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

%------------------------------------------------------------------------------
% File     : LEO-II---2.3.1
% Problem  : ITP257^3 : TPTP v9.3.1. Bugfixed v9.2.1.
% 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 : n013.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 10:25:17 AM UTC 2026

% Result   : Theorem 174.34s 35.23s
% Output   : CNFRefutation 174.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   36
%            Number of leaves      :  427
% Syntax   : Number of formulae    : 4974 (2500 unt;   0 typ;   0 def)
%            Number of atoms       : 30200 (15632 equ;   0 cnn)
%            Maximal formula atoms :    8 (   6 avg)
%            Number of connectives : 58001 (7141   ~;6741   |;  81   &;43552   @)
%                                         (   0 <=>; 486  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   4 avg)
%            Number of types       :   93 (  92 usr)
%            Number of type conns  :  306 ( 306   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  916 ( 913 usr;  62 con; 0-8 aty)
%            Number of variables   : 12311 ( 299   ^;11967   !;  45   ?;12311   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_char,type,
    char: $tType ).

thf(tp_code_integer,type,
    code_integer: $tType ).

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

thf(tp_extended_enat,type,
    extended_enat: $tType ).

thf(tp_filter1242075044329608583at_nat,type,
    filter1242075044329608583at_nat: $tType ).

thf(tp_filter2146258269922977983l_real,type,
    filter2146258269922977983l_real: $tType ).

thf(tp_filter6041513312241820739omplex,type,
    filter6041513312241820739omplex: $tType ).

thf(tp_filter_nat,type,
    filter_nat: $tType ).

thf(tp_filter_real,type,
    filter_real: $tType ).

thf(tp_int,type,
    int: $tType ).

thf(tp_list_Code_integer,type,
    list_Code_integer: $tType ).

thf(tp_list_P1726324292696863441at_num,type,
    list_P1726324292696863441at_num: $tType ).

thf(tp_list_P3126845725202233233VEBT_o,type,
    list_P3126845725202233233VEBT_o: $tType ).

thf(tp_list_P3744719386663036955um_num,type,
    list_P3744719386663036955um_num: $tType ).

thf(tp_list_P3795440434834930179_o_int,type,
    list_P3795440434834930179_o_int: $tType ).

thf(tp_list_P4002435161011370285od_o_o,type,
    list_P4002435161011370285od_o_o: $tType ).

thf(tp_list_P4547456442757143711BT_int,type,
    list_P4547456442757143711BT_int: $tType ).

thf(tp_list_P5087981734274514673_int_o,type,
    list_P5087981734274514673_int_o: $tType ).

thf(tp_list_P5707943133018811711nt_int,type,
    list_P5707943133018811711nt_int: $tType ).

thf(tp_list_P6011104703257516679at_nat,type,
    list_P6011104703257516679at_nat: $tType ).

thf(tp_list_P7413028617227757229T_VEBT,type,
    list_P7413028617227757229T_VEBT: $tType ).

thf(tp_list_P7495141550334521929T_VEBT,type,
    list_P7495141550334521929T_VEBT: $tType ).

thf(tp_list_P7524865323317820941T_VEBT,type,
    list_P7524865323317820941T_VEBT: $tType ).

thf(tp_list_P8526636022914148096eger_o,type,
    list_P8526636022914148096eger_o: $tType ).

thf(tp_list_VEBT_VEBT,type,
    list_VEBT_VEBT: $tType ).

thf(tp_list_complex,type,
    list_complex: $tType ).

thf(tp_list_int,type,
    list_int: $tType ).

thf(tp_list_nat,type,
    list_nat: $tType ).

thf(tp_list_num,type,
    list_num: $tType ).

thf(tp_list_o,type,
    list_o: $tType ).

thf(tp_list_real,type,
    list_real: $tType ).

thf(tp_list_set_nat,type,
    list_set_nat: $tType ).

thf(tp_nat,type,
    nat: $tType ).

thf(tp_num,type,
    num: $tType ).

thf(tp_option4927543243414619207at_nat,type,
    option4927543243414619207at_nat: $tType ).

thf(tp_option_nat,type,
    option_nat: $tType ).

thf(tp_option_num,type,
    option_num: $tType ).

thf(tp_produc1193250871479095198on_num,type,
    produc1193250871479095198on_num: $tType ).

thf(tp_produc2233624965454879586on_nat,type,
    produc2233624965454879586on_nat: $tType ).

thf(tp_produc2422161461964618553l_real,type,
    produc2422161461964618553l_real: $tType ).

thf(tp_produc2504756804600209347T_VEBT,type,
    produc2504756804600209347T_VEBT: $tType ).

thf(tp_produc2963631642982155120at_num,type,
    produc2963631642982155120at_num: $tType ).

thf(tp_produc334124729049499915VEBT_o,type,
    produc334124729049499915VEBT_o: $tType ).

thf(tp_produc3368934014287244435at_num,type,
    produc3368934014287244435at_num: $tType ).

thf(tp_produc3447558737645232053on_num,type,
    produc3447558737645232053on_num: $tType ).

thf(tp_produc4411394909380815293omplex,type,
    produc4411394909380815293omplex: $tType ).

thf(tp_produc4471711990508489141at_nat,type,
    produc4471711990508489141at_nat: $tType ).

thf(tp_produc4894624898956917775BT_int,type,
    produc4894624898956917775BT_int: $tType ).

thf(tp_produc4953844613479565601on_nat,type,
    produc4953844613479565601on_nat: $tType ).

thf(tp_produc5491161045314408544at_nat,type,
    produc5491161045314408544at_nat: $tType ).

thf(tp_produc5542196010084753463at_nat,type,
    produc5542196010084753463at_nat: $tType ).

thf(tp_produc6121120109295599847at_nat,type,
    produc6121120109295599847at_nat: $tType ).

thf(tp_produc6271795597528267376eger_o,type,
    produc6271795597528267376eger_o: $tType ).

thf(tp_produc7036089656553540234on_num,type,
    produc7036089656553540234on_num: $tType ).

thf(tp_produc7248412053542808358at_nat,type,
    produc7248412053542808358at_nat: $tType ).

thf(tp_produc8243902056947475879T_VEBT,type,
    produc8243902056947475879T_VEBT: $tType ).

thf(tp_produc8306885398267862888on_nat,type,
    produc8306885398267862888on_nat: $tType ).

thf(tp_produc8923325533196201883nteger,type,
    produc8923325533196201883nteger: $tType ).

thf(tp_produc9072475918466114483BT_nat,type,
    produc9072475918466114483BT_nat: $tType ).

thf(tp_product_prod_int_int,type,
    product_prod_int_int: $tType ).

thf(tp_product_prod_nat_nat,type,
    product_prod_nat_nat: $tType ).

thf(tp_product_prod_nat_num,type,
    product_prod_nat_num: $tType ).

thf(tp_product_prod_num_num,type,
    product_prod_num_num: $tType ).

thf(tp_product_prod_o_int,type,
    product_prod_o_int: $tType ).

thf(tp_product_prod_o_o,type,
    product_prod_o_o: $tType ).

thf(tp_rat,type,
    rat: $tType ).

thf(tp_real,type,
    real: $tType ).

thf(tp_set_Code_integer,type,
    set_Code_integer: $tType ).

thf(tp_set_Pr5085853215250843933omplex,type,
    set_Pr5085853215250843933omplex: $tType ).

thf(tp_set_Pr6218003697084177305l_real,type,
    set_Pr6218003697084177305l_real: $tType ).

thf(tp_set_Pr958786334691620121nt_int,type,
    set_Pr958786334691620121nt_int: $tType ).

thf(tp_set_Product_unit,type,
    set_Product_unit: $tType ).

thf(tp_set_VEBT_VEBT,type,
    set_VEBT_VEBT: $tType ).

thf(tp_set_char,type,
    set_char: $tType ).

thf(tp_set_complex,type,
    set_complex: $tType ).

thf(tp_set_fi4554929511873752355omplex,type,
    set_fi4554929511873752355omplex: $tType ).

thf(tp_set_fi7789364187291644575l_real,type,
    set_fi7789364187291644575l_real: $tType ).

thf(tp_set_int,type,
    set_int: $tType ).

thf(tp_set_list_VEBT_VEBT,type,
    set_list_VEBT_VEBT: $tType ).

thf(tp_set_list_complex,type,
    set_list_complex: $tType ).

thf(tp_set_list_int,type,
    set_list_int: $tType ).

thf(tp_set_list_nat,type,
    set_list_nat: $tType ).

thf(tp_set_list_o,type,
    set_list_o: $tType ).

thf(tp_set_nat,type,
    set_nat: $tType ).

thf(tp_set_num,type,
    set_num: $tType ).

thf(tp_set_o,type,
    set_o: $tType ).

thf(tp_set_rat,type,
    set_rat: $tType ).

thf(tp_set_real,type,
    set_real: $tType ).

thf(tp_set_set_complex,type,
    set_set_complex: $tType ).

thf(tp_set_set_int,type,
    set_set_int: $tType ).

thf(tp_set_set_nat,type,
    set_set_nat: $tType ).

thf(tp_vEBT_VEBT,type,
    vEBT_VEBT: $tType ).

thf(tp_abs_Integ,type,
    abs_Integ: product_prod_nat_nat > int ).

thf(tp_abs_abs_Code_integer,type,
    abs_abs_Code_integer: code_integer > code_integer ).

thf(tp_abs_abs_complex,type,
    abs_abs_complex: complex > complex ).

thf(tp_abs_abs_int,type,
    abs_abs_int: int > int ).

thf(tp_abs_abs_rat,type,
    abs_abs_rat: rat > rat ).

thf(tp_abs_abs_real,type,
    abs_abs_real: real > real ).

thf(tp_accp_P1096762738010456898nt_int,type,
    accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).

thf(tp_accp_P2887432264394892906BT_nat,type,
    accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).

thf(tp_accp_P4275260045618599050at_nat,type,
    accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).

thf(tp_accp_VEBT_VEBT,type,
    accp_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > vEBT_VEBT > $o ).

thf(tp_accp_nat,type,
    accp_nat: ( nat > nat > $o ) > nat > $o ).

thf(tp_adjust_div,type,
    adjust_div: product_prod_int_int > int ).

thf(tp_adjust_mod,type,
    adjust_mod: int > int > int ).

thf(tp_append_VEBT_VEBT,type,
    append_VEBT_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_VEBT_VEBT ).

thf(tp_append_int,type,
    append_int: list_int > list_int > list_int ).

thf(tp_arccos,type,
    arccos: real > real ).

thf(tp_archim3151403230148437115or_rat,type,
    archim3151403230148437115or_rat: rat > int ).

thf(tp_archim6058952711729229775r_real,type,
    archim6058952711729229775r_real: real > int ).

thf(tp_archim7778729529865785530nd_rat,type,
    archim7778729529865785530nd_rat: rat > int ).

thf(tp_archim7802044766580827645g_real,type,
    archim7802044766580827645g_real: real > int ).

thf(tp_archim8280529875227126926d_real,type,
    archim8280529875227126926d_real: real > int ).

thf(tp_arcosh_real,type,
    arcosh_real: real > real ).

thf(tp_arcsin,type,
    arcsin: real > real ).

thf(tp_arctan,type,
    arctan: real > real ).

thf(tp_arg,type,
    arg: complex > real ).

thf(tp_arsinh_real,type,
    arsinh_real: real > real ).

thf(tp_artanh_real,type,
    artanh_real: real > real ).

thf(tp_ascii_of,type,
    ascii_of: char > char ).

thf(tp_at_bot_real,type,
    at_bot_real: filter_real ).

thf(tp_at_top_nat,type,
    at_top_nat: filter_nat ).

thf(tp_at_top_real,type,
    at_top_real: filter_real ).

thf(tp_bezw,type,
    bezw: nat > nat > product_prod_int_int ).

thf(tp_bezw_rel,type,
    bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(tp_bfun_nat_real,type,
    bfun_nat_real: ( nat > real ) > filter_nat > $o ).

thf(tp_bij_be1856998921033663316omplex,type,
    bij_be1856998921033663316omplex: ( complex > complex ) > set_complex > set_complex > $o ).

thf(tp_bij_betw_nat_complex,type,
    bij_betw_nat_complex: ( nat > complex ) > set_nat > set_complex > $o ).

thf(tp_bij_betw_nat_nat,type,
    bij_betw_nat_nat: ( nat > nat ) > set_nat > set_nat > $o ).

thf(tp_binomial,type,
    binomial: nat > nat > nat ).

thf(tp_bit0,type,
    bit0: num > num ).

thf(tp_bit1,type,
    bit1: num > num ).

thf(tp_bitM,type,
    bitM: num > num ).

thf(tp_bit_and_int_rel,type,
    bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o ).

thf(tp_bit_and_not_num,type,
    bit_and_not_num: num > num > option_num ).

thf(tp_bit_concat_bit,type,
    bit_concat_bit: nat > int > int > int ).

thf(tp_bit_or_not_num_neg,type,
    bit_or_not_num_neg: num > num > num ).

thf(tp_bit_ri631733984087533419it_int,type,
    bit_ri631733984087533419it_int: nat > int > int ).

thf(tp_bit_ri6519982836138164636nteger,type,
    bit_ri6519982836138164636nteger: nat > code_integer > code_integer ).

thf(tp_bit_ri7919022796975470100ot_int,type,
    bit_ri7919022796975470100ot_int: int > int ).

thf(tp_bit_se1146084159140164899it_int,type,
    bit_se1146084159140164899it_int: int > nat > $o ).

thf(tp_bit_se1148574629649215175it_nat,type,
    bit_se1148574629649215175it_nat: nat > nat > $o ).

thf(tp_bit_se1345352211410354436nteger,type,
    bit_se1345352211410354436nteger: nat > code_integer > code_integer ).

thf(tp_bit_se1409905431419307370or_int,type,
    bit_se1409905431419307370or_int: int > int > int ).

thf(tp_bit_se1412395901928357646or_nat,type,
    bit_se1412395901928357646or_nat: nat > nat > nat ).

thf(tp_bit_se2000444600071755411sk_int,type,
    bit_se2000444600071755411sk_int: nat > int ).

thf(tp_bit_se2002935070580805687sk_nat,type,
    bit_se2002935070580805687sk_nat: nat > nat ).

thf(tp_bit_se2159334234014336723it_int,type,
    bit_se2159334234014336723it_int: nat > int > int ).

thf(tp_bit_se2161824704523386999it_nat,type,
    bit_se2161824704523386999it_nat: nat > nat > nat ).

thf(tp_bit_se2793503036327961859nteger,type,
    bit_se2793503036327961859nteger: nat > code_integer > code_integer ).

thf(tp_bit_se2923211474154528505it_int,type,
    bit_se2923211474154528505it_int: nat > int > int ).

thf(tp_bit_se2925701944663578781it_nat,type,
    bit_se2925701944663578781it_nat: nat > nat > nat ).

thf(tp_bit_se4203085406695923979it_int,type,
    bit_se4203085406695923979it_int: nat > int > int ).

thf(tp_bit_se4205575877204974255it_nat,type,
    bit_se4205575877204974255it_nat: nat > nat > nat ).

thf(tp_bit_se545348938243370406it_int,type,
    bit_se545348938243370406it_int: nat > int > int ).

thf(tp_bit_se547839408752420682it_nat,type,
    bit_se547839408752420682it_nat: nat > nat > nat ).

thf(tp_bit_se6526347334894502574or_int,type,
    bit_se6526347334894502574or_int: int > int > int ).

thf(tp_bit_se6528837805403552850or_nat,type,
    bit_se6528837805403552850or_nat: nat > nat > nat ).

thf(tp_bit_se725231765392027082nd_int,type,
    bit_se725231765392027082nd_int: int > int > int ).

thf(tp_bit_se727722235901077358nd_nat,type,
    bit_se727722235901077358nd_nat: nat > nat > nat ).

thf(tp_bit_se7879613467334960850it_int,type,
    bit_se7879613467334960850it_int: nat > int > int ).

thf(tp_bit_se7882103937844011126it_nat,type,
    bit_se7882103937844011126it_nat: nat > nat > nat ).

thf(tp_bit_se8260200283734997820nteger,type,
    bit_se8260200283734997820nteger: nat > code_integer > code_integer ).

thf(tp_bit_se8568078237143864401it_int,type,
    bit_se8568078237143864401it_int: nat > int > int ).

thf(tp_bit_se8570568707652914677it_nat,type,
    bit_se8570568707652914677it_nat: nat > nat > nat ).

thf(tp_bit_take_bit_num,type,
    bit_take_bit_num: nat > num > option_num ).

thf(tp_bit_un1837492267222099188nd_num,type,
    bit_un1837492267222099188nd_num: num > num > option_num ).

thf(tp_bit_un2480387367778600638or_num,type,
    bit_un2480387367778600638or_num: num > num > option_num ).

thf(tp_bit_un6178654185764691216or_num,type,
    bit_un6178654185764691216or_num: num > num > option_num ).

thf(tp_bit_un7362597486090784418nd_num,type,
    bit_un7362597486090784418nd_num: num > num > option_num ).

thf(tp_bot_bo1796632182523588997nt_int,type,
    bot_bo1796632182523588997nt_int: set_Pr958786334691620121nt_int ).

thf(tp_bot_bot_nat,type,
    bot_bot_nat: nat ).

thf(tp_bot_bot_set_complex,type,
    bot_bot_set_complex: set_complex ).

thf(tp_bot_bot_set_int,type,
    bot_bot_set_int: set_int ).

thf(tp_bot_bot_set_nat,type,
    bot_bot_set_nat: set_nat ).

thf(tp_bot_bot_set_num,type,
    bot_bot_set_num: set_num ).

thf(tp_bot_bot_set_rat,type,
    bot_bot_set_rat: set_rat ).

thf(tp_bot_bot_set_real,type,
    bot_bot_set_real: set_real ).

thf(tp_bot_bot_set_set_nat,type,
    bot_bot_set_set_nat: set_set_nat ).

thf(tp_case_nat_nat,type,
    case_nat_nat: nat > ( nat > nat ) > nat > nat ).

thf(tp_case_nat_o,type,
    case_nat_o: $o > ( nat > $o ) > nat > $o ).

thf(tp_case_nat_option_num,type,
    case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).

thf(tp_case_num_option_num,type,
    case_num_option_num: option_num > ( num > option_num ) > ( num > option_num ) > num > option_num ).

thf(tp_case_o184042715313410164at_nat,type,
    case_o184042715313410164at_nat: $o > ( product_prod_nat_nat > $o ) > option4927543243414619207at_nat > $o ).

thf(tp_case_o6005452278849405969um_num,type,
    case_o6005452278849405969um_num: option_num > ( num > option_num ) > option_num > option_num ).

thf(tp_case_option_int_num,type,
    case_option_int_num: int > ( num > int ) > option_num > int ).

thf(tp_case_option_num_num,type,
    case_option_num_num: num > ( num > num ) > option_num > num ).

thf(tp_char2,type,
    char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).

thf(tp_char_of_integer,type,
    char_of_integer: code_integer > char ).

thf(tp_cis,type,
    cis: real > complex ).

thf(tp_cnj,type,
    cnj: complex > complex ).

thf(tp_code_bit_cut_integer,type,
    code_bit_cut_integer: code_integer > produc6271795597528267376eger_o ).

thf(tp_code_divmod_abs,type,
    code_divmod_abs: code_integer > code_integer > produc8923325533196201883nteger ).

thf(tp_code_divmod_integer,type,
    code_divmod_integer: code_integer > code_integer > produc8923325533196201883nteger ).

thf(tp_code_int_of_integer,type,
    code_int_of_integer: code_integer > int ).

thf(tp_code_integer_of_int,type,
    code_integer_of_int: int > code_integer ).

thf(tp_code_integer_of_num,type,
    code_integer_of_num: num > code_integer ).

thf(tp_code_nat_of_integer,type,
    code_nat_of_integer: code_integer > nat ).

thf(tp_code_num_of_integer,type,
    code_num_of_integer: code_integer > num ).

thf(tp_collec213857154873943460nt_int,type,
    collec213857154873943460nt_int: ( product_prod_int_int > $o ) > set_Pr958786334691620121nt_int ).

thf(tp_collec3799799289383736868l_real,type,
    collec3799799289383736868l_real: ( produc2422161461964618553l_real > $o ) > set_Pr6218003697084177305l_real ).

thf(tp_collec5608196760682091941T_VEBT,type,
    collec5608196760682091941T_VEBT: ( list_VEBT_VEBT > $o ) > set_list_VEBT_VEBT ).

thf(tp_collec8663557070575231912omplex,type,
    collec8663557070575231912omplex: ( produc4411394909380815293omplex > $o ) > set_Pr5085853215250843933omplex ).

thf(tp_collect_Code_integer,type,
    collect_Code_integer: ( code_integer > $o ) > set_Code_integer ).

thf(tp_collect_complex,type,
    collect_complex: ( complex > $o ) > set_complex ).

thf(tp_collect_int,type,
    collect_int: ( int > $o ) > set_int ).

thf(tp_collect_list_complex,type,
    collect_list_complex: ( list_complex > $o ) > set_list_complex ).

thf(tp_collect_list_int,type,
    collect_list_int: ( list_int > $o ) > set_list_int ).

