 ) @ ( hAPP_int_nat @ number_number_of_nat @ SV756 ) )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV607 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8319]) ).

thf(8407,plain,
    ! [SV814: $i,SV757: $i] :
      ( ( ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV757 ) @ ( hAPP_int_nat @ number_number_of_nat @ SV814 ) )
           != zero_zero_int )
          | ( ( hAPP_int_nat @ number_number_of_nat @ SV814 )
           != zero_zero_nat ) )
        = $true )
      | ( ( is_int @ SV757 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8320]) ).

thf(8408,plain,
    ! [SV758: $i] :
      ( ( ( ! [SY1279: $i] :
              ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV758 ) @ ( hAPP_int_nat @ number_number_of_nat @ SY1279 ) )
             != zero_zero_int ) )
        = $true )
      | ( ( SV758 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV758 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8321]) ).

thf(8409,plain,
    ! [SV694: $i,SV613: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV613 ) @ SV694 )
          = zero_zero_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ ( hAPP_int_int @ uminus_uminus_int @ SV613 ) ) @ SV694 )
          = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV613 ) @ SV694 ) ) )
        = $true )
      | ( ( SV694 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV694 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8324]) ).

thf(8410,plain,
    ! [SV314: $i,SV486: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK1_A_4 @ SV486 @ SV314 ) )
                          | ~ ( is_int @ ( sK2_SY713 @ SV486 @ SV314 ) ) )
                    | ( SV314
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK1_A_4 @ SV486 @ SV314 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 ) ) ) )
              | ( SV486
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK2_SY713 @ SV486 @ SV314 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 ) ) ) ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV314 )
        = $false )
      | ( ( is_int @ SV486 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[8326]) ).

thf(8411,plain,
    ! [SV314: $i,SV486: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( sK1_A_4 @ SV486 @ SV314 ) ) @ ( sK2_SY713 @ SV486 @ SV314 ) )
          = one_one_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV314 )
        = $false )
      | ( ( is_int @ SV486 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[8327]) ).

thf(8412,plain,
    ! [SV696: $i,SV619: $i] :
      ( ( ( ( hAPP_int_int @ number_number_of_int @ SV619 )
         != ( hAPP_int_int @ number_number_of_int @ SV696 ) )
        = $true )
      | ( ( SV619 = SV696 )
        = $true )
      | ( ( is_int @ SV619 )
        = $false )
      | ( ( is_int @ SV696 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8328]) ).

thf(8413,plain,
    ! [SV697: $i,SV620: $i] :
      ( ( ( SV620 != SV697 )
        = $true )
      | ( ( ( hAPP_int_int @ number_number_of_int @ SV620 )
          = ( hAPP_int_int @ number_number_of_int @ SV697 ) )
        = $true )
      | ( ( is_int @ SV620 )
        = $false )
      | ( ( is_int @ SV697 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8329]) ).

thf(8414,plain,
    ! [SV759: $i,SV623: $i] :
      ( ( ( SV623 = zero_zero_int )
        = $false )
      | ( ( SV759 = zero_zero_nat )
        = $true )
      | ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV623 ) @ SV759 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV623 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8330]) ).

thf(8415,plain,
    ! [SV815: $i,SV760: $i] :
      ( ( ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV760 ) @ SV815 )
           != zero_zero_int )
          | ( SV815 != zero_zero_nat ) )
        = $true )
      | ( ( is_int @ SV760 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8331]) ).

thf(8416,plain,
    ! [SV761: $i] :
      ( ( ( ! [SY1281: $i] :
              ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV761 ) @ SY1281 )
             != zero_zero_int ) )
        = $true )
      | ( ( SV761 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV761 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8332]) ).

thf(8417,plain,
    ! [SV762: $i,SV742: $i,SV487: $i,SV315: $i] :
      ( ( ( ~ ( is_int @ SV315 )
          | ~ ( is_int @ SV487 ) )
        = $true )
      | ( ( ~ ( is_int @ SV742 ) )
        = $true )
      | ( ( ~ ( is_int @ SV762 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV742 ) @ SV762 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV762 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV742 ) @ SV487 ) ) )
          | ( SV315 = SV742 )
          | ( SV487 = SV762 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8333]) ).

thf(8418,plain,
    ! [SV816: $i,SV803: $i,SV487: $i,SV315: $i] :
      ( ( ~ ( is_int @ SV315 )
        | ~ ( is_int @ SV487 )
        | ~ ( is_int @ SV803 )
        | ~ ( is_int @ SV816 )
        | ( SV315 != SV803 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV803 ) @ SV816 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV816 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV803 ) @ SV487 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8334]) ).

thf(8419,plain,
    ! [SV817: $i,SV804: $i,SV487: $i,SV315: $i] :
      ( ( ~ ( is_int @ SV315 )
        | ~ ( is_int @ SV487 )
        | ~ ( is_int @ SV804 )
        | ~ ( is_int @ SV817 )
        | ( SV487 != SV817 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV804 ) @ SV817 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV817 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV804 ) @ SV487 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8335]) ).

thf(8420,plain,
    ! [SV700: $i,SV624: $i] :
      ( ( ( SV624
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV624 ) @ SV700 ) )
        = $true )
      | ( ( SV700 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV624 )
        = $false )
      | ( ( is_int @ SV700 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8336]) ).

thf(8421,plain,
    ! [SV625: $i,SV701: $i] :
      ( ( ( SV701 != zero_zero_int )
        = $true )
      | ( ( SV625
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV625 ) @ SV701 ) )
        = $true )
      | ( ( is_int @ SV625 )
        = $false )
      | ( ( is_int @ SV701 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8337]) ).

thf(8422,plain,
    ! [SV316: $i,SV704: $i,SV743: $i] :
      ( ( ( is_int @ SV743 )
        = $false )
      | ( ( is_int @ SV704 )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SV704 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SV743 ) )
          | ( SV704 = SV743 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8338]) ).

thf(8423,plain,
    ! [SV316: $i,SV705: $i,SV744: $i] :
      ( ( ( is_int @ SV744 )
        = $false )
      | ( ( is_int @ SV705 )
        = $false )
      | ( ( ( SV705 != SV744 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SV705 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SV744 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8339]) ).

thf(8424,plain,
    ! [SV630: $i,SV706: $i] :
      ( ( ( SV706 = zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV706 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV706 ) @ SV630 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV630 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV706 ) @ SV630 ) ) )
          = one_one_int )
        = $true )
      | ( ( is_int @ SV630 )
        = $false )
      | ( ( is_int @ SV706 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8340]) ).

thf(8425,plain,
    ! [SV707: $i,SV631: $i] :
      ( ( ( SV631 = zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV707 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV707 ) @ SV631 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV631 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV707 ) @ SV631 ) ) )
          = one_one_int )
        = $true )
      | ( ( is_int @ SV631 )
        = $false )
      | ( ( is_int @ SV707 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8341]) ).

thf(8426,plain,
    ! [SV708: $i,SV632: $i] :
      ( ( ( ( hAPP_int_int @ bit1 @ SV632 )
         != ( hAPP_int_int @ bit1 @ SV708 ) )
        = $true )
      | ( ( SV632 = SV708 )
        = $true )
      | ( ( is_int @ SV632 )
        = $false )
      | ( ( is_int @ SV708 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8342]) ).

thf(8427,plain,
    ! [SV709: $i,SV633: $i] :
      ( ( ( SV633 != SV709 )
        = $true )
      | ( ( ( hAPP_int_int @ bit1 @ SV633 )
          = ( hAPP_int_int @ bit1 @ SV709 ) )
        = $true )
      | ( ( is_int @ SV633 )
        = $false )
      | ( ( is_int @ SV709 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8343]) ).

thf(8428,plain,
    ! [SV805: $i,SV763: $i] :
      ( ( ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV763 ) )
          = ( hAPP_nat_int @ semiri1621563631at_int @ SV805 ) )
        = $false )
      | ( ( SV763 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8345]) ).

thf(8429,plain,
    ! [SV788: $i,SV764: $i] :
      ( ( ( ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_nat_int @ semiri1621563631at_int @ SV764 ) )
          = ( hAPP_nat_int @ semiri1621563631at_int @ SV788 ) )
        = $false )
      | ( ( SV788 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8346]) ).

thf(8430,plain,
    ! [SV635: $i,SV711: $i] :
      ( ( ( SV711 = zero_zero_int )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK7_C_3 @ SV711 @ SV635 ) )
                                | ~ ( is_int @ ( sK8_SY715 @ SV711 @ SV635 ) ) )
                          | ( SV711
                           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV711 ) @ SV635 ) ) @ ( sK7_C_3 @ SV711 @ SV635 ) ) ) )
                    | ( SV635
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV711 ) @ SV635 ) ) @ ( sK8_SY715 @ SV711 @ SV635 ) ) ) )
              | ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK7_C_3 @ SV711 @ SV635 ) ) @ ( sK8_SY715 @ SV711 @ SV635 ) )
               != one_one_int ) ) )
        = $true )
      | ( ( is_int @ SV635 )
        = $false )
      | ( ( is_int @ SV711 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8347]) ).

thf(8431,plain,
    ! [SV712: $i,SV636: $i] :
      ( ( ( SV636 = zero_zero_int )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK5_C_3 @ SV712 @ SV636 ) )
                                | ~ ( is_int @ ( sK6_SY714 @ SV712 @ SV636 ) ) )
                          | ( SV712
                           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV712 ) @ SV636 ) ) @ ( sK5_C_3 @ SV712 @ SV636 ) ) ) )
                    | ( SV636
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV712 ) @ SV636 ) ) @ ( sK6_SY714 @ SV712 @ SV636 ) ) ) )
              | ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK5_C_3 @ SV712 @ SV636 ) ) @ ( sK6_SY714 @ SV712 @ SV636 ) )
               != one_one_int ) ) )
        = $true )
      | ( ( is_int @ SV636 )
        = $false )
      | ( ( is_int @ SV712 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8348]) ).

thf(8432,plain,
    ! [SV715: $i,SV317: $i,SV745: $i] :
      ( ( ( is_int @ SV745 )
        = $false )
      | ( ( is_int @ SV317 )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV317 ) @ SV715 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV745 ) @ SV715 ) )
          | ( SV317 = SV745 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8351]) ).

thf(8433,plain,
    ! [SV716: $i,SV317: $i,SV746: $i] :
      ( ( ( is_int @ SV746 )
        = $false )
      | ( ( is_int @ SV317 )
        = $false )
      | ( ( ( SV317 != SV746 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV317 ) @ SV716 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV746 ) @ SV716 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8352]) ).

thf(8434,plain,
    ! [SV639: $i,SV717: $i] :
      ( ( ( SV717 = zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV717 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV717 ) @ SV639 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV639 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV717 ) @ SV639 ) ) )
          = one_one_int )
        = $true )
      | ( ( is_int @ SV639 )
        = $false )
      | ( ( is_int @ SV717 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8353]) ).

thf(8435,plain,
    ! [SV718: $i,SV640: $i] :
      ( ( ( SV640 = zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( legacy_zgcd @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV718 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV718 ) @ SV640 ) ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV640 ) @ ( hAPP_int_int @ ( legacy_zgcd @ SV718 ) @ SV640 ) ) )
          = one_one_int )
        = $true )
      | ( ( is_int @ SV640 )
        = $false )
      | ( ( is_int @ SV718 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8354]) ).

thf(8436,plain,
    ! [SV818: $i,SV806: $i,SV569: $i,SV488: $i,SV318: $i] :
      ( ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV318 ) @ SV488 ) ) @ SV569 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV806 ) @ SV488 ) ) @ SV818 ) )
          | ( SV569
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV806 ) @ SV318 ) ) @ SV488 ) ) @ SV818 ) ) )
        = $true )
      | ( ( is_int @ SV569 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8355]) ).

thf(8437,plain,
    ! [SV819: $i,SV488: $i,SV318: $i,SV807: $i,SV569: $i] :
      ( ( ( ( SV569
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV807 ) @ SV318 ) ) @ SV488 ) ) @ SV819 ) )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV318 ) @ SV488 ) ) @ SV569 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV807 ) @ SV488 ) ) @ SV819 ) ) )
        = $true )
      | ( ( is_int @ SV569 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8356]) ).

thf(8438,plain,
    ! [SV765: $i,SV747: $i,SV489: $i,SV319: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
         != one_one_int )
        = $true )
      | ( ( ( ( hAPP_int_int @ abs_abs_int @ SV747 )
           != ( hAPP_int_int @ abs_abs_int @ SV319 ) )
          | ( ( hAPP_int_int @ abs_abs_int @ SV489 )
           != ( hAPP_int_int @ abs_abs_int @ SV765 ) )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV747 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV765 ) ) ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV747 ) @ SV765 )
          = one_one_int )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8357]) ).

thf(8439,plain,
    ! [SV489: $i,SV319: $i,SV820: $i,SV808: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV808 ) @ SV820 )
         != one_one_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
         != one_one_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV808 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV820 ) ) )
        | ( ( hAPP_int_int @ abs_abs_int @ SV808 )
          = ( hAPP_int_int @ abs_abs_int @ SV319 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8358]) ).

thf(8440,plain,
    ! [SV489: $i,SV319: $i,SV821: $i,SV809: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV809 ) @ SV821 )
         != one_one_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
         != one_one_int )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV809 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV821 ) ) )
        | ( ( hAPP_int_int @ abs_abs_int @ SV489 )
          = ( hAPP_int_int @ abs_abs_int @ SV821 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8359]) ).

thf(8441,plain,
    ! [SV766: $i,SV748: $i,SV490: $i,SV320: $i] :
      ( ( ( ~ ( is_int @ SV320 )
          | ~ ( is_int @ SV490 ) )
        = $true )
      | ( ( ~ ( is_int @ SV748 ) )
        = $true )
      | ( ( ~ ( is_int @ SV766 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV748 ) @ SV766 ) )
          | ( SV320 != SV490 )
          | ( SV748 = SV766 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8360]) ).

thf(8442,plain,
    ! [SV767: $i,SV749: $i,SV490: $i,SV320: $i] :
      ( ( ( ~ ( is_int @ SV320 )
          | ~ ( is_int @ SV490 ) )
        = $true )
      | ( ( ~ ( is_int @ SV749 ) )
        = $true )
      | ( ( ~ ( is_int @ SV767 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV749 ) @ SV767 ) )
          | ( SV749 != SV767 )
          | ( SV320 = SV490 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8361]) ).

thf(8443,plain,
    ! [SV822: $i] :
      ( ( ! [SY1307: $i] :
            ( ~ ( is_int @ SV822 )
            | ~ ( is_int @ SY1307 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV822 ) @ SY1307 )
             != one_one_int )
            | ( SV822 = one_one_int )
            | ( SV822
              = ( hAPP_int_int @ number_number_of_int @ min ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8362]) ).

thf(8444,plain,
    ! [SV823: $i] :
      ( ( ! [SY1308: $i] :
            ( ~ ( is_int @ SV823 )
            | ~ ( is_int @ SY1308 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV823 ) @ SY1308 )
             != one_one_int )
            | ( SV823 = one_one_int )
            | ( SY1308
              = ( hAPP_int_int @ number_number_of_int @ min ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8363]) ).

thf(8445,plain,
    ! [SV824: $i] :
      ( ( ! [SY1309: $i] :
            ( ~ ( is_int @ SV824 )
            | ~ ( is_int @ SY1309 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV824 ) @ SY1309 )
             != one_one_int )
            | ( SY1309 = one_one_int )
            | ( SV824
              = ( hAPP_int_int @ number_number_of_int @ min ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8364]) ).

thf(8446,plain,
    ! [SV825: $i] :
      ( ( ! [SY1310: $i] :
            ( ~ ( is_int @ SV825 )
            | ~ ( is_int @ SY1310 )
            | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV825 ) @ SY1310 )
             != one_one_int )
            | ( SY1310 = one_one_int )
            | ( SY1310
              = ( hAPP_int_int @ number_number_of_int @ min ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8365]) ).

thf(8447,plain,
    ! [SV789: $i,SV768: $i] :
      ( ( ( ~ ( is_int @ SV768 ) )
        = $true )
      | ( ( ~ ( is_int @ SV789 ) )
        = $true )
      | ( ( ( SV768 != one_one_int )
          | ( SV789 != one_one_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV768 ) @ SV789 )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8366]) ).

thf(8448,plain,
    ! [SV790: $i,SV769: $i] :
      ( ( ( ~ ( is_int @ SV769 ) )
        = $true )
      | ( ( ~ ( is_int @ SV790 ) )
        = $true )
      | ( ( ( SV769
           != ( hAPP_int_int @ number_number_of_int @ min ) )
          | ( SV790
           != ( hAPP_int_int @ number_number_of_int @ min ) )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV769 ) @ SV790 )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8367]) ).

thf(8449,plain,
    ! [SV770: $i] :
      ( ( ( SV770 != one_one_int )
        = $true )
      | ( ( ( hAPP_int_int @ abs_abs_int @ SV770 )
          = one_one_int )
        = $true )
      | ( ( is_int @ SV770 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8369]) ).

thf(8450,plain,
    ! [SV771: $i] :
      ( ( ( SV771
         != ( hAPP_int_int @ number_number_of_int @ min ) )
        = $true )
      | ( ( ( hAPP_int_int @ abs_abs_int @ SV771 )
          = one_one_int )
        = $true )
      | ( ( is_int @ SV771 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8370]) ).

thf(8451,plain,
    ! [SV826: $i,SV810: $i,SV491: $i,SV321: $i] :
      ( ( ~ ( is_int @ SV321 )
        | ~ ( is_int @ SV491 )
        | ~ ( is_int @ SV810 )
        | ~ ( is_int @ SV826 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV810 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV826 ) @ SV491 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV810 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV826 ) @ SV321 ) ) )
        | ( SV810 != SV826 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8371]) ).

thf(8452,plain,
    ! [SV827: $i,SV811: $i,SV491: $i,SV321: $i] :
      ( ( ~ ( is_int @ SV321 )
        | ~ ( is_int @ SV491 )
        | ~ ( is_int @ SV811 )
        | ~ ( is_int @ SV827 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV811 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV827 ) @ SV491 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV811 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV827 ) @ SV321 ) ) )
        | ( SV321 != SV491 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8372]) ).

thf(8453,plain,
    ! [SV772: $i,SV750: $i,SV491: $i,SV321: $i] :
      ( ( ( ~ ( is_int @ SV321 )
          | ~ ( is_int @ SV491 ) )
        = $true )
      | ( ( ~ ( is_int @ SV750 ) )
        = $true )
      | ( ( ~ ( is_int @ SV772 ) )
        = $true )
      | ( ( ( SV750 = SV772 )
          | ( SV321 = SV491 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV750 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV772 ) @ SV491 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV750 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV772 ) @ SV321 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8373]) ).

thf(8454,plain,
    ! [SV719: $i,SV644: $i] :
      ( ( ( ( SV644 != zero_zero_int )
          | ( SV719 != zero_zero_int ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV644 ) @ SV719 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV644 )
        = $false )
      | ( ( is_int @ SV719 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8374]) ).

thf(8455,plain,
    ! [SV791: $i,SV773: $i] :
      ( ( ( ~ ( is_int @ SV773 ) )
        = $true )
      | ( ( ~ ( is_int @ SV791 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV773 ) @ SV791 )
           != zero_zero_int )
          | ( SV773 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8375]) ).

thf(8456,plain,
    ! [SV792: $i,SV774: $i] :
      ( ( ( ~ ( is_int @ SV774 ) )
        = $true )
      | ( ( ~ ( is_int @ SV792 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV774 ) @ SV792 )
           != zero_zero_int )
          | ( SV792 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8376]) ).

thf(8457,plain,
    ! [SV720: $i,SV645: $i] :
      ( ( ( ( hAPP_int_int @ ( div_mod_int @ SV645 ) @ SV720 )
          = zero_zero_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV645 ) @ ( hAPP_int_int @ uminus_uminus_int @ SV720 ) )
          = ( hAPP_int_int @ uminus_uminus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV645 ) @ SV720 ) ) )
        = $true )
      | ( ( SV720 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV720 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8377]) ).

thf(8458,plain,
    ! [SV724: $i,SV751: $i,SV322: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SV751 )
          = one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SV724 )
          = one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV724 ) @ SV751 ) )
          = one_one_int )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8379]) ).

thf(8459,plain,
    ! [SV828: $i,SV793: $i,SV322: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV793 ) @ SV828 ) )
         != one_one_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SV793 )
          = one_one_int )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[8380]) ).

thf(8460,plain,
    ! [SV812: $i,SV794: $i,SV322: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV794 ) @ SV812 ) )
         != one_one_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SV812 )
          = one_one_int )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8381]) ).

thf(8461,plain,
    ! [SV775: $i,SV570: $i,SV492: $i,SV323: $i,SV795: $i] :
      ( ( ( is_int @ SV795 )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV323 ) @ SV492 ) ) @ SV570 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV775 ) @ SV492 ) ) @ SV795 ) )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV323 ) @ SV775 ) ) @ SV492 ) ) @ SV570 )
            = SV795 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8382]) ).

thf(8462,plain,
    ! [SV570: $i,SV492: $i,SV776: $i,SV323: $i,SV796: $i] :
      ( ( ( is_int @ SV796 )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV323 ) @ SV776 ) ) @ SV492 ) ) @ SV570 )
           != SV796 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV323 ) @ SV492 ) ) @ SV570 )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV776 ) @ SV492 ) ) @ SV796 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8383]) ).

thf(8463,plain,
    ! [SV777: $i,SV651: $i] :
      ( ( ( ( SV651
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV777 ) @ ( sK12_Q_4 @ SV777 @ SV651 ) ) )
          | ~ ( is_int @ ( sK12_Q_4 @ SV777 @ SV651 ) ) )
        = $false )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ SV651 ) @ SV777 )
          = zero_zero_int )
        = $false )
      | ( ( is_int @ SV651 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8384]) ).

thf(8464,plain,
    ! [SV813: $i,SV778: $i,SV652: $i] :
      ( ( ( SV652
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV778 ) @ SV813 ) )
        = $true )
      | ( ( ~ ( is_int @ SV813 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ SV652 ) @ SV778 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV652 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8385]) ).

thf(8465,plain,
    ! [SV727: $i,SV655: $i] :
      ( ( ( ( hAPP_int_int @ bit0 @ SV655 )
         != ( hAPP_int_int @ bit0 @ SV727 ) )
        = $true )
      | ( ( SV655 = SV727 )
        = $true )
      | ( ( is_int @ SV655 )
        = $false )
      | ( ( is_int @ SV727 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8386]) ).

thf(8466,plain,
    ! [SV728: $i,SV656: $i] :
      ( ( ( SV656 != SV728 )
        = $true )
      | ( ( ( hAPP_int_int @ bit0 @ SV656 )
          = ( hAPP_int_int @ bit0 @ SV728 ) )
        = $true )
      | ( ( is_int @ SV656 )
        = $false )
      | ( ( is_int @ SV728 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8387]) ).

thf(8467,plain,
    ! [SV731: $i,SV663: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV663 ) @ SV731 )
         != zero_zero_int )
        = $true )
      | ( ( SV663 = SV731 )
        = $true )
      | ( ( is_int @ SV663 )
        = $false )
      | ( ( is_int @ SV731 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8388]) ).

thf(8468,plain,
    ! [SV732: $i,SV664: $i] :
      ( ( ( SV664 != SV732 )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV664 ) @ SV732 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV664 )
        = $false )
      | ( ( is_int @ SV732 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8389]) ).

thf(8469,plain,
    ! [SV733: $i,SV665: $i] :
      ( ( ( SV665 != SV733 )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV665 ) @ SV733 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV665 )
        = $false )
      | ( ( is_int @ SV733 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8390]) ).

thf(8470,plain,
    ! [SV734: $i,SV666: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV666 ) @ SV734 )
         != zero_zero_int )
        = $true )
      | ( ( SV666 = SV734 )
        = $true )
      | ( ( is_int @ SV666 )
        = $false )
      | ( ( is_int @ SV734 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8391]) ).

thf(8471,plain,
    ! [SV737: $i,SV677: $i] :
      ( ( ( ( SV677 != zero_zero_int )
          | ( SV737 != zero_zero_int ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV677 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV737 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV677 )
        = $false )
      | ( ( is_int @ SV737 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8392]) ).

thf(8472,plain,
    ! [SV797: $i,SV779: $i] :
      ( ( ( ~ ( is_int @ SV779 ) )
        = $true )
      | ( ( ~ ( is_int @ SV797 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV779 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV797 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
           != zero_zero_int )
          | ( SV779 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8393]) ).

thf(8473,plain,
    ! [SV798: $i,SV780: $i] :
      ( ( ( ~ ( is_int @ SV780 ) )
        = $true )
      | ( ( ~ ( is_int @ SV798 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV780 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV798 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
           != zero_zero_int )
          | ( SV798 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8394]) ).

thf(8474,plain,
    ! [SV738: $i,SV678: $i] :
      ( ( ( ( SV678 != zero_zero_int )
          | ( SV738 != zero_zero_int ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV678 ) @ SV678 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV738 ) @ SV738 ) )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV678 )
        = $false )
      | ( ( is_int @ SV738 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8395]) ).

thf(8475,plain,
    ! [SV799: $i,SV781: $i] :
      ( ( ( ~ ( is_int @ SV781 ) )
        = $true )
      | ( ( ~ ( is_int @ SV799 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV781 ) @ SV781 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV799 ) @ SV799 ) )
           != zero_zero_int )
          | ( SV781 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8396]) ).

thf(8476,plain,
    ! [SV800: $i,SV782: $i] :
      ( ( ( ~ ( is_int @ SV782 ) )
        = $true )
      | ( ( ~ ( is_int @ SV800 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV782 ) @ SV782 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV800 ) @ SV800 ) )
           != zero_zero_int )
          | ( SV800 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8397]) ).

thf(8477,plain,
    ! [SV739: $i,SV679: $i] :
      ( ( ( ( SV679 != zero_zero_int )
          | ( SV739 != zero_zero_int ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV679 ) @ SV739 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV679 )
        = $false )
      | ( ( is_int @ SV739 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8398]) ).

thf(8478,plain,
    ! [SV801: $i,SV783: $i] :
      ( ( ( ~ ( is_int @ SV783 ) )
        = $true )
      | ( ( ~ ( is_int @ SV801 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV783 ) @ SV801 )
           != zero_zero_int )
          | ( SV783 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8399]) ).

thf(8479,plain,
    ! [SV802: $i,SV784: $i] :
      ( ( ( ~ ( is_int @ SV784 ) )
        = $true )
      | ( ( ~ ( is_int @ SV802 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV784 ) @ SV802 )
           != zero_zero_int )
          | ( SV802 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8400]) ).

thf(8480,plain,
    ! [SV576: $i,SV524: $i,SV380: $i,SV104: $i,SV680: $i] :
      ( ( ( is_int @ SV680 )
        = $false )
      | ( ( is_int @ SV104 )
        = $false )
      | ( ( is_int @ SV380 )
        = $false )
      | ( ( ( SV680 = zero_zero_int )
          | ( SV104 = SV380 )
          | ( SV524 != SV576 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV524 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV680 ) @ SV104 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV576 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV680 ) @ SV380 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8401]) ).

thf(8481,plain,
    ! [SV753: $i,SV684: $i,SV587: $i,SV785: $i,SV564: $i,SV741: $i,SV475: $i,SV287: $i] :
      ( ( ( SV287
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV475 ) @ SV741 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV564 ) @ SV785 ) ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ SV587 ) @ SV287 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV684 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV587 ) @ SV287 ) ) @ SV475 ) ) ) @ SV741 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV753 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV587 ) @ SV287 ) ) @ SV564 ) ) ) @ SV785 ) ) )
        = $true )
      | ( ( SV587
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV684 ) @ SV741 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV753 ) @ SV785 ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8402]) ).

thf(8482,plain,
    ! [SV691: $i,SV606: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV606 ) @ SV691 )
          = zero_zero_int )
        = $false )
      | ( ( ( SV606 = zero_zero_int )
          | ( SV691 = zero_zero_int ) )
        = $true )
      | ( ( is_int @ SV606 )
        = $false )
      | ( ( is_int @ SV691 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8403]) ).

thf(8483,plain,
    ! [SV786: $i,SV754: $i] :
      ( ( ( is_int @ SV754 )
        = $false )
      | ( ( ~ ( is_int @ SV786 ) )
        = $true )
      | ( ( ( SV754 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV754 ) @ SV786 )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8404]) ).

thf(8484,plain,
    ! [SV787: $i,SV755: $i] :
      ( ( ( is_int @ SV755 )
        = $false )
      | ( ( ~ ( is_int @ SV787 ) )
        = $true )
      | ( ( ( SV787 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV755 ) @ SV787 )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8405]) ).

thf(8485,plain,
    ! [SV814: $i,SV757: $i] :
      ( ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV757 ) @ ( hAPP_int_nat @ number_number_of_nat @ SV814 ) )
         != zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_nat @ number_number_of_nat @ SV814 )
         != zero_zero_nat )
        = $true )
      | ( ( is_int @ SV757 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8407]) ).

thf(8486,plain,
    ! [SV829: $i,SV758: $i] :
      ( ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV758 ) @ ( hAPP_int_nat @ number_number_of_nat @ SV829 ) )
         != zero_zero_int )
        = $true )
      | ( ( SV758 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV758 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8408]) ).

thf(8487,plain,
    ! [SV314: $i,SV486: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK1_A_4 @ SV486 @ SV314 ) )
                      | ~ ( is_int @ ( sK2_SY713 @ SV486 @ SV314 ) ) )
                | ( SV314
                 != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK1_A_4 @ SV486 @ SV314 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 ) ) ) )
          | ( SV486
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK2_SY713 @ SV486 @ SV314 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 ) ) ) )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV314 )
        = $false )
      | ( ( is_int @ SV486 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8410]) ).

thf(8488,plain,
    ! [SV696: $i,SV619: $i] :
      ( ( ( ( hAPP_int_int @ number_number_of_int @ SV619 )
          = ( hAPP_int_int @ number_number_of_int @ SV696 ) )
        = $false )
      | ( ( SV619 = SV696 )
        = $true )
      | ( ( is_int @ SV619 )
        = $false )
      | ( ( is_int @ SV696 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8412]) ).

thf(8489,plain,
    ! [SV697: $i,SV620: $i] :
      ( ( ( SV620 = SV697 )
        = $false )
      | ( ( ( hAPP_int_int @ number_number_of_int @ SV620 )
          = ( hAPP_int_int @ number_number_of_int @ SV697 ) )
        = $true )
      | ( ( is_int @ SV620 )
        = $false )
      | ( ( is_int @ SV697 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8413]) ).

thf(8490,plain,
    ! [SV815: $i,SV760: $i] :
      ( ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV760 ) @ SV815 )
         != zero_zero_int )
        = $true )
      | ( ( SV815 != zero_zero_nat )
        = $true )
      | ( ( is_int @ SV760 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8415]) ).

thf(8491,plain,
    ! [SV830: $i,SV761: $i] :
      ( ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV761 ) @ SV830 )
         != zero_zero_int )
        = $true )
      | ( ( SV761 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV761 )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[8416]) ).

thf(8492,plain,
    ! [SV762: $i,SV742: $i,SV487: $i,SV315: $i] :
      ( ( ( ~ ( is_int @ SV315 ) )
        = $true )
      | ( ( ~ ( is_int @ SV487 ) )
        = $true )
      | ( ( ~ ( is_int @ SV742 ) )
        = $true )
      | ( ( ~ ( is_int @ SV762 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV742 ) @ SV762 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV762 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV742 ) @ SV487 ) ) )
          | ( SV315 = SV742 )
          | ( SV487 = SV762 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8417]) ).

thf(8493,plain,
    ! [SV816: $i,SV803: $i,SV487: $i,SV315: $i] :
      ( ( ( ~ ( is_int @ SV315 )
          | ~ ( is_int @ SV487 )
          | ~ ( is_int @ SV803 )
          | ~ ( is_int @ SV816 ) )
        = $true )
      | ( ( ( SV315 != SV803 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV803 ) @ SV816 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV816 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV803 ) @ SV487 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8418]) ).

thf(8494,plain,
    ! [SV817: $i,SV804: $i,SV487: $i,SV315: $i] :
      ( ( ( ~ ( is_int @ SV315 )
          | ~ ( is_int @ SV487 )
          | ~ ( is_int @ SV804 )
          | ~ ( is_int @ SV817 ) )
        = $true )
      | ( ( ( SV487 != SV817 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV804 ) @ SV817 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV817 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV804 ) @ SV487 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8419]) ).

thf(8495,plain,
    ! [SV700: $i,SV624: $i] :
      ( ( ( SV624
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV624 ) @ SV700 ) )
        = $false )
      | ( ( SV700 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV624 )
        = $false )
      | ( ( is_int @ SV700 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8420]) ).

thf(8496,plain,
    ! [SV625: $i,SV701: $i] :
      ( ( ( SV701 = zero_zero_int )
        = $false )
      | ( ( SV625
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV625 ) @ SV701 ) )
        = $true )
      | ( ( is_int @ SV625 )
        = $false )
      | ( ( is_int @ SV701 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8421]) ).

thf(8497,plain,
    ! [SV743: $i,SV704: $i,SV316: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SV704 )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SV743 ) )
        = $true )
      | ( ( SV704 = SV743 )
        = $true )
      | ( ( is_int @ SV704 )
        = $false )
      | ( ( is_int @ SV743 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8422]) ).

thf(8498,plain,
    ! [SV316: $i,SV744: $i,SV705: $i] :
      ( ( ( SV705 != SV744 )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SV705 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SV744 ) )
        = $true )
      | ( ( is_int @ SV705 )
        = $false )
      | ( ( is_int @ SV744 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8423]) ).

thf(8499,plain,
    ! [SV708: $i,SV632: $i] :
      ( ( ( ( hAPP_int_int @ bit1 @ SV632 )
          = ( hAPP_int_int @ bit1 @ SV708 ) )
        = $false )
      | ( ( SV632 = SV708 )
        = $true )
      | ( ( is_int @ SV632 )
        = $false )
      | ( ( is_int @ SV708 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8426]) ).

thf(8500,plain,
    ! [SV709: $i,SV633: $i] :
      ( ( ( SV633 = SV709 )
        = $false )
      | ( ( ( hAPP_int_int @ bit1 @ SV633 )
          = ( hAPP_int_int @ bit1 @ SV709 ) )
        = $true )
      | ( ( is_int @ SV633 )
        = $false )
      | ( ( is_int @ SV709 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8427]) ).

thf(8501,plain,
    ! [SV635: $i,SV711: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK7_C_3 @ SV711 @ SV635 ) )
                            | ~ ( is_int @ ( sK8_SY715 @ SV711 @ SV635 ) ) )
                      | ( SV711
                       != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV711 ) @ SV635 ) ) @ ( sK7_C_3 @ SV711 @ SV635 ) ) ) )
                | ( SV635
                 != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV711 ) @ SV635 ) ) @ ( sK8_SY715 @ SV711 @ SV635 ) ) ) )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK7_C_3 @ SV711 @ SV635 ) ) @ ( sK8_SY715 @ SV711 @ SV635 ) )
           != one_one_int ) )
        = $false )
      | ( ( SV711 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV635 )
        = $false )
      | ( ( is_int @ SV711 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8430]) ).

thf(8502,plain,
    ! [SV636: $i,SV712: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK5_C_3 @ SV712 @ SV636 ) )
                            | ~ ( is_int @ ( sK6_SY714 @ SV712 @ SV636 ) ) )
                      | ( SV712
                       != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV712 ) @ SV636 ) ) @ ( sK5_C_3 @ SV712 @ SV636 ) ) ) )
                | ( SV636
                 != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV712 ) @ SV636 ) ) @ ( sK6_SY714 @ SV712 @ SV636 ) ) ) )
          | ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK5_C_3 @ SV712 @ SV636 ) ) @ ( sK6_SY714 @ SV712 @ SV636 ) )
           != one_one_int ) )
        = $false )
      | ( ( SV636 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV636 )
        = $false )
      | ( ( is_int @ SV712 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8431]) ).

thf(8503,plain,
    ! [SV745: $i,SV715: $i,SV317: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV317 ) @ SV715 )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV745 ) @ SV715 ) )
        = $true )
      | ( ( SV317 = SV745 )
        = $true )
      | ( ( is_int @ SV317 )
        = $false )
      | ( ( is_int @ SV745 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8432]) ).

thf(8504,plain,
    ! [SV716: $i,SV746: $i,SV317: $i] :
      ( ( ( SV317 != SV746 )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV317 ) @ SV716 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV746 ) @ SV716 ) )
        = $true )
      | ( ( is_int @ SV317 )
        = $false )
      | ( ( is_int @ SV746 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8433]) ).

thf(8505,plain,
    ! [SV818: $i,SV806: $i,SV569: $i,SV488: $i,SV318: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV318 ) @ SV488 ) ) @ SV569 )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV806 ) @ SV488 ) ) @ SV818 ) )
        = $true )
      | ( ( SV569
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV806 ) @ SV318 ) ) @ SV488 ) ) @ SV818 ) )
        = $true )
      | ( ( is_int @ SV569 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8436]) ).

thf(8506,plain,
    ! [SV819: $i,SV488: $i,SV318: $i,SV807: $i,SV569: $i] :
      ( ( ( SV569
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV807 ) @ SV318 ) ) @ SV488 ) ) @ SV819 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV318 ) @ SV488 ) ) @ SV569 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV807 ) @ SV488 ) ) @ SV819 ) )
        = $true )
      | ( ( is_int @ SV569 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8437]) ).