thf(tp_collect_list_nat,type,
    collect_list_nat: ( list_nat > $o ) > set_list_nat ).

thf(tp_collect_list_o,type,
    collect_list_o: ( list_o > $o ) > set_list_o ).

thf(tp_collect_nat,type,
    collect_nat: ( nat > $o ) > set_nat ).

thf(tp_collect_num,type,
    collect_num: ( num > $o ) > set_num ).

thf(tp_collect_rat,type,
    collect_rat: ( rat > $o ) > set_rat ).

thf(tp_collect_real,type,
    collect_real: ( real > $o ) > set_real ).

thf(tp_collect_set_complex,type,
    collect_set_complex: ( set_complex > $o ) > set_set_complex ).

thf(tp_collect_set_int,type,
    collect_set_int: ( set_int > $o ) > set_set_int ).

thf(tp_collect_set_nat,type,
    collect_set_nat: ( set_nat > $o ) > set_set_nat ).

thf(tp_comm_s2602460028002588243omplex,type,
    comm_s2602460028002588243omplex: complex > nat > complex ).

thf(tp_comm_s4028243227959126397er_rat,type,
    comm_s4028243227959126397er_rat: rat > nat > rat ).

thf(tp_comm_s4660882817536571857er_int,type,
    comm_s4660882817536571857er_int: int > nat > int ).

thf(tp_comm_s4663373288045622133er_nat,type,
    comm_s4663373288045622133er_nat: nat > nat > nat ).

thf(tp_comm_s629917340098488124ar_nat,type,
    comm_s629917340098488124ar_nat: char > nat ).

thf(tp_comm_s7457072308508201937r_real,type,
    comm_s7457072308508201937r_real: real > nat > real ).

thf(tp_comm_s8582702949713902594nteger,type,
    comm_s8582702949713902594nteger: code_integer > nat > code_integer ).

thf(tp_comp_C1593894019821074884nteger,type,
    comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(tp_comp_C8797469213163452608nteger,type,
    comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(tp_comp_int_nat_int,type,
    comp_int_nat_int: ( int > nat ) > ( int > int ) > int > nat ).

thf(tp_comp_nat_nat_nat,type,
    comp_nat_nat_nat: ( nat > nat ) > ( nat > nat ) > nat > nat ).

thf(tp_comp_nat_real_nat,type,
    comp_nat_real_nat: ( nat > real ) > ( nat > nat ) > nat > real ).

thf(tp_comple1385675409528146559p_real,type,
    comple1385675409528146559p_real: set_real > real ).

thf(tp_comple2936214249959783750l_real,type,
    comple2936214249959783750l_real: set_fi7789364187291644575l_real > filter2146258269922977983l_real ).

thf(tp_comple4887499456419720421f_real,type,
    comple4887499456419720421f_real: set_real > real ).

thf(tp_comple7399068483239264473et_nat,type,
    comple7399068483239264473et_nat: set_set_nat > set_nat ).

thf(tp_comple7806235888213564991et_nat,type,
    comple7806235888213564991et_nat: set_set_nat > set_nat ).

thf(tp_comple8358262395181532106omplex,type,
    comple8358262395181532106omplex: set_fi4554929511873752355omplex > filter6041513312241820739omplex ).

thf(tp_complete_Sup_Sup_int,type,
    complete_Sup_Sup_int: set_int > int ).

thf(tp_complex2,type,
    complex2: real > real > complex ).

thf(tp_compow_nat_nat,type,
    compow_nat_nat: nat > ( nat > nat ) > nat > nat ).

thf(tp_cons_VEBT_VEBT,type,
    cons_VEBT_VEBT: vEBT_VEBT > list_VEBT_VEBT > list_VEBT_VEBT ).

thf(tp_cons_int,type,
    cons_int: int > list_int > list_int ).

thf(tp_cos_coeff,type,
    cos_coeff: nat > real ).

thf(tp_cos_complex,type,
    cos_complex: complex > complex ).

thf(tp_cos_real,type,
    cos_real: real > real ).

thf(tp_cosh_real,type,
    cosh_real: real > real ).

thf(tp_cot_real,type,
    cot_real: real > real ).

thf(tp_csqrt,type,
    csqrt: complex > complex ).

thf(tp_deg,type,
    deg: nat ).

thf(tp_differ6690327859849518006l_real,type,
    differ6690327859849518006l_real: ( real > real ) > filter_real > $o ).

thf(tp_diffs_Code_integer,type,
    diffs_Code_integer: ( nat > code_integer ) > nat > code_integer ).

thf(tp_diffs_complex,type,
    diffs_complex: ( nat > complex ) > nat > complex ).

thf(tp_diffs_int,type,
    diffs_int: ( nat > int ) > nat > int ).

thf(tp_diffs_rat,type,
    diffs_rat: ( nat > rat ) > nat > rat ).

thf(tp_diffs_real,type,
    diffs_real: ( nat > real ) > nat > real ).

thf(tp_distinct_int,type,
    distinct_int: list_int > $o ).

thf(tp_divide1717551699836669952omplex,type,
    divide1717551699836669952omplex: complex > complex > complex ).

thf(tp_divide6298287555418463151nteger,type,
    divide6298287555418463151nteger: code_integer > code_integer > code_integer ).

thf(tp_divide_divide_int,type,
    divide_divide_int: int > int > int ).

thf(tp_divide_divide_nat,type,
    divide_divide_nat: nat > nat > nat ).

thf(tp_divide_divide_rat,type,
    divide_divide_rat: rat > rat > rat ).

thf(tp_divide_divide_real,type,
    divide_divide_real: real > real > real ).

thf(tp_divmod_nat,type,
    divmod_nat: nat > nat > product_prod_nat_nat ).

thf(tp_drop_VEBT_VEBT,type,
    drop_VEBT_VEBT: nat > list_VEBT_VEBT > list_VEBT_VEBT ).

thf(tp_dvd_dvd_Code_integer,type,
    dvd_dvd_Code_integer: code_integer > code_integer > $o ).

thf(tp_dvd_dvd_complex,type,
    dvd_dvd_complex: complex > complex > $o ).

thf(tp_dvd_dvd_int,type,
    dvd_dvd_int: int > int > $o ).

thf(tp_dvd_dvd_nat,type,
    dvd_dvd_nat: nat > nat > $o ).

thf(tp_dvd_dvd_rat,type,
    dvd_dvd_rat: rat > rat > $o ).

thf(tp_dvd_dvd_real,type,
    dvd_dvd_real: real > real > $o ).

thf(tp_eucl_rel_int,type,
    eucl_rel_int: int > int > product_prod_int_int > $o ).

thf(tp_eventu1038000079068216329at_nat,type,
    eventu1038000079068216329at_nat: ( product_prod_nat_nat > $o ) > filter1242075044329608583at_nat > $o ).

thf(tp_eventu3244425730907250241l_real,type,
    eventu3244425730907250241l_real: ( produc2422161461964618553l_real > $o ) > filter2146258269922977983l_real > $o ).

thf(tp_eventu5826381225784669381omplex,type,
    eventu5826381225784669381omplex: ( produc4411394909380815293omplex > $o ) > filter6041513312241820739omplex > $o ).

thf(tp_eventually_nat,type,
    eventually_nat: ( nat > $o ) > filter_nat > $o ).

thf(tp_eventually_real,type,
    eventually_real: ( real > $o ) > filter_real > $o ).

thf(tp_exp_complex,type,
    exp_complex: complex > complex ).

thf(tp_exp_real,type,
    exp_real: real > real ).

thf(tp_fChoice_real,type,
    fChoice_real: ( real > $o ) > real ).

thf(tp_filterlim_nat_nat,type,
    filterlim_nat_nat: ( nat > nat ) > filter_nat > filter_nat > $o ).

thf(tp_filterlim_nat_real,type,
    filterlim_nat_real: ( nat > real ) > filter_real > filter_nat > $o ).

thf(tp_filterlim_real_real,type,
    filterlim_real_real: ( real > real ) > filter_real > filter_real > $o ).

thf(tp_filtermap_real_real,type,
    filtermap_real_real: ( real > real ) > filter_real > filter_real ).

thf(tp_finite1152437895449049373et_nat,type,
    finite1152437895449049373et_nat: set_set_nat > $o ).

thf(tp_finite2998713641127702882nt_int,type,
    finite2998713641127702882nt_int: set_Pr958786334691620121nt_int > $o ).

thf(tp_finite3004134309566078307T_VEBT,type,
    finite3004134309566078307T_VEBT: set_list_VEBT_VEBT > $o ).

thf(tp_finite3207457112153483333omplex,type,
    finite3207457112153483333omplex: set_complex > $o ).

thf(tp_finite3922522038869484883st_int,type,
    finite3922522038869484883st_int: set_list_int > $o ).

thf(tp_finite410649719033368117t_unit,type,
    finite410649719033368117t_unit: set_Product_unit > nat ).

thf(tp_finite5795047828879050333T_VEBT,type,
    finite5795047828879050333T_VEBT: set_VEBT_VEBT > $o ).

thf(tp_finite6197958912794628473et_int,type,
    finite6197958912794628473et_int: set_set_int > $o ).

thf(tp_finite6551019134538273531omplex,type,
    finite6551019134538273531omplex: set_set_complex > $o ).

thf(tp_finite8100373058378681591st_nat,type,
    finite8100373058378681591st_nat: set_list_nat > $o ).

thf(tp_finite8712137658972009173omplex,type,
    finite8712137658972009173omplex: set_list_complex > $o ).

thf(tp_finite_card_char,type,
    finite_card_char: set_char > nat ).

thf(tp_finite_card_complex,type,
    finite_card_complex: set_complex > nat ).

thf(tp_finite_card_int,type,
    finite_card_int: set_int > nat ).

thf(tp_finite_card_nat,type,
    finite_card_nat: set_nat > nat ).

thf(tp_finite_card_o,type,
    finite_card_o: set_o > nat ).

thf(tp_finite_card_set_nat,type,
    finite_card_set_nat: set_set_nat > nat ).

thf(tp_finite_finite_int,type,
    finite_finite_int: set_int > $o ).

thf(tp_finite_finite_list_o,type,
    finite_finite_list_o: set_list_o > $o ).

thf(tp_finite_finite_nat,type,
    finite_finite_nat: set_nat > $o ).

thf(tp_finite_finite_num,type,
    finite_finite_num: set_num > $o ).

thf(tp_finite_finite_o,type,
    finite_finite_o: set_o > $o ).

thf(tp_finite_finite_rat,type,
    finite_finite_rat: set_rat > $o ).

thf(tp_finite_finite_real,type,
    finite_finite_real: set_real > $o ).

thf(tp_frct,type,
    frct: product_prod_int_int > rat ).

thf(tp_gcd_Gcd_int,type,
    gcd_Gcd_int: set_int > int ).

thf(tp_gcd_Gcd_nat,type,
    gcd_Gcd_nat: set_nat > nat ).

thf(tp_gcd_gcd_int,type,
    gcd_gcd_int: int > int > int ).

thf(tp_gcd_gcd_nat,type,
    gcd_gcd_nat: nat > nat > nat ).

thf(tp_gcd_nat_rel,type,
    gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(tp_groups1072433553688619179nt_rat,type,
    groups1072433553688619179nt_rat: ( int > rat ) > set_int > rat ).

thf(tp_groups129246275422532515t_real,type,
    groups129246275422532515t_real: ( nat > real ) > set_nat > real ).

thf(tp_groups1300246762558778688al_rat,type,
    groups1300246762558778688al_rat: ( real > rat ) > set_real > rat ).

thf(tp_groups1681761925125756287l_real,type,
    groups1681761925125756287l_real: ( real > real ) > set_real > real ).

thf(tp_groups1705073143266064639nt_int,type,
    groups1705073143266064639nt_int: ( int > int ) > set_int > int ).

thf(tp_groups1707563613775114915nt_nat,type,
    groups1707563613775114915nt_nat: ( int > nat ) > set_int > nat ).

thf(tp_groups1932886352136224148al_int,type,
    groups1932886352136224148al_int: ( real > int ) > set_real > int ).

thf(tp_groups1935376822645274424al_nat,type,
    groups1935376822645274424al_nat: ( real > nat ) > set_real > nat ).

thf(tp_groups2073611262835488442omplex,type,
    groups2073611262835488442omplex: ( nat > complex ) > set_nat > complex ).

thf(tp_groups225925009352817453ex_rat,type,
    groups225925009352817453ex_rat: ( complex > rat ) > set_complex > rat ).

thf(tp_groups2316167850115554303t_real,type,
    groups2316167850115554303t_real: ( int > real ) > set_int > real ).

thf(tp_groups2906978787729119204at_rat,type,
    groups2906978787729119204at_rat: ( nat > rat ) > set_nat > rat ).

thf(tp_groups3049146728041665814omplex,type,
    groups3049146728041665814omplex: ( int > complex ) > set_int > complex ).

thf(tp_groups3455450783089532116nteger,type,
    groups3455450783089532116nteger: ( nat > code_integer ) > set_nat > code_integer ).

thf(tp_groups3539618377306564664at_int,type,
    groups3539618377306564664at_int: ( nat > int ) > set_nat > int ).

thf(tp_groups3542108847815614940at_nat,type,
    groups3542108847815614940at_nat: ( nat > nat ) > set_nat > nat ).

thf(tp_groups3708469109370488835omplex,type,
    groups3708469109370488835omplex: ( complex > complex ) > set_complex > complex ).

thf(tp_groups3827104343326376752nteger,type,
    groups3827104343326376752nteger: ( int > code_integer ) > set_int > code_integer ).

thf(tp_groups3906332499630173760nt_rat,type,
    groups3906332499630173760nt_rat: ( int > rat ) > set_int > rat ).

thf(tp_groups4061424788464935467al_rat,type,
    groups4061424788464935467al_rat: ( real > rat ) > set_real > rat ).

thf(tp_groups4246057289670975065at_int,type,
    groups4246057289670975065at_int: ( set_nat > int ) > set_set_nat > int ).

thf(tp_groups4538972089207619220nt_int,type,
    groups4538972089207619220nt_int: ( int > int ) > set_int > int ).

thf(tp_groups4541462559716669496nt_nat,type,
    groups4541462559716669496nt_nat: ( int > nat ) > set_int > nat ).

thf(tp_groups4694064378042380927al_int,type,
    groups4694064378042380927al_int: ( real > int ) > set_real > int ).

thf(tp_groups4696554848551431203al_nat,type,
    groups4696554848551431203al_nat: ( real > nat ) > set_real > nat ).

thf(tp_groups5058264527183730370ex_rat,type,
    groups5058264527183730370ex_rat: ( complex > rat ) > set_complex > rat ).

thf(tp_groups5107569545109728110t_real,type,
    groups5107569545109728110t_real: ( set_nat > real ) > set_set_nat > real ).

thf(tp_groups5690904116761175830ex_int,type,
    groups5690904116761175830ex_int: ( complex > int ) > set_complex > int ).

thf(tp_groups5693394587270226106ex_nat,type,
    groups5693394587270226106ex_nat: ( complex > nat ) > set_complex > nat ).

thf(tp_groups5754745047067104278omplex,type,
    groups5754745047067104278omplex: ( real > complex ) > set_real > complex ).

thf(tp_groups5808333547571424918x_real,type,
    groups5808333547571424918x_real: ( complex > real ) > set_complex > real ).

thf(tp_groups6225526099057966256nteger,type,
    groups6225526099057966256nteger: ( real > code_integer ) > set_real > code_integer ).

thf(tp_groups6464643781859351333omplex,type,
    groups6464643781859351333omplex: ( nat > complex ) > set_nat > complex ).

thf(tp_groups6591440286371151544t_real,type,
    groups6591440286371151544t_real: ( nat > real ) > set_nat > real ).

thf(tp_groups6621422865394947399nteger,type,
    groups6621422865394947399nteger: ( complex > code_integer ) > set_complex > code_integer ).

thf(tp_groups705719431365010083at_int,type,
    groups705719431365010083at_int: ( nat > int ) > set_nat > int ).

thf(tp_groups708209901874060359at_nat,type,
    groups708209901874060359at_nat: ( nat > nat ) > set_nat > nat ).

thf(tp_groups713298508707869441omplex,type,
    groups713298508707869441omplex: ( real > complex ) > set_real > complex ).

thf(tp_groups73079841787564623at_rat,type,
    groups73079841787564623at_rat: ( nat > rat ) > set_nat > rat ).

thf(tp_groups7440179247065528705omplex,type,
    groups7440179247065528705omplex: ( int > complex ) > set_int > complex ).

thf(tp_groups7501900531339628137nteger,type,
    groups7501900531339628137nteger: ( nat > code_integer ) > set_nat > code_integer ).

thf(tp_groups766887009212190081x_real,type,
    groups766887009212190081x_real: ( complex > real ) > set_complex > real ).

thf(tp_groups7713935264441627589nteger,type,
    groups7713935264441627589nteger: ( real > code_integer ) > set_real > code_integer ).

thf(tp_groups7754918857620584856omplex,type,
    groups7754918857620584856omplex: ( complex > complex ) > set_complex > complex ).

thf(tp_groups7873554091576472773nteger,type,
    groups7873554091576472773nteger: ( int > code_integer ) > set_int > code_integer ).

thf(tp_groups8097168146408367636l_real,type,
    groups8097168146408367636l_real: ( real > real ) > set_real > real ).

thf(tp_groups8255218700646806128omplex,type,
    groups8255218700646806128omplex: ( set_nat > complex ) > set_set_nat > complex ).

thf(tp_groups8294997508430121362at_nat,type,
    groups8294997508430121362at_nat: ( set_nat > nat ) > set_set_nat > nat ).

thf(tp_groups858564598930262913ex_int,type,
    groups858564598930262913ex_int: ( complex > int ) > set_complex > int ).

thf(tp_groups861055069439313189ex_nat,type,
    groups861055069439313189ex_nat: ( complex > nat ) > set_complex > nat ).

thf(tp_groups8682486955453173170nteger,type,
    groups8682486955453173170nteger: ( complex > code_integer ) > set_complex > code_integer ).

thf(tp_groups8778361861064173332t_real,type,
    groups8778361861064173332t_real: ( int > real ) > set_int > real ).

thf(tp_groups9116527308978886569_o_int,type,
    groups9116527308978886569_o_int: ( $o > int ) > int > list_o > int ).

thf(tp_has_de1759254742604945161l_real,type,
    has_de1759254742604945161l_real: ( real > real ) > ( real > real ) > filter_real > $o ).

thf(tp_has_fi5821293074295781190e_real,type,
    has_fi5821293074295781190e_real: ( real > real ) > real > filter_real > $o ).

thf(tp_if_Code_integer,type,
    if_Code_integer: $o > code_integer > code_integer > code_integer ).

thf(tp_if_Pro3027730157355071871nt_int,type,
    if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int ).

thf(tp_if_Pro5737122678794959658eger_o,type,
    if_Pro5737122678794959658eger_o: $o > produc6271795597528267376eger_o > produc6271795597528267376eger_o > produc6271795597528267376eger_o ).

thf(tp_if_Pro6119634080678213985nteger,type,
    if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(tp_if_Pro6206227464963214023at_nat,type,
    if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).

thf(tp_if_VEBT_VEBT,type,
    if_VEBT_VEBT: $o > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).

thf(tp_if_complex,type,
    if_complex: $o > complex > complex > complex ).

thf(tp_if_int,type,
    if_int: $o > int > int > int ).

thf(tp_if_list_int,type,
    if_list_int: $o > list_int > list_int > list_int ).

thf(tp_if_nat,type,
    if_nat: $o > nat > nat > nat ).

thf(tp_if_num,type,
    if_num: $o > num > num > num ).

thf(tp_if_option_nat,type,
    if_option_nat: $o > option_nat > option_nat > option_nat ).

thf(tp_if_option_num,type,
    if_option_num: $o > option_num > option_num > option_num ).

thf(tp_if_rat,type,
    if_rat: $o > rat > rat > rat ).

thf(tp_if_real,type,
    if_real: $o > real > real > real ).

thf(tp_if_set_int,type,
    if_set_int: $o > set_int > set_int > set_int ).

thf(tp_if_set_nat,type,
    if_set_nat: $o > set_nat > set_nat > set_nat ).

thf(tp_im,type,
    im: complex > real ).

thf(tp_image_2178119161166701260l_real,type,
    image_2178119161166701260l_real: ( real > filter2146258269922977983l_real ) > set_real > set_fi7789364187291644575l_real ).

thf(tp_image_5971271580939081552omplex,type,
    image_5971271580939081552omplex: ( real > filter6041513312241820739omplex ) > set_real > set_fi4554929511873752355omplex ).

thf(tp_image_char_nat,type,
    image_char_nat: ( char > nat ) > set_char > set_nat ).

thf(tp_image_int_int,type,
    image_int_int: ( int > int ) > set_int > set_int ).

thf(tp_image_int_nat,type,
    image_int_nat: ( int > nat ) > set_int > set_nat ).

thf(tp_image_nat_char,type,
    image_nat_char: ( nat > char ) > set_nat > set_char ).

thf(tp_image_nat_int,type,
    image_nat_int: ( nat > int ) > set_nat > set_int ).

thf(tp_image_nat_nat,type,
    image_nat_nat: ( nat > nat ) > set_nat > set_nat ).

thf(tp_image_nat_real,type,
    image_nat_real: ( nat > real ) > set_nat > set_real ).

thf(tp_image_nat_set_nat,type,
    image_nat_set_nat: ( nat > set_nat ) > set_nat > set_set_nat ).

thf(tp_image_real_real,type,
    image_real_real: ( real > real ) > set_real > set_real ).

thf(tp_imaginary_unit,type,
    imaginary_unit: complex ).

thf(tp_inc,type,
    inc: num > num ).

thf(tp_inj_on_nat_char,type,
    inj_on_nat_char: ( nat > char ) > set_nat > $o ).

thf(tp_inj_on_nat_nat,type,
    inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).

thf(tp_inj_on_real_real,type,
    inj_on_real_real: ( real > real ) > set_real > $o ).

thf(tp_insert_int,type,
    insert_int: int > set_int > set_int ).

thf(tp_insert_nat,type,
    insert_nat: nat > set_nat > set_nat ).

thf(tp_insert_real,type,
    insert_real: real > set_real > set_real ).

thf(tp_int_ge_less_than,type,
    int_ge_less_than: int > set_Pr958786334691620121nt_int ).

thf(tp_int_ge_less_than2,type,
    int_ge_less_than2: int > set_Pr958786334691620121nt_int ).

thf(tp_integer_of_char,type,
    integer_of_char: char > code_integer ).

thf(tp_invers8013647133539491842omplex,type,
    invers8013647133539491842omplex: complex > complex ).

thf(tp_inverse_inverse_rat,type,
    inverse_inverse_rat: rat > rat ).

thf(tp_inverse_inverse_real,type,
    inverse_inverse_real: real > real ).

thf(tp_lattic8263393255366662781ax_int,type,
    lattic8263393255366662781ax_int: set_int > int ).

thf(tp_lattic8265883725875713057ax_nat,type,
    lattic8265883725875713057ax_nat: set_nat > nat ).

thf(tp_list_u1324408373059187874T_VEBT,type,
    list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(tp_list_update_complex,type,
    list_update_complex: list_complex > nat > complex > list_complex ).

thf(tp_list_update_int,type,
    list_update_int: list_int > nat > int > list_int ).

thf(tp_list_update_nat,type,
    list_update_nat: list_nat > nat > nat > list_nat ).

thf(tp_list_update_o,type,
    list_update_o: list_o > nat > $o > list_o ).

thf(tp_list_update_real,type,
    list_update_real: list_real > nat > real > list_real ).

thf(tp_list_update_set_nat,type,
    list_update_set_nat: list_set_nat > nat > set_nat > list_set_nat ).

thf(tp_ln_ln_real,type,
    ln_ln_real: real > real ).

thf(tp_log,type,
    log: real > real > real ).

thf(tp_lx,type,
    lx: nat ).

thf(tp_m,type,
    m: nat ).

thf(tp_ma,type,
    ma: nat ).

thf(tp_map_option_num_num,type,
    map_option_num_num: ( num > num ) > option_num > option_num ).

thf(tp_maxi,type,
    maxi: nat ).

thf(tp_maxs,type,
    maxs: nat ).

thf(tp_member2936631157270082147T_VEBT,type,
    member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).

thf(tp_member5262025264175285858nt_int,type,
    member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o ).

thf(tp_member_VEBT_VEBT,type,
    member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).

thf(tp_member_complex,type,
    member_complex: complex > set_complex > $o ).

thf(tp_member_int,type,
    member_int: int > set_int > $o ).

thf(tp_member_list_int,type,
    member_list_int: list_int > set_list_int > $o ).

thf(tp_member_list_o,type,
    member_list_o: list_o > set_list_o > $o ).

thf(tp_member_nat,type,
    member_nat: nat > set_nat > $o ).

thf(tp_member_num,type,
    member_num: num > set_num > $o ).

thf(tp_member_o,type,
    member_o: $o > set_o > $o ).

thf(tp_member_rat,type,
    member_rat: rat > set_rat > $o ).

thf(tp_member_real,type,
    member_real: real > set_real > $o ).

thf(tp_member_set_nat,type,
    member_set_nat: set_nat > set_set_nat > $o ).

thf(tp_mi,type,
    mi: nat ).

thf(tp_minus_1052850069191792384nt_int,type,
    minus_1052850069191792384nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).

thf(tp_minus_2163939370556025621et_nat,type,
    minus_2163939370556025621et_nat: set_set_nat > set_set_nat > set_set_nat ).

thf(tp_minus_3235023915231533773d_enat,type,
    minus_3235023915231533773d_enat: extended_enat > extended_enat > extended_enat ).

thf(tp_minus_6910147592129066416_nat_o,type,
    minus_6910147592129066416_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > set_nat > $o ).

thf(tp_minus_711738161318947805_int_o,type,
    minus_711738161318947805_int_o: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ).

thf(tp_minus_811609699411566653omplex,type,
    minus_811609699411566653omplex: set_complex > set_complex > set_complex ).

thf(tp_minus_8373710615458151222nteger,type,
    minus_8373710615458151222nteger: code_integer > code_integer > code_integer ).

thf(tp_minus_8727706125548526216plex_o,type,
    minus_8727706125548526216plex_o: ( complex > $o ) > ( complex > $o ) > complex > $o ).

thf(tp_minus_minus_complex,type,
    minus_minus_complex: complex > complex > complex ).

thf(tp_minus_minus_int,type,
    minus_minus_int: int > int > int ).

thf(tp_minus_minus_int_o,type,
    minus_minus_int_o: ( int > $o ) > ( int > $o ) > int > $o ).

thf(tp_minus_minus_nat,type,
    minus_minus_nat: nat > nat > nat ).

thf(tp_minus_minus_nat_o,type,
    minus_minus_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).

thf(tp_minus_minus_rat,type,
    minus_minus_rat: rat > rat > rat ).

thf(tp_minus_minus_real,type,
    minus_minus_real: real > real > real ).

thf(tp_minus_minus_real_o,type,
    minus_minus_real_o: ( real > $o ) > ( real > $o ) > real > $o ).

thf(tp_minus_minus_set_int,type,
    minus_minus_set_int: set_int > set_int > set_int ).

thf(tp_minus_minus_set_nat,type,
    minus_minus_set_nat: set_nat > set_nat > set_nat ).

thf(tp_minus_minus_set_real,type,
    minus_minus_set_real: set_real > set_real > set_real ).

thf(tp_modulo364778990260209775nteger,type,
    modulo364778990260209775nteger: code_integer > code_integer > code_integer ).

thf(tp_modulo_modulo_int,type,
    modulo_modulo_int: int > int > int ).

thf(tp_modulo_modulo_nat,type,
    modulo_modulo_nat: nat > nat > nat ).

thf(tp_na,type,
    na: nat ).

thf(tp_nat2,type,
    nat2: int > nat ).

thf(tp_nat_pr5047031295181774490ux_rel,type,
    nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(tp_nat_prod_decode_aux,type,
    nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).

thf(tp_nat_prod_encode,type,
    nat_prod_encode: product_prod_nat_nat > nat ).

thf(tp_nat_set_decode,type,
    nat_set_decode: nat > set_nat ).

thf(tp_nat_set_encode,type,
    nat_set_encode: set_nat > nat ).

thf(tp_nat_triangle,type,
    nat_triangle: nat > nat ).

thf(tp_neg_nu3179335615603231917ec_rat,type,
    neg_nu3179335615603231917ec_rat: rat > rat ).

thf(tp_neg_nu3811975205180677377ec_int,type,
    neg_nu3811975205180677377ec_int: int > int ).

thf(tp_neg_nu5219082963157363817nc_rat,type,
    neg_nu5219082963157363817nc_rat: rat > rat ).

thf(tp_neg_nu5831290666863070958nteger,type,
    neg_nu5831290666863070958nteger: code_integer > code_integer ).

thf(tp_neg_nu5851722552734809277nc_int,type,
    neg_nu5851722552734809277nc_int: int > int ).

thf(tp_neg_nu6075765906172075777c_real,type,
    neg_nu6075765906172075777c_real: real > real ).

thf(tp_neg_nu6511756317524482435omplex,type,
    neg_nu6511756317524482435omplex: complex > complex ).

thf(tp_neg_nu7009210354673126013omplex,type,
    neg_nu7009210354673126013omplex: complex > complex ).

thf(tp_neg_nu7757733837767384882nteger,type,
    neg_nu7757733837767384882nteger: code_integer > code_integer ).

thf(tp_neg_nu8295874005876285629c_real,type,
    neg_nu8295874005876285629c_real: real > real ).

thf(tp_neg_nu8557863876264182079omplex,type,
    neg_nu8557863876264182079omplex: complex > complex ).

thf(tp_neg_nu8804712462038260780nteger,type,
    neg_nu8804712462038260780nteger: code_integer > code_integer ).

thf(tp_neg_numeral_dbl_int,type,
    neg_numeral_dbl_int: int > int ).

thf(tp_neg_numeral_dbl_rat,type,
    neg_numeral_dbl_rat: rat > rat ).

thf(tp_neg_numeral_dbl_real,type,
    neg_numeral_dbl_real: real > real ).

thf(tp_neg_numeral_sub_int,type,
    neg_numeral_sub_int: num > num > int ).

thf(tp_nil_VEBT_VEBT,type,
    nil_VEBT_VEBT: list_VEBT_VEBT ).

thf(tp_nil_int,type,
    nil_int: list_int ).

thf(tp_none_P5556105721700978146at_nat,type,
    none_P5556105721700978146at_nat: option4927543243414619207at_nat ).

thf(tp_none_nat,type,
    none_nat: option_nat ).

thf(tp_none_num,type,
    none_num: option_num ).

thf(tp_normalize,type,
    normalize: product_prod_int_int > product_prod_int_int ).

thf(tp_nth_Code_integer,type,
    nth_Code_integer: list_Code_integer > nat > code_integer ).

thf(tp_nth_Pr1649062631805364268_o_int,type,
    nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int ).

thf(tp_nth_Pr4606735188037164562VEBT_o,type,
    nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).

thf(tp_nth_Pr4953567300277697838T_VEBT,type,
    nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).

thf(tp_nth_Pr6456567536196504476um_num,type,
    nth_Pr6456567536196504476um_num: list_P3744719386663036955um_num > nat > product_prod_num_num ).

thf(tp_nth_Pr6777367263587873994T_VEBT,type,
    nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT ).

thf(tp_nth_Pr6837108013167703752BT_int,type,
    nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int ).

thf(tp_nth_Pr7617993195940197384at_nat,type,
    nth_Pr7617993195940197384at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat ).

thf(tp_nth_Pr8326237132889035090at_num,type,
    nth_Pr8326237132889035090at_num: list_P1726324292696863441at_num > nat > product_prod_nat_num ).

thf(tp_nth_Pr8522763379788166057eger_o,type,
    nth_Pr8522763379788166057eger_o: list_P8526636022914148096eger_o > nat > produc6271795597528267376eger_o ).

thf(tp_nth_Product_prod_o_o,type,
    nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o ).

thf(tp_nth_VEBT_VEBT,type,
    nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).

thf(tp_nth_complex,type,
    nth_complex: list_complex > nat > complex ).

thf(tp_nth_int,type,
    nth_int: list_int > nat > int ).

thf(tp_nth_nat,type,
    nth_nat: list_nat > nat > nat ).

thf(tp_nth_num,type,
    nth_num: list_num > nat > num ).

thf(tp_nth_o,type,
    nth_o: list_o > nat > $o ).

thf(tp_nth_real,type,
    nth_real: list_real > nat > real ).

thf(tp_nth_set_nat,type,
    nth_set_nat: list_set_nat > nat > set_nat ).

thf(tp_num_of_nat,type,
    num_of_nat: nat > num ).

thf(tp_numera1916890842035813515d_enat,type,
    numera1916890842035813515d_enat: num > extended_enat ).

thf(tp_numera6620942414471956472nteger,type,
    numera6620942414471956472nteger: num > code_integer ).

thf(tp_numera6690914467698888265omplex,type,
    numera6690914467698888265omplex: num > complex ).

thf(tp_numeral_numeral_int,type,
    numeral_numeral_int: num > int ).

thf(tp_numeral_numeral_nat,type,
    numeral_numeral_nat: num > nat ).

thf(tp_numeral_numeral_rat,type,
    numeral_numeral_rat: num > rat ).

thf(tp_numeral_numeral_real,type,
    numeral_numeral_real: num > real ).

thf(tp_of_int,type,
    of_int: int > rat ).

thf(tp_one,type,
    one: num ).

thf(tp_one_on7984719198319812577d_enat,type,
    one_on7984719198319812577d_enat: extended_enat ).

thf(tp_one_one_Code_integer,type,
    one_one_Code_integer: code_integer ).

thf(tp_one_one_complex,type,
    one_one_complex: complex ).

thf(tp_one_one_int,type,
    one_one_int: int ).

thf(tp_one_one_nat,type,
    one_one_nat: nat ).

thf(tp_one_one_rat,type,
    one_one_rat: rat ).

thf(tp_one_one_real,type,
    one_one_real: real ).

thf(tp_ord_le1307284697595431911nteger,type,
    ord_le1307284697595431911nteger: set_Code_integer > set_Code_integer > $o ).

thf(tp_ord_le211207098394363844omplex,type,
    ord_le211207098394363844omplex: set_complex > set_complex > $o ).

thf(tp_ord_le2510731241096832064er_nat,type,
    ord_le2510731241096832064er_nat: filter_nat > filter_nat > $o ).

thf(tp_ord_le2843351958646193337nt_int,type,
    ord_le2843351958646193337nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > $o ).

thf(tp_ord_le2932123472753598470d_enat,type,
    ord_le2932123472753598470d_enat: extended_enat > extended_enat > $o ).

thf(tp_ord_le3102999989581377725nteger,type,
    ord_le3102999989581377725nteger: code_integer > code_integer > $o ).

thf(tp_ord_le3964352015994296041_nat_o,type,
    ord_le3964352015994296041_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > $o ).

thf(tp_ord_le4337996190870823476T_VEBT,type,
    ord_le4337996190870823476T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o ).

thf(tp_ord_le4573692005234683329plex_o,type,
    ord_le4573692005234683329plex_o: ( complex > $o ) > ( complex > $o ) > $o ).

thf(tp_ord_le6747313008572928689nteger,type,
    ord_le6747313008572928689nteger: code_integer > code_integer > $o ).

thf(tp_ord_le6893508408891458716et_nat,type,
    ord_le6893508408891458716et_nat: set_set_nat > set_set_nat > $o ).

thf(tp_ord_le7084787975880047091nteger,type,
    ord_le7084787975880047091nteger: set_Code_integer > set_Code_integer > $o ).

thf(tp_ord_le72135733267957522d_enat,type,
    ord_le72135733267957522d_enat: extended_enat > extended_enat > $o ).

thf(tp_ord_less_complex_o,type,
    ord_less_complex_o: ( complex > $o ) > ( complex > $o ) > $o ).

thf(tp_ord_less_eq_int,type,
    ord_less_eq_int: int > int > $o ).

thf(tp_ord_less_eq_int_o,type,
    ord_less_eq_int_o: ( int > $o ) > ( int > $o ) > $o ).

thf(tp_ord_less_eq_nat,type,
    ord_less_eq_nat: nat > nat > $o ).

thf(tp_ord_less_eq_nat_o,type,
    ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).

thf(tp_ord_less_eq_num,type,
    ord_less_eq_num: num > num > $o ).

thf(tp_ord_less_eq_rat,type,
    ord_less_eq_rat: rat > rat > $o ).

thf(tp_ord_less_eq_real,type,
    ord_less_eq_real: real > real > $o ).

thf(tp_ord_less_eq_real_o,type,
    ord_less_eq_real_o: ( real > $o ) > ( real > $o ) > $o ).

thf(tp_ord_less_eq_set_int,type,
    ord_less_eq_set_int: set_int > set_int > $o ).

thf(tp_ord_less_eq_set_nat,type,
    ord_less_eq_set_nat: set_nat > set_nat > $o ).

thf(tp_ord_less_eq_set_num,type,
    ord_less_eq_set_num: set_num > set_num > $o ).

thf(tp_ord_less_eq_set_o,type,
    ord_less_eq_set_o: set_o > set_o > $o ).

thf(tp_ord_less_eq_set_rat,type,
    ord_less_eq_set_rat: set_rat > set_rat > $o ).

thf(tp_ord_less_eq_set_real,type,
    ord_less_eq_set_real: set_real > set_real > $o ).

thf(tp_ord_less_int,type,
    ord_less_int: int > int > $o ).

thf(tp_ord_less_int_o,type,
    ord_less_int_o: ( int > $o ) > ( int > $o ) > $o ).

thf(tp_ord_less_nat,type,
    ord_less_nat: nat > nat > $o ).

thf(tp_ord_less_nat_o,type,
    ord_less_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).

thf(tp_ord_less_num,type,
    ord_less_num: num > num > $o ).

thf(tp_ord_less_rat,type,
    ord_less_rat: rat > rat > $o ).

thf(tp_ord_less_real,type,
    ord_less_real: real > real > $o ).

thf(tp_ord_less_real_o,type,
    ord_less_real_o: ( real > $o ) > ( real > $o ) > $o ).

thf(tp_ord_less_set_complex,type,
    ord_less_set_complex: set_complex > set_complex > $o ).

thf(tp_ord_less_set_int,type,
    ord_less_set_int: set_int > set_int > $o ).

thf(tp_ord_less_set_nat,type,
    ord_less_set_nat: set_nat > set_nat > $o ).

thf(tp_ord_less_set_nat_o,type,
    ord_less_set_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > $o ).

thf(tp_ord_less_set_num,type,
    ord_less_set_num: set_num > set_num > $o ).

thf(tp_ord_less_set_rat,type,
    ord_less_set_rat: set_rat > set_rat > $o ).

thf(tp_ord_less_set_real,type,
    ord_less_set_real: set_real > set_real > $o ).

thf(tp_ord_less_set_set_nat,type,
    ord_less_set_set_nat: set_set_nat > set_set_nat > $o ).

thf(tp_ord_max_Code_integer,type,
    ord_max_Code_integer: code_integer > code_integer > code_integer ).

thf(tp_ord_max_int,type,
    ord_max_int: int > int > int ).

thf(tp_ord_max_nat,type,
    ord_max_nat: nat > nat > nat ).

thf(tp_ord_max_num,type,
    ord_max_num: num > num > num ).

thf(tp_ord_max_rat,type,
    ord_max_rat: rat > rat > rat ).

thf(tp_ord_max_real,type,
    ord_max_real: real > real > real ).

thf(tp_ord_max_set_nat,type,
    ord_max_set_nat: set_nat > set_nat > set_nat ).

thf(tp_order_5726023648592871131at_nat,type,
    order_5726023648592871131at_nat: ( nat > nat ) > $o ).

thf(tp_order_7092887310737990675l_real,type,
    order_7092887310737990675l_real: ( real > real ) > $o ).

thf(tp_order_9091379641038594480t_real,type,
    order_9091379641038594480t_real: ( nat > real ) > $o ).

thf(tp_order_Greatest_nat,type,
    order_Greatest_nat: ( nat > $o ) > nat ).

thf(tp_order_mono_nat_nat,type,
    order_mono_nat_nat: ( nat > nat ) > $o ).

thf(tp_order_mono_nat_real,type,
    order_mono_nat_real: ( nat > real ) > $o ).

thf(tp_order_mono_real_real,type,
    order_mono_real_real: ( real > real ) > $o ).

thf(tp_pi,type,
    pi: real ).

thf(tp_plus_p3455044024723400733d_enat,type,
    plus_p3455044024723400733d_enat: extended_enat > extended_enat > extended_enat ).

thf(tp_plus_p5714425477246183910nteger,type,
    plus_p5714425477246183910nteger: code_integer > code_integer > code_integer ).

thf(tp_plus_plus_complex,type,
    plus_plus_complex: complex > complex > complex ).

thf(tp_plus_plus_int,type,
    plus_plus_int: int > int > int ).

thf(tp_plus_plus_nat,type,
    plus_plus_nat: nat > nat > nat ).

thf(tp_plus_plus_num,type,
    plus_plus_num: num > num > num ).

thf(tp_plus_plus_rat,type,
    plus_plus_rat: rat > rat > rat ).

thf(tp_plus_plus_real,type,
    plus_plus_real: real > real > real ).

thf(tp_pow,type,
    pow: num > num > num ).

thf(tp_pow_nat,type,
    pow_nat: set_nat > set_set_nat ).

thf(tp_power_8256067586552552935nteger,type,
    power_8256067586552552935nteger: code_integer > nat > code_integer ).

thf(tp_power_power_complex,type,
    power_power_complex: complex > nat > complex ).

thf(tp_power_power_int,type,
    power_power_int: int > nat > int ).

thf(tp_power_power_nat,type,
    power_power_nat: nat > nat > nat ).

thf(tp_power_power_rat,type,
    power_power_rat: rat > nat > rat ).

thf(tp_power_power_real,type,
    power_power_real: real > nat > real ).