thf(8507,plain,
    ! [SV765: $i,SV747: $i,SV489: $i,SV319: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
          = one_one_int )
        = $false )
      | ( ( ( ( hAPP_int_int @ abs_abs_int @ SV747 )
           != ( hAPP_int_int @ abs_abs_int @ SV319 ) )
          | ( ( hAPP_int_int @ abs_abs_int @ SV489 )
           != ( hAPP_int_int @ abs_abs_int @ SV765 ) )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV747 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV765 ) ) ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV747 ) @ SV765 )
          = one_one_int )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8438]) ).

thf(8508,plain,
    ! [SV489: $i,SV319: $i,SV820: $i,SV808: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV808 ) @ SV820 )
         != one_one_int )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
           != one_one_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV808 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV820 ) ) )
          | ( ( hAPP_int_int @ abs_abs_int @ SV808 )
            = ( hAPP_int_int @ abs_abs_int @ SV319 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8439]) ).

thf(8509,plain,
    ! [SV489: $i,SV319: $i,SV821: $i,SV809: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV809 ) @ SV821 )
         != one_one_int )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
           != one_one_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV809 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV821 ) ) )
          | ( ( hAPP_int_int @ abs_abs_int @ SV489 )
            = ( hAPP_int_int @ abs_abs_int @ SV821 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8440]) ).

thf(8510,plain,
    ! [SV766: $i,SV748: $i,SV490: $i,SV320: $i] :
      ( ( ( ~ ( is_int @ SV320 ) )
        = $true )
      | ( ( ~ ( is_int @ SV490 ) )
        = $true )
      | ( ( ~ ( is_int @ SV748 ) )
        = $true )
      | ( ( ~ ( is_int @ SV766 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV748 ) @ SV766 ) )
          | ( SV320 != SV490 )
          | ( SV748 = SV766 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8441]) ).

thf(8511,plain,
    ! [SV767: $i,SV749: $i,SV490: $i,SV320: $i] :
      ( ( ( ~ ( is_int @ SV320 ) )
        = $true )
      | ( ( ~ ( is_int @ SV490 ) )
        = $true )
      | ( ( ~ ( is_int @ SV749 ) )
        = $true )
      | ( ( ~ ( is_int @ SV767 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV749 ) @ SV767 ) )
          | ( SV749 != SV767 )
          | ( SV320 = SV490 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8442]) ).

thf(8512,plain,
    ! [SV831: $i,SV822: $i] :
      ( ( ~ ( is_int @ SV822 )
        | ~ ( is_int @ SV831 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV822 ) @ SV831 )
         != one_one_int )
        | ( SV822 = one_one_int )
        | ( SV822
          = ( hAPP_int_int @ number_number_of_int @ min ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8443]) ).

thf(8513,plain,
    ! [SV832: $i,SV823: $i] :
      ( ( ~ ( is_int @ SV823 )
        | ~ ( is_int @ SV832 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV823 ) @ SV832 )
         != one_one_int )
        | ( SV823 = one_one_int )
        | ( SV832
          = ( hAPP_int_int @ number_number_of_int @ min ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8444]) ).

thf(8514,plain,
    ! [SV833: $i,SV824: $i] :
      ( ( ~ ( is_int @ SV824 )
        | ~ ( is_int @ SV833 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV824 ) @ SV833 )
         != one_one_int )
        | ( SV833 = one_one_int )
        | ( SV824
          = ( hAPP_int_int @ number_number_of_int @ min ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8445]) ).

thf(8515,plain,
    ! [SV834: $i,SV825: $i] :
      ( ( ~ ( is_int @ SV825 )
        | ~ ( is_int @ SV834 )
        | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV825 ) @ SV834 )
         != one_one_int )
        | ( SV834 = one_one_int )
        | ( SV834
          = ( hAPP_int_int @ number_number_of_int @ min ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[8446]) ).

thf(8516,plain,
    ! [SV789: $i,SV768: $i] :
      ( ( ( is_int @ SV768 )
        = $false )
      | ( ( ~ ( is_int @ SV789 ) )
        = $true )
      | ( ( ( SV768 != one_one_int )
          | ( SV789 != one_one_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV768 ) @ SV789 )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8447]) ).

thf(8517,plain,
    ! [SV790: $i,SV769: $i] :
      ( ( ( is_int @ SV769 )
        = $false )
      | ( ( ~ ( is_int @ SV790 ) )
        = $true )
      | ( ( ( SV769
           != ( hAPP_int_int @ number_number_of_int @ min ) )
          | ( SV790
           != ( hAPP_int_int @ number_number_of_int @ min ) )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV769 ) @ SV790 )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8448]) ).

thf(8518,plain,
    ! [SV770: $i] :
      ( ( ( SV770 = one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ abs_abs_int @ SV770 )
          = one_one_int )
        = $true )
      | ( ( is_int @ SV770 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8449]) ).

thf(8519,plain,
    ! [SV771: $i] :
      ( ( ( SV771
          = ( hAPP_int_int @ number_number_of_int @ min ) )
        = $false )
      | ( ( ( hAPP_int_int @ abs_abs_int @ SV771 )
          = one_one_int )
        = $true )
      | ( ( is_int @ SV771 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8450]) ).

thf(8520,plain,
    ! [SV826: $i,SV810: $i,SV491: $i,SV321: $i] :
      ( ( ( ~ ( is_int @ SV321 )
          | ~ ( is_int @ SV491 )
          | ~ ( is_int @ SV810 )
          | ~ ( is_int @ SV826 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV810 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV826 ) @ SV491 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV810 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV826 ) @ SV321 ) ) )
          | ( SV810 != SV826 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8451]) ).

thf(8521,plain,
    ! [SV827: $i,SV811: $i,SV491: $i,SV321: $i] :
      ( ( ( ~ ( is_int @ SV321 )
          | ~ ( is_int @ SV491 )
          | ~ ( is_int @ SV811 )
          | ~ ( is_int @ SV827 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV811 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV827 ) @ SV491 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV811 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV827 ) @ SV321 ) ) )
          | ( SV321 != SV491 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8452]) ).

thf(8522,plain,
    ! [SV772: $i,SV750: $i,SV491: $i,SV321: $i] :
      ( ( ( ~ ( is_int @ SV321 ) )
        = $true )
      | ( ( ~ ( is_int @ SV491 ) )
        = $true )
      | ( ( ~ ( is_int @ SV750 ) )
        = $true )
      | ( ( ~ ( is_int @ SV772 ) )
        = $true )
      | ( ( ( SV750 = SV772 )
          | ( SV321 = SV491 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV750 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV772 ) @ SV491 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV750 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV772 ) @ SV321 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8453]) ).

thf(8523,plain,
    ! [SV719: $i,SV644: $i] :
      ( ( ( SV644 != zero_zero_int )
        = $true )
      | ( ( SV719 != zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV644 ) @ SV719 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV644 )
        = $false )
      | ( ( is_int @ SV719 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8454]) ).

thf(8524,plain,
    ! [SV791: $i,SV773: $i] :
      ( ( ( is_int @ SV773 )
        = $false )
      | ( ( ~ ( is_int @ SV791 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV773 ) @ SV791 )
           != zero_zero_int )
          | ( SV773 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8455]) ).

thf(8525,plain,
    ! [SV792: $i,SV774: $i] :
      ( ( ( is_int @ SV774 )
        = $false )
      | ( ( ~ ( is_int @ SV792 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV774 ) @ SV792 )
           != zero_zero_int )
          | ( SV792 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8456]) ).

thf(8526,plain,
    ! [SV828: $i,SV793: $i,SV322: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV793 ) @ SV828 ) )
          = one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SV793 )
          = one_one_int )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8459]) ).

thf(8527,plain,
    ! [SV812: $i,SV794: $i,SV322: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV794 ) @ SV812 ) )
          = one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV322 ) @ SV812 )
          = one_one_int )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8460]) ).

thf(8528,plain,
    ! [SV795: $i,SV775: $i,SV570: $i,SV492: $i,SV323: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV323 ) @ SV492 ) ) @ SV570 )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV775 ) @ SV492 ) ) @ SV795 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV323 ) @ SV775 ) ) @ SV492 ) ) @ SV570 )
          = SV795 )
        = $true )
      | ( ( is_int @ SV795 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8461]) ).

thf(8529,plain,
    ! [SV796: $i,SV570: $i,SV492: $i,SV776: $i,SV323: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV323 ) @ SV776 ) ) @ SV492 ) ) @ SV570 )
         != SV796 )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV323 ) @ SV492 ) ) @ SV570 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV776 ) @ SV492 ) ) @ SV796 ) )
        = $true )
      | ( ( is_int @ SV796 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8462]) ).

thf(8530,plain,
    ! [SV777: $i,SV651: $i] :
      ( ( ( SV651
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV777 ) @ ( sK12_Q_4 @ SV777 @ SV651 ) ) )
        = $false )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ SV651 ) @ SV777 )
          = zero_zero_int )
        = $false )
      | ( ( is_int @ SV651 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[8463]) ).

thf(8531,plain,
    ! [SV651: $i,SV777: $i] :
      ( ( ( ~ ( is_int @ ( sK12_Q_4 @ SV777 @ SV651 ) ) )
        = $false )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ SV651 ) @ SV777 )
          = zero_zero_int )
        = $false )
      | ( ( is_int @ SV651 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[8463]) ).

thf(8532,plain,
    ! [SV813: $i,SV778: $i,SV652: $i] :
      ( ( ( SV652
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV778 ) @ SV813 ) )
        = $false )
      | ( ( ~ ( is_int @ SV813 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ SV652 ) @ SV778 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV652 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8464]) ).

thf(8533,plain,
    ! [SV727: $i,SV655: $i] :
      ( ( ( ( hAPP_int_int @ bit0 @ SV655 )
          = ( hAPP_int_int @ bit0 @ SV727 ) )
        = $false )
      | ( ( SV655 = SV727 )
        = $true )
      | ( ( is_int @ SV655 )
        = $false )
      | ( ( is_int @ SV727 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8465]) ).

thf(8534,plain,
    ! [SV728: $i,SV656: $i] :
      ( ( ( SV656 = SV728 )
        = $false )
      | ( ( ( hAPP_int_int @ bit0 @ SV656 )
          = ( hAPP_int_int @ bit0 @ SV728 ) )
        = $true )
      | ( ( is_int @ SV656 )
        = $false )
      | ( ( is_int @ SV728 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8466]) ).

thf(8535,plain,
    ! [SV731: $i,SV663: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV663 ) @ SV731 )
          = zero_zero_int )
        = $false )
      | ( ( SV663 = SV731 )
        = $true )
      | ( ( is_int @ SV663 )
        = $false )
      | ( ( is_int @ SV731 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8467]) ).

thf(8536,plain,
    ! [SV732: $i,SV664: $i] :
      ( ( ( SV664 = SV732 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV664 ) @ SV732 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV664 )
        = $false )
      | ( ( is_int @ SV732 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8468]) ).

thf(8537,plain,
    ! [SV733: $i,SV665: $i] :
      ( ( ( SV665 = SV733 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV665 ) @ SV733 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV665 )
        = $false )
      | ( ( is_int @ SV733 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8469]) ).

thf(8538,plain,
    ! [SV734: $i,SV666: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV666 ) @ SV734 )
          = zero_zero_int )
        = $false )
      | ( ( SV666 = SV734 )
        = $true )
      | ( ( is_int @ SV666 )
        = $false )
      | ( ( is_int @ SV734 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8470]) ).

thf(8539,plain,
    ! [SV737: $i,SV677: $i] :
      ( ( ( SV677 != zero_zero_int )
        = $true )
      | ( ( SV737 != zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV677 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV737 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV677 )
        = $false )
      | ( ( is_int @ SV737 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8471]) ).

thf(8540,plain,
    ! [SV797: $i,SV779: $i] :
      ( ( ( is_int @ SV779 )
        = $false )
      | ( ( ~ ( is_int @ SV797 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV779 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV797 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
           != zero_zero_int )
          | ( SV779 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8472]) ).

thf(8541,plain,
    ! [SV798: $i,SV780: $i] :
      ( ( ( is_int @ SV780 )
        = $false )
      | ( ( ~ ( is_int @ SV798 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV780 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV798 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
           != zero_zero_int )
          | ( SV798 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8473]) ).

thf(8542,plain,
    ! [SV738: $i,SV678: $i] :
      ( ( ( SV678 != zero_zero_int )
        = $true )
      | ( ( SV738 != zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV678 ) @ SV678 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV738 ) @ SV738 ) )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV678 )
        = $false )
      | ( ( is_int @ SV738 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8474]) ).

thf(8543,plain,
    ! [SV799: $i,SV781: $i] :
      ( ( ( is_int @ SV781 )
        = $false )
      | ( ( ~ ( is_int @ SV799 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV781 ) @ SV781 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV799 ) @ SV799 ) )
           != zero_zero_int )
          | ( SV781 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8475]) ).

thf(8544,plain,
    ! [SV800: $i,SV782: $i] :
      ( ( ( is_int @ SV782 )
        = $false )
      | ( ( ~ ( is_int @ SV800 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV782 ) @ SV782 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV800 ) @ SV800 ) )
           != zero_zero_int )
          | ( SV800 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8476]) ).

thf(8545,plain,
    ! [SV739: $i,SV679: $i] :
      ( ( ( SV679 != zero_zero_int )
        = $true )
      | ( ( SV739 != zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV679 ) @ SV739 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV679 )
        = $false )
      | ( ( is_int @ SV739 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8477]) ).

thf(8546,plain,
    ! [SV801: $i,SV783: $i] :
      ( ( ( is_int @ SV783 )
        = $false )
      | ( ( ~ ( is_int @ SV801 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV783 ) @ SV801 )
           != zero_zero_int )
          | ( SV783 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8478]) ).

thf(8547,plain,
    ! [SV802: $i,SV784: $i] :
      ( ( ( is_int @ SV784 )
        = $false )
      | ( ( ~ ( is_int @ SV802 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV784 ) @ SV802 )
           != zero_zero_int )
          | ( SV802 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8479]) ).

thf(8548,plain,
    ! [SV576: $i,SV524: $i,SV380: $i,SV104: $i,SV680: $i] :
      ( ( ( SV680 = zero_zero_int )
        = $true )
      | ( ( ( SV104 = SV380 )
          | ( SV524 != SV576 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV524 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV680 ) @ SV104 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV576 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV680 ) @ SV380 ) ) ) )
        = $true )
      | ( ( is_int @ SV380 )
        = $false )
      | ( ( is_int @ SV104 )
        = $false )
      | ( ( is_int @ SV680 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8480]) ).

thf(8549,plain,
    ! [SV753: $i,SV684: $i,SV587: $i,SV785: $i,SV564: $i,SV741: $i,SV475: $i,SV287: $i] :
      ( ( ( SV287
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV475 ) @ SV741 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV564 ) @ SV785 ) ) )
        = $false )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ SV587 ) @ SV287 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV684 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV587 ) @ SV287 ) ) @ SV475 ) ) ) @ SV741 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV753 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ div_div_int @ SV587 ) @ SV287 ) ) @ SV564 ) ) ) @ SV785 ) ) )
        = $true )
      | ( ( SV587
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV684 ) @ SV741 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV753 ) @ SV785 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8481]) ).

thf(8550,plain,
    ! [SV691: $i,SV606: $i] :
      ( ( ( SV606 = zero_zero_int )
        = $true )
      | ( ( SV691 = zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV606 ) @ SV691 )
          = zero_zero_int )
        = $false )
      | ( ( is_int @ SV606 )
        = $false )
      | ( ( is_int @ SV691 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8482]) ).

thf(8551,plain,
    ! [SV754: $i,SV786: $i] :
      ( ( ( is_int @ SV786 )
        = $false )
      | ( ( is_int @ SV754 )
        = $false )
      | ( ( ( SV754 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV754 ) @ SV786 )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8483]) ).

thf(8552,plain,
    ! [SV755: $i,SV787: $i] :
      ( ( ( is_int @ SV787 )
        = $false )
      | ( ( is_int @ SV755 )
        = $false )
      | ( ( ( SV787 != zero_zero_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV755 ) @ SV787 )
            = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8484]) ).

thf(8553,plain,
    ! [SV814: $i,SV757: $i] :
      ( ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV757 ) @ ( hAPP_int_nat @ number_number_of_nat @ SV814 ) )
          = zero_zero_int )
        = $false )
      | ( ( ( hAPP_int_nat @ number_number_of_nat @ SV814 )
         != zero_zero_nat )
        = $true )
      | ( ( is_int @ SV757 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8485]) ).

thf(8554,plain,
    ! [SV829: $i,SV758: $i] :
      ( ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV758 ) @ ( hAPP_int_nat @ number_number_of_nat @ SV829 ) )
          = zero_zero_int )
        = $false )
      | ( ( SV758 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV758 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8486]) ).

thf(8555,plain,
    ! [SV314: $i,SV486: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK1_A_4 @ SV486 @ SV314 ) )
                      | ~ ( is_int @ ( sK2_SY713 @ SV486 @ SV314 ) ) )
                | ( SV314
                 != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK1_A_4 @ SV486 @ SV314 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 ) ) ) ) )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV314 )
        = $false )
      | ( ( is_int @ SV486 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[8487]) ).

thf(8556,plain,
    ! [SV314: $i,SV486: $i] :
      ( ( ( SV486
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK2_SY713 @ SV486 @ SV314 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 ) ) )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV314 )
        = $false )
      | ( ( is_int @ SV486 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[8487]) ).

thf(8557,plain,
    ! [SV815: $i,SV760: $i] :
      ( ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV760 ) @ SV815 )
          = zero_zero_int )
        = $false )
      | ( ( SV815 != zero_zero_nat )
        = $true )
      | ( ( is_int @ SV760 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8490]) ).

thf(8558,plain,
    ! [SV830: $i,SV761: $i] :
      ( ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV761 ) @ SV830 )
          = zero_zero_int )
        = $false )
      | ( ( SV761 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV761 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8491]) ).

thf(8559,plain,
    ! [SV762: $i,SV742: $i,SV487: $i,SV315: $i] :
      ( ( ( is_int @ SV315 )
        = $false )
      | ( ( ~ ( is_int @ SV487 ) )
        = $true )
      | ( ( ~ ( is_int @ SV742 ) )
        = $true )
      | ( ( ~ ( is_int @ SV762 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV742 ) @ SV762 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV762 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV742 ) @ SV487 ) ) )
          | ( SV315 = SV742 )
          | ( SV487 = SV762 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8492]) ).