thf(tp_powr_real,type,
    powr_real: real > real > real ).

thf(tp_pred,type,
    pred: nat > nat ).

thf(tp_pred_numeral,type,
    pred_numeral: num > nat ).

thf(tp_princi3496590319149328850omplex,type,
    princi3496590319149328850omplex: set_Pr5085853215250843933omplex > filter6041513312241820739omplex ).

thf(tp_princi6114159922880469582l_real,type,
    princi6114159922880469582l_real: set_Pr6218003697084177305l_real > filter2146258269922977983l_real ).

thf(tp_prod_filter_nat_nat,type,
    prod_filter_nat_nat: filter_nat > filter_nat > filter1242075044329608583at_nat ).

thf(tp_produc1043322548047392435omplex,type,
    produc1043322548047392435omplex: ( code_integer > $o > set_complex ) > produc6271795597528267376eger_o > set_complex ).

thf(tp_produc1086072967326762835nteger,type,
    produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger ).

thf(tp_produc1195630363706982562at_num,type,
    produc1195630363706982562at_num: nat > product_prod_nat_num > produc2963631642982155120at_num ).

thf(tp_produc1253318751659547953et_int,type,
    produc1253318751659547953et_int: ( code_integer > $o > set_int ) > produc6271795597528267376eger_o > set_int ).

thf(tp_produc1361121860356118632et_nat,type,
    produc1361121860356118632et_nat: ( num > num > set_nat ) > product_prod_num_num > set_nat ).

thf(tp_produc1435849484188172666t_real,type,
    produc1435849484188172666t_real: ( nat > num > set_real ) > product_prod_nat_num > set_real ).

thf(tp_produc1553301316500091796er_int,type,
    produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).

thf(tp_produc1555791787009142072er_nat,type,
    produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).

thf(tp_produc1703576794950452218t_real,type,
    produc1703576794950452218t_real: ( nat > nat > real ) > product_prod_nat_nat > real ).

thf(tp_produc1917071388513777916omplex,type,
    produc1917071388513777916omplex: ( nat > nat > complex ) > product_prod_nat_nat > complex ).

thf(tp_produc242741666403216561t_real,type,
    produc242741666403216561t_real: ( code_integer > $o > set_real ) > produc6271795597528267376eger_o > set_real ).

thf(tp_produc2626176000494625587at_nat,type,
    produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).

thf(tp_produc27273713700761075at_nat,type,
    produc27273713700761075at_nat: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).

thf(tp_produc2866383454006189126omplex,type,
    produc2866383454006189126omplex: ( num > num > set_complex ) > product_prod_num_num > set_complex ).

thf(tp_produc2899441246263362727at_nat,type,
    produc2899441246263362727at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > produc6121120109295599847at_nat > produc5542196010084753463at_nat ).

thf(tp_produc2982872950893828659T_VEBT,type,
    produc2982872950893828659T_VEBT: $o > vEBT_VEBT > produc2504756804600209347T_VEBT ).

thf(tp_produc3209952032786966637at_nat,type,
    produc3209952032786966637at_nat: ( nat > nat > nat ) > produc7248412053542808358at_nat > produc4471711990508489141at_nat ).

thf(tp_produc3576312749637752826on_num,type,
    produc3576312749637752826on_num: ( num > num > $o ) > produc3447558737645232053on_num > produc7036089656553540234on_num ).

thf(tp_produc3607205314601156340eger_o,type,
    produc3607205314601156340eger_o: list_Code_integer > list_o > list_P8526636022914148096eger_o ).

thf(tp_produc3994169339658061776at_nat,type,
    produc3994169339658061776at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > produc6121120109295599847at_nat > produc5491161045314408544at_nat ).

thf(tp_produc4035269172776083154on_nat,type,
    produc4035269172776083154on_nat: ( nat > nat > $o ) > produc4953844613479565601on_nat > produc2233624965454879586on_nat ).

thf(tp_produc4130284055270567454et_nat,type,
    produc4130284055270567454et_nat: ( nat > num > set_nat ) > product_prod_nat_num > set_nat ).

thf(tp_produc4188289175737317920o_char,type,
    produc4188289175737317920o_char: ( code_integer > $o > char ) > produc6271795597528267376eger_o > char ).

thf(tp_produc4245557441103728435nt_int,type,
    produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).

thf(tp_produc4743750530478302277T_VEBT,type,
    produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).

thf(tp_produc478579273971653890on_num,type,
    produc478579273971653890on_num: ( nat > num > option_num ) > product_prod_nat_num > option_num ).

thf(tp_produc487386426758144856at_nat,type,
    produc487386426758144856at_nat: nat > product_prod_nat_nat > produc7248412053542808358at_nat ).

thf(tp_produc488173922507101015at_nat,type,
    produc488173922507101015at_nat: option4927543243414619207at_nat > option4927543243414619207at_nat > produc6121120109295599847at_nat ).

thf(tp_produc4927758841916487424_num_o,type,
    produc4927758841916487424_num_o: ( nat > num > $o ) > product_prod_nat_num > $o ).

thf(tp_produc4947309494688390418_int_o,type,
    produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).

thf(tp_produc5098337634421038937on_nat,type,
    produc5098337634421038937on_nat: option_nat > option_nat > produc4953844613479565601on_nat ).

thf(tp_produc537772716801021591T_VEBT,type,
    produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT ).

thf(tp_produc5414030515140494994real_o,type,
    produc5414030515140494994real_o: ( real > real > $o ) > produc2422161461964618553l_real > $o ).

thf(tp_produc5431169771168744661et_nat,type,
    produc5431169771168744661et_nat: ( code_integer > $o > set_nat ) > produc6271795597528267376eger_o > set_nat ).

thf(tp_produc5703948589228662326_num_o,type,
    produc5703948589228662326_num_o: ( num > num > $o ) > product_prod_num_num > $o ).

thf(tp_produc5778274026573060048on_num,type,
    produc5778274026573060048on_num: ( num > num > num ) > produc3447558737645232053on_num > produc1193250871479095198on_num ).

thf(tp_produc6081775807080527818_nat_o,type,
    produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).

thf(tp_produc6207742614233964070at_rat,type,
    produc6207742614233964070at_rat: ( nat > nat > rat ) > product_prod_nat_nat > rat ).

thf(tp_produc6406642877701697732et_int,type,
    produc6406642877701697732et_int: ( num > num > set_int ) > product_prod_num_num > set_int ).

thf(tp_produc6499014454317279255nteger,type,
    produc6499014454317279255nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(tp_produc662631939642741121T_VEBT,type,
    produc662631939642741121T_VEBT: list_int > list_VEBT_VEBT > list_P7524865323317820941T_VEBT ).

thf(tp_produc6677183202524767010eger_o,type,
    produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o ).

thf(tp_produc6771430404735790350plex_o,type,
    produc6771430404735790350plex_o: ( complex > complex > $o ) > produc4411394909380815293omplex > $o ).

thf(tp_produc6840382203811409530at_int,type,
    produc6840382203811409530at_int: ( nat > nat > int ) > product_prod_nat_nat > int ).

thf(tp_produc6842872674320459806at_nat,type,
    produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).

thf(tp_produc6916734918728496179nteger,type,
    produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(tp_produc7292646706713671643BT_int,type,
    produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).

thf(tp_produc7336495610019696514er_num,type,
    produc7336495610019696514er_num: ( code_integer > code_integer > num ) > produc8923325533196201883nteger > num ).

thf(tp_produc736041933913180425BT_int,type,
    produc736041933913180425BT_int: vEBT_VEBT > int > produc4894624898956917775BT_int ).

thf(tp_produc738532404422230701BT_nat,type,
    produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat ).

thf(tp_produc7828578312038201481er_o_o,type,
    produc7828578312038201481er_o_o: ( code_integer > $o > $o ) > produc6271795597528267376eger_o > $o ).

thf(tp_produc8211389475949308722nt_int,type,
    produc8211389475949308722nt_int: ( int > int > int ) > product_prod_int_int > int ).

thf(tp_produc8296048397933160132t_real,type,
    produc8296048397933160132t_real: ( num > num > set_real ) > product_prod_num_num > set_real ).

thf(tp_produc8508995932063986495nteger,type,
    produc8508995932063986495nteger: produc8923325533196201883nteger > code_integer ).

thf(tp_produc851828971589881931at_num,type,
    produc851828971589881931at_num: ( nat > num > num ) > produc2963631642982155120at_num > produc3368934014287244435at_num ).

thf(tp_produc8585076106096196333on_num,type,
    produc8585076106096196333on_num: option_num > option_num > produc3447558737645232053on_num ).

thf(tp_produc8721562602347293563VEBT_o,type,
    produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o ).

thf(tp_produc8739625826339149834_nat_o,type,
    produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(tp_produc8929957630744042906on_nat,type,
    produc8929957630744042906on_nat: ( nat > nat > nat ) > produc4953844613479565601on_nat > produc8306885398267862888on_nat ).

thf(tp_produc9125791028180074456eger_o,type,
    produc9125791028180074456eger_o: ( code_integer > code_integer > produc6271795597528267376eger_o ) > produc8923325533196201883nteger > produc6271795597528267376eger_o ).

thf(tp_product_Pair_int_int,type,
    product_Pair_int_int: int > int > product_prod_int_int ).

thf(tp_product_Pair_nat_nat,type,
    product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).

thf(tp_product_Pair_nat_num,type,
    product_Pair_nat_num: nat > num > product_prod_nat_num ).

thf(tp_product_Pair_num_num,type,
    product_Pair_num_num: num > num > product_prod_num_num ).

thf(tp_product_Pair_o_int,type,
    product_Pair_o_int: $o > int > product_prod_o_int ).

thf(tp_product_Pair_o_o,type,
    product_Pair_o_o: $o > $o > product_prod_o_o ).

thf(tp_product_VEBT_VEBT_o,type,
    product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).

thf(tp_product_fst_int_int,type,
    product_fst_int_int: product_prod_int_int > int ).

thf(tp_product_fst_nat_nat,type,
    product_fst_nat_nat: product_prod_nat_nat > nat ).

thf(tp_product_int_int,type,
    product_int_int: list_int > list_int > list_P5707943133018811711nt_int ).

thf(tp_product_int_o,type,
    product_int_o: list_int > list_o > list_P5087981734274514673_int_o ).

thf(tp_product_nat_nat,type,
    product_nat_nat: list_nat > list_nat > list_P6011104703257516679at_nat ).

thf(tp_product_nat_num,type,
    product_nat_num: list_nat > list_num > list_P1726324292696863441at_num ).

thf(tp_product_num_num,type,
    product_num_num: list_num > list_num > list_P3744719386663036955um_num ).

thf(tp_product_o_VEBT_VEBT,type,
    product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).

thf(tp_product_o_int,type,
    product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).

thf(tp_product_o_o,type,
    product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).

thf(tp_product_snd_int_int,type,
    product_snd_int_int: product_prod_int_int > int ).

thf(tp_product_snd_nat_nat,type,
    product_snd_nat_nat: product_prod_nat_nat > nat ).

thf(tp_quotient_of,type,
    quotient_of: rat > product_prod_int_int ).

thf(tp_re,type,
    re: complex > real ).

thf(tp_real_V1022390504157884413omplex,type,
    real_V1022390504157884413omplex: complex > real ).

thf(tp_real_V1485227260804924795R_real,type,
    real_V1485227260804924795R_real: real > real > real ).

thf(tp_real_V2046097035970521341omplex,type,
    real_V2046097035970521341omplex: real > complex > complex ).

thf(tp_real_V2521375963428798218omplex,type,
    real_V2521375963428798218omplex: set_complex ).

thf(tp_real_V3694042436643373181omplex,type,
    real_V3694042436643373181omplex: complex > complex > real ).

thf(tp_real_V4546457046886955230omplex,type,
    real_V4546457046886955230omplex: real > complex ).

thf(tp_real_V5970128139526366754l_real,type,
    real_V5970128139526366754l_real: ( real > real ) > $o ).

thf(tp_real_V7735802525324610683m_real,type,
    real_V7735802525324610683m_real: real > real ).

thf(tp_real_V975177566351809787t_real,type,
    real_V975177566351809787t_real: real > real > real ).

thf(tp_rep_Integ,type,
    rep_Integ: int > product_prod_nat_nat ).

thf(tp_replicate_VEBT_VEBT,type,
    replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).

thf(tp_replicate_complex,type,
    replicate_complex: nat > complex > list_complex ).

thf(tp_replicate_int,type,
    replicate_int: nat > int > list_int ).

thf(tp_replicate_nat,type,
    replicate_nat: nat > nat > list_nat ).

thf(tp_replicate_o,type,
    replicate_o: nat > $o > list_o ).

thf(tp_replicate_real,type,
    replicate_real: nat > real > list_real ).

thf(tp_replicate_set_nat,type,
    replicate_set_nat: nat > set_nat > list_set_nat ).

thf(tp_ring_17405671764205052669omplex,type,
    ring_17405671764205052669omplex: int > complex ).

thf(tp_ring_18347121197199848620nteger,type,
    ring_18347121197199848620nteger: int > code_integer ).

thf(tp_ring_1_Ints_real,type,
    ring_1_Ints_real: set_real ).

thf(tp_ring_1_of_int_int,type,
    ring_1_of_int_int: int > int ).

thf(tp_ring_1_of_int_rat,type,
    ring_1_of_int_rat: int > rat ).

thf(tp_ring_1_of_int_real,type,
    ring_1_of_int_real: int > real ).

thf(tp_root,type,
    root: nat > real > real ).

thf(tp_sK10_SY1755,type,
    sK10_SY1755: nat > nat > nat ).

thf(tp_sK11_SY1419,type,
    sK11_SY1419: nat > nat > ( nat > nat > $o ) > nat ).

thf(tp_sK12_SY1817,type,
    sK12_SY1817: nat > nat > nat ).

thf(tp_sK13_SY1869,type,
    sK13_SY1869: nat > nat > nat > nat ).

thf(tp_sK14_SY1883,type,
    sK14_SY1883: nat > nat > nat > nat ).

thf(tp_sK15_SY1414,type,
    sK15_SY1414: num > ( num > $o ) > num ).

thf(tp_sK16_SY1934,type,
    sK16_SY1934: nat > nat > ( nat > nat > $o ) > nat ).

thf(tp_sK17_SY1466,type,
    sK17_SY1466: nat > nat ).

thf(tp_sK18_SY1926,type,
    sK18_SY1926: nat > nat > nat ).

thf(tp_sK19_SY1550,type,
    sK19_SY1550: num > num ).

thf(tp_sK1_SX0,type,
    sK1_SX0: nat ).

thf(tp_sK20_SY1935,type,
    sK20_SY1935: nat > nat > nat > nat ).

thf(tp_sK21_SY1534,type,
    sK21_SY1534: nat > ( nat > $o ) > nat ).

thf(tp_sK22_SY1936,type,
    sK22_SY1936: nat > nat > nat > nat ).

thf(tp_sK23_SY1937,type,
    sK23_SY1937: nat > nat > nat ).

thf(tp_sK24_SY1534,type,
    sK24_SY1534: nat > ( nat > $o ) > nat ).

thf(tp_sK25_SY1939,type,
    sK25_SY1939: nat > ( nat > $o ) > $o ).

thf(tp_sK26_SY1551,type,
    sK26_SY1551: num > num ).

thf(tp_sK27_SY1421,type,
    sK27_SY1421: nat > nat > ( nat > nat > $o ) > nat ).

thf(tp_sK28_SY1940,type,
    sK28_SY1940: nat > ( nat > $o ) > $o ).

thf(tp_sK29_SY1874,type,
    sK29_SY1874: nat > nat > nat > nat ).

thf(tp_sK2_SX0,type,
    sK2_SX0: nat ).

thf(tp_sK30_SY1919,type,
    sK30_SY1919: nat > nat > nat ).

thf(tp_sK31_SY1924,type,
    sK31_SY1924: nat > nat > nat ).

thf(tp_sK32_SY1929,type,
    sK32_SY1929: nat > nat > nat ).

thf(tp_sK33_SY1887,type,
    sK33_SY1887: nat > nat > nat > nat > nat > nat ).

thf(tp_sK34_SY1887,type,
    sK34_SY1887: nat > nat > nat > nat > nat > nat ).

thf(tp_sK35_SY1421,type,
    sK35_SY1421: nat > nat > ( nat > nat > $o ) > nat ).

thf(tp_sK36_SY1422,type,
    sK36_SY1422: nat > nat > ( nat > nat > $o ) > nat ).

thf(tp_sK37_SY1941,type,
    sK37_SY1941: nat > nat > nat > nat ).

thf(tp_sK38_SY1944,type,
    sK38_SY1944: nat > nat > ( nat > nat > $o ) > nat ).

thf(tp_sK39_SY1919,type,
    sK39_SY1919: nat > nat > nat > nat ).

thf(tp_sK3_SX0,type,
    sK3_SX0: nat ).

thf(tp_sK40_SY1421,type,
    sK40_SY1421: nat > nat > ( nat > nat > $o ) > nat ).

thf(tp_sK41_SY1924,type,
    sK41_SY1924: nat > nat > nat > nat ).

thf(tp_sK42_SY1929,type,
    sK42_SY1929: nat > nat > nat > nat ).

thf(tp_sK43_SY1942,type,
    sK43_SY1942: nat > nat > nat > nat > nat > nat ).

thf(tp_sK44_SY1943,type,
    sK44_SY1943: nat > nat > nat > nat > nat > nat ).

thf(tp_sK45_SY1422,type,
    sK45_SY1422: nat > nat > ( nat > nat > $o ) > nat ).

thf(tp_sK46_SY1874,type,
    sK46_SY1874: nat > nat > nat > nat > nat > nat ).

thf(tp_sK47_SY1945,type,
    sK47_SY1945: nat > nat > ( nat > nat > $o ) > nat ).

thf(tp_sK48_SY1422,type,
    sK48_SY1422: nat > nat > ( nat > nat > $o ) > nat ).

thf(tp_sK49_SY1947,type,
    sK49_SY1947: nat > nat > ( nat > nat > $o ) > nat ).

thf(tp_sK4_SX0,type,
    sK4_SX0: nat ).

thf(tp_sK50_SY1946,type,
    sK50_SY1946: nat > nat > nat > nat > nat > nat ).

thf(tp_sK5_SY1465,type,
    sK5_SY1465: nat > nat ).

thf(tp_sK6_SY1803,type,
    sK6_SY1803: nat > nat > nat ).

thf(tp_sK7_SY1343,type,
    sK7_SY1343: nat > nat ).

thf(tp_sK8_SY1533,type,
    sK8_SY1533: nat > ( nat > $o ) > nat ).

thf(tp_sK9_SY1748,type,
    sK9_SY1748: nat > nat > nat ).

thf(tp_semila1623282765462674594er_nat,type,
    semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).

thf(tp_semiri1314217659103216013at_int,type,
    semiri1314217659103216013at_int: nat > int ).

thf(tp_semiri1316708129612266289at_nat,type,
    semiri1316708129612266289at_nat: nat > nat ).

thf(tp_semiri1406184849735516958ct_int,type,
    semiri1406184849735516958ct_int: nat > int ).

thf(tp_semiri1408675320244567234ct_nat,type,
    semiri1408675320244567234ct_nat: nat > nat ).

thf(tp_semiri2265585572941072030t_real,type,
    semiri2265585572941072030t_real: nat > real ).

thf(tp_semiri3624122377584611663nteger,type,
    semiri3624122377584611663nteger: nat > code_integer ).

thf(tp_semiri4939895301339042750nteger,type,
    semiri4939895301339042750nteger: nat > code_integer ).

thf(tp_semiri5044797733671781792omplex,type,
    semiri5044797733671781792omplex: nat > complex ).

thf(tp_semiri5074537144036343181t_real,type,
    semiri5074537144036343181t_real: nat > real ).

thf(tp_semiri681578069525770553at_rat,type,
    semiri681578069525770553at_rat: nat > rat ).

thf(tp_semiri773545260158071498ct_rat,type,
    semiri773545260158071498ct_rat: nat > rat ).

thf(tp_semiri8010041392384452111omplex,type,
    semiri8010041392384452111omplex: nat > complex ).

thf(tp_set_VEBT_VEBT2,type,
    set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).

thf(tp_set_complex2,type,
    set_complex2: list_complex > set_complex ).

thf(tp_set_fo1517530859248394432omplex,type,
    set_fo1517530859248394432omplex: ( nat > complex > complex ) > nat > nat > complex > complex ).

thf(tp_set_fo1949268297981939178at_rat,type,
    set_fo1949268297981939178at_rat: ( nat > rat > rat ) > nat > nat > rat > rat ).

thf(tp_set_fo2581907887559384638at_int,type,
    set_fo2581907887559384638at_int: ( nat > int > int ) > nat > nat > int > int ).

thf(tp_set_fo2584398358068434914at_nat,type,
    set_fo2584398358068434914at_nat: ( nat > nat > nat ) > nat > nat > nat > nat ).

thf(tp_set_fo3111899725591712190t_real,type,
    set_fo3111899725591712190t_real: ( nat > real > real ) > nat > nat > real > real ).

thf(tp_set_int2,type,
    set_int2: list_int > set_int ).

thf(tp_set_nat2,type,
    set_nat2: list_nat > set_nat ).

thf(tp_set_o2,type,
    set_o2: list_o > set_o ).

thf(tp_set_or1210151606488870762an_nat,type,
    set_or1210151606488870762an_nat: nat > set_nat ).

thf(tp_set_or1222579329274155063t_real,type,
    set_or1222579329274155063t_real: real > real > set_real ).

thf(tp_set_or1266510415728281911st_int,type,
    set_or1266510415728281911st_int: int > int > set_int ).

thf(tp_set_or1269000886237332187st_nat,type,
    set_or1269000886237332187st_nat: nat > nat > set_nat ).

thf(tp_set_or1633881224788618240n_real,type,
    set_or1633881224788618240n_real: real > real > set_real ).

thf(tp_set_or4548717258645045905et_nat,type,
    set_or4548717258645045905et_nat: set_nat > set_nat > set_set_nat ).

thf(tp_set_or4662586982721622107an_int,type,
    set_or4662586982721622107an_int: int > int > set_int ).

thf(tp_set_or4665077453230672383an_nat,type,
    set_or4665077453230672383an_nat: nat > nat > set_nat ).

thf(tp_set_or5832277885323065728an_int,type,
    set_or5832277885323065728an_int: int > int > set_int ).

thf(tp_set_or5834768355832116004an_nat,type,
    set_or5834768355832116004an_nat: nat > nat > set_nat ).

thf(tp_set_or5849166863359141190n_real,type,
    set_or5849166863359141190n_real: real > set_real ).

thf(tp_set_or5984915006950818249n_real,type,
    set_or5984915006950818249n_real: real > set_real ).

thf(tp_set_or633870826150836451st_rat,type,
    set_or633870826150836451st_rat: rat > rat > set_rat ).

thf(tp_set_or6656581121297822940st_int,type,
    set_or6656581121297822940st_int: int > int > set_int ).

thf(tp_set_or6659071591806873216st_nat,type,
    set_or6659071591806873216st_nat: nat > nat > set_nat ).

thf(tp_set_or7049704709247886629st_num,type,
    set_or7049704709247886629st_num: num > num > set_num ).

thf(tp_set_or890127255671739683et_nat,type,
    set_or890127255671739683et_nat: set_nat > set_set_nat ).

thf(tp_set_ord_atLeast_nat,type,
    set_ord_atLeast_nat: nat > set_nat ).

thf(tp_set_ord_atLeast_real,type,
    set_ord_atLeast_real: real > set_real ).

thf(tp_set_ord_atMost_nat,type,
    set_ord_atMost_nat: nat > set_nat ).

thf(tp_set_ord_lessThan_int,type,
    set_ord_lessThan_int: int > set_int ).

thf(tp_set_ord_lessThan_nat,type,
    set_ord_lessThan_nat: nat > set_nat ).

thf(tp_set_ord_lessThan_num,type,
    set_ord_lessThan_num: num > set_num ).

thf(tp_set_ord_lessThan_rat,type,
    set_ord_lessThan_rat: rat > set_rat ).

thf(tp_set_real2,type,
    set_real2: list_real > set_real ).

thf(tp_set_set_nat2,type,
    set_set_nat2: list_set_nat > set_set_nat ).

thf(tp_sgn_sgn_Code_integer,type,
    sgn_sgn_Code_integer: code_integer > code_integer ).

thf(tp_sgn_sgn_complex,type,
    sgn_sgn_complex: complex > complex ).

thf(tp_sgn_sgn_int,type,
    sgn_sgn_int: int > int ).

thf(tp_sgn_sgn_rat,type,
    sgn_sgn_rat: rat > rat ).

thf(tp_sgn_sgn_real,type,
    sgn_sgn_real: real > real ).

thf(tp_sin_coeff,type,
    sin_coeff: nat > real ).

thf(tp_sin_complex,type,
    sin_complex: complex > complex ).

thf(tp_sin_real,type,
    sin_real: real > real ).

thf(tp_sinh_real,type,
    sinh_real: real > real ).

thf(tp_size_list_VEBT_VEBT,type,
    size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).

thf(tp_size_num,type,
    size_num: num > nat ).

thf(tp_size_o8335143837870341156at_nat,type,
    size_o8335143837870341156at_nat: ( product_prod_nat_nat > nat ) > option4927543243414619207at_nat > nat ).

thf(tp_size_option_nat,type,
    size_option_nat: ( nat > nat ) > option_nat > nat ).

thf(tp_size_option_num,type,
    size_option_num: ( num > nat ) > option_num > nat ).

thf(tp_size_s1515746228057227161od_o_o,type,
    size_s1515746228057227161od_o_o: list_P4002435161011370285od_o_o > nat ).

thf(tp_size_s170228958280169651at_nat,type,
    size_s170228958280169651at_nat: option4927543243414619207at_nat > nat ).

thf(tp_size_s2953683556165314199_o_int,type,
    size_s2953683556165314199_o_int: list_P3795440434834930179_o_int > nat ).

thf(tp_size_s3254054031482475050et_nat,type,
    size_s3254054031482475050et_nat: list_set_nat > nat ).

thf(tp_size_s3445333598471063425nteger,type,
    size_s3445333598471063425nteger: list_Code_integer > nat ).

thf(tp_size_s3451745648224563538omplex,type,
    size_s3451745648224563538omplex: list_complex > nat ).

thf(tp_size_s3661962791536183091BT_int,type,
    size_s3661962791536183091BT_int: list_P4547456442757143711BT_int > nat ).

thf(tp_size_s4246224855604898693_int_o,type,
    size_s4246224855604898693_int_o: list_P5087981734274514673_int_o > nat ).

thf(tp_size_s4313452262239582901T_VEBT,type,
    size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat ).

thf(tp_size_s5157815400016825771nt_int,type,
    size_s5157815400016825771nt_int: list_P5707943133018811711nt_int > nat ).

thf(tp_size_s6639371672096860321T_VEBT,type,
    size_s6639371672096860321T_VEBT: list_P7524865323317820941T_VEBT > nat ).

thf(tp_size_s6755466524823107622T_VEBT,type,
    size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).

thf(tp_size_s7466405169056248089T_VEBT,type,
    size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).

thf(tp_size_s9168528473962070013VEBT_o,type,
    size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat ).

thf(tp_size_size_VEBT_VEBT,type,
    size_size_VEBT_VEBT: vEBT_VEBT > nat ).

thf(tp_size_size_list_int,type,
    size_size_list_int: list_int > nat ).

thf(tp_size_size_list_nat,type,
    size_size_list_nat: list_nat > nat ).

thf(tp_size_size_list_num,type,
    size_size_list_num: list_num > nat ).

thf(tp_size_size_list_o,type,
    size_size_list_o: list_o > nat ).

thf(tp_size_size_list_real,type,
    size_size_list_real: list_real > nat ).

thf(tp_size_size_num,type,
    size_size_num: num > nat ).

thf(tp_size_size_option_nat,type,
    size_size_option_nat: option_nat > nat ).

thf(tp_size_size_option_num,type,
    size_size_option_num: option_num > nat ).

thf(tp_some_P7363390416028606310at_nat,type,
    some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat ).

thf(tp_some_nat,type,
    some_nat: nat > option_nat ).

thf(tp_some_num,type,
    some_num: num > option_num ).

thf(tp_sqrt,type,
    sqrt: real > real ).

thf(tp_strict1292158309912662752at_nat,type,
    strict1292158309912662752at_nat: ( nat > nat ) > set_nat > $o ).

thf(tp_suc,type,
    suc: nat > nat ).

thf(tp_suminf_complex,type,
    suminf_complex: ( nat > complex ) > complex ).

thf(tp_suminf_int,type,
    suminf_int: ( nat > int ) > int ).

thf(tp_suminf_nat,type,
    suminf_nat: ( nat > nat ) > nat ).

thf(tp_suminf_real,type,
    suminf_real: ( nat > real ) > real ).

thf(tp_summable_complex,type,
    summable_complex: ( nat > complex ) > $o ).

thf(tp_summable_int,type,
    summable_int: ( nat > int ) > $o ).

thf(tp_summable_nat,type,
    summable_nat: ( nat > nat ) > $o ).

thf(tp_summable_real,type,
    summable_real: ( nat > real ) > $o ).

thf(tp_summary,type,
    summary: vEBT_VEBT ).

thf(tp_summin,type,
    summin: nat ).

thf(tp_sums_complex,type,
    sums_complex: ( nat > complex ) > complex > $o ).

thf(tp_sums_int,type,
    sums_int: ( nat > int ) > int > $o ).

thf(tp_sums_nat,type,
    sums_nat: ( nat > nat ) > nat > $o ).

thf(tp_sums_real,type,
    sums_real: ( nat > real ) > real > $o ).

thf(tp_take_VEBT_VEBT,type,
    take_VEBT_VEBT: nat > list_VEBT_VEBT > list_VEBT_VEBT ).

thf(tp_tan_complex,type,
    tan_complex: complex > complex ).

thf(tp_tan_real,type,
    tan_real: real > real ).

thf(tp_tanh_complex,type,
    tanh_complex: complex > complex ).

thf(tp_tanh_real,type,
    tanh_real: real > real ).

thf(tp_the_Pr8591224930841456533at_nat,type,
    the_Pr8591224930841456533at_nat: option4927543243414619207at_nat > product_prod_nat_nat ).

thf(tp_the_in5290026491893676941l_real,type,
    the_in5290026491893676941l_real: set_real > ( real > real ) > real > real ).

thf(tp_the_int,type,
    the_int: ( int > $o ) > int ).

thf(tp_the_nat,type,
    the_nat: option_nat > nat ).

thf(tp_the_num,type,
    the_num: option_num > num ).

thf(tp_the_real,type,
    the_real: ( real > $o ) > real ).

thf(tp_times_3573771949741848930nteger,type,
    times_3573771949741848930nteger: code_integer > code_integer > code_integer ).

thf(tp_times_7803423173614009249d_enat,type,
    times_7803423173614009249d_enat: extended_enat > extended_enat > extended_enat ).

thf(tp_times_times_complex,type,
    times_times_complex: complex > complex > complex ).

thf(tp_times_times_int,type,
    times_times_int: int > int > int ).

thf(tp_times_times_nat,type,
    times_times_nat: nat > nat > nat ).

thf(tp_times_times_num,type,
    times_times_num: num > num > num ).

thf(tp_times_times_rat,type,
    times_times_rat: rat > rat > rat ).

thf(tp_times_times_real,type,
    times_times_real: real > real > real ).

thf(tp_top_to1996260823553986621t_unit,type,
    top_to1996260823553986621t_unit: set_Product_unit ).

thf(tp_top_top_set_char,type,
    top_top_set_char: set_char ).

thf(tp_top_top_set_nat,type,
    top_top_set_nat: set_nat ).

thf(tp_top_top_set_o,type,
    top_top_set_o: set_o ).

thf(tp_top_top_set_real,type,
    top_top_set_real: set_real ).

thf(tp_topolo1459490580787246023eq_num,type,
    topolo1459490580787246023eq_num: ( nat > num ) > $o ).

thf(tp_topolo1511823702728130853y_real,type,
    topolo1511823702728130853y_real: filter2146258269922977983l_real ).

thf(tp_topolo2177554685111907308n_real,type,
    topolo2177554685111907308n_real: real > set_real > filter_real ).

thf(tp_topolo2815343760600316023s_real,type,
    topolo2815343760600316023s_real: real > filter_real ).

thf(tp_topolo2919662092509805066nteger,type,
    topolo2919662092509805066nteger: ( nat > code_integer ) > $o ).

thf(tp_topolo4055970368930404560y_real,type,
    topolo4055970368930404560y_real: ( nat > real ) > $o ).

thf(tp_topolo4110288021797289639omplex,type,
    topolo4110288021797289639omplex: set_complex > $o ).

thf(tp_topolo4267028734544971653eq_rat,type,
    topolo4267028734544971653eq_rat: ( nat > rat ) > $o ).

thf(tp_topolo4422821103128117721l_real,type,
    topolo4422821103128117721l_real: filter_real > ( real > real ) > $o ).

thf(tp_topolo4860482606490270245n_real,type,
    topolo4860482606490270245n_real: set_real > $o ).

thf(tp_topolo4899668324122417113eq_int,type,
    topolo4899668324122417113eq_int: ( nat > int ) > $o ).

thf(tp_topolo4902158794631467389eq_nat,type,
    topolo4902158794631467389eq_nat: ( nat > nat ) > $o ).

thf(tp_topolo5044208981011980120l_real,type,
    topolo5044208981011980120l_real: set_real > ( real > real ) > $o ).

thf(tp_topolo6517432010174082258omplex,type,
    topolo6517432010174082258omplex: ( nat > complex ) > $o ).

thf(tp_topolo6980174941875973593q_real,type,
    topolo6980174941875973593q_real: ( nat > real ) > $o ).

thf(tp_topolo7278393974255667507et_nat,type,
    topolo7278393974255667507et_nat: ( nat > set_nat ) > $o ).

thf(tp_topolo896644834953643431omplex,type,
    topolo896644834953643431omplex: filter6041513312241820739omplex ).

thf(tp_treeList,type,
    treeList: list_VEBT_VEBT ).

thf(tp_uminus1351360451143612070nteger,type,
    uminus1351360451143612070nteger: code_integer > code_integer ).

thf(tp_uminus1482373934393186551omplex,type,
    uminus1482373934393186551omplex: complex > complex ).

thf(tp_uminus1532241313380277803et_int,type,
    uminus1532241313380277803et_int: set_int > set_int ).

thf(tp_uminus1680532995456772888plex_o,type,
    uminus1680532995456772888plex_o: ( complex > $o ) > complex > $o ).

thf(tp_uminus5710092332889474511et_nat,type,
    uminus5710092332889474511et_nat: set_nat > set_nat ).

thf(tp_uminus612125837232591019t_real,type,
    uminus612125837232591019t_real: set_real > set_real ).

thf(tp_uminus613421341184616069et_nat,type,
    uminus613421341184616069et_nat: set_set_nat > set_set_nat ).

thf(tp_uminus6221592323253981072nt_int,type,
    uminus6221592323253981072nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).

thf(tp_uminus6401447641752708672_nat_o,type,
    uminus6401447641752708672_nat_o: ( set_nat > $o ) > set_nat > $o ).

thf(tp_uminus7117520113953359693_int_o,type,
    uminus7117520113953359693_int_o: ( product_prod_int_int > $o ) > product_prod_int_int > $o ).

thf(tp_uminus8566677241136511917omplex,type,
    uminus8566677241136511917omplex: set_complex > set_complex ).

thf(tp_uminus_uminus_int,type,
    uminus_uminus_int: int > int ).

thf(tp_uminus_uminus_int_o,type,
    uminus_uminus_int_o: ( int > $o ) > int > $o ).

thf(tp_uminus_uminus_nat_o,type,
    uminus_uminus_nat_o: ( nat > $o ) > nat > $o ).

thf(tp_uminus_uminus_rat,type,
    uminus_uminus_rat: rat > rat ).

thf(tp_uminus_uminus_real,type,
    uminus_uminus_real: real > real ).

thf(tp_uminus_uminus_real_o,type,
    uminus_uminus_real_o: ( real > $o ) > real > $o ).

thf(tp_unique3096191561947761185of_nat,type,
    unique3096191561947761185of_nat: nat > char ).

thf(tp_unique3479559517661332726nteger,type,
    unique3479559517661332726nteger: num > num > produc8923325533196201883nteger ).

thf(tp_unique4921790084139445826nteger,type,
    unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(tp_unique5024387138958732305ep_int,type,
    unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int ).

thf(tp_unique5026877609467782581ep_nat,type,
    unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat ).

thf(tp_unique5052692396658037445od_int,type,
    unique5052692396658037445od_int: num > num > product_prod_int_int ).

thf(tp_unique5055182867167087721od_nat,type,
    unique5055182867167087721od_nat: num > num > product_prod_nat_nat ).

thf(tp_unique5706413561485394159nteger,type,
    unique5706413561485394159nteger: produc8923325533196201883nteger > $o ).

thf(tp_unique6319869463603278526ux_int,type,
    unique6319869463603278526ux_int: product_prod_int_int > $o ).

thf(tp_unique6322359934112328802ux_nat,type,
    unique6322359934112328802ux_nat: product_prod_nat_nat > $o ).

thf(tp_upto,type,
    upto: int > int > list_int ).

thf(tp_upto_aux,type,
    upto_aux: int > int > list_int > list_int ).

thf(tp_upto_rel,type,
    upto_rel: product_prod_int_int > product_prod_int_int > $o ).

thf(tp_vEBT_Leaf,type,
    vEBT_Leaf: $o > $o > vEBT_VEBT ).

thf(tp_vEBT_Node,type,
    vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).

thf(tp_vEBT_V1502963449132264192at_nat,type,
    vEBT_V1502963449132264192at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat ).

thf(tp_vEBT_V4262088993061758097ft_nat,type,
    vEBT_V4262088993061758097ft_nat: ( nat > nat > nat ) > option_nat > option_nat > option_nat ).

thf(tp_vEBT_V4351362008482014158ma_rel,type,
    vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(tp_vEBT_V5719532721284313246member,type,
    vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).

thf(tp_vEBT_V5765760719290551771er_rel,type,
    vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(tp_vEBT_V5917875025757280293ildren,type,
    vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).

thf(tp_vEBT_V6963167321098673237ll_rel,type,
    vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o ).

thf(tp_vEBT_V819420779217536731ft_num,type,
    vEBT_V819420779217536731ft_num: ( num > num > num ) > option_num > option_num > option_num ).

thf(tp_vEBT_V8194947554948674370ptions,type,
    vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).

thf(tp_vEBT_VEBT_add,type,
    vEBT_VEBT_add: option_nat > option_nat > option_nat ).

thf(tp_vEBT_VEBT_bit_concat,type,
    vEBT_VEBT_bit_concat: nat > nat > nat > nat ).

thf(tp_vEBT_VEBT_greater,type,
    vEBT_VEBT_greater: option_nat > option_nat > $o ).

thf(tp_vEBT_VEBT_high,type,
    vEBT_VEBT_high: nat > nat > nat ).

thf(tp_vEBT_VEBT_less,type,
    vEBT_VEBT_less: option_nat > option_nat > $o ).

thf(tp_vEBT_VEBT_lesseq,type,
    vEBT_VEBT_lesseq: option_nat > option_nat > $o ).

thf(tp_vEBT_VEBT_low,type,
    vEBT_VEBT_low: nat > nat > nat ).

thf(tp_vEBT_VEBT_max_in_set,type,
    vEBT_VEBT_max_in_set: set_nat > nat > $o ).

thf(tp_vEBT_VEBT_membermima,type,
    vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).

thf(tp_vEBT_VEBT_minNull,type,
    vEBT_VEBT_minNull: vEBT_VEBT > $o ).

thf(tp_vEBT_VEBT_min_in_set,type,
    vEBT_VEBT_min_in_set: set_nat > nat > $o ).

thf(tp_vEBT_VEBT_mul,type,
    vEBT_VEBT_mul: option_nat > option_nat > option_nat ).

thf(tp_vEBT_VEBT_power,type,
    vEBT_VEBT_power: option_nat > option_nat > option_nat ).

thf(tp_vEBT_VEBT_set_vebt,type,
    vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).

thf(tp_vEBT_VEBT_valid,type,
    vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).

thf(tp_vEBT_VEBT_valid_rel,type,
    vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(tp_vEBT_invar_vebt,type,
    vEBT_invar_vebt: vEBT_VEBT > nat > $o ).

thf(tp_vEBT_is_pred_in_set,type,
    vEBT_is_pred_in_set: set_nat > nat > nat > $o ).

thf(tp_vEBT_is_succ_in_set,type,
    vEBT_is_succ_in_set: set_nat > nat > nat > $o ).

thf(tp_vEBT_set_vebt,type,
    vEBT_set_vebt: vEBT_VEBT > set_nat ).

thf(tp_vEBT_size_VEBT,type,
    vEBT_size_VEBT: vEBT_VEBT > nat ).

thf(tp_vEBT_v4011308405150292612up_rel,type,
    vEBT_v4011308405150292612up_rel: nat > nat > $o ).

thf(tp_vEBT_vebt_buildup,type,
    vEBT_vebt_buildup: nat > vEBT_VEBT ).

thf(tp_vEBT_vebt_delete,type,
    vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT ).

thf(tp_vEBT_vebt_delete_rel,type,
    vEBT_vebt_delete_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(tp_vEBT_vebt_insert,type,
    vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).

thf(tp_vEBT_vebt_insert_rel,type,
    vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(tp_vEBT_vebt_maxt,type,
    vEBT_vebt_maxt: vEBT_VEBT > option_nat ).

thf(tp_vEBT_vebt_maxt_rel,type,
    vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o ).

thf(tp_vEBT_vebt_member,type,
    vEBT_vebt_member: vEBT_VEBT > nat > $o ).

thf(tp_vEBT_vebt_member_rel,type,
    vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(tp_vEBT_vebt_mint,type,
    vEBT_vebt_mint: vEBT_VEBT > option_nat ).

thf(tp_vEBT_vebt_mint_rel,type,
    vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o ).