thf(8560,plain,
    ! [SV816: $i,SV803: $i,SV487: $i,SV315: $i] :
      ( ( ( ~ ( is_int @ SV315 )
          | ~ ( is_int @ SV487 )
          | ~ ( is_int @ SV803 ) )
        = $true )
      | ( ( ~ ( is_int @ SV816 ) )
        = $true )
      | ( ( ( SV315 != SV803 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV803 ) @ SV816 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV816 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV803 ) @ SV487 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8493]) ).

thf(8561,plain,
    ! [SV817: $i,SV804: $i,SV487: $i,SV315: $i] :
      ( ( ( ~ ( is_int @ SV315 )
          | ~ ( is_int @ SV487 )
          | ~ ( is_int @ SV804 ) )
        = $true )
      | ( ( ~ ( is_int @ SV817 ) )
        = $true )
      | ( ( ( SV487 != SV817 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV804 ) @ SV817 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV817 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV804 ) @ SV487 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8494]) ).

thf(8562,plain,
    ! [SV743: $i,SV704: $i,SV316: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SV704 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SV743 ) )
        = $false )
      | ( ( SV704 = SV743 )
        = $true )
      | ( ( is_int @ SV704 )
        = $false )
      | ( ( is_int @ SV743 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8497]) ).

thf(8563,plain,
    ! [SV316: $i,SV744: $i,SV705: $i] :
      ( ( ( SV705 = SV744 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SV705 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV316 ) @ SV744 ) )
        = $true )
      | ( ( is_int @ SV705 )
        = $false )
      | ( ( is_int @ SV744 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8498]) ).

thf(8564,plain,
    ! [SV635: $i,SV711: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK7_C_3 @ SV711 @ SV635 ) )
                            | ~ ( is_int @ ( sK8_SY715 @ SV711 @ SV635 ) ) )
                      | ( SV711
                       != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV711 ) @ SV635 ) ) @ ( sK7_C_3 @ SV711 @ SV635 ) ) ) )
                | ( SV635
                 != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV711 ) @ SV635 ) ) @ ( sK8_SY715 @ SV711 @ SV635 ) ) ) ) )
        = $false )
      | ( ( SV711 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV635 )
        = $false )
      | ( ( is_int @ SV711 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[8501]) ).

thf(8565,plain,
    ! [SV635: $i,SV711: $i] :
      ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK7_C_3 @ SV711 @ SV635 ) ) @ ( sK8_SY715 @ SV711 @ SV635 ) )
         != one_one_int )
        = $false )
      | ( ( SV711 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV635 )
        = $false )
      | ( ( is_int @ SV711 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[8501]) ).

thf(8566,plain,
    ! [SV636: $i,SV712: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK5_C_3 @ SV712 @ SV636 ) )
                            | ~ ( is_int @ ( sK6_SY714 @ SV712 @ SV636 ) ) )
                      | ( SV712
                       != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV712 ) @ SV636 ) ) @ ( sK5_C_3 @ SV712 @ SV636 ) ) ) )
                | ( SV636
                 != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV712 ) @ SV636 ) ) @ ( sK6_SY714 @ SV712 @ SV636 ) ) ) ) )
        = $false )
      | ( ( SV636 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV636 )
        = $false )
      | ( ( is_int @ SV712 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[8502]) ).

thf(8567,plain,
    ! [SV636: $i,SV712: $i] :
      ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK5_C_3 @ SV712 @ SV636 ) ) @ ( sK6_SY714 @ SV712 @ SV636 ) )
         != one_one_int )
        = $false )
      | ( ( SV636 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV636 )
        = $false )
      | ( ( is_int @ SV712 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[8502]) ).

thf(8568,plain,
    ! [SV745: $i,SV715: $i,SV317: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV317 ) @ SV715 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV745 ) @ SV715 ) )
        = $false )
      | ( ( SV317 = SV745 )
        = $true )
      | ( ( is_int @ SV317 )
        = $false )
      | ( ( is_int @ SV745 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8503]) ).

thf(8569,plain,
    ! [SV716: $i,SV746: $i,SV317: $i] :
      ( ( ( SV317 = SV746 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV317 ) @ SV716 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV746 ) @ SV716 ) )
        = $true )
      | ( ( is_int @ SV317 )
        = $false )
      | ( ( is_int @ SV746 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8504]) ).

thf(8570,plain,
    ! [SV818: $i,SV806: $i,SV569: $i,SV488: $i,SV318: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV318 ) @ SV488 ) ) @ SV569 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV806 ) @ SV488 ) ) @ SV818 ) )
        = $false )
      | ( ( SV569
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV806 ) @ SV318 ) ) @ SV488 ) ) @ SV818 ) )
        = $true )
      | ( ( is_int @ SV569 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8505]) ).

thf(8571,plain,
    ! [SV819: $i,SV488: $i,SV318: $i,SV807: $i,SV569: $i] :
      ( ( ( SV569
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV807 ) @ SV318 ) ) @ SV488 ) ) @ SV819 ) )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV318 ) @ SV488 ) ) @ SV569 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV807 ) @ SV488 ) ) @ SV819 ) )
        = $true )
      | ( ( is_int @ SV569 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8506]) ).

thf(8572,plain,
    ! [SV765: $i,SV489: $i,SV319: $i,SV747: $i] :
      ( ( ( ( ( hAPP_int_int @ abs_abs_int @ SV747 )
           != ( hAPP_int_int @ abs_abs_int @ SV319 ) )
          | ( ( hAPP_int_int @ abs_abs_int @ SV489 )
           != ( hAPP_int_int @ abs_abs_int @ SV765 ) ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV747 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV765 ) ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
          = one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV747 ) @ SV765 )
          = one_one_int )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8507]) ).

thf(8573,plain,
    ! [SV489: $i,SV319: $i,SV820: $i,SV808: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV808 ) @ SV820 )
          = one_one_int )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
           != one_one_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV808 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV820 ) ) )
          | ( ( hAPP_int_int @ abs_abs_int @ SV808 )
            = ( hAPP_int_int @ abs_abs_int @ SV319 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8508]) ).

thf(8574,plain,
    ! [SV489: $i,SV319: $i,SV821: $i,SV809: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV809 ) @ SV821 )
          = one_one_int )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
           != one_one_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV809 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV821 ) ) )
          | ( ( hAPP_int_int @ abs_abs_int @ SV489 )
            = ( hAPP_int_int @ abs_abs_int @ SV821 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8509]) ).

thf(8575,plain,
    ! [SV766: $i,SV748: $i,SV490: $i,SV320: $i] :
      ( ( ( is_int @ SV320 )
        = $false )
      | ( ( ~ ( is_int @ SV490 ) )
        = $true )
      | ( ( ~ ( is_int @ SV748 ) )
        = $true )
      | ( ( ~ ( is_int @ SV766 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV748 ) @ SV766 ) )
          | ( SV320 != SV490 )
          | ( SV748 = SV766 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8510]) ).

thf(8576,plain,
    ! [SV767: $i,SV749: $i,SV490: $i,SV320: $i] :
      ( ( ( is_int @ SV320 )
        = $false )
      | ( ( ~ ( is_int @ SV490 ) )
        = $true )
      | ( ( ~ ( is_int @ SV749 ) )
        = $true )
      | ( ( ~ ( is_int @ SV767 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV749 ) @ SV767 ) )
          | ( SV749 != SV767 )
          | ( SV320 = SV490 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8511]) ).

thf(8577,plain,
    ! [SV831: $i,SV822: $i] :
      ( ( ( ~ ( is_int @ SV822 )
          | ~ ( is_int @ SV831 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV822 ) @ SV831 )
           != one_one_int )
          | ( SV822 = one_one_int )
          | ( SV822
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8512]) ).

thf(8578,plain,
    ! [SV832: $i,SV823: $i] :
      ( ( ( ~ ( is_int @ SV823 )
          | ~ ( is_int @ SV832 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV823 ) @ SV832 )
           != one_one_int )
          | ( SV823 = one_one_int )
          | ( SV832
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8513]) ).

thf(8579,plain,
    ! [SV833: $i,SV824: $i] :
      ( ( ( ~ ( is_int @ SV824 )
          | ~ ( is_int @ SV833 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV824 ) @ SV833 )
           != one_one_int )
          | ( SV833 = one_one_int )
          | ( SV824
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8514]) ).

thf(8580,plain,
    ! [SV834: $i,SV825: $i] :
      ( ( ( ~ ( is_int @ SV825 )
          | ~ ( is_int @ SV834 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV825 ) @ SV834 )
           != one_one_int )
          | ( SV834 = one_one_int )
          | ( SV834
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8515]) ).

thf(8581,plain,
    ! [SV768: $i,SV789: $i] :
      ( ( ( is_int @ SV789 )
        = $false )
      | ( ( is_int @ SV768 )
        = $false )
      | ( ( ( SV768 != one_one_int )
          | ( SV789 != one_one_int )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV768 ) @ SV789 )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8516]) ).

thf(8582,plain,
    ! [SV769: $i,SV790: $i] :
      ( ( ( is_int @ SV790 )
        = $false )
      | ( ( is_int @ SV769 )
        = $false )
      | ( ( ( SV769
           != ( hAPP_int_int @ number_number_of_int @ min ) )
          | ( SV790
           != ( hAPP_int_int @ number_number_of_int @ min ) )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV769 ) @ SV790 )
            = one_one_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8517]) ).

thf(8583,plain,
    ! [SV826: $i,SV810: $i,SV491: $i,SV321: $i] :
      ( ( ( ~ ( is_int @ SV321 )
          | ~ ( is_int @ SV491 )
          | ~ ( is_int @ SV810 ) )
        = $true )
      | ( ( ~ ( is_int @ SV826 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV810 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV826 ) @ SV491 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV810 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV826 ) @ SV321 ) ) )
          | ( SV810 != SV826 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8520]) ).

thf(8584,plain,
    ! [SV827: $i,SV811: $i,SV491: $i,SV321: $i] :
      ( ( ( ~ ( is_int @ SV321 )
          | ~ ( is_int @ SV491 )
          | ~ ( is_int @ SV811 ) )
        = $true )
      | ( ( ~ ( is_int @ SV827 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV811 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV827 ) @ SV491 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV811 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV827 ) @ SV321 ) ) )
          | ( SV321 != SV491 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8521]) ).

thf(8585,plain,
    ! [SV772: $i,SV750: $i,SV491: $i,SV321: $i] :
      ( ( ( is_int @ SV321 )
        = $false )
      | ( ( ~ ( is_int @ SV491 ) )
        = $true )
      | ( ( ~ ( is_int @ SV750 ) )
        = $true )
      | ( ( ~ ( is_int @ SV772 ) )
        = $true )
      | ( ( ( SV750 = SV772 )
          | ( SV321 = SV491 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV750 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV772 ) @ SV491 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV750 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV772 ) @ SV321 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8522]) ).

thf(8586,plain,
    ! [SV719: $i,SV644: $i] :
      ( ( ( SV644 = zero_zero_int )
        = $false )
      | ( ( SV719 != zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV644 ) @ SV719 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV644 )
        = $false )
      | ( ( is_int @ SV719 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8523]) ).

thf(8587,plain,
    ! [SV773: $i,SV791: $i] :
      ( ( ( is_int @ SV791 )
        = $false )
      | ( ( is_int @ SV773 )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV773 ) @ SV791 )
           != zero_zero_int )
          | ( SV773 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8524]) ).

thf(8588,plain,
    ! [SV774: $i,SV792: $i] :
      ( ( ( is_int @ SV792 )
        = $false )
      | ( ( is_int @ SV774 )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV774 ) @ SV792 )
           != zero_zero_int )
          | ( SV792 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8525]) ).

thf(8589,plain,
    ! [SV795: $i,SV775: $i,SV570: $i,SV492: $i,SV323: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV323 ) @ SV492 ) ) @ SV570 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV775 ) @ SV492 ) ) @ SV795 ) )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV323 ) @ SV775 ) ) @ SV492 ) ) @ SV570 )
          = SV795 )
        = $true )
      | ( ( is_int @ SV795 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8528]) ).

thf(8590,plain,
    ! [SV796: $i,SV570: $i,SV492: $i,SV776: $i,SV323: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV323 ) @ SV776 ) ) @ SV492 ) ) @ SV570 )
          = SV796 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV323 ) @ SV492 ) ) @ SV570 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV776 ) @ SV492 ) ) @ SV796 ) )
        = $true )
      | ( ( is_int @ SV796 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8529]) ).

thf(8591,plain,
    ! [SV777: $i,SV651: $i] :
      ( ( ( SV651
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV777 ) @ ( sK12_Q_4 @ SV777 @ SV651 ) ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ SV651 ) @ SV777 )
          = zero_zero_int )
        = $false )
      | ( ( is_int @ SV651 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[8530]) ).

thf(8592,plain,
    ! [SV651: $i,SV777: $i] :
      ( ( ( is_int @ ( sK12_Q_4 @ SV777 @ SV651 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ SV651 ) @ SV777 )
          = zero_zero_int )
        = $false )
      | ( ( is_int @ SV651 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[8531]) ).

thf(8593,plain,
    ! [SV778: $i,SV652: $i,SV813: $i] :
      ( ( ( is_int @ SV813 )
        = $false )
      | ( ( SV652
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV778 ) @ SV813 ) )
        = $false )
      | ( ( ( hAPP_int_int @ ( div_mod_int @ SV652 ) @ SV778 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV652 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8532]) ).

thf(8594,plain,
    ! [SV737: $i,SV677: $i] :
      ( ( ( SV677 = zero_zero_int )
        = $false )
      | ( ( SV737 != zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV677 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV737 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV677 )
        = $false )
      | ( ( is_int @ SV737 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8539]) ).

thf(8595,plain,
    ! [SV779: $i,SV797: $i] :
      ( ( ( is_int @ SV797 )
        = $false )
      | ( ( is_int @ SV779 )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV779 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV797 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
           != zero_zero_int )
          | ( SV779 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8540]) ).

thf(8596,plain,
    ! [SV780: $i,SV798: $i] :
      ( ( ( is_int @ SV798 )
        = $false )
      | ( ( is_int @ SV780 )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV780 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV798 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
           != zero_zero_int )
          | ( SV798 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8541]) ).

thf(8597,plain,
    ! [SV738: $i,SV678: $i] :
      ( ( ( SV678 = zero_zero_int )
        = $false )
      | ( ( SV738 != zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV678 ) @ SV678 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV738 ) @ SV738 ) )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV678 )
        = $false )
      | ( ( is_int @ SV738 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8542]) ).

thf(8598,plain,
    ! [SV781: $i,SV799: $i] :
      ( ( ( is_int @ SV799 )
        = $false )
      | ( ( is_int @ SV781 )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV781 ) @ SV781 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV799 ) @ SV799 ) )
           != zero_zero_int )
          | ( SV781 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8543]) ).

thf(8599,plain,
    ! [SV782: $i,SV800: $i] :
      ( ( ( is_int @ SV800 )
        = $false )
      | ( ( is_int @ SV782 )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV782 ) @ SV782 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV800 ) @ SV800 ) )
           != zero_zero_int )
          | ( SV800 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8544]) ).

thf(8600,plain,
    ! [SV739: $i,SV679: $i] :
      ( ( ( SV679 = zero_zero_int )
        = $false )
      | ( ( SV739 != zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV679 ) @ SV739 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV679 )
        = $false )
      | ( ( is_int @ SV739 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8545]) ).

thf(8601,plain,
    ! [SV783: $i,SV801: $i] :
      ( ( ( is_int @ SV801 )
        = $false )
      | ( ( is_int @ SV783 )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV783 ) @ SV801 )
           != zero_zero_int )
          | ( SV783 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8546]) ).

thf(8602,plain,
    ! [SV784: $i,SV802: $i] :
      ( ( ( is_int @ SV802 )
        = $false )
      | ( ( is_int @ SV784 )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV784 ) @ SV802 )
           != zero_zero_int )
          | ( SV802 = zero_zero_int ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8547]) ).

thf(8603,plain,
    ! [SV680: $i,SV576: $i,SV524: $i,SV380: $i,SV104: $i] :
      ( ( ( ( SV104 = SV380 )
          | ( SV524 != SV576 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV524 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV680 ) @ SV104 ) )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV576 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV680 ) @ SV380 ) ) )
        = $true )
      | ( ( SV680 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV380 )
        = $false )
      | ( ( is_int @ SV104 )
        = $false )
      | ( ( is_int @ SV680 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8548]) ).

thf(8604,plain,
    ! [SV786: $i,SV754: $i] :
      ( ( ( SV754 != zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV754 ) @ SV786 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV754 )
        = $false )
      | ( ( is_int @ SV786 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8551]) ).

thf(8605,plain,
    ! [SV755: $i,SV787: $i] :
      ( ( ( SV787 != zero_zero_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV755 ) @ SV787 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV755 )
        = $false )
      | ( ( is_int @ SV787 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8552]) ).

thf(8606,plain,
    ! [SV757: $i,SV814: $i] :
      ( ( ( ( hAPP_int_nat @ number_number_of_nat @ SV814 )
          = zero_zero_nat )
        = $false )
      | ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV757 ) @ ( hAPP_int_nat @ number_number_of_nat @ SV814 ) )
          = zero_zero_int )
        = $false )
      | ( ( is_int @ SV757 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8553]) ).

thf(8607,plain,
    ! [SV314: $i,SV486: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ( is_int @ ( sK1_A_4 @ SV486 @ SV314 ) )
                    | ~ ( is_int @ ( sK2_SY713 @ SV486 @ SV314 ) ) )
              | ( SV314
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK1_A_4 @ SV486 @ SV314 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 ) ) ) ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV314 )
        = $false )
      | ( ( is_int @ SV486 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[8555]) ).

thf(8608,plain,
    ! [SV314: $i,SV486: $i] :
      ( ( ( SV486
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK2_SY713 @ SV486 @ SV314 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 ) ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV314 )
        = $false )
      | ( ( is_int @ SV486 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[8556]) ).

thf(8609,plain,
    ! [SV760: $i,SV815: $i] :
      ( ( ( SV815 = zero_zero_nat )
        = $false )
      | ( ( ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV760 ) @ SV815 )
          = zero_zero_int )
        = $false )
      | ( ( is_int @ SV760 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8557]) ).

thf(8610,plain,
    ! [SV762: $i,SV742: $i,SV315: $i,SV487: $i] :
      ( ( ( is_int @ SV487 )
        = $false )
      | ( ( is_int @ SV315 )
        = $false )
      | ( ( ~ ( is_int @ SV742 ) )
        = $true )
      | ( ( ~ ( is_int @ SV762 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV742 ) @ SV762 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV762 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV742 ) @ SV487 ) ) )
          | ( SV315 = SV742 )
          | ( SV487 = SV762 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8559]) ).

thf(8611,plain,
    ! [SV816: $i,SV803: $i,SV487: $i,SV315: $i] :
      ( ( ( ~ ( is_int @ SV315 )
          | ~ ( is_int @ SV487 ) )
        = $true )
      | ( ( ~ ( is_int @ SV803 ) )
        = $true )
      | ( ( ~ ( is_int @ SV816 ) )
        = $true )
      | ( ( ( SV315 != SV803 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV803 ) @ SV816 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV816 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV803 ) @ SV487 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8560]) ).

thf(8612,plain,
    ! [SV817: $i,SV804: $i,SV487: $i,SV315: $i] :
      ( ( ( ~ ( is_int @ SV315 )
          | ~ ( is_int @ SV487 ) )
        = $true )
      | ( ( ~ ( is_int @ SV804 ) )
        = $true )
      | ( ( ~ ( is_int @ SV817 ) )
        = $true )
      | ( ( ( SV487 != SV817 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV804 ) @ SV817 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV817 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV804 ) @ SV487 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8561]) ).

thf(8613,plain,
    ! [SV635: $i,SV711: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK7_C_3 @ SV711 @ SV635 ) )
                          | ~ ( is_int @ ( sK8_SY715 @ SV711 @ SV635 ) ) )
                    | ( SV711
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV711 ) @ SV635 ) ) @ ( sK7_C_3 @ SV711 @ SV635 ) ) ) )
              | ( SV635
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV711 ) @ SV635 ) ) @ ( sK8_SY715 @ SV711 @ SV635 ) ) ) ) )
        = $true )
      | ( ( SV711 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV635 )
        = $false )
      | ( ( is_int @ SV711 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[8564]) ).

thf(8614,plain,
    ! [SV635: $i,SV711: $i] :
      ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK7_C_3 @ SV711 @ SV635 ) ) @ ( sK8_SY715 @ SV711 @ SV635 ) )
          = one_one_int )
        = $true )
      | ( ( SV711 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV635 )
        = $false )
      | ( ( is_int @ SV711 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[8565]) ).

thf(8615,plain,
    ! [SV636: $i,SV712: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK5_C_3 @ SV712 @ SV636 ) )
                          | ~ ( is_int @ ( sK6_SY714 @ SV712 @ SV636 ) ) )
                    | ( SV712
                     != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV712 ) @ SV636 ) ) @ ( sK5_C_3 @ SV712 @ SV636 ) ) ) )
              | ( SV636
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV712 ) @ SV636 ) ) @ ( sK6_SY714 @ SV712 @ SV636 ) ) ) ) )
        = $true )
      | ( ( SV636 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV636 )
        = $false )
      | ( ( is_int @ SV712 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[8566]) ).

thf(8616,plain,
    ! [SV636: $i,SV712: $i] :
      ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ ( sK5_C_3 @ SV712 @ SV636 ) ) @ ( sK6_SY714 @ SV712 @ SV636 ) )
          = one_one_int )
        = $true )
      | ( ( SV636 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV636 )
        = $false )
      | ( ( is_int @ SV712 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[8567]) ).

thf(8617,plain,
    ! [SV765: $i,SV489: $i,SV319: $i,SV747: $i] :
      ( ( ( ( hAPP_int_int @ abs_abs_int @ SV747 )
         != ( hAPP_int_int @ abs_abs_int @ SV319 ) )
        = $true )
      | ( ( ( hAPP_int_int @ abs_abs_int @ SV489 )
         != ( hAPP_int_int @ abs_abs_int @ SV765 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV747 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV765 ) ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
          = one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV747 ) @ SV765 )
          = one_one_int )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8572]) ).

thf(8618,plain,
    ! [SV820: $i,SV808: $i,SV489: $i,SV319: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
         != one_one_int )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV808 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV820 ) ) )
          | ( ( hAPP_int_int @ abs_abs_int @ SV808 )
            = ( hAPP_int_int @ abs_abs_int @ SV319 ) ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV808 ) @ SV820 )
          = one_one_int )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8573]) ).

thf(8619,plain,
    ! [SV821: $i,SV809: $i,SV489: $i,SV319: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
         != one_one_int )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV809 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV821 ) ) )
          | ( ( hAPP_int_int @ abs_abs_int @ SV489 )
            = ( hAPP_int_int @ abs_abs_int @ SV821 ) ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV809 ) @ SV821 )
          = one_one_int )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8574]) ).

thf(8620,plain,
    ! [SV766: $i,SV748: $i,SV320: $i,SV490: $i] :
      ( ( ( is_int @ SV490 )
        = $false )
      | ( ( is_int @ SV320 )
        = $false )
      | ( ( ~ ( is_int @ SV748 ) )
        = $true )
      | ( ( ~ ( is_int @ SV766 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV748 ) @ SV766 ) )
          | ( SV320 != SV490 )
          | ( SV748 = SV766 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8575]) ).

thf(8621,plain,
    ! [SV767: $i,SV749: $i,SV320: $i,SV490: $i] :
      ( ( ( is_int @ SV490 )
        = $false )
      | ( ( is_int @ SV320 )
        = $false )
      | ( ( ~ ( is_int @ SV749 ) )
        = $true )
      | ( ( ~ ( is_int @ SV767 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV749 ) @ SV767 ) )
          | ( SV749 != SV767 )
          | ( SV320 = SV490 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8576]) ).

thf(8622,plain,
    ! [SV831: $i,SV822: $i] :
      ( ( ( ~ ( is_int @ SV822 ) )
        = $true )
      | ( ( ~ ( is_int @ SV831 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV822 ) @ SV831 )
           != one_one_int )
          | ( SV822 = one_one_int )
          | ( SV822
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8577]) ).

thf(8623,plain,
    ! [SV832: $i,SV823: $i] :
      ( ( ( ~ ( is_int @ SV823 ) )
        = $true )
      | ( ( ~ ( is_int @ SV832 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV823 ) @ SV832 )
           != one_one_int )
          | ( SV823 = one_one_int )
          | ( SV832
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8578]) ).

thf(8624,plain,
    ! [SV833: $i,SV824: $i] :
      ( ( ( ~ ( is_int @ SV824 ) )
        = $true )
      | ( ( ~ ( is_int @ SV833 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV824 ) @ SV833 )
           != one_one_int )
          | ( SV833 = one_one_int )
          | ( SV824
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8579]) ).

thf(8625,plain,
    ! [SV834: $i,SV825: $i] :
      ( ( ( ~ ( is_int @ SV825 ) )
        = $true )
      | ( ( ~ ( is_int @ SV834 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV825 ) @ SV834 )
           != one_one_int )
          | ( SV834 = one_one_int )
          | ( SV834
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8580]) ).

thf(8626,plain,
    ! [SV789: $i,SV768: $i] :
      ( ( ( ( SV768 != one_one_int )
          | ( SV789 != one_one_int ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV768 ) @ SV789 )
          = one_one_int )
        = $true )
      | ( ( is_int @ SV768 )
        = $false )
      | ( ( is_int @ SV789 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8581]) ).

thf(8627,plain,
    ! [SV790: $i,SV769: $i] :
      ( ( ( ( SV769
           != ( hAPP_int_int @ number_number_of_int @ min ) )
          | ( SV790
           != ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV769 ) @ SV790 )
          = one_one_int )
        = $true )
      | ( ( is_int @ SV769 )
        = $false )
      | ( ( is_int @ SV790 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8582]) ).

thf(8628,plain,
    ! [SV826: $i,SV810: $i,SV491: $i,SV321: $i] :
      ( ( ( ~ ( is_int @ SV321 )
          | ~ ( is_int @ SV491 ) )
        = $true )
      | ( ( ~ ( is_int @ SV810 ) )
        = $true )
      | ( ( ~ ( is_int @ SV826 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV810 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV826 ) @ SV491 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV810 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV826 ) @ SV321 ) ) )
          | ( SV810 != SV826 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8583]) ).

thf(8629,plain,
    ! [SV827: $i,SV811: $i,SV491: $i,SV321: $i] :
      ( ( ( ~ ( is_int @ SV321 )
          | ~ ( is_int @ SV491 ) )
        = $true )
      | ( ( ~ ( is_int @ SV811 ) )
        = $true )
      | ( ( ~ ( is_int @ SV827 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV811 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV827 ) @ SV491 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV811 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV827 ) @ SV321 ) ) )
          | ( SV321 != SV491 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8584]) ).

thf(8630,plain,
    ! [SV772: $i,SV750: $i,SV321: $i,SV491: $i] :
      ( ( ( is_int @ SV491 )
        = $false )
      | ( ( is_int @ SV321 )
        = $false )
      | ( ( ~ ( is_int @ SV750 ) )
        = $true )
      | ( ( ~ ( is_int @ SV772 ) )
        = $true )
      | ( ( ( SV750 = SV772 )
          | ( SV321 = SV491 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV750 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV772 ) @ SV491 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV750 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV772 ) @ SV321 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8585]) ).

thf(8631,plain,
    ! [SV644: $i,SV719: $i] :
      ( ( ( SV719 = zero_zero_int )
        = $false )
      | ( ( SV644 = zero_zero_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV644 ) @ SV719 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV644 )
        = $false )
      | ( ( is_int @ SV719 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8586]) ).

thf(8632,plain,
    ! [SV791: $i,SV773: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV773 ) @ SV791 )
         != zero_zero_int )
        = $true )
      | ( ( SV773 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV773 )
        = $false )
      | ( ( is_int @ SV791 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8587]) ).

thf(8633,plain,
    ! [SV792: $i,SV774: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV774 ) @ SV792 )
         != zero_zero_int )
        = $true )
      | ( ( SV792 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV774 )
        = $false )
      | ( ( is_int @ SV792 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8588]) ).

thf(8634,plain,
    ! [SV677: $i,SV737: $i] :
      ( ( ( SV737 = zero_zero_int )
        = $false )
      | ( ( SV677 = zero_zero_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV677 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV737 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV677 )
        = $false )
      | ( ( is_int @ SV737 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8594]) ).

thf(8635,plain,
    ! [SV797: $i,SV779: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV779 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV797 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
         != zero_zero_int )
        = $true )
      | ( ( SV779 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV779 )
        = $false )
      | ( ( is_int @ SV797 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8595]) ).

thf(8636,plain,
    ! [SV798: $i,SV780: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV780 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV798 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
         != zero_zero_int )
        = $true )
      | ( ( SV798 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV780 )
        = $false )
      | ( ( is_int @ SV798 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8596]) ).

thf(8637,plain,
    ! [SV678: $i,SV738: $i] :
      ( ( ( SV738 = zero_zero_int )
        = $false )
      | ( ( SV678 = zero_zero_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV678 ) @ SV678 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV738 ) @ SV738 ) )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV678 )
        = $false )
      | ( ( is_int @ SV738 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8597]) ).

thf(8638,plain,
    ! [SV799: $i,SV781: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV781 ) @ SV781 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV799 ) @ SV799 ) )
         != zero_zero_int )
        = $true )
      | ( ( SV781 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV781 )
        = $false )
      | ( ( is_int @ SV799 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8598]) ).

thf(8639,plain,
    ! [SV800: $i,SV782: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV782 ) @ SV782 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV800 ) @ SV800 ) )
         != zero_zero_int )
        = $true )
      | ( ( SV800 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV782 )
        = $false )
      | ( ( is_int @ SV800 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8599]) ).

thf(8640,plain,
    ! [SV679: $i,SV739: $i] :
      ( ( ( SV739 = zero_zero_int )
        = $false )
      | ( ( SV679 = zero_zero_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV679 ) @ SV739 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV679 )
        = $false )
      | ( ( is_int @ SV739 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8600]) ).

thf(8641,plain,
    ! [SV801: $i,SV783: $i] :
      ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV783 ) @ SV801 )
         != zero_zero_int )
        = $true )
      | ( ( SV783 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV783 )
        = $false )
      | ( ( is_int @ SV801 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8601]) ).

thf(8642,plain,
    ! [SV802: $i,SV784: $i] :
      ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV784 ) @ SV802 )
         != zero_zero_int )
        = $true )
      | ( ( SV802 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV784 )
        = $false )
      | ( ( is_int @ SV802 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8602]) ).

thf(8643,plain,
    ! [SV680: $i,SV576: $i,SV524: $i,SV380: $i,SV104: $i] :
      ( ( ( SV104 = SV380 )
        = $true )
      | ( ( SV524 != SV576 )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV524 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV680 ) @ SV104 ) )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV576 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV680 ) @ SV380 ) ) )
        = $true )
      | ( ( SV680 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV380 )
        = $false )
      | ( ( is_int @ SV104 )
        = $false )
      | ( ( is_int @ SV680 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8603]) ).

thf(8644,plain,
    ! [SV786: $i,SV754: $i] :
      ( ( ( SV754 = zero_zero_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV754 ) @ SV786 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV754 )
        = $false )
      | ( ( is_int @ SV786 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8604]) ).

thf(8645,plain,
    ! [SV755: $i,SV787: $i] :
      ( ( ( SV787 = zero_zero_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV755 ) @ SV787 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV755 )
        = $false )
      | ( ( is_int @ SV787 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8605]) ).

thf(8646,plain,
    ! [SV314: $i,SV486: $i] :
      ( ( ( ~ ~ ( ~ ( is_int @ ( sK1_A_4 @ SV486 @ SV314 ) )
                | ~ ( is_int @ ( sK2_SY713 @ SV486 @ SV314 ) ) )
          | ( SV314
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK1_A_4 @ SV486 @ SV314 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 ) ) ) )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV314 )
        = $false )
      | ( ( is_int @ SV486 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8607]) ).

thf(8647,plain,
    ! [SV762: $i,SV487: $i,SV315: $i,SV742: $i] :
      ( ( ( is_int @ SV742 )
        = $false )
      | ( ( is_int @ SV315 )
        = $false )
      | ( ( is_int @ SV487 )
        = $false )
      | ( ( ~ ( is_int @ SV762 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV742 ) @ SV762 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV762 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV742 ) @ SV487 ) ) )
          | ( SV315 = SV742 )
          | ( SV487 = SV762 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8610]) ).

thf(8648,plain,
    ! [SV816: $i,SV803: $i,SV487: $i,SV315: $i] :
      ( ( ( ~ ( is_int @ SV315 ) )
        = $true )
      | ( ( ~ ( is_int @ SV487 ) )
        = $true )
      | ( ( ~ ( is_int @ SV803 ) )
        = $true )
      | ( ( ~ ( is_int @ SV816 ) )
        = $true )
      | ( ( ( SV315 != SV803 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV803 ) @ SV816 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV816 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV803 ) @ SV487 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8611]) ).

thf(8649,plain,
    ! [SV817: $i,SV804: $i,SV487: $i,SV315: $i] :
      ( ( ( ~ ( is_int @ SV315 ) )
        = $true )
      | ( ( ~ ( is_int @ SV487 ) )
        = $true )
      | ( ( ~ ( is_int @ SV804 ) )
        = $true )
      | ( ( ~ ( is_int @ SV817 ) )
        = $true )
      | ( ( ( SV487 != SV817 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV804 ) @ SV817 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV817 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV804 ) @ SV487 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8612]) ).

thf(8650,plain,
    ! [SV635: $i,SV711: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK7_C_3 @ SV711 @ SV635 ) )
                      | ~ ( is_int @ ( sK8_SY715 @ SV711 @ SV635 ) ) )
                | ( SV711
                 != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV711 ) @ SV635 ) ) @ ( sK7_C_3 @ SV711 @ SV635 ) ) ) )
          | ( SV635
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV711 ) @ SV635 ) ) @ ( sK8_SY715 @ SV711 @ SV635 ) ) ) )
        = $false )
      | ( ( SV711 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV635 )
        = $false )
      | ( ( is_int @ SV711 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8613]) ).

thf(8651,plain,
    ! [SV636: $i,SV712: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK5_C_3 @ SV712 @ SV636 ) )
                      | ~ ( is_int @ ( sK6_SY714 @ SV712 @ SV636 ) ) )
                | ( SV712
                 != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV712 ) @ SV636 ) ) @ ( sK5_C_3 @ SV712 @ SV636 ) ) ) )
          | ( SV636
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV712 ) @ SV636 ) ) @ ( sK6_SY714 @ SV712 @ SV636 ) ) ) )
        = $false )
      | ( ( SV636 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV636 )
        = $false )
      | ( ( is_int @ SV712 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8615]) ).

thf(8652,plain,
    ! [SV765: $i,SV489: $i,SV319: $i,SV747: $i] :
      ( ( ( ( hAPP_int_int @ abs_abs_int @ SV747 )
          = ( hAPP_int_int @ abs_abs_int @ SV319 ) )
        = $false )
      | ( ( ( hAPP_int_int @ abs_abs_int @ SV489 )
         != ( hAPP_int_int @ abs_abs_int @ SV765 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV747 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV765 ) ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
          = one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV747 ) @ SV765 )
          = one_one_int )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8617]) ).

thf(8653,plain,
    ! [SV820: $i,SV808: $i,SV489: $i,SV319: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
          = one_one_int )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV808 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV820 ) ) )
          | ( ( hAPP_int_int @ abs_abs_int @ SV808 )
            = ( hAPP_int_int @ abs_abs_int @ SV319 ) ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV808 ) @ SV820 )
          = one_one_int )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8618]) ).

thf(8654,plain,
    ! [SV821: $i,SV809: $i,SV489: $i,SV319: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
          = one_one_int )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV809 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV821 ) ) )
          | ( ( hAPP_int_int @ abs_abs_int @ SV489 )
            = ( hAPP_int_int @ abs_abs_int @ SV821 ) ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV809 ) @ SV821 )
          = one_one_int )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8619]) ).

thf(8655,plain,
    ! [SV766: $i,SV490: $i,SV320: $i,SV748: $i] :
      ( ( ( is_int @ SV748 )
        = $false )
      | ( ( is_int @ SV320 )
        = $false )
      | ( ( is_int @ SV490 )
        = $false )
      | ( ( ~ ( is_int @ SV766 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV748 ) @ SV766 ) )
          | ( SV320 != SV490 )
          | ( SV748 = SV766 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8620]) ).

thf(8656,plain,
    ! [SV767: $i,SV490: $i,SV320: $i,SV749: $i] :
      ( ( ( is_int @ SV749 )
        = $false )
      | ( ( is_int @ SV320 )
        = $false )
      | ( ( is_int @ SV490 )
        = $false )
      | ( ( ~ ( is_int @ SV767 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV749 ) @ SV767 ) )
          | ( SV749 != SV767 )
          | ( SV320 = SV490 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8621]) ).

thf(8657,plain,
    ! [SV831: $i,SV822: $i] :
      ( ( ( is_int @ SV822 )
        = $false )
      | ( ( ~ ( is_int @ SV831 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV822 ) @ SV831 )
           != one_one_int )
          | ( SV822 = one_one_int )
          | ( SV822
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8622]) ).