thf(tp_vEBT_vebt_pred,type,
    vEBT_vebt_pred: vEBT_VEBT > nat > option_nat ).

thf(tp_vEBT_vebt_pred_rel,type,
    vEBT_vebt_pred_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(tp_vEBT_vebt_succ,type,
    vEBT_vebt_succ: vEBT_VEBT > nat > option_nat ).

thf(tp_vEBT_vebt_succ_rel,type,
    vEBT_vebt_succ_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).

thf(tp_xa,type,
    xa: nat ).

thf(tp_ya,type,
    ya: nat ).

thf(tp_zero_n1201886186963655149omplex,type,
    zero_n1201886186963655149omplex: $o > complex ).

thf(tp_zero_n2052037380579107095ol_rat,type,
    zero_n2052037380579107095ol_rat: $o > rat ).

thf(tp_zero_n2684676970156552555ol_int,type,
    zero_n2684676970156552555ol_int: $o > int ).

thf(tp_zero_n2687167440665602831ol_nat,type,
    zero_n2687167440665602831ol_nat: $o > nat ).

thf(tp_zero_n3304061248610475627l_real,type,
    zero_n3304061248610475627l_real: $o > real ).

thf(tp_zero_n356916108424825756nteger,type,
    zero_n356916108424825756nteger: $o > code_integer ).

thf(tp_zero_z3403309356797280102nteger,type,
    zero_z3403309356797280102nteger: code_integer ).

thf(tp_zero_z5237406670263579293d_enat,type,
    zero_z5237406670263579293d_enat: extended_enat ).

thf(tp_zero_zero_complex,type,
    zero_zero_complex: complex ).

thf(tp_zero_zero_int,type,
    zero_zero_int: int ).

thf(tp_zero_zero_nat,type,
    zero_zero_nat: nat ).

thf(tp_zero_zero_rat,type,
    zero_zero_rat: rat ).

thf(tp_zero_zero_real,type,
    zero_zero_real: real ).

thf(3,axiom,
    ! [P: $o] :
      ( ( P = $true )
      | ( P = $false ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T) ).

thf(402,axiom,
    ! [K: nat,M: nat,N2: nat] :
      ( ( times_times_nat @ K @ ( gcd_gcd_nat @ M @ N2 ) )
      = ( gcd_gcd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9836_gcd__mult__distrib__nat) ).

thf(413,axiom,
    ! [Q2: num] :
      ( ( num_of_nat @ ( numeral_numeral_nat @ Q2 ) )
      = Q2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9825_num__of__nat__numeral__eq) ).

thf(466,axiom,
    ( bit_se8570568707652914677it_nat
    = ( ^ [N: nat,M6: nat] : ( divide_divide_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9772_drop__bit__nat__def) ).

thf(692,axiom,
    ( bit_se547839408752420682it_nat
    = ( ^ [N: nat,M6: nat] : ( times_times_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9546_push__bit__nat__def) ).

thf(770,axiom,
    ! [N2: num] :
      ( ( bit_or_not_num_neg @ ( bit0 @ N2 ) @ one )
      = ( bit0 @ one ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9468_or__not__num__neg_Osimps_I4_J) ).

thf(773,axiom,
    ( ( bit_or_not_num_neg @ one @ one )
    = one ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9465_or__not__num__neg_Osimps_I1_J) ).

thf(834,axiom,
    ! [X: num] :
      ( ( pow @ X @ one )
      = X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9404_pow_Osimps_I1_J) ).

thf(862,axiom,
    ( ( inc @ one )
    = ( bit0 @ one ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9376_inc_Osimps_I1_J) ).

thf(864,axiom,
    ! [P: num > $o,X: num] :
      ( ( P @ one )
     => ( ! [X4: num] :
            ( ( P @ X4 )
           => ( P @ ( inc @ X4 ) ) )
       => ( P @ X ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9374_num__induct) ).

thf(997,axiom,
    ! [M: nat,N2: nat,X: real] :
      ( ( root @ ( times_times_nat @ M @ N2 ) @ X )
      = ( root @ M @ ( root @ N2 @ X ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9241_real__root__mult__exp) ).

thf(1289,axiom,
    ! [M: nat,R: nat,K: nat] :
      ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R ) @ K ) @ ( plus_plus_nat @ M @ K ) ) @ ( binomial @ ( plus_plus_nat @ M @ K ) @ K ) )
      = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M @ R ) @ M ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8949_choose__mult__lemma) ).

thf(1604,axiom,
    ! [F: nat > nat,A2: set_nat,N2: nat] :
      ( ( power_power_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ N2 )
      = ( groups708209901874060359at_nat
        @ ^ [X2: nat] : ( power_power_nat @ ( F @ X2 ) @ N2 )
        @ A2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8634_prod__power__distrib) ).

thf(1607,axiom,
    ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
      ( ( groups708209901874060359at_nat
        @ ^ [X2: nat] : ( times_times_nat @ ( G @ X2 ) @ ( H2 @ X2 ) )
        @ A2 )
      = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ A2 ) @ ( groups708209901874060359at_nat @ H2 @ A2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8631_prod_Odistrib) ).

thf(2069,axiom,
    ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
    = ( numeral_numeral_nat @ ( bit0 @ one ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8169_fact__2) ).

thf(2385,axiom,
    ! [F: nat > nat,A: nat,G: nat > nat,B: nat] :
      ( ( sums_nat @ F @ A )
     => ( ( sums_nat @ G @ B )
       => ( sums_nat
          @ ^ [N: nat] : ( plus_plus_nat @ ( F @ N ) @ ( G @ N ) )
          @ ( plus_plus_nat @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7853_sums__add) ).

thf(2534,axiom,
    ! [F: nat > complex,K: nat] :
      ( ( summable_complex @ F )
     => ( summable_complex
        @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7704_summable__ignore__initial__segment) ).

thf(2535,axiom,
    ! [F: nat > real,K: nat] :
      ( ( summable_real @ F )
     => ( summable_real
        @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7703_summable__ignore__initial__segment) ).

thf(2547,axiom,
    ! [F: nat > nat,G: nat > nat] :
      ( ( summable_nat @ F )
     => ( ( summable_nat @ G )
       => ( summable_nat
          @ ^ [N: nat] : ( plus_plus_nat @ ( F @ N ) @ ( G @ N ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7691_summable__add) ).

thf(2558,axiom,
    ! [F: nat > complex,K: nat] :
      ( ( summable_complex
        @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
      = ( summable_complex @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7680_summable__iff__shift) ).

thf(2559,axiom,
    ! [F: nat > real,K: nat] :
      ( ( summable_real
        @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
      = ( summable_real @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7679_summable__iff__shift) ).

thf(2949,axiom,
    ! [M: nat,N2: nat] :
      ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ M @ N2 ) )
      = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7289_unique__euclidean__semiring__with__nat__class_Oof__nat__div) ).

thf(2963,axiom,
    ! [A: nat,M: nat,N2: nat] :
      ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) )
      = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7275_div__mult2__eq_H) ).

thf(2978,axiom,
    ( ( bitM @ one )
    = one ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7260_semiring__norm_I26_J) ).

thf(2981,axiom,
    ! [X: nat,Y: nat] :
      ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X ) @ Y )
      = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7257_mult__of__nat__commute) ).

thf(3125,axiom,
    ! [Y: nat,X: num,N2: nat] :
      ( ( ( semiri1316708129612266289at_nat @ Y )
        = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) )
      = ( Y
        = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7113_real__of__nat__eq__numeral__power__cancel__iff) ).

thf(3130,axiom,
    ! [X: num,N2: nat,Y: nat] :
      ( ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 )
        = ( semiri1316708129612266289at_nat @ Y ) )
      = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 )
        = Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7108_numeral__power__eq__of__nat__cancel__iff) ).

thf(3239,axiom,
    ! [X: nat,B: nat,W: nat] :
      ( ( ( semiri1316708129612266289at_nat @ X )
        = ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
      = ( X
        = ( power_power_nat @ B @ W ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6999_of__nat__power__eq__of__nat__cancel__iff) ).

thf(3243,axiom,
    ! [B: nat,W: nat,X: nat] :
      ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W )
        = ( semiri1316708129612266289at_nat @ X ) )
      = ( ( power_power_nat @ B @ W )
        = X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6995_of__nat__eq__of__nat__power__cancel__iff) ).

thf(3247,axiom,
    ! [M: nat,N2: nat] :
      ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ M @ N2 ) )
      = ( power_power_nat @ ( semiri1316708129612266289at_nat @ M ) @ N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6991_of__nat__power) ).

thf(3266,axiom,
    ! [M: nat,N2: nat] :
      ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N2 ) )
      = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6972_of__nat__mult) ).

thf(3271,axiom,
    ! [M: nat,N2: nat] :
      ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N2 ) )
      = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6967_of__nat__add) ).

thf(3284,axiom,
    ! [N2: num] :
      ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N2 ) )
      = ( numeral_numeral_nat @ N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6954_of__nat__numeral) ).

thf(3495,axiom,
    ! [A: nat] :
      ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
      = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6743_power3__eq__cube) ).

thf(3506,axiom,
    ! [N2: num] :
      ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
      = ( numeral_numeral_nat @ N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6732_numeral__Bit1__div__2) ).

thf(3534,axiom,
    ! [Z: nat,W: num] :
      ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
      = ( times_times_nat @ ( times_times_nat @ Z @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6704_power__numeral__odd) ).

thf(3646,axiom,
    ! [Y: num] :
      ( ( Y != one )
     => ( ! [X23: num] :
            ( Y
           != ( bit0 @ X23 ) )
       => ~ ! [X33: num] :
              ( Y
             != ( bit1 @ X33 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6592_num_Oexhaust) ).

thf(3716,axiom,
    ! [X32: num] :
      ( one
     != ( bit1 @ X32 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6522_verit__eq__simplify_I12_J) ).

thf(3717,axiom,
    ! [X22: num,X32: num] :
      ( ( bit0 @ X22 )
     != ( bit1 @ X32 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6521_verit__eq__simplify_I14_J) ).

thf(3911,axiom,
    ! [N2: num] :
      ( one
     != ( bit1 @ N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6327_semiring__norm_I84_J) ).

thf(3912,axiom,
    ! [M: num] :
      ( ( bit1 @ M )
     != one ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6326_semiring__norm_I86_J) ).

thf(3913,axiom,
    ! [M: num,N2: num] :
      ( ( bit0 @ M )
     != ( bit1 @ N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6325_semiring__norm_I88_J) ).

thf(3914,axiom,
    ! [M: num,N2: num] :
      ( ( bit1 @ M )
     != ( bit0 @ N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6324_semiring__norm_I89_J) ).

thf(3967,axiom,
    ! [W: nat,Y: nat,X: nat,Z: nat] :
      ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y ) @ ( times_times_nat @ X @ Z ) )
        = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X @ Y ) ) )
      = ( ( W = X )
        | ( Y = Z ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6271_crossproduct__eq) ).

thf(3971,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( A != B )
        & ( C != D ) )
      = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) )
       != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6267_crossproduct__noteq) ).

thf(3975,axiom,
    ! [B: nat,A: nat] :
      ( ( B
        = ( plus_plus_nat @ B @ A ) )
      = ( A = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6263_add__0__iff) ).

thf(4626,axiom,
    ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
      ( ( groups3542108847815614940at_nat
        @ ^ [X2: nat] : ( plus_plus_nat @ ( G @ X2 ) @ ( H2 @ X2 ) )
        @ A2 )
      = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ A2 ) @ ( groups3542108847815614940at_nat @ H2 @ A2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5612_sum_Odistrib) ).

thf(4630,axiom,
    ! [R: nat,F: nat > nat,A2: set_nat] :
      ( ( times_times_nat @ R @ ( groups3542108847815614940at_nat @ F @ A2 ) )
      = ( groups3542108847815614940at_nat
        @ ^ [N: nat] : ( times_times_nat @ R @ ( F @ N ) )
        @ A2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5608_sum__distrib__left) ).

thf(4634,axiom,
    ! [F: nat > nat,A2: set_nat,R: nat] :
      ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ R )
      = ( groups3542108847815614940at_nat
        @ ^ [N: nat] : ( times_times_nat @ ( F @ N ) @ R )
        @ A2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5604_sum__distrib__right) ).

thf(4638,axiom,
    ! [F: nat > nat,A2: set_nat,G: nat > nat,B3: set_nat] :
      ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ B3 ) )
      = ( groups3542108847815614940at_nat
        @ ^ [I3: nat] :
            ( groups3542108847815614940at_nat
            @ ^ [J3: nat] : ( times_times_nat @ ( F @ I3 ) @ ( G @ J3 ) )
            @ B3 )
        @ A2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5600_sum__product) ).

thf(5158,axiom,
    ! [R: nat,A: nat,B: nat,C: nat,D: nat] :
      ( ( R != zero_zero_nat )
     => ( ( ( A = B )
          & ( C != D ) )
       => ( ( plus_plus_nat @ A @ ( times_times_nat @ R @ C ) )
         != ( plus_plus_nat @ B @ ( times_times_nat @ R @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5080_add__scale__eq__noteq) ).

thf(5181,axiom,
    ! [P: nat > $o,A: nat] :
      ( ! [A3: nat] :
          ( ( ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
            = A3 )
         => ( P @ A3 ) )
     => ( ! [A3: nat,B2: $o] :
            ( ( P @ A3 )
           => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                = A3 )
             => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
       => ( P @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5057_bits__induct) ).

thf(5233,axiom,
    ! [P: $o,Q: $o] :
      ( ( zero_n2687167440665602831ol_nat
        @ ( P
          & Q ) )
      = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5005_of__bool__conj) ).

thf(5652,axiom,
    ! [A: nat] :
      ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
     => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4586_even__two__times__div__two) ).

thf(5675,axiom,
    ( ( ^ [Y3: nat,Z2: nat] : ( Y3 = Z2 ) )
    = ( ^ [A5: nat,B5: nat] :
          ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 )
            = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B5 ) )
          & ( ( divide_divide_nat @ A5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
            = ( divide_divide_nat @ B5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4563_bit__eq__rec) ).

thf(5681,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
     => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
       => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4557_odd__even__add) ).

thf(5693,axiom,
    ! [A: nat] :
      ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
     => ~ ! [B2: nat] :
            ( A
           != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4545_evenE) ).

thf(6049,axiom,
    ! [N2: num] : ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4189_even__numeral) ).

thf(6072,axiom,
    ! [X: nat,Y: nat] :
      ( ( ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
        = ( divide_divide_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
     => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y ) )
       => ( X = Y ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4166_div2__even__ext__nat) ).

thf(6082,axiom,
    ! [A: nat,B: nat] :
    ? [D4: nat,X4: nat,Y4: nat] :
      ( ( dvd_dvd_nat @ D4 @ A )
      & ( dvd_dvd_nat @ D4 @ B )
      & ( ( ( times_times_nat @ A @ X4 )
          = ( plus_plus_nat @ ( times_times_nat @ B @ Y4 ) @ D4 ) )
        | ( ( times_times_nat @ B @ X4 )
          = ( plus_plus_nat @ ( times_times_nat @ A @ Y4 ) @ D4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4156_bezout__add__nat) ).

thf(6083,axiom,
    ! [D: nat,A: nat,B: nat,X: nat,Y: nat] :
      ( ( dvd_dvd_nat @ D @ A )
     => ( ( dvd_dvd_nat @ D @ B )
       => ( ( ( ( times_times_nat @ A @ X )
              = ( plus_plus_nat @ ( times_times_nat @ B @ Y ) @ D ) )
            | ( ( times_times_nat @ B @ X )
              = ( plus_plus_nat @ ( times_times_nat @ A @ Y ) @ D ) ) )
         => ? [X4: nat,Y4: nat] :
              ( ( dvd_dvd_nat @ D @ A )
              & ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
              & ( ( ( times_times_nat @ A @ X4 )
                  = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y4 ) @ D ) )
                | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X4 )
                  = ( plus_plus_nat @ ( times_times_nat @ A @ Y4 ) @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4155_bezout__lemma__nat) ).

thf(6108,axiom,
    ! [B: nat,A: nat,N2: nat] :
      ( ( dvd_dvd_nat @ B @ A )
     => ( ( power_power_nat @ ( divide_divide_nat @ A @ B ) @ N2 )
        = ( divide_divide_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4130_div__power) ).

thf(6120,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( ( dvd_dvd_nat @ C @ A )
     => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
        = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4118_div__plus__div__distrib__dvd__left) ).

thf(6123,axiom,
    ! [C: nat,B: nat,A: nat] :
      ( ( dvd_dvd_nat @ C @ B )
     => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
        = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4115_div__plus__div__distrib__dvd__right) ).

thf(6126,axiom,
    ! [C: nat,B: nat,A: nat] :
      ( ( dvd_dvd_nat @ C @ B )
     => ( ( times_times_nat @ ( divide_divide_nat @ B @ C ) @ A )
        = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4112_dvd__div__mult) ).

thf(6129,axiom,
    ! [C: nat,B: nat,A: nat] :
      ( ( dvd_dvd_nat @ C @ B )
     => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
        = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4109_div__mult__swap) ).

thf(6132,axiom,
    ! [C: nat,B: nat,A: nat] :
      ( ( dvd_dvd_nat @ C @ B )
     => ( ( dvd_dvd_nat @ B @ A )
       => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C ) )
          = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4106_div__div__eq__right) ).

thf(6135,axiom,
    ! [B: nat,C: nat,A: nat] :
      ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C ) @ A )
     => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
        = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4103_dvd__div__mult2__eq) ).

thf(6138,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B )
     => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4100_dvd__mult__imp__div) ).

thf(6141,axiom,
    ! [B: nat,A: nat,D: nat,C: nat] :
      ( ( dvd_dvd_nat @ B @ A )
     => ( ( dvd_dvd_nat @ D @ C )
       => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C @ D ) )
          = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4097_div__mult__div__if__dvd) ).

thf(6197,axiom,
    ! [N2: nat,K: int,M: nat,L2: int,R: int] :
      ( ( bit_concat_bit @ N2 @ K @ ( bit_concat_bit @ M @ L2 @ R ) )
      = ( bit_concat_bit @ ( plus_plus_nat @ M @ N2 ) @ ( bit_concat_bit @ N2 @ K @ L2 ) @ R ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4041_concat__bit__assoc) ).

thf(6213,axiom,
    ! [X: nat,Y: nat,N2: nat] :
      ( ( dvd_dvd_nat @ X @ Y )
     => ( dvd_dvd_nat @ ( power_power_nat @ X @ N2 ) @ ( power_power_nat @ Y @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4025_dvd__power__same) ).

thf(6216,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( ( dvd_dvd_nat @ C @ A )
     => ( ( dvd_dvd_nat @ C @ B )
       => ( ( ( divide_divide_nat @ A @ C )
            = ( divide_divide_nat @ B @ C ) )
          = ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4022_dvd__div__eq__iff) ).

thf(6222,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( ( ( divide_divide_nat @ A @ C )
        = ( divide_divide_nat @ B @ C ) )
     => ( ( dvd_dvd_nat @ C @ A )
       => ( ( dvd_dvd_nat @ C @ B )
         => ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4016_dvd__div__eq__cancel) ).

thf(6228,axiom,
    ! [D: nat,B: nat,A: nat] :
      ( ( dvd_dvd_nat @ D @ B )
     => ( ( dvd_dvd_nat @ B @ A )
       => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D ) @ ( divide_divide_nat @ B @ D ) )
          = ( divide_divide_nat @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4010_div__div__div__same) ).

thf(6249,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( dvd_dvd_nat @ A @ B )
     => ( ( dvd_dvd_nat @ A @ C )
       => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3989_dvd__add) ).

thf(6254,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( ( dvd_dvd_nat @ A @ C )
     => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
        = ( dvd_dvd_nat @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3984_dvd__add__left__iff) ).

thf(6259,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( dvd_dvd_nat @ A @ B )
     => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
        = ( dvd_dvd_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3979_dvd__add__right__iff) ).

thf(6264,axiom,
    ! [P4: nat,A: nat,B: nat] :
      ( ( dvd_dvd_nat @ P4 @ ( times_times_nat @ A @ B ) )
     => ~ ! [X4: nat,Y4: nat] :
            ( ( P4
              = ( times_times_nat @ X4 @ Y4 ) )
           => ( ( dvd_dvd_nat @ X4 @ A )
             => ~ ( dvd_dvd_nat @ Y4 @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3974_dvd__productE) ).

thf(6266,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
     => ? [B8: nat,C5: nat] :
          ( ( A
            = ( times_times_nat @ B8 @ C5 ) )
          & ( dvd_dvd_nat @ B8 @ B )
          & ( dvd_dvd_nat @ C5 @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3972_division__decomp) ).

thf(6268,axiom,
    ! [B: nat,A: nat] :
      ( ( dvd_dvd_nat @ B @ A )
     => ~ ! [K2: nat] :
            ( A
           != ( times_times_nat @ B @ K2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3970_dvdE) ).

thf(6273,axiom,
    ! [A: nat,B: nat,K: nat] :
      ( ( A
        = ( times_times_nat @ B @ K ) )
     => ( dvd_dvd_nat @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3965_dvdI) ).