thf(8658,plain,
    ! [SV832: $i,SV823: $i] :
      ( ( ( is_int @ SV823 )
        = $false )
      | ( ( ~ ( is_int @ SV832 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV823 ) @ SV832 )
           != one_one_int )
          | ( SV823 = one_one_int )
          | ( SV832
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8623]) ).

thf(8659,plain,
    ! [SV833: $i,SV824: $i] :
      ( ( ( is_int @ SV824 )
        = $false )
      | ( ( ~ ( is_int @ SV833 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV824 ) @ SV833 )
           != one_one_int )
          | ( SV833 = one_one_int )
          | ( SV824
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8624]) ).

thf(8660,plain,
    ! [SV834: $i,SV825: $i] :
      ( ( ( is_int @ SV825 )
        = $false )
      | ( ( ~ ( is_int @ SV834 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV825 ) @ SV834 )
           != one_one_int )
          | ( SV834 = one_one_int )
          | ( SV834
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8625]) ).

thf(8661,plain,
    ! [SV789: $i,SV768: $i] :
      ( ( ( SV768 != one_one_int )
        = $true )
      | ( ( SV789 != one_one_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV768 ) @ SV789 )
          = one_one_int )
        = $true )
      | ( ( is_int @ SV768 )
        = $false )
      | ( ( is_int @ SV789 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8626]) ).

thf(8662,plain,
    ! [SV790: $i,SV769: $i] :
      ( ( ( SV769
         != ( hAPP_int_int @ number_number_of_int @ min ) )
        = $true )
      | ( ( SV790
         != ( hAPP_int_int @ number_number_of_int @ min ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV769 ) @ SV790 )
          = one_one_int )
        = $true )
      | ( ( is_int @ SV769 )
        = $false )
      | ( ( is_int @ SV790 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8627]) ).

thf(8663,plain,
    ! [SV826: $i,SV810: $i,SV491: $i,SV321: $i] :
      ( ( ( ~ ( is_int @ SV321 ) )
        = $true )
      | ( ( ~ ( is_int @ SV491 ) )
        = $true )
      | ( ( ~ ( is_int @ SV810 ) )
        = $true )
      | ( ( ~ ( is_int @ SV826 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV810 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV826 ) @ SV491 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV810 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV826 ) @ SV321 ) ) )
          | ( SV810 != SV826 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8628]) ).

thf(8664,plain,
    ! [SV827: $i,SV811: $i,SV491: $i,SV321: $i] :
      ( ( ( ~ ( is_int @ SV321 ) )
        = $true )
      | ( ( ~ ( is_int @ SV491 ) )
        = $true )
      | ( ( ~ ( is_int @ SV811 ) )
        = $true )
      | ( ( ~ ( is_int @ SV827 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV811 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV827 ) @ SV491 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV811 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV827 ) @ SV321 ) ) )
          | ( SV321 != SV491 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[8629]) ).

thf(8665,plain,
    ! [SV772: $i,SV491: $i,SV321: $i,SV750: $i] :
      ( ( ( is_int @ SV750 )
        = $false )
      | ( ( is_int @ SV321 )
        = $false )
      | ( ( is_int @ SV491 )
        = $false )
      | ( ( ~ ( is_int @ SV772 ) )
        = $true )
      | ( ( ( SV750 = SV772 )
          | ( SV321 = SV491 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV750 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV772 ) @ SV491 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV750 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV772 ) @ SV321 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8630]) ).

thf(8666,plain,
    ! [SV791: $i,SV773: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV773 ) @ SV791 )
          = zero_zero_int )
        = $false )
      | ( ( SV773 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV773 )
        = $false )
      | ( ( is_int @ SV791 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8632]) ).

thf(8667,plain,
    ! [SV792: $i,SV774: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV774 ) @ SV792 )
          = zero_zero_int )
        = $false )
      | ( ( SV792 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV774 )
        = $false )
      | ( ( is_int @ SV792 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8633]) ).

thf(8668,plain,
    ! [SV797: $i,SV779: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV779 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV797 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
          = zero_zero_int )
        = $false )
      | ( ( SV779 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV779 )
        = $false )
      | ( ( is_int @ SV797 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8635]) ).

thf(8669,plain,
    ! [SV798: $i,SV780: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV780 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) ) @ ( hAPP_nat_int @ ( hAPP_int_fun_nat_int @ power_power_int @ SV798 ) @ ( hAPP_int_nat @ number_number_of_nat @ ( hAPP_int_int @ bit0 @ ( hAPP_int_int @ bit1 @ pls ) ) ) ) )
          = zero_zero_int )
        = $false )
      | ( ( SV798 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV780 )
        = $false )
      | ( ( is_int @ SV798 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8636]) ).

thf(8670,plain,
    ! [SV799: $i,SV781: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV781 ) @ SV781 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV799 ) @ SV799 ) )
          = zero_zero_int )
        = $false )
      | ( ( SV781 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV781 )
        = $false )
      | ( ( is_int @ SV799 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8638]) ).

thf(8671,plain,
    ! [SV800: $i,SV782: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV782 ) @ SV782 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV800 ) @ SV800 ) )
          = zero_zero_int )
        = $false )
      | ( ( SV800 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV782 )
        = $false )
      | ( ( is_int @ SV800 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8639]) ).

thf(8672,plain,
    ! [SV801: $i,SV783: $i] :
      ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV783 ) @ SV801 )
          = zero_zero_int )
        = $false )
      | ( ( SV783 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV783 )
        = $false )
      | ( ( is_int @ SV801 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8641]) ).

thf(8673,plain,
    ! [SV802: $i,SV784: $i] :
      ( ( ( ( hAPP_int_int @ ( legacy_zgcd @ SV784 ) @ SV802 )
          = zero_zero_int )
        = $false )
      | ( ( SV802 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV784 )
        = $false )
      | ( ( is_int @ SV802 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8642]) ).

thf(8674,plain,
    ! [SV680: $i,SV380: $i,SV104: $i,SV576: $i,SV524: $i] :
      ( ( ( SV524 = SV576 )
        = $false )
      | ( ( SV104 = SV380 )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV524 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV680 ) @ SV104 ) )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV576 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV680 ) @ SV380 ) ) )
        = $true )
      | ( ( SV680 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV380 )
        = $false )
      | ( ( is_int @ SV104 )
        = $false )
      | ( ( is_int @ SV680 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8643]) ).

thf(8675,plain,
    ! [SV314: $i,SV486: $i] :
      ( ( ( ~ ~ ( ~ ( is_int @ ( sK1_A_4 @ SV486 @ SV314 ) )
                | ~ ( is_int @ ( sK2_SY713 @ SV486 @ SV314 ) ) ) )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV314 )
        = $false )
      | ( ( is_int @ SV486 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[8646]) ).

thf(8676,plain,
    ! [SV486: $i,SV314: $i] :
      ( ( ( SV314
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK1_A_4 @ SV486 @ SV314 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 ) ) )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV314 )
        = $false )
      | ( ( is_int @ SV486 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[8646]) ).

thf(8677,plain,
    ! [SV742: $i,SV315: $i,SV487: $i,SV762: $i] :
      ( ( ( is_int @ SV762 )
        = $false )
      | ( ( is_int @ SV487 )
        = $false )
      | ( ( is_int @ SV315 )
        = $false )
      | ( ( is_int @ SV742 )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV742 ) @ SV762 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV762 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV742 ) @ SV487 ) ) )
          | ( SV315 = SV742 )
          | ( SV487 = SV762 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8647]) ).

thf(8678,plain,
    ! [SV816: $i,SV803: $i,SV487: $i,SV315: $i] :
      ( ( ( is_int @ SV315 )
        = $false )
      | ( ( ~ ( is_int @ SV487 ) )
        = $true )
      | ( ( ~ ( is_int @ SV803 ) )
        = $true )
      | ( ( ~ ( is_int @ SV816 ) )
        = $true )
      | ( ( ( SV315 != SV803 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV803 ) @ SV816 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV816 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV803 ) @ SV487 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8648]) ).

thf(8679,plain,
    ! [SV817: $i,SV804: $i,SV487: $i,SV315: $i] :
      ( ( ( is_int @ SV315 )
        = $false )
      | ( ( ~ ( is_int @ SV487 ) )
        = $true )
      | ( ( ~ ( is_int @ SV804 ) )
        = $true )
      | ( ( ~ ( is_int @ SV817 ) )
        = $true )
      | ( ( ( SV487 != SV817 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV804 ) @ SV817 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV817 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV804 ) @ SV487 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8649]) ).

thf(8680,plain,
    ! [SV635: $i,SV711: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK7_C_3 @ SV711 @ SV635 ) )
                      | ~ ( is_int @ ( sK8_SY715 @ SV711 @ SV635 ) ) )
                | ( SV711
                 != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV711 ) @ SV635 ) ) @ ( sK7_C_3 @ SV711 @ SV635 ) ) ) ) )
        = $false )
      | ( ( SV711 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV635 )
        = $false )
      | ( ( is_int @ SV711 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[8650]) ).

thf(8681,plain,
    ! [SV711: $i,SV635: $i] :
      ( ( ( SV635
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV711 ) @ SV635 ) ) @ ( sK8_SY715 @ SV711 @ SV635 ) ) )
        = $false )
      | ( ( SV711 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV635 )
        = $false )
      | ( ( is_int @ SV711 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[8650]) ).

thf(8682,plain,
    ! [SV636: $i,SV712: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( is_int @ ( sK5_C_3 @ SV712 @ SV636 ) )
                      | ~ ( is_int @ ( sK6_SY714 @ SV712 @ SV636 ) ) )
                | ( SV712
                 != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV712 ) @ SV636 ) ) @ ( sK5_C_3 @ SV712 @ SV636 ) ) ) ) )
        = $false )
      | ( ( SV636 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV636 )
        = $false )
      | ( ( is_int @ SV712 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[8651]) ).

thf(8683,plain,
    ! [SV712: $i,SV636: $i] :
      ( ( ( SV636
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV712 ) @ SV636 ) ) @ ( sK6_SY714 @ SV712 @ SV636 ) ) )
        = $false )
      | ( ( SV636 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV636 )
        = $false )
      | ( ( is_int @ SV712 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[8651]) ).

thf(8684,plain,
    ! [SV319: $i,SV747: $i,SV765: $i,SV489: $i] :
      ( ( ( ( hAPP_int_int @ abs_abs_int @ SV489 )
          = ( hAPP_int_int @ abs_abs_int @ SV765 ) )
        = $false )
      | ( ( ( hAPP_int_int @ abs_abs_int @ SV747 )
          = ( hAPP_int_int @ abs_abs_int @ SV319 ) )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV747 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV765 ) ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
          = one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV747 ) @ SV765 )
          = one_one_int )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8652]) ).

thf(8685,plain,
    ! [SV820: $i,SV319: $i,SV489: $i,SV808: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV808 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV820 ) ) )
        = $true )
      | ( ( ( hAPP_int_int @ abs_abs_int @ SV808 )
          = ( hAPP_int_int @ abs_abs_int @ SV319 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
          = one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV808 ) @ SV820 )
          = one_one_int )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8653]) ).

thf(8686,plain,
    ! [SV821: $i,SV319: $i,SV489: $i,SV809: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV809 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV821 ) ) )
        = $true )
      | ( ( ( hAPP_int_int @ abs_abs_int @ SV489 )
          = ( hAPP_int_int @ abs_abs_int @ SV821 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
          = one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV809 ) @ SV821 )
          = one_one_int )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8654]) ).

thf(8687,plain,
    ! [SV748: $i,SV320: $i,SV490: $i,SV766: $i] :
      ( ( ( is_int @ SV766 )
        = $false )
      | ( ( is_int @ SV490 )
        = $false )
      | ( ( is_int @ SV320 )
        = $false )
      | ( ( is_int @ SV748 )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV748 ) @ SV766 ) )
          | ( SV320 != SV490 )
          | ( SV748 = SV766 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8655]) ).

thf(8688,plain,
    ! [SV749: $i,SV320: $i,SV490: $i,SV767: $i] :
      ( ( ( is_int @ SV767 )
        = $false )
      | ( ( is_int @ SV490 )
        = $false )
      | ( ( is_int @ SV320 )
        = $false )
      | ( ( is_int @ SV749 )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV749 ) @ SV767 ) )
          | ( SV749 != SV767 )
          | ( SV320 = SV490 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8656]) ).

thf(8689,plain,
    ! [SV822: $i,SV831: $i] :
      ( ( ( is_int @ SV831 )
        = $false )
      | ( ( is_int @ SV822 )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV822 ) @ SV831 )
           != one_one_int )
          | ( SV822 = one_one_int )
          | ( SV822
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8657]) ).

thf(8690,plain,
    ! [SV823: $i,SV832: $i] :
      ( ( ( is_int @ SV832 )
        = $false )
      | ( ( is_int @ SV823 )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV823 ) @ SV832 )
           != one_one_int )
          | ( SV823 = one_one_int )
          | ( SV832
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8658]) ).

thf(8691,plain,
    ! [SV824: $i,SV833: $i] :
      ( ( ( is_int @ SV833 )
        = $false )
      | ( ( is_int @ SV824 )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV824 ) @ SV833 )
           != one_one_int )
          | ( SV833 = one_one_int )
          | ( SV824
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8659]) ).

thf(8692,plain,
    ! [SV825: $i,SV834: $i] :
      ( ( ( is_int @ SV834 )
        = $false )
      | ( ( is_int @ SV825 )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV825 ) @ SV834 )
           != one_one_int )
          | ( SV834 = one_one_int )
          | ( SV834
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8660]) ).

thf(8693,plain,
    ! [SV789: $i,SV768: $i] :
      ( ( ( SV768 = one_one_int )
        = $false )
      | ( ( SV789 != one_one_int )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV768 ) @ SV789 )
          = one_one_int )
        = $true )
      | ( ( is_int @ SV768 )
        = $false )
      | ( ( is_int @ SV789 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8661]) ).

thf(8694,plain,
    ! [SV790: $i,SV769: $i] :
      ( ( ( SV769
          = ( hAPP_int_int @ number_number_of_int @ min ) )
        = $false )
      | ( ( SV790
         != ( hAPP_int_int @ number_number_of_int @ min ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV769 ) @ SV790 )
          = one_one_int )
        = $true )
      | ( ( is_int @ SV769 )
        = $false )
      | ( ( is_int @ SV790 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8662]) ).

thf(8695,plain,
    ! [SV826: $i,SV810: $i,SV491: $i,SV321: $i] :
      ( ( ( is_int @ SV321 )
        = $false )
      | ( ( ~ ( is_int @ SV491 ) )
        = $true )
      | ( ( ~ ( is_int @ SV810 ) )
        = $true )
      | ( ( ~ ( is_int @ SV826 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV810 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV826 ) @ SV491 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV810 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV826 ) @ SV321 ) ) )
          | ( SV810 != SV826 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8663]) ).

thf(8696,plain,
    ! [SV827: $i,SV811: $i,SV491: $i,SV321: $i] :
      ( ( ( is_int @ SV321 )
        = $false )
      | ( ( ~ ( is_int @ SV491 ) )
        = $true )
      | ( ( ~ ( is_int @ SV811 ) )
        = $true )
      | ( ( ~ ( is_int @ SV827 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV811 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV827 ) @ SV491 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV811 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV827 ) @ SV321 ) ) )
          | ( SV321 != SV491 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8664]) ).

thf(8697,plain,
    ! [SV750: $i,SV321: $i,SV491: $i,SV772: $i] :
      ( ( ( is_int @ SV772 )
        = $false )
      | ( ( is_int @ SV491 )
        = $false )
      | ( ( is_int @ SV321 )
        = $false )
      | ( ( is_int @ SV750 )
        = $false )
      | ( ( ( SV750 = SV772 )
          | ( SV321 = SV491 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV750 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV772 ) @ SV491 ) )
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV750 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV772 ) @ SV321 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8665]) ).

thf(8698,plain,
    ! [SV380: $i,SV576: $i,SV104: $i,SV680: $i,SV524: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV524 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV680 ) @ SV104 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ SV576 ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV680 ) @ SV380 ) ) )
        = $false )
      | ( ( SV104 = SV380 )
        = $true )
      | ( ( SV524 = SV576 )
        = $false )
      | ( ( SV680 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV380 )
        = $false )
      | ( ( is_int @ SV104 )
        = $false )
      | ( ( is_int @ SV680 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8674]) ).

thf(8699,plain,
    ! [SV314: $i,SV486: $i] :
      ( ( ( ~ ( ~ ( is_int @ ( sK1_A_4 @ SV486 @ SV314 ) )
              | ~ ( is_int @ ( sK2_SY713 @ SV486 @ SV314 ) ) ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV314 )
        = $false )
      | ( ( is_int @ SV486 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[8675]) ).

thf(8700,plain,
    ! [SV486: $i,SV314: $i] :
      ( ( ( SV314
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( sK1_A_4 @ SV486 @ SV314 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 ) ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV314 )
        = $false )
      | ( ( is_int @ SV486 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[8676]) ).

thf(8701,plain,
    ! [SV762: $i,SV742: $i,SV487: $i,SV315: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV742 ) @ SV762 ) )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV762 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV742 ) @ SV487 ) ) )
        = $true )
      | ( ( ( SV315 = SV742 )
          | ( SV487 = SV762 ) )
        = $true )
      | ( ( is_int @ SV742 )
        = $false )
      | ( ( is_int @ SV315 )
        = $false )
      | ( ( is_int @ SV487 )
        = $false )
      | ( ( is_int @ SV762 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8677]) ).

thf(8702,plain,
    ! [SV816: $i,SV803: $i,SV315: $i,SV487: $i] :
      ( ( ( is_int @ SV487 )
        = $false )
      | ( ( is_int @ SV315 )
        = $false )
      | ( ( ~ ( is_int @ SV803 ) )
        = $true )
      | ( ( ~ ( is_int @ SV816 ) )
        = $true )
      | ( ( ( SV315 != SV803 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV803 ) @ SV816 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV816 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV803 ) @ SV487 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8678]) ).

thf(8703,plain,
    ! [SV817: $i,SV804: $i,SV315: $i,SV487: $i] :
      ( ( ( is_int @ SV487 )
        = $false )
      | ( ( is_int @ SV315 )
        = $false )
      | ( ( ~ ( is_int @ SV804 ) )
        = $true )
      | ( ( ~ ( is_int @ SV817 ) )
        = $true )
      | ( ( ( SV487 != SV817 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV804 ) @ SV817 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV817 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV804 ) @ SV487 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8679]) ).

thf(8704,plain,
    ! [SV635: $i,SV711: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ( is_int @ ( sK7_C_3 @ SV711 @ SV635 ) )
                    | ~ ( is_int @ ( sK8_SY715 @ SV711 @ SV635 ) ) )
              | ( SV711
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV711 ) @ SV635 ) ) @ ( sK7_C_3 @ SV711 @ SV635 ) ) ) ) )
        = $true )
      | ( ( SV711 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV635 )
        = $false )
      | ( ( is_int @ SV711 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[8680]) ).

thf(8705,plain,
    ! [SV711: $i,SV635: $i] :
      ( ( ( SV635
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV711 ) @ SV635 ) ) @ ( sK8_SY715 @ SV711 @ SV635 ) ) )
        = $true )
      | ( ( SV711 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV635 )
        = $false )
      | ( ( is_int @ SV711 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[8681]) ).

thf(8706,plain,
    ! [SV636: $i,SV712: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ( is_int @ ( sK5_C_3 @ SV712 @ SV636 ) )
                    | ~ ( is_int @ ( sK6_SY714 @ SV712 @ SV636 ) ) )
              | ( SV712
               != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV712 ) @ SV636 ) ) @ ( sK5_C_3 @ SV712 @ SV636 ) ) ) ) )
        = $true )
      | ( ( SV636 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV636 )
        = $false )
      | ( ( is_int @ SV712 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[8682]) ).

thf(8707,plain,
    ! [SV712: $i,SV636: $i] :
      ( ( ( SV636
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV712 ) @ SV636 ) ) @ ( sK6_SY714 @ SV712 @ SV636 ) ) )
        = $true )
      | ( ( SV636 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV636 )
        = $false )
      | ( ( is_int @ SV712 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[8683]) ).

thf(8708,plain,
    ! [SV820: $i,SV319: $i,SV489: $i,SV808: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV808 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV820 ) ) )
        = $false )
      | ( ( ( hAPP_int_int @ abs_abs_int @ SV808 )
          = ( hAPP_int_int @ abs_abs_int @ SV319 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
          = one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV808 ) @ SV820 )
          = one_one_int )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8685]) ).

thf(8709,plain,
    ! [SV821: $i,SV319: $i,SV489: $i,SV809: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV809 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV489 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ abs_abs_int @ SV319 ) ) @ ( hAPP_int_int @ abs_abs_int @ SV821 ) ) )
        = $false )
      | ( ( ( hAPP_int_int @ abs_abs_int @ SV489 )
          = ( hAPP_int_int @ abs_abs_int @ SV821 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV319 ) @ SV489 )
          = one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV809 ) @ SV821 )
          = one_one_int )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8686]) ).

thf(8710,plain,
    ! [SV766: $i,SV748: $i,SV490: $i,SV320: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV748 ) @ SV766 ) )
        = $true )
      | ( ( ( SV320 != SV490 )
          | ( SV748 = SV766 ) )
        = $true )
      | ( ( is_int @ SV748 )
        = $false )
      | ( ( is_int @ SV320 )
        = $false )
      | ( ( is_int @ SV490 )
        = $false )
      | ( ( is_int @ SV766 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8687]) ).

thf(8711,plain,
    ! [SV767: $i,SV749: $i,SV490: $i,SV320: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV749 ) @ SV767 ) )
        = $true )
      | ( ( ( SV749 != SV767 )
          | ( SV320 = SV490 ) )
        = $true )
      | ( ( is_int @ SV749 )
        = $false )
      | ( ( is_int @ SV320 )
        = $false )
      | ( ( is_int @ SV490 )
        = $false )
      | ( ( is_int @ SV767 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8688]) ).

thf(8712,plain,
    ! [SV831: $i,SV822: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV822 ) @ SV831 )
         != one_one_int )
        = $true )
      | ( ( ( SV822 = one_one_int )
          | ( SV822
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true )
      | ( ( is_int @ SV822 )
        = $false )
      | ( ( is_int @ SV831 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8689]) ).

thf(8713,plain,
    ! [SV832: $i,SV823: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV823 ) @ SV832 )
         != one_one_int )
        = $true )
      | ( ( ( SV823 = one_one_int )
          | ( SV832
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true )
      | ( ( is_int @ SV823 )
        = $false )
      | ( ( is_int @ SV832 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8690]) ).

thf(8714,plain,
    ! [SV833: $i,SV824: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV824 ) @ SV833 )
         != one_one_int )
        = $true )
      | ( ( ( SV833 = one_one_int )
          | ( SV824
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true )
      | ( ( is_int @ SV824 )
        = $false )
      | ( ( is_int @ SV833 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8691]) ).

thf(8715,plain,
    ! [SV834: $i,SV825: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV825 ) @ SV834 )
         != one_one_int )
        = $true )
      | ( ( ( SV834 = one_one_int )
          | ( SV834
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true )
      | ( ( is_int @ SV825 )
        = $false )
      | ( ( is_int @ SV834 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8692]) ).

thf(8716,plain,
    ! [SV768: $i,SV789: $i] :
      ( ( ( SV789 = one_one_int )
        = $false )
      | ( ( SV768 = one_one_int )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV768 ) @ SV789 )
          = one_one_int )
        = $true )
      | ( ( is_int @ SV768 )
        = $false )
      | ( ( is_int @ SV789 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8693]) ).

thf(8717,plain,
    ! [SV769: $i,SV790: $i] :
      ( ( ( SV790
          = ( hAPP_int_int @ number_number_of_int @ min ) )
        = $false )
      | ( ( SV769
          = ( hAPP_int_int @ number_number_of_int @ min ) )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV769 ) @ SV790 )
          = one_one_int )
        = $true )
      | ( ( is_int @ SV769 )
        = $false )
      | ( ( is_int @ SV790 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8694]) ).

thf(8718,plain,
    ! [SV826: $i,SV810: $i,SV321: $i,SV491: $i] :
      ( ( ( is_int @ SV491 )
        = $false )
      | ( ( is_int @ SV321 )
        = $false )
      | ( ( ~ ( is_int @ SV810 ) )
        = $true )
      | ( ( ~ ( is_int @ SV826 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV810 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV826 ) @ SV491 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV810 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV826 ) @ SV321 ) ) )
          | ( SV810 != SV826 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8695]) ).

thf(8719,plain,
    ! [SV827: $i,SV811: $i,SV321: $i,SV491: $i] :
      ( ( ( is_int @ SV491 )
        = $false )
      | ( ( is_int @ SV321 )
        = $false )
      | ( ( ~ ( is_int @ SV811 ) )
        = $true )
      | ( ( ~ ( is_int @ SV827 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV811 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV827 ) @ SV491 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV811 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV827 ) @ SV321 ) ) )
          | ( SV321 != SV491 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8696]) ).

thf(8720,plain,
    ! [SV491: $i,SV321: $i,SV772: $i,SV750: $i] :
      ( ( ( ( SV750 = SV772 )
          | ( SV321 = SV491 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV750 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV772 ) @ SV491 ) )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV750 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV772 ) @ SV321 ) ) )
        = $true )
      | ( ( is_int @ SV750 )
        = $false )
      | ( ( is_int @ SV321 )
        = $false )
      | ( ( is_int @ SV491 )
        = $false )
      | ( ( is_int @ SV772 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8697]) ).

thf(8721,plain,
    ! [SV314: $i,SV486: $i] :
      ( ( ( ~ ( is_int @ ( sK1_A_4 @ SV486 @ SV314 ) )
          | ~ ( is_int @ ( sK2_SY713 @ SV486 @ SV314 ) ) )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV314 )
        = $false )
      | ( ( is_int @ SV486 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8699]) ).

thf(8722,plain,
    ! [SV762: $i,SV742: $i,SV487: $i,SV315: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV742 ) @ SV762 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV762 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV742 ) @ SV487 ) ) )
        = $false )
      | ( ( ( SV315 = SV742 )
          | ( SV487 = SV762 ) )
        = $true )
      | ( ( is_int @ SV742 )
        = $false )
      | ( ( is_int @ SV315 )
        = $false )
      | ( ( is_int @ SV487 )
        = $false )
      | ( ( is_int @ SV762 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8701]) ).

thf(8723,plain,
    ! [SV816: $i,SV487: $i,SV315: $i,SV803: $i] :
      ( ( ( is_int @ SV803 )
        = $false )
      | ( ( is_int @ SV315 )
        = $false )
      | ( ( is_int @ SV487 )
        = $false )
      | ( ( ~ ( is_int @ SV816 ) )
        = $true )
      | ( ( ( SV315 != SV803 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV803 ) @ SV816 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV816 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV803 ) @ SV487 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8702]) ).

thf(8724,plain,
    ! [SV817: $i,SV487: $i,SV315: $i,SV804: $i] :
      ( ( ( is_int @ SV804 )
        = $false )
      | ( ( is_int @ SV315 )
        = $false )
      | ( ( is_int @ SV487 )
        = $false )
      | ( ( ~ ( is_int @ SV817 ) )
        = $true )
      | ( ( ( SV487 != SV817 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV804 ) @ SV817 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV817 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV804 ) @ SV487 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8703]) ).

thf(8725,plain,
    ! [SV635: $i,SV711: $i] :
      ( ( ( ~ ~ ( ~ ( is_int @ ( sK7_C_3 @ SV711 @ SV635 ) )
                | ~ ( is_int @ ( sK8_SY715 @ SV711 @ SV635 ) ) )
          | ( SV711
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV711 ) @ SV635 ) ) @ ( sK7_C_3 @ SV711 @ SV635 ) ) ) )
        = $false )
      | ( ( SV711 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV635 )
        = $false )
      | ( ( is_int @ SV711 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8704]) ).

thf(8726,plain,
    ! [SV636: $i,SV712: $i] :
      ( ( ( ~ ~ ( ~ ( is_int @ ( sK5_C_3 @ SV712 @ SV636 ) )
                | ~ ( is_int @ ( sK6_SY714 @ SV712 @ SV636 ) ) )
          | ( SV712
           != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV712 ) @ SV636 ) ) @ ( sK5_C_3 @ SV712 @ SV636 ) ) ) )
        = $false )
      | ( ( SV636 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV636 )
        = $false )
      | ( ( is_int @ SV712 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8706]) ).

thf(8727,plain,
    ! [SV766: $i,SV748: $i,SV490: $i,SV320: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV748 ) @ SV766 ) )
        = $false )
      | ( ( ( SV320 != SV490 )
          | ( SV748 = SV766 ) )
        = $true )
      | ( ( is_int @ SV748 )
        = $false )
      | ( ( is_int @ SV320 )
        = $false )
      | ( ( is_int @ SV490 )
        = $false )
      | ( ( is_int @ SV766 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8710]) ).

thf(8728,plain,
    ! [SV767: $i,SV749: $i,SV490: $i,SV320: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV749 ) @ SV767 ) )
        = $false )
      | ( ( ( SV749 != SV767 )
          | ( SV320 = SV490 ) )
        = $true )
      | ( ( is_int @ SV749 )
        = $false )
      | ( ( is_int @ SV320 )
        = $false )
      | ( ( is_int @ SV490 )
        = $false )
      | ( ( is_int @ SV767 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8711]) ).

thf(8729,plain,
    ! [SV831: $i,SV822: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV822 ) @ SV831 )
          = one_one_int )
        = $false )
      | ( ( ( SV822 = one_one_int )
          | ( SV822
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true )
      | ( ( is_int @ SV822 )
        = $false )
      | ( ( is_int @ SV831 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8712]) ).

thf(8730,plain,
    ! [SV832: $i,SV823: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV823 ) @ SV832 )
          = one_one_int )
        = $false )
      | ( ( ( SV823 = one_one_int )
          | ( SV832
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true )
      | ( ( is_int @ SV823 )
        = $false )
      | ( ( is_int @ SV832 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8713]) ).

thf(8731,plain,
    ! [SV833: $i,SV824: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV824 ) @ SV833 )
          = one_one_int )
        = $false )
      | ( ( ( SV833 = one_one_int )
          | ( SV824
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true )
      | ( ( is_int @ SV824 )
        = $false )
      | ( ( is_int @ SV833 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8714]) ).

thf(8732,plain,
    ! [SV834: $i,SV825: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV825 ) @ SV834 )
          = one_one_int )
        = $false )
      | ( ( ( SV834 = one_one_int )
          | ( SV834
            = ( hAPP_int_int @ number_number_of_int @ min ) ) )
        = $true )
      | ( ( is_int @ SV825 )
        = $false )
      | ( ( is_int @ SV834 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8715]) ).

thf(8733,plain,
    ! [SV826: $i,SV491: $i,SV321: $i,SV810: $i] :
      ( ( ( is_int @ SV810 )
        = $false )
      | ( ( is_int @ SV321 )
        = $false )
      | ( ( is_int @ SV491 )
        = $false )
      | ( ( ~ ( is_int @ SV826 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV810 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV826 ) @ SV491 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV810 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV826 ) @ SV321 ) ) )
          | ( SV810 != SV826 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8718]) ).

thf(8734,plain,
    ! [SV827: $i,SV491: $i,SV321: $i,SV811: $i] :
      ( ( ( is_int @ SV811 )
        = $false )
      | ( ( is_int @ SV321 )
        = $false )
      | ( ( is_int @ SV491 )
        = $false )
      | ( ( ~ ( is_int @ SV827 ) )
        = $true )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV811 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV827 ) @ SV491 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV811 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV827 ) @ SV321 ) ) )
          | ( SV321 != SV491 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8719]) ).

thf(8735,plain,
    ! [SV491: $i,SV321: $i,SV772: $i,SV750: $i] :
      ( ( ( SV750 = SV772 )
        = $true )
      | ( ( SV321 = SV491 )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV750 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV772 ) @ SV491 ) )
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV750 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV772 ) @ SV321 ) ) )
        = $true )
      | ( ( is_int @ SV750 )
        = $false )
      | ( ( is_int @ SV321 )
        = $false )
      | ( ( is_int @ SV491 )
        = $false )
      | ( ( is_int @ SV772 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8720]) ).

thf(8736,plain,
    ! [SV314: $i,SV486: $i] :
      ( ( ( ~ ( is_int @ ( sK1_A_4 @ SV486 @ SV314 ) ) )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV314 )
        = $false )
      | ( ( is_int @ SV486 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[8721]) ).

thf(8737,plain,
    ! [SV314: $i,SV486: $i] :
      ( ( ( ~ ( is_int @ ( sK2_SY713 @ SV486 @ SV314 ) ) )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV314 )
        = $false )
      | ( ( is_int @ SV486 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[8721]) ).

thf(8738,plain,
    ! [SV762: $i,SV487: $i,SV742: $i,SV315: $i] :
      ( ( ( SV315 = SV742 )
        = $true )
      | ( ( SV487 = SV762 )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV742 ) @ SV762 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV762 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV742 ) @ SV487 ) ) )
        = $false )
      | ( ( is_int @ SV742 )
        = $false )
      | ( ( is_int @ SV315 )
        = $false )
      | ( ( is_int @ SV487 )
        = $false )
      | ( ( is_int @ SV762 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8722]) ).

thf(8739,plain,
    ! [SV803: $i,SV315: $i,SV487: $i,SV816: $i] :
      ( ( ( is_int @ SV816 )
        = $false )
      | ( ( is_int @ SV487 )
        = $false )
      | ( ( is_int @ SV315 )
        = $false )
      | ( ( is_int @ SV803 )
        = $false )
      | ( ( ( SV315 != SV803 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV803 ) @ SV816 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV816 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV803 ) @ SV487 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8723]) ).

thf(8740,plain,
    ! [SV804: $i,SV315: $i,SV487: $i,SV817: $i] :
      ( ( ( is_int @ SV817 )
        = $false )
      | ( ( is_int @ SV487 )
        = $false )
      | ( ( is_int @ SV315 )
        = $false )
      | ( ( is_int @ SV804 )
        = $false )
      | ( ( ( SV487 != SV817 )
          | ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV804 ) @ SV817 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV817 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV804 ) @ SV487 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8724]) ).

thf(8741,plain,
    ! [SV635: $i,SV711: $i] :
      ( ( ( ~ ~ ( ~ ( is_int @ ( sK7_C_3 @ SV711 @ SV635 ) )
                | ~ ( is_int @ ( sK8_SY715 @ SV711 @ SV635 ) ) ) )
        = $false )
      | ( ( SV711 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV635 )
        = $false )
      | ( ( is_int @ SV711 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[8725]) ).

thf(8742,plain,
    ! [SV635: $i,SV711: $i] :
      ( ( ( SV711
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV711 ) @ SV635 ) ) @ ( sK7_C_3 @ SV711 @ SV635 ) ) )
        = $false )
      | ( ( SV711 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV635 )
        = $false )
      | ( ( is_int @ SV711 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[8725]) ).

thf(8743,plain,
    ! [SV636: $i,SV712: $i] :
      ( ( ( ~ ~ ( ~ ( is_int @ ( sK5_C_3 @ SV712 @ SV636 ) )
                | ~ ( is_int @ ( sK6_SY714 @ SV712 @ SV636 ) ) ) )
        = $false )
      | ( ( SV636 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV636 )
        = $false )
      | ( ( is_int @ SV712 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[8726]) ).

thf(8744,plain,
    ! [SV636: $i,SV712: $i] :
      ( ( ( SV712
         != ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV712 ) @ SV636 ) ) @ ( sK5_C_3 @ SV712 @ SV636 ) ) )
        = $false )
      | ( ( SV636 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV636 )
        = $false )
      | ( ( is_int @ SV712 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[8726]) ).

thf(8745,plain,
    ! [SV766: $i,SV748: $i,SV490: $i,SV320: $i] :
      ( ( ( SV320 != SV490 )
        = $true )
      | ( ( SV748 = SV766 )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV748 ) @ SV766 ) )
        = $false )
      | ( ( is_int @ SV748 )
        = $false )
      | ( ( is_int @ SV320 )
        = $false )
      | ( ( is_int @ SV490 )
        = $false )
      | ( ( is_int @ SV766 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8727]) ).

thf(8746,plain,
    ! [SV490: $i,SV320: $i,SV767: $i,SV749: $i] :
      ( ( ( SV749 != SV767 )
        = $true )
      | ( ( SV320 = SV490 )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV749 ) @ SV767 ) )
        = $false )
      | ( ( is_int @ SV749 )
        = $false )
      | ( ( is_int @ SV320 )
        = $false )
      | ( ( is_int @ SV490 )
        = $false )
      | ( ( is_int @ SV767 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8728]) ).

thf(8747,plain,
    ! [SV831: $i,SV822: $i] :
      ( ( ( SV822 = one_one_int )
        = $true )
      | ( ( SV822
          = ( hAPP_int_int @ number_number_of_int @ min ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV822 ) @ SV831 )
          = one_one_int )
        = $false )
      | ( ( is_int @ SV822 )
        = $false )
      | ( ( is_int @ SV831 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8729]) ).

thf(8748,plain,
    ! [SV832: $i,SV823: $i] :
      ( ( ( SV823 = one_one_int )
        = $true )
      | ( ( SV832
          = ( hAPP_int_int @ number_number_of_int @ min ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV823 ) @ SV832 )
          = one_one_int )
        = $false )
      | ( ( is_int @ SV823 )
        = $false )
      | ( ( is_int @ SV832 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8730]) ).