thf(6278,axiom,
    ( dvd_dvd_nat
    = ( ^ [B5: nat,A5: nat] :
        ? [K3: nat] :
          ( A5
          = ( times_times_nat @ B5 @ K3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3960_dvd__def) ).

thf(6283,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( ( dvd_dvd_nat @ A @ C )
     => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3955_dvd__mult) ).

thf(6288,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( dvd_dvd_nat @ A @ B )
     => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3950_dvd__mult2) ).

thf(6293,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
     => ( dvd_dvd_nat @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3945_dvd__mult__left) ).

thf(6298,axiom,
    ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3940_dvd__triv__left) ).

thf(6303,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( dvd_dvd_nat @ A @ B )
     => ( ( dvd_dvd_nat @ C @ D )
       => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3935_mult__dvd__mono) ).

thf(6308,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
     => ( dvd_dvd_nat @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3930_dvd__mult__right) ).

thf(6313,axiom,
    ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3925_dvd__triv__right) ).

thf(6364,axiom,
    ! [A: nat,B: nat] :
      ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) )
      = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
       != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3874_odd__add) ).

thf(6367,axiom,
    ! [A: nat,B: nat] :
      ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) )
      = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
        = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3871_even__add) ).

thf(6370,axiom,
    ! [A: nat,B: nat] :
      ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
      = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
        | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3868_even__mult__iff) ).

thf(6400,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( ( dvd_dvd_nat @ C @ A )
     => ( ( dvd_dvd_nat @ C @ B )
       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
          = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3838_div__add) ).

thf(6403,axiom,
    ! [A: nat,B: nat] :
      ( ( dvd_dvd_nat @ A @ B )
     => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3835_dvd__div__mult__self) ).

thf(6406,axiom,
    ! [A: nat,B: nat] :
      ( ( dvd_dvd_nat @ A @ B )
     => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3832_dvd__mult__div__cancel) ).

thf(6412,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
      = ( dvd_dvd_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3826_dvd__add__times__triv__left__iff) ).

thf(6417,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
      = ( dvd_dvd_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3821_dvd__add__times__triv__right__iff) ).

thf(6444,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( dvd_dvd_nat @ A @ B )
     => ( ( dvd_dvd_nat @ A @ C )
       => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B @ A ) @ ( divide_divide_nat @ C @ A ) )
          = ( dvd_dvd_nat @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3794_div__dvd__div) ).

thf(6449,axiom,
    ! [A: nat,B: nat] :
      ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
      = ( dvd_dvd_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3789_dvd__add__triv__left__iff) ).

thf(6454,axiom,
    ! [A: nat,B: nat] :
      ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
      = ( dvd_dvd_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3784_dvd__add__triv__right__iff) ).

thf(6480,axiom,
    ! [P: nat > nat > $o,A: nat,B: nat] :
      ( ! [A3: nat,B2: nat] :
          ( ( P @ A3 @ B2 )
          = ( P @ B2 @ A3 ) )
     => ( ! [A3: nat] : ( P @ A3 @ zero_zero_nat )
       => ( ! [A3: nat,B2: nat] :
              ( ( P @ A3 @ B2 )
             => ( P @ A3 @ ( plus_plus_nat @ A3 @ B2 ) ) )
         => ( P @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3758_Euclid__induct) ).

thf(6909,axiom,
    ! [X22: num] :
      ( one
     != ( bit0 @ X22 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3329_verit__eq__simplify_I10_J) ).

thf(6911,axiom,
    ! [A: nat] :
      ( ( plus_plus_nat @ A @ zero_zero_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3327_verit__sum__simplify) ).

thf(6985,axiom,
    ! [X22: num,Y22: num] :
      ( ( ( bit0 @ X22 )
        = ( bit0 @ Y22 ) )
      = ( X22 = Y22 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3253_verit__eq__simplify_I8_J) ).

thf(6989,axiom,
    ! [A2: nat,N2: nat] :
      ( A2
      = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ N2 ) @ N2 ) @ ( modulo_modulo_nat @ A2 @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3249_div__mod__decomp) ).

thf(7049,axiom,
    ! [A: nat,N2: nat,M: nat] :
      ( ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
      = ( divide_divide_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3189_div__exp__mod__exp__eq) ).

thf(7070,axiom,
    ! [M: nat,N2: nat] :
      ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
       != zero_zero_nat )
     => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
       != zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3168_exp__add__not__zero__imp__left) ).

thf(7072,axiom,
    ! [M: nat,N2: nat] :
      ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
       != zero_zero_nat )
     => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
       != zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3166_exp__add__not__zero__imp__right) ).

thf(7140,axiom,
    ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
    = zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3098_zero__power2) ).

thf(7465,axiom,
    ! [M: nat,N2: nat,Q2: nat] :
      ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N2 @ Q2 ) )
      = ( plus_plus_nat @ ( times_times_nat @ N2 @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N2 ) @ Q2 ) ) @ ( modulo_modulo_nat @ M @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2773_mod__mult2__eq) ).

thf(7480,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
      = ( plus_plus_nat @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2758_cancel__div__mod__rules_I2_J) ).

thf(7483,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
      = ( plus_plus_nat @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2755_cancel__div__mod__rules_I1_J) ).

thf(7486,axiom,
    ! [A: nat,B: nat] :
      ( A
      = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2752_mod__div__decomp) ).

thf(7489,axiom,
    ! [A: nat,B: nat] :
      ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2749_div__mult__mod__eq) ).

thf(7492,axiom,
    ! [A: nat,B: nat] :
      ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2746_mod__div__mult__eq) ).

thf(7495,axiom,
    ! [A: nat,B: nat] :
      ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2743_mod__mult__div__eq) ).

thf(7498,axiom,
    ! [B: nat,A: nat] :
      ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2740_mult__div__mod__eq) ).

thf(7501,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
      = ( plus_plus_nat @ ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2737_div__mult1__eq) ).

thf(7862,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
      = ( plus_plus_nat @ ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2376_div__add1__eq) ).

thf(7867,axiom,
    ! [M: num,Q2: num] :
      ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
     != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2371_cong__exp__iff__simps_I8_J) ).

thf(7870,axiom,
    ! [Q2: num,N2: num] :
      ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
     != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2368_cong__exp__iff__simps_I6_J) ).

thf(7882,axiom,
    ( ( ^ [H: nat] : zero_zero_nat )
    = ( times_times_nat @ zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2356_lambda__zero) ).

thf(7898,axiom,
    ! [X: nat,N2: nat,Y: nat] :
      ( ( ( modulo_modulo_nat @ X @ N2 )
        = ( modulo_modulo_nat @ Y @ N2 ) )
      = ( ? [Q1: nat,Q22: nat] :
            ( ( plus_plus_nat @ X @ ( times_times_nat @ N2 @ Q1 ) )
            = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q22 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2340_nat__mod__eq__iff) ).

thf(7902,axiom,
    ! [K: nat,M: nat,N2: nat] :
      ( ( ( times_times_nat @ K @ M )
        = ( times_times_nat @ K @ N2 ) )
      = ( ( K = zero_zero_nat )
        | ( M = N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2336_nat__mult__eq__cancel__disj) ).

thf(7903,axiom,
    ! [N2: nat] :
      ( ( times_times_nat @ zero_zero_nat @ N2 )
      = zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2335_mult__0) ).

thf(7904,axiom,
    ! [N2: nat] :
      ( ( plus_plus_nat @ zero_zero_nat @ N2 )
      = N2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2334_plus__nat_Oadd__0) ).

thf(7905,axiom,
    ! [M: nat,N2: nat] :
      ( ( ( plus_plus_nat @ M @ N2 )
        = M )
     => ( N2 = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2333_add__eq__self__zero) ).

thf(7937,axiom,
    ! [A: nat,N2: nat] :
      ( ( A != zero_zero_nat )
     => ( ( power_power_nat @ A @ N2 )
       != zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2301_power__not__zero) ).

thf(7950,axiom,
    ! [A: nat] :
      ( ( plus_plus_nat @ zero_zero_nat @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2288_comm__monoid__add__class_Oadd__0) ).

thf(7955,axiom,
    ! [A: nat] :
      ( ( plus_plus_nat @ A @ zero_zero_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2283_add_Ocomm__neutral) ).

thf(7964,axiom,
    ! [A: nat,B: nat] :
      ( ( ( times_times_nat @ A @ B )
       != zero_zero_nat )
     => ( ( A != zero_zero_nat )
        & ( B != zero_zero_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2274_mult__not__zero) ).

thf(7969,axiom,
    ! [A: nat,B: nat] :
      ( ( ( times_times_nat @ A @ B )
        = zero_zero_nat )
     => ( ( A = zero_zero_nat )
        | ( B = zero_zero_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2269_divisors__zero) ).

thf(7974,axiom,
    ! [A: nat,B: nat] :
      ( ( A != zero_zero_nat )
     => ( ( B != zero_zero_nat )
       => ( ( times_times_nat @ A @ B )
         != zero_zero_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2264_no__zero__divisors) ).

thf(7979,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( ( C != zero_zero_nat )
     => ( ( ( times_times_nat @ C @ A )
          = ( times_times_nat @ C @ B ) )
        = ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2259_mult__left__cancel) ).

thf(7984,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( ( C != zero_zero_nat )
     => ( ( ( times_times_nat @ A @ C )
          = ( times_times_nat @ B @ C ) )
        = ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2254_mult__right__cancel) ).

thf(7990,axiom,
    ! [M: num,N2: num] :
      ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ one ) )
      = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ one ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2248_cong__exp__iff__simps_I4_J) ).

thf(7993,axiom,
    ! [M: num,Q2: num,N2: num] :
      ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
        = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
      = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
        = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2245_cong__exp__iff__simps_I9_J) ).

thf(7995,axiom,
    ! [N2: num] :
      ( zero_zero_nat
     != ( numeral_numeral_nat @ N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2243_zero__neq__numeral) ).

thf(8025,axiom,
    ! [A: nat,B: nat,N2: nat] :
      ( ( modulo_modulo_nat @ ( power_power_nat @ ( modulo_modulo_nat @ A @ B ) @ N2 ) @ B )
      = ( modulo_modulo_nat @ ( power_power_nat @ A @ N2 ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2213_power__mod) ).

thf(8036,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
      = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2202_mod__add__eq) ).

thf(8039,axiom,
    ! [A: nat,C: nat,A6: nat,B: nat,B6: nat] :
      ( ( ( modulo_modulo_nat @ A @ C )
        = ( modulo_modulo_nat @ A6 @ C ) )
     => ( ( ( modulo_modulo_nat @ B @ C )
          = ( modulo_modulo_nat @ B6 @ C ) )
       => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C )
          = ( modulo_modulo_nat @ ( plus_plus_nat @ A6 @ B6 ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2199_mod__add__cong) ).

thf(8042,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
      = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2196_mod__add__left__eq) ).

thf(8045,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
      = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2193_mod__add__right__eq) ).

thf(8048,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
      = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2190_mod__mult__eq) ).

thf(8051,axiom,
    ! [A: nat,C: nat,A6: nat,B: nat,B6: nat] :
      ( ( ( modulo_modulo_nat @ A @ C )
        = ( modulo_modulo_nat @ A6 @ C ) )
     => ( ( ( modulo_modulo_nat @ B @ C )
          = ( modulo_modulo_nat @ B6 @ C ) )
       => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C )
          = ( modulo_modulo_nat @ ( times_times_nat @ A6 @ B6 ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2187_mod__mult__cong) ).

thf(8054,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
      = ( times_times_nat @ ( modulo_modulo_nat @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2184_mod__mult__mult2) ).

thf(8057,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( ( times_times_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
      = ( modulo_modulo_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2181_mult__mod__right) ).

thf(8060,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
      = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2178_mod__mult__left__eq) ).

thf(8063,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
      = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2175_mod__mult__right__eq) ).

thf(8161,axiom,
    ! [A: nat] :
      ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
        = zero_zero_nat )
      = ( A = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2077_zero__eq__power2) ).

thf(8197,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( ( B != zero_zero_nat )
     => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
        = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2041_div__mult__self1) ).

thf(8199,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( ( B != zero_zero_nat )
     => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
        = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2039_div__mult__self2) ).

thf(8201,axiom,
    ! [B: nat,C: nat,A: nat] :
      ( ( B != zero_zero_nat )
     => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
        = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2037_div__mult__self3) ).

thf(8203,axiom,
    ! [B: nat,C: nat,A: nat] :
      ( ( B != zero_zero_nat )
     => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
        = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2035_div__mult__self4) ).

thf(8227,axiom,
    ! [K: nat,M: nat,N2: nat] :
      ( ( ( K = zero_zero_nat )
       => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
          = zero_zero_nat ) )
      & ( ( K != zero_zero_nat )
       => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
          = ( divide_divide_nat @ M @ N2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2011_nat__mult__div__cancel__disj) ).

thf(8263,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
      = ( modulo_modulo_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1975_mod__mult__self1) ).

thf(8266,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
      = ( modulo_modulo_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1972_mod__mult__self2) ).

thf(8269,axiom,
    ! [C: nat,B: nat,A: nat] :
      ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
      = ( modulo_modulo_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1969_mod__mult__self3) ).

thf(8272,axiom,
    ! [B: nat,C: nat,A: nat] :
      ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
      = ( modulo_modulo_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1966_mod__mult__self4) ).

thf(8298,axiom,
    ! [K: num] :
      ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
      = zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1940_power__zero__numeral) ).

thf(8351,axiom,
    ! [A: nat,B: nat] :
      ( ( A != zero_zero_nat )
     => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1887_nonzero__mult__div__cancel__left) ).

thf(8356,axiom,
    ! [B: nat,A: nat] :
      ( ( B != zero_zero_nat )
     => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1882_nonzero__mult__div__cancel__right) ).

thf(8361,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( ( C != zero_zero_nat )
     => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
        = ( divide_divide_nat @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1877_div__mult__mult1) ).

thf(8363,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( ( C != zero_zero_nat )
     => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
        = ( divide_divide_nat @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1875_div__mult__mult2) ).

thf(8365,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( ( ( C = zero_zero_nat )
       => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
          = zero_zero_nat ) )
      & ( ( C != zero_zero_nat )
       => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
          = ( divide_divide_nat @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1873_div__mult__mult1__if) ).

thf(8444,axiom,
    ! [M: nat,N2: nat] :
      ( ( ( times_times_nat @ M @ N2 )
        = zero_zero_nat )
      = ( ( M = zero_zero_nat )
        | ( N2 = zero_zero_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1794_mult__is__0) ).

thf(8445,axiom,
    ! [M: nat] :
      ( ( times_times_nat @ M @ zero_zero_nat )
      = zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1793_mult__0__right) ).

thf(8446,axiom,
    ! [K: nat,M: nat,N2: nat] :
      ( ( ( times_times_nat @ K @ M )
        = ( times_times_nat @ K @ N2 ) )
      = ( ( M = N2 )
        | ( K = zero_zero_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1792_mult__cancel1) ).

thf(8447,axiom,
    ! [M: nat,K: nat,N2: nat] :
      ( ( ( times_times_nat @ M @ K )
        = ( times_times_nat @ N2 @ K ) )
      = ( ( M = N2 )
        | ( K = zero_zero_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1791_mult__cancel2) ).

thf(8450,axiom,
    ! [M: nat,N2: nat] :
      ( ( ( plus_plus_nat @ M @ N2 )
        = zero_zero_nat )
      = ( ( M = zero_zero_nat )
        & ( N2 = zero_zero_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1788_add__is__0) ).

thf(8451,axiom,
    ! [M: nat] :
      ( ( plus_plus_nat @ M @ zero_zero_nat )
      = M ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1787_Nat_Oadd__0__right) ).

thf(8454,axiom,
    ! [B: nat,A: nat] :
      ( ( modulo_modulo_nat @ ( plus_plus_nat @ B @ A ) @ B )
      = ( modulo_modulo_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1784_mod__add__self1) ).

thf(8457,axiom,
    ! [A: nat,B: nat] :
      ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ B )
      = ( modulo_modulo_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1781_mod__add__self2) ).

thf(8479,axiom,
    ! [A: nat] :
      ( ( divide_divide_nat @ zero_zero_nat @ A )
      = zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1759_div__0) ).

thf(8484,axiom,
    ! [A: nat] :
      ( ( divide_divide_nat @ A @ zero_zero_nat )
      = zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1754_div__by__0) ).

thf(8489,axiom,
    ! [A: nat] :
      ( ( divide_divide_nat @ zero_zero_nat @ A )
      = zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1749_bits__div__0) ).

thf(8491,axiom,
    ! [A: nat] :
      ( ( divide_divide_nat @ A @ zero_zero_nat )
      = zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1747_bits__div__by__0) ).

thf(8512,axiom,
    ! [A: nat] :
      ( ( plus_plus_nat @ A @ zero_zero_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1726_add_Oright__neutral) ).

thf(8520,axiom,
    ! [B: nat,A: nat] :
      ( ( ( plus_plus_nat @ B @ A )
        = A )
      = ( B = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1718_add__cancel__left__left) ).

thf(8525,axiom,
    ! [A: nat,B: nat] :
      ( ( ( plus_plus_nat @ A @ B )
        = A )
      = ( B = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1713_add__cancel__left__right) ).

thf(8530,axiom,
    ! [A: nat,B: nat] :
      ( ( A
        = ( plus_plus_nat @ B @ A ) )
      = ( B = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1708_add__cancel__right__left) ).

thf(8535,axiom,
    ! [A: nat,B: nat] :
      ( ( A
        = ( plus_plus_nat @ A @ B ) )
      = ( B = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1703_add__cancel__right__right) ).

thf(8539,axiom,
    ! [X: nat,Y: nat] :
      ( ( ( plus_plus_nat @ X @ Y )
        = zero_zero_nat )
      = ( ( X = zero_zero_nat )
        & ( Y = zero_zero_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1699_add__eq__0__iff__both__eq__0) ).

thf(8540,axiom,
    ! [X: nat,Y: nat] :
      ( ( zero_zero_nat
        = ( plus_plus_nat @ X @ Y ) )
      = ( ( X = zero_zero_nat )
        & ( Y = zero_zero_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1698_zero__eq__add__iff__both__eq__0) ).

thf(8542,axiom,
    ! [A: nat] :
      ( ( plus_plus_nat @ zero_zero_nat @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1696_add__0) ).

thf(8547,axiom,
    ! [A: nat] :
      ( ( times_times_nat @ zero_zero_nat @ A )
      = zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1691_mult__zero__left) ).

thf(8552,axiom,
    ! [A: nat] :
      ( ( times_times_nat @ A @ zero_zero_nat )
      = zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1686_mult__zero__right) ).

thf(8557,axiom,
    ! [A: nat,B: nat] :
      ( ( ( times_times_nat @ A @ B )
        = zero_zero_nat )
      = ( ( A = zero_zero_nat )
        | ( B = zero_zero_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1681_mult__eq__0__iff) ).

thf(8562,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( ( ( times_times_nat @ C @ A )
        = ( times_times_nat @ C @ B ) )
      = ( ( C = zero_zero_nat )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1676_mult__cancel__left) ).

thf(8567,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( ( ( times_times_nat @ A @ C )
        = ( times_times_nat @ B @ C ) )
      = ( ( C = zero_zero_nat )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1671_mult__cancel__right) ).

thf(8589,axiom,
    ( vEBT_VEBT_low
    = ( ^ [X2: nat,N: nat] : ( modulo_modulo_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1649_low__def) ).

thf(8648,axiom,
    ! [X: nat,Y: nat,Z: nat] :
      ( ( plus_plus_nat @ X @ ( ord_max_nat @ Y @ Z ) )
      = ( ord_max_nat @ ( plus_plus_nat @ X @ Y ) @ ( plus_plus_nat @ X @ Z ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1590_max__add__distrib__right) ).

thf(8652,axiom,
    ! [X: nat,Y: nat,Z: nat] :
      ( ( plus_plus_nat @ ( ord_max_nat @ X @ Y ) @ Z )
      = ( ord_max_nat @ ( plus_plus_nat @ X @ Z ) @ ( plus_plus_nat @ Y @ Z ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1586_max__add__distrib__left) ).

thf(8662,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
      = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1576_diff__diff__eq) ).

thf(8666,axiom,
    ! [C: nat,B: nat,A: nat] :
      ( ( ( plus_plus_nat @ C @ B )
        = A )
     => ( C
        = ( minus_minus_nat @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1572_add__implies__diff) ).

thf(8700,axiom,
    ! [A: nat] :
      ( ( times_times_nat @ A @ one_one_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1538_mult_Ocomm__neutral) ).

thf(8705,axiom,
    ! [A: nat] :
      ( ( times_times_nat @ one_one_nat @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1533_comm__monoid__mult__class_Omult__1) ).

thf(8734,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
     => ( ord_less_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1504_add__less__imp__less__right) ).

thf(8738,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
     => ( ord_less_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1500_add__less__imp__less__left) ).

thf(8742,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1496_add__strict__right__mono) ).

thf(8746,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1492_add__strict__left__mono) ).

thf(8750,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_nat @ A @ B )
     => ( ( ord_less_nat @ C @ D )
       => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1488_add__strict__mono) ).