thf(8749,plain,
    ! [SV824: $i,SV833: $i] :
      ( ( ( SV833 = one_one_int )
        = $true )
      | ( ( SV824
          = ( hAPP_int_int @ number_number_of_int @ min ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV824 ) @ SV833 )
          = one_one_int )
        = $false )
      | ( ( is_int @ SV824 )
        = $false )
      | ( ( is_int @ SV833 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8731]) ).

thf(8750,plain,
    ! [SV825: $i,SV834: $i] :
      ( ( ( SV834 = one_one_int )
        = $true )
      | ( ( SV834
          = ( hAPP_int_int @ number_number_of_int @ min ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV825 ) @ SV834 )
          = one_one_int )
        = $false )
      | ( ( is_int @ SV825 )
        = $false )
      | ( ( is_int @ SV834 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8732]) ).

thf(8751,plain,
    ! [SV810: $i,SV321: $i,SV491: $i,SV826: $i] :
      ( ( ( is_int @ SV826 )
        = $false )
      | ( ( is_int @ SV491 )
        = $false )
      | ( ( is_int @ SV321 )
        = $false )
      | ( ( is_int @ SV810 )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV810 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV826 ) @ SV491 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV810 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV826 ) @ SV321 ) ) )
          | ( SV810 != SV826 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8733]) ).

thf(8752,plain,
    ! [SV811: $i,SV321: $i,SV491: $i,SV827: $i] :
      ( ( ( is_int @ SV827 )
        = $false )
      | ( ( is_int @ SV491 )
        = $false )
      | ( ( is_int @ SV321 )
        = $false )
      | ( ( is_int @ SV811 )
        = $false )
      | ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV811 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV827 ) @ SV491 ) )
            = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV811 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV827 ) @ SV321 ) ) )
          | ( SV321 != SV491 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[8734]) ).

thf(8753,plain,
    ! [SV491: $i,SV772: $i,SV321: $i,SV750: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV750 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV772 ) @ SV491 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV750 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV772 ) @ SV321 ) ) )
        = $false )
      | ( ( SV321 = SV491 )
        = $true )
      | ( ( SV750 = SV772 )
        = $true )
      | ( ( is_int @ SV750 )
        = $false )
      | ( ( is_int @ SV321 )
        = $false )
      | ( ( is_int @ SV491 )
        = $false )
      | ( ( is_int @ SV772 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8735]) ).

thf(8754,plain,
    ! [SV314: $i,SV486: $i] :
      ( ( ( is_int @ ( sK1_A_4 @ SV486 @ SV314 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV314 )
        = $false )
      | ( ( is_int @ SV486 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[8736]) ).

thf(8755,plain,
    ! [SV314: $i,SV486: $i] :
      ( ( ( is_int @ ( sK2_SY713 @ SV486 @ SV314 ) )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ gcd_gcd_int @ SV314 ) @ SV486 )
          = zero_zero_int )
        = $true )
      | ( ( is_int @ SV314 )
        = $false )
      | ( ( is_int @ SV486 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[8737]) ).

thf(8756,plain,
    ! [SV816: $i,SV487: $i,SV803: $i,SV315: $i] :
      ( ( ( SV315 != SV803 )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV803 ) @ SV816 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV816 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV803 ) @ SV487 ) ) )
        = $true )
      | ( ( is_int @ SV803 )
        = $false )
      | ( ( is_int @ SV315 )
        = $false )
      | ( ( is_int @ SV487 )
        = $false )
      | ( ( is_int @ SV816 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8739]) ).

thf(8757,plain,
    ! [SV804: $i,SV315: $i,SV817: $i,SV487: $i] :
      ( ( ( SV487 != SV817 )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV804 ) @ SV817 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV817 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV804 ) @ SV487 ) ) )
        = $true )
      | ( ( is_int @ SV804 )
        = $false )
      | ( ( is_int @ SV315 )
        = $false )
      | ( ( is_int @ SV487 )
        = $false )
      | ( ( is_int @ SV817 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8740]) ).

thf(8758,plain,
    ! [SV635: $i,SV711: $i] :
      ( ( ( ~ ( ~ ( is_int @ ( sK7_C_3 @ SV711 @ SV635 ) )
              | ~ ( is_int @ ( sK8_SY715 @ SV711 @ SV635 ) ) ) )
        = $true )
      | ( ( SV711 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV635 )
        = $false )
      | ( ( is_int @ SV711 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[8741]) ).

thf(8759,plain,
    ! [SV635: $i,SV711: $i] :
      ( ( ( SV711
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV711 ) @ SV635 ) ) @ ( sK7_C_3 @ SV711 @ SV635 ) ) )
        = $true )
      | ( ( SV711 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV635 )
        = $false )
      | ( ( is_int @ SV711 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[8742]) ).

thf(8760,plain,
    ! [SV636: $i,SV712: $i] :
      ( ( ( ~ ( ~ ( is_int @ ( sK5_C_3 @ SV712 @ SV636 ) )
              | ~ ( is_int @ ( sK6_SY714 @ SV712 @ SV636 ) ) ) )
        = $true )
      | ( ( SV636 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV636 )
        = $false )
      | ( ( is_int @ SV712 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[8743]) ).

thf(8761,plain,
    ! [SV636: $i,SV712: $i] :
      ( ( ( SV712
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ ( hAPP_int_int @ ( legacy_zgcd @ SV712 ) @ SV636 ) ) @ ( sK5_C_3 @ SV712 @ SV636 ) ) )
        = $true )
      | ( ( SV636 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV636 )
        = $false )
      | ( ( is_int @ SV712 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[8744]) ).

thf(8762,plain,
    ! [SV766: $i,SV748: $i,SV490: $i,SV320: $i] :
      ( ( ( SV320 = SV490 )
        = $false )
      | ( ( SV748 = SV766 )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV748 ) @ SV766 ) )
        = $false )
      | ( ( is_int @ SV748 )
        = $false )
      | ( ( is_int @ SV320 )
        = $false )
      | ( ( is_int @ SV490 )
        = $false )
      | ( ( is_int @ SV766 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8745]) ).

thf(8763,plain,
    ! [SV490: $i,SV320: $i,SV767: $i,SV749: $i] :
      ( ( ( SV749 = SV767 )
        = $false )
      | ( ( SV320 = SV490 )
        = $true )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV320 ) @ SV490 )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ minus_minus_int @ SV749 ) @ SV767 ) )
        = $false )
      | ( ( is_int @ SV749 )
        = $false )
      | ( ( is_int @ SV320 )
        = $false )
      | ( ( is_int @ SV490 )
        = $false )
      | ( ( is_int @ SV767 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8746]) ).

thf(8764,plain,
    ! [SV491: $i,SV826: $i,SV321: $i,SV810: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV810 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV826 ) @ SV491 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV810 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV826 ) @ SV321 ) ) )
        = $true )
      | ( ( SV810 != SV826 )
        = $true )
      | ( ( is_int @ SV810 )
        = $false )
      | ( ( is_int @ SV321 )
        = $false )
      | ( ( is_int @ SV491 )
        = $false )
      | ( ( is_int @ SV826 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8751]) ).

thf(8765,plain,
    ! [SV491: $i,SV827: $i,SV321: $i,SV811: $i] :
      ( ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV811 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV827 ) @ SV491 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV811 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV827 ) @ SV321 ) ) )
        = $true )
      | ( ( SV321 != SV491 )
        = $true )
      | ( ( is_int @ SV811 )
        = $false )
      | ( ( is_int @ SV321 )
        = $false )
      | ( ( is_int @ SV491 )
        = $false )
      | ( ( is_int @ SV827 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[8752]) ).

thf(8766,plain,
    ! [SV816: $i,SV487: $i,SV803: $i,SV315: $i] :
      ( ( ( SV315 = SV803 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV803 ) @ SV816 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV816 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV803 ) @ SV487 ) ) )
        = $true )
      | ( ( is_int @ SV803 )
        = $false )
      | ( ( is_int @ SV315 )
        = $false )
      | ( ( is_int @ SV487 )
        = $false )
      | ( ( is_int @ SV816 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8756]) ).

thf(8767,plain,
    ! [SV804: $i,SV315: $i,SV817: $i,SV487: $i] :
      ( ( ( SV487 = SV817 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV487 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV804 ) @ SV817 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV315 ) @ SV817 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV804 ) @ SV487 ) ) )
        = $true )
      | ( ( is_int @ SV804 )
        = $false )
      | ( ( is_int @ SV315 )
        = $false )
      | ( ( is_int @ SV487 )
        = $false )
      | ( ( is_int @ SV817 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8757]) ).

thf(8768,plain,
    ! [SV635: $i,SV711: $i] :
      ( ( ( ~ ( is_int @ ( sK7_C_3 @ SV711 @ SV635 ) )
          | ~ ( is_int @ ( sK8_SY715 @ SV711 @ SV635 ) ) )
        = $false )
      | ( ( SV711 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV635 )
        = $false )
      | ( ( is_int @ SV711 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8758]) ).

thf(8769,plain,
    ! [SV636: $i,SV712: $i] :
      ( ( ( ~ ( is_int @ ( sK5_C_3 @ SV712 @ SV636 ) )
          | ~ ( is_int @ ( sK6_SY714 @ SV712 @ SV636 ) ) )
        = $false )
      | ( ( SV636 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV636 )
        = $false )
      | ( ( is_int @ SV712 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8760]) ).

thf(8770,plain,
    ! [SV491: $i,SV321: $i,SV826: $i,SV810: $i] :
      ( ( ( SV810 = SV826 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV810 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV826 ) @ SV491 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV810 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV826 ) @ SV321 ) ) )
        = $true )
      | ( ( is_int @ SV810 )
        = $false )
      | ( ( is_int @ SV321 )
        = $false )
      | ( ( is_int @ SV491 )
        = $false )
      | ( ( is_int @ SV826 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8764]) ).

thf(8771,plain,
    ! [SV827: $i,SV811: $i,SV491: $i,SV321: $i] :
      ( ( ( SV321 = SV491 )
        = $false )
      | ( ( ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV811 ) @ SV321 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV827 ) @ SV491 ) )
          = ( hAPP_int_int @ ( hAPP_int_fun_int_int @ plus_plus_int @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV811 ) @ SV491 ) ) @ ( hAPP_int_int @ ( hAPP_int_fun_int_int @ times_times_int @ SV827 ) @ SV321 ) ) )
        = $true )
      | ( ( is_int @ SV811 )
        = $false )
      | ( ( is_int @ SV321 )
        = $false )
      | ( ( is_int @ SV491 )
        = $false )
      | ( ( is_int @ SV827 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[8765]) ).

thf(8772,plain,
    ! [SV635: $i,SV711: $i] :
      ( ( ( ~ ( is_int @ ( sK7_C_3 @ SV711 @ SV635 ) ) )
        = $false )
      | ( ( SV711 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV635 )
        = $false )
      | ( ( is_int @ SV711 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[8768]) ).

thf(8773,plain,
    ! [SV635: $i,SV711: $i] :
      ( ( ( ~ ( is_int @ ( sK8_SY715 @ SV711 @ SV635 ) ) )
        = $false )
      | ( ( SV711 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV635 )
        = $false )
      | ( ( is_int @ SV711 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[8768]) ).

thf(8774,plain,
    ! [SV636: $i,SV712: $i] :
      ( ( ( ~ ( is_int @ ( sK5_C_3 @ SV712 @ SV636 ) ) )
        = $false )
      | ( ( SV636 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV636 )
        = $false )
      | ( ( is_int @ SV712 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[8769]) ).

thf(8775,plain,
    ! [SV636: $i,SV712: $i] :
      ( ( ( ~ ( is_int @ ( sK6_SY714 @ SV712 @ SV636 ) ) )
        = $false )
      | ( ( SV636 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV636 )
        = $false )
      | ( ( is_int @ SV712 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[8769]) ).

thf(8776,plain,
    ! [SV635: $i,SV711: $i] :
      ( ( ( is_int @ ( sK7_C_3 @ SV711 @ SV635 ) )
        = $true )
      | ( ( SV711 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV635 )
        = $false )
      | ( ( is_int @ SV711 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[8772]) ).

thf(8777,plain,
    ! [SV635: $i,SV711: $i] :
      ( ( ( is_int @ ( sK8_SY715 @ SV711 @ SV635 ) )
        = $true )
      | ( ( SV711 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV635 )
        = $false )
      | ( ( is_int @ SV711 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[8773]) ).

thf(8778,plain,
    ! [SV636: $i,SV712: $i] :
      ( ( ( is_int @ ( sK5_C_3 @ SV712 @ SV636 ) )
        = $true )
      | ( ( SV636 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV636 )
        = $false )
      | ( ( is_int @ SV712 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[8774]) ).

thf(8779,plain,
    ! [SV636: $i,SV712: $i] :
      ( ( ( is_int @ ( sK6_SY714 @ SV712 @ SV636 ) )
        = $true )
      | ( ( SV636 = zero_zero_int )
        = $true )
      | ( ( is_int @ SV636 )
        = $false )
      | ( ( is_int @ SV712 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[8775]) ).

thf(8780,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[6108,8779,8778,8777,8776,8771,8770,8767,8766,8763,8762,8761,8759,8755,8754,8753,8750,8749,8748,8747,8738,8717,8716,8709,8708,8707,8705,8700,8698,8684,8673,8672,8671,8670,8669,8668,8667,8666,8645,8644,8640,8637,8634,8631,8616,8614,8609,8608,8606,8593,8592,8591,8590,8589,8571,8570,8569,8568,8563,8562,8558,8554,8550,8549,8538,8537,8536,8535,8534,8533,8527,8526,8519,8518,8500,8499,8496,8495,8489,8488,8458,8457,8435,8434,8429,8428,8425,8424,8414,8411,8409,8406,8378,8368,8350,8349,8344,8325,8323,8322,8314,8312,8311,8310,8309,8308,8298,8297,8296,8295,8290,8289,8288,8287,8269,8268,8234,8233,8221,8220,8219,8218,8207,8206,8205,8204,8186,8175,8174,8169,8168,8160,8159,8115,8114,8105,8104,8094,8093,8085,8082,8081,8080,8079,8075,8073,8072,8071,8070,8054,8053,8052,8050,8049,8026,8025,7958,7957,7956,7955,7945,7941,7940,7936,7932,7931,7926,7916,7794,7792,7789,7780,7776,7775,7773,7772,7770,7769,7767,7635,7634,7632,7631,7618,7617,7616,7615,7612,7611,7610,7609,7607,7604,7603,7602,7601,7596,7506,7476,7474,7473,7471,7469,7468,7467,7464,7463,7461,7460,7459,7458,7452,7451,7450,7448,7444,7443,7442,7441,7436,7435,7434,7433,7432,7431,7430,7429,7427,7423,7421,7420,7419,7415,7414,7413,7411,7410,7409,7408,7407,7406,7405,7404,7403,7402,7401,7400,7399,7398,7397,7395,7392,7391,7387,7386,7385,7384,7383,7382,7381,7380,7379,7378,7377,7376,7375,7374,7373,7372,7371,7365,7364,7363,7362,7361,7360,7359,7358,7357,7356,7355,7354,7353,7231,7230,7229,7228,7226,7225,7224,7223,7222,7219,7218,7213,7212,7211,7210,7209,7208,7207,7206,7204,7203,7202,7201,7195,7194,7193,7192,7184,7183,7180,7178,7176,7175,7174,7173,7172,7171,7168,7164,7163,7160,7158,7155,7154,7151,7150,7149,7148,7147,7146,7145,7144,7143,7139,7133,7132,7128,7127,7126,7125,7124,7121,7119,7118,7114,7108,7107,7106,7105,7104,7103,7102,7098,7093,7090,7076,7075,7072,7063,7062,7061,7053,7052,7039,7038,7037,7036,7035,7029,7024,7023,7022,7019,7018,6953,6950,6947,6946,6941,6939,6938,6936,6933,6921,6907,6901,6900,6896,6895,6894,6893,6891,6890,6889,6873,6872,6871,6867,6862,6861,6858,6857,6856,6855,6844,6843,6838,6837,6836,6835,6834,6833,6832,6827,6821,6818,6815,6807,6806,6804,6801,6799,6798,6797,6796,6794,6793,6792,6787,6786,6781,6780,6779,6777,6776,6764,6762,6759,6758,6756,6755,6754,6753,6752,6751,6750,6749,6748,6747,6743,6733,6718,6717,6714,6713,6688,6687,6676,6675,6674,6673,6672,6670,6669,6666,6665,6664,6663,6661,6651,6647,6638,6637,6636,6570,6562,6556,6555,6550,6549,6548,6529,6528,6527,6525,6524,6521,6520,6512,6498,6488,6480,6479,6476,6475,6474,6473,6472,6471,6470,6469,6468,6467,6466,6461,6400,6399,6392,6391,6387,6384,6371,6369,6347,6345,6344,6340,6339,6333,6329,6300,6292,6199,6196,6193,6192,6183,6181,6180,6179,6178,6163,6162,6161,6160,6152,6151,6134,6133,6132,6131,6129,6128,6127,6126,6124,6123,6120,6119,6115,6114,6110,6109]) ).

thf(8781,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[8780]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : NUM925+4 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05  % Command  : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.20  % Computer : n002.cluster.edu
% 0.07/0.20  % Model    : x86_64 x86_64
% 0.07/0.20  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20  % Memory   : 8046.5625MB
% 0.07/0.20  % OS       : Linux 6.8.0-71-generic
% 0.07/0.20  % CPULimit : 300
% 0.07/0.20  % WCLimit  : 300
% 0.07/0.20  % DateTime : Tue Oct  6 13:47:27 UTC 2026
% 0.07/0.20  % CPUTime  : 
% 0.07/0.20  Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 178.56/36.30  ...........................................
% 178.56/36.30  
% 178.56/36.30   No.of.Axioms: 5486
% 178.56/36.30  
% 178.56/36.30   Length.of.Defs: 0
% 178.56/36.30  
% 178.56/36.30   Contains.Choice.Funs: false
% 178.56/36.30  .....................................................................................................................................................................................................................
% 178.56/36.30  
% 178.56/36.30  ********************************
% 178.56/36.30  *   All subproblems solved!    *
% 178.56/36.30  ********************************
% 178.56/36.30  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:462,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:69,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:8780,loop_count:0,foatp_calls:1,translation:fof_full)
% 178.56/36.30  
% 178.56/36.30  %**** Beginning of derivation protocol ****
% 178.56/36.30  % SZS output start CNFRefutation
% See solution above
% 178.56/36.36  
% 178.56/36.36  %**** End of derivation protocol ****
% 178.56/36.36  %**** no. of clauses in derivation: 3757 ****
% 178.56/36.36  %**** clause counter: 8780 ****
% 178.56/36.36  
% 178.56/36.36  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:2,axioms:462,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:69,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:8780,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------