thf(8754,axiom,
    ! [I2: nat,J: nat,K: nat,L2: nat] :
      ( ( ( ord_less_nat @ I2 @ J )
        & ( K = L2 ) )
     => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1484_add__mono__thms__linordered__field_I1_J) ).

thf(8758,axiom,
    ! [I2: nat,J: nat,K: nat,L2: nat] :
      ( ( ( I2 = J )
        & ( ord_less_nat @ K @ L2 ) )
     => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1480_add__mono__thms__linordered__field_I2_J) ).

thf(8762,axiom,
    ! [I2: nat,J: nat,K: nat,L2: nat] :
      ( ( ( ord_less_nat @ I2 @ J )
        & ( ord_less_nat @ K @ L2 ) )
     => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1476_add__mono__thms__linordered__field_I5_J) ).

thf(8766,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
     => ( ord_less_eq_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1472_add__le__imp__le__right) ).

thf(8770,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
     => ( ord_less_eq_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1468_add__le__imp__le__left) ).

thf(8773,axiom,
    ( ord_less_eq_nat
    = ( ^ [A5: nat,B5: nat] :
        ? [C4: nat] :
          ( B5
          = ( plus_plus_nat @ A5 @ C4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1465_le__iff__add) ).

thf(8775,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1463_add__right__mono) ).

thf(8778,axiom,
    ! [A: nat,B: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ~ ! [C3: nat] :
            ( B
           != ( plus_plus_nat @ A @ C3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1460_less__eqE) ).

thf(8780,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1458_add__left__mono) ).

thf(8784,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ord_less_eq_nat @ A @ B )
     => ( ( ord_less_eq_nat @ C @ D )
       => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1454_add__mono) ).

thf(8788,axiom,
    ! [I2: nat,J: nat,K: nat,L2: nat] :
      ( ( ( ord_less_eq_nat @ I2 @ J )
        & ( ord_less_eq_nat @ K @ L2 ) )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1450_add__mono__thms__linordered__semiring_I1_J) ).

thf(8792,axiom,
    ! [I2: nat,J: nat,K: nat,L2: nat] :
      ( ( ( I2 = J )
        & ( ord_less_eq_nat @ K @ L2 ) )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1446_add__mono__thms__linordered__semiring_I2_J) ).

thf(8796,axiom,
    ! [I2: nat,J: nat,K: nat,L2: nat] :
      ( ( ( ord_less_eq_nat @ I2 @ J )
        & ( K = L2 ) )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1442_add__mono__thms__linordered__semiring_I3_J) ).

thf(8812,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( ( ( plus_plus_nat @ B @ A )
        = ( plus_plus_nat @ C @ A ) )
     => ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1426_add__right__imp__eq) ).

thf(8816,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( plus_plus_nat @ A @ B )
        = ( plus_plus_nat @ A @ C ) )
     => ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1422_add__left__imp__eq) ).

thf(8820,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
      = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1418_add_Oleft__commute) ).

thf(8824,axiom,
    ( plus_plus_nat
    = ( ^ [A5: nat,B5: nat] : ( plus_plus_nat @ B5 @ A5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1414_add_Ocommute) ).

thf(8834,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
      = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1404_add_Oassoc) ).

thf(8838,axiom,
    ! [B3: nat,K: nat,B: nat,A: nat] :
      ( ( B3
        = ( plus_plus_nat @ K @ B ) )
     => ( ( plus_plus_nat @ A @ B3 )
        = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1400_group__cancel_Oadd2) ).

thf(8842,axiom,
    ! [A2: nat,K: nat,A: nat,B: nat] :
      ( ( A2
        = ( plus_plus_nat @ K @ A ) )
     => ( ( plus_plus_nat @ A2 @ B )
        = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1396_group__cancel_Oadd1) ).

thf(8846,axiom,
    ! [I2: nat,J: nat,K: nat,L2: nat] :
      ( ( ( I2 = J )
        & ( K = L2 ) )
     => ( ( plus_plus_nat @ I2 @ K )
        = ( plus_plus_nat @ J @ L2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1392_add__mono__thms__linordered__semiring_I4_J) ).

thf(8850,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
      = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1388_ab__semigroup__add__class_Oadd__ac_I1_J) ).

thf(8854,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
      = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1384_mult_Oleft__commute) ).

thf(8858,axiom,
    ( times_times_nat
    = ( ^ [A5: nat,B5: nat] : ( times_times_nat @ B5 @ A5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1380_mult_Ocommute) ).

thf(8862,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
      = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1376_mult_Oassoc) ).

thf(8866,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
      = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1372_ab__semigroup__mult__class_Omult__ac_I1_J) ).

thf(8890,axiom,
    ! [A: nat] :
      ( ( times_times_nat @ one_one_nat @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1348_mult__1) ).

thf(8895,axiom,
    ! [A: nat] :
      ( ( times_times_nat @ A @ one_one_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1343_mult_Oright__neutral) ).

thf(8900,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
      = ( ord_less_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1338_add__less__cancel__right) ).

thf(8904,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
      = ( ord_less_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1334_add__less__cancel__left) ).

thf(8908,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
      = ( ord_less_eq_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1330_add__le__cancel__right) ).

thf(8912,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
      = ( ord_less_eq_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1326_add__le__cancel__left) ).

thf(8916,axiom,
    ! [B: nat,A: nat,C: nat] :
      ( ( ( plus_plus_nat @ B @ A )
        = ( plus_plus_nat @ C @ A ) )
      = ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1322_add__right__cancel) ).

thf(8920,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( plus_plus_nat @ A @ B )
        = ( plus_plus_nat @ A @ C ) )
      = ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1318_add__left__cancel) ).

thf(8936,axiom,
    ! [C: nat,A: nat,B: nat] :
      ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
      = ( minus_minus_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1302_add__diff__cancel__left) ).

thf(8940,axiom,
    ! [A: nat,B: nat] :
      ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1298_add__diff__cancel__left_H) ).

thf(8944,axiom,
    ! [A: nat,C: nat,B: nat] :
      ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
      = ( minus_minus_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1294_add__diff__cancel__right) ).

thf(8948,axiom,
    ! [A: nat,B: nat] :
      ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1290_add__diff__cancel__right_H) ).

thf(8951,axiom,
    ! [M: nat,N2: nat] :
      ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
     != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1287_Suc__double__not__eq__double) ).

thf(8952,axiom,
    ! [M: nat,N2: nat] :
      ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
     != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1286_double__not__eq__Suc__double) ).

thf(9048,axiom,
    ! [C: nat] :
      ( ( ^ [X2: nat] : ( times_times_nat @ X2 @ C ) )
      = ( times_times_nat @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1190_mult__commute__abs) ).

thf(9257,axiom,
    ( ( ^ [X2: nat] : X2 )
    = ( times_times_nat @ one_one_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_981_lambda__one) ).

thf(9262,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
      = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_976_right__diff__distrib_H) ).

thf(9266,axiom,
    ! [B: nat,C: nat,A: nat] :
      ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
      = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_972_left__diff__distrib_H) ).

thf(9276,axiom,
    ! [A: nat,E: nat,B: nat,C: nat] :
      ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C ) )
      = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_962_combine__common__factor) ).

thf(9280,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
      = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_958_distrib__right) ).

thf(9284,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
      = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_954_distrib__left) ).

thf(9288,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
      = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_950_comm__semiring__class_Odistrib) ).

thf(9301,axiom,
    ! [M: nat,N2: nat,Q2: nat] :
      ( ( times_times_nat @ M @ ( ord_max_nat @ N2 @ Q2 ) )
      = ( ord_max_nat @ ( times_times_nat @ M @ N2 ) @ ( times_times_nat @ M @ Q2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_937_nat__mult__max__right) ).

thf(9302,axiom,
    ! [M: nat,N2: nat,Q2: nat] :
      ( ( times_times_nat @ ( ord_max_nat @ M @ N2 ) @ Q2 )
      = ( ord_max_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N2 @ Q2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_936_nat__mult__max__left) ).

thf(9303,axiom,
    ! [M: nat,N2: nat,Q2: nat] :
      ( ( plus_plus_nat @ M @ ( ord_max_nat @ N2 @ Q2 ) )
      = ( ord_max_nat @ ( plus_plus_nat @ M @ N2 ) @ ( plus_plus_nat @ M @ Q2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_935_nat__add__max__right) ).

thf(9304,axiom,
    ! [M: nat,N2: nat,Q2: nat] :
      ( ( plus_plus_nat @ ( ord_max_nat @ M @ N2 ) @ Q2 )
      = ( ord_max_nat @ ( plus_plus_nat @ M @ Q2 ) @ ( plus_plus_nat @ N2 @ Q2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_934_nat__add__max__left) ).

thf(9321,axiom,
    ! [A: nat] :
      ( ( divide_divide_nat @ A @ one_one_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_917_div__by__1) ).

thf(9361,axiom,
    ! [N2: nat] :
      ( ( times_times_nat @ one_one_nat @ N2 )
      = N2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_877_nat__mult__1) ).

thf(9362,axiom,
    ! [N2: nat] :
      ( ( times_times_nat @ N2 @ one_one_nat )
      = N2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_876_nat__mult__1__right) ).

thf(9363,axiom,
    ! [M: nat,N2: nat,K: nat] :
      ( ( times_times_nat @ ( plus_plus_nat @ M @ N2 ) @ K )
      = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_875_add__mult__distrib) ).

thf(9364,axiom,
    ! [K: nat,M: nat,N2: nat] :
      ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N2 ) )
      = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_874_add__mult__distrib2) ).

thf(9365,axiom,
    ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_873_le__cube) ).

thf(9366,axiom,
    ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_872_le__square) ).

thf(9367,axiom,
    ! [I2: nat,J: nat,K: nat,L2: nat] :
      ( ( ord_less_eq_nat @ I2 @ J )
     => ( ( ord_less_eq_nat @ K @ L2 )
       => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ L2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_871_mult__le__mono) ).

thf(9368,axiom,
    ! [I2: nat,J: nat,K: nat] :
      ( ( ord_less_eq_nat @ I2 @ J )
     => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ K ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_870_mult__le__mono1) ).

thf(9369,axiom,
    ! [I2: nat,J: nat,K: nat] :
      ( ( ord_less_eq_nat @ I2 @ J )
     => ( ord_less_eq_nat @ ( times_times_nat @ K @ I2 ) @ ( times_times_nat @ K @ J ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_869_mult__le__mono2) ).

thf(9370,axiom,
    ! [M: nat,K: nat,N2: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
     => ~ ( ( ord_less_eq_nat @ M @ N2 )
         => ~ ( ord_less_eq_nat @ K @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_868_add__leE) ).

thf(9371,axiom,
    ! [N2: nat,M: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ N2 @ M ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_867_le__add1) ).

thf(9372,axiom,
    ! [N2: nat,M: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ M @ N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_866_le__add2) ).

thf(9373,axiom,
    ! [M: nat,K: nat,N2: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
     => ( ord_less_eq_nat @ M @ N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_865_add__leD1) ).

thf(9374,axiom,
    ! [M: nat,K: nat,N2: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
     => ( ord_less_eq_nat @ K @ N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_864_add__leD2) ).

thf(9375,axiom,
    ! [K: nat,L2: nat] :
      ( ( ord_less_eq_nat @ K @ L2 )
     => ? [N4: nat] :
          ( L2
          = ( plus_plus_nat @ K @ N4 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_863_le__Suc__ex) ).

thf(9376,axiom,
    ! [I2: nat,J: nat,K: nat,L2: nat] :
      ( ( ord_less_eq_nat @ I2 @ J )
     => ( ( ord_less_eq_nat @ K @ L2 )
       => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_862_add__le__mono) ).

thf(9377,axiom,
    ! [I2: nat,J: nat,K: nat] :
      ( ( ord_less_eq_nat @ I2 @ J )
     => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_861_add__le__mono1) ).

thf(9378,axiom,
    ! [I2: nat,J: nat,M: nat] :
      ( ( ord_less_eq_nat @ I2 @ J )
     => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_860_trans__le__add1) ).

thf(9379,axiom,
    ! [I2: nat,J: nat,M: nat] :
      ( ( ord_less_eq_nat @ I2 @ J )
     => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_859_trans__le__add2) ).

thf(9380,axiom,
    ( ord_less_eq_nat
    = ( ^ [M6: nat,N: nat] :
        ? [K3: nat] :
          ( N
          = ( plus_plus_nat @ M6 @ K3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_858_nat__le__iff__add) ).

thf(9381,axiom,
    ! [I2: nat,J: nat,K: nat] :
      ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ K )
     => ( ord_less_nat @ I2 @ K ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_857_add__lessD1) ).

thf(9382,axiom,
    ! [I2: nat,J: nat,K: nat,L2: nat] :
      ( ( ord_less_nat @ I2 @ J )
     => ( ( ord_less_nat @ K @ L2 )
       => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_856_add__less__mono) ).

thf(9383,axiom,
    ! [I2: nat,J: nat] :
      ~ ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ I2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_855_not__add__less1) ).

thf(9384,axiom,
    ! [J: nat,I2: nat] :
      ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I2 ) @ I2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_854_not__add__less2) ).

thf(9385,axiom,
    ! [I2: nat,J: nat,K: nat] :
      ( ( ord_less_nat @ I2 @ J )
     => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_853_add__less__mono1) ).

thf(9386,axiom,
    ! [I2: nat,J: nat,M: nat] :
      ( ( ord_less_nat @ I2 @ J )
     => ( ord_less_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_852_trans__less__add1) ).

thf(9387,axiom,
    ! [I2: nat,J: nat,M: nat] :
      ( ( ord_less_nat @ I2 @ J )
     => ( ord_less_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_851_trans__less__add2) ).

thf(9388,axiom,
    ! [K: nat,L2: nat,M: nat,N2: nat] :
      ( ( ord_less_nat @ K @ L2 )
     => ( ( ( plus_plus_nat @ M @ L2 )
          = ( plus_plus_nat @ K @ N2 ) )
       => ( ord_less_nat @ M @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_850_less__add__eq__less) ).

thf(9400,axiom,
    ! [A: nat,N2: nat] :
      ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
      = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_838_power__odd__eq) ).

thf(9445,axiom,
    ! [A: nat,N2: nat] :
      ( ( power_power_nat @ A @ ( suc @ N2 ) )
      = ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_793_power__Suc) ).

thf(9450,axiom,
    ! [A: nat,N2: nat] :
      ( ( power_power_nat @ A @ ( suc @ N2 ) )
      = ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_788_power__Suc2) ).

thf(9459,axiom,
    ! [Z: nat,W: num] :
      ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
      = ( times_times_nat @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_779_power__numeral__even) ).

thf(9466,axiom,
    ! [M: nat,N2: nat] :
      ( ( times_times_nat @ ( suc @ M ) @ N2 )
      = ( plus_plus_nat @ N2 @ ( times_times_nat @ M @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_772_mult__Suc) ).

thf(9513,axiom,
    ! [N2: num] :
      ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
      = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_725_numeral__code_I2_J) ).

thf(9521,axiom,
    ! [K: nat,M: nat,N2: nat] :
      ( ( ( times_times_nat @ ( suc @ K ) @ M )
        = ( times_times_nat @ ( suc @ K ) @ N2 ) )
      = ( M = N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_717_Suc__mult__cancel1) ).

thf(9522,axiom,
    ! [M: nat,N2: nat,K: nat] :
      ( ( times_times_nat @ ( minus_minus_nat @ M @ N2 ) @ K )
      = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_716_diff__mult__distrib) ).

thf(9523,axiom,
    ! [K: nat,M: nat,N2: nat] :
      ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
      = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_715_diff__mult__distrib2) ).

thf(9524,axiom,
    ! [A2: nat,K: nat,A: nat] :
      ( ( A2
        = ( plus_plus_nat @ K @ A ) )
     => ( ( suc @ A2 )
        = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_714_nat__arith_Osuc1) ).

thf(9525,axiom,
    ! [M: nat,N2: nat] :
      ( ( plus_plus_nat @ ( suc @ M ) @ N2 )
      = ( suc @ ( plus_plus_nat @ M @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_713_add__Suc) ).

thf(9526,axiom,
    ! [M: nat,N2: nat] :
      ( ( plus_plus_nat @ ( suc @ M ) @ N2 )
      = ( plus_plus_nat @ M @ ( suc @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_712_add__Suc__shift) ).

thf(9537,axiom,
    ! [K: nat,M: nat,N2: nat] :
      ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
      = ( minus_minus_nat @ M @ N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_701_Nat_Odiff__cancel) ).

thf(9538,axiom,
    ! [M: nat,K: nat,N2: nat] :
      ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) )
      = ( minus_minus_nat @ M @ N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_700_diff__cancel2) ).

thf(9539,axiom,
    ! [N2: nat,M: nat] :
      ( ( minus_minus_nat @ ( plus_plus_nat @ N2 @ M ) @ N2 )
      = M ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_699_diff__add__inverse) ).

thf(9540,axiom,
    ! [M: nat,N2: nat] :
      ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ N2 )
      = M ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_698_diff__add__inverse2) ).

thf(9590,axiom,
    ! [M: nat] :
      ( ( divide_divide_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
      = ( suc @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_648_div2__Suc__Suc) ).

thf(9591,axiom,
    ! [N2: nat] :
      ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
      = ( suc @ ( suc @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_647_add__2__eq__Suc) ).

thf(9592,axiom,
    ! [N2: nat] :
      ( ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
      = ( suc @ ( suc @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_646_add__2__eq__Suc_H) ).

thf(9602,axiom,
    ! [M: nat,N2: nat] :
      ( ( times_times_nat @ M @ ( suc @ N2 ) )
      = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_636_mult__Suc__right) ).

thf(9611,axiom,
    ! [M: nat,N2: nat] :
      ( ( ( times_times_nat @ M @ N2 )
        = one_one_nat )
      = ( ( M = one_one_nat )
        & ( N2 = one_one_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_627_nat__mult__eq__1__iff) ).

thf(9612,axiom,
    ! [I2: nat,J: nat,K: nat] :
      ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
      = ( minus_minus_nat @ I2 @ ( plus_plus_nat @ J @ K ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_626_diff__diff__left) ).

thf(9614,axiom,
    ! [K: nat,M: nat,N2: nat] :
      ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
      = ( ord_less_eq_nat @ M @ N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_624_nat__add__left__cancel__le) ).

thf(9617,axiom,
    ! [K: nat,M: nat,N2: nat] :
      ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
      = ( ord_less_nat @ M @ N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_621_nat__add__left__cancel__less) ).

thf(9618,axiom,
    ! [M: nat,N2: nat] :
      ( ( plus_plus_nat @ M @ ( suc @ N2 ) )
      = ( suc @ ( plus_plus_nat @ M @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_620_add__Suc__right) ).

thf(9634,axiom,
    ! [X: nat] :
      ( ! [N4: nat] :
          ( X
         != ( plus_plus_nat @ N4 @ N4 ) )
     => ~ ! [N4: nat] :
            ( X
           != ( plus_plus_nat @ N4 @ ( suc @ N4 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_604_even__odd__cases) ).

thf(9635,axiom,
    ! [M: nat,N2: nat] :
      ( ( one_one_nat
        = ( times_times_nat @ M @ N2 ) )
      = ( ( M = one_one_nat )
        & ( N2 = one_one_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_603_nat__1__eq__mult__iff) ).

thf(9682,axiom,
    ! [I2: nat,U: nat,J: nat,K: nat] :
      ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
      = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I2 @ J ) @ U ) @ K ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_556_left__add__mult__distrib) ).

thf(9683,axiom,
    ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
    = ( numeral_numeral_nat @ ( bit0 @ one ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_555_nat__1__add__1) ).

thf(9687,axiom,
    ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
    = one_one_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_551_one__power2) ).

thf(9719,axiom,
    ( ( numeral_numeral_nat @ one )
    = one_one_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_519_numerals_I1_J) ).

thf(9724,axiom,
    ! [X: nat,Y: nat,N2: nat] :
      ( ( ( times_times_nat @ X @ Y )
        = one_one_nat )
     => ( ( times_times_nat @ ( power_power_nat @ X @ N2 ) @ ( power_power_nat @ Y @ N2 ) )
        = one_one_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_514_left__right__inverse__power) ).

thf(9733,axiom,
    ( ( numeral_numeral_nat @ one )
    = one_one_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_505_numeral__One) ).

thf(9738,axiom,
    ! [X: num] :
      ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
      = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_500_one__plus__numeral__commute) ).

thf(9766,axiom,
    ! [X: num] :
      ( ( ord_less_eq_num @ X @ one )
      = ( X = one ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_472_le__num__One__iff) ).

thf(9792,axiom,
    ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
    = ( numeral_numeral_nat @ ( bit0 @ one ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_446_one__add__one) ).

thf(9800,axiom,
    ! [M: num] :
      ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_438_semiring__norm_I69_J) ).

thf(9806,axiom,
    ! [N2: num] :
      ( ( ( numeral_numeral_nat @ N2 )
        = one_one_nat )
      = ( N2 = one ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_432_numeral__eq__one__iff) ).

thf(9811,axiom,
    ! [N2: num] :
      ( ( one_one_nat
        = ( numeral_numeral_nat @ N2 ) )
      = ( one = N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_427_one__eq__numeral__iff) ).

thf(9815,axiom,
    ! [N2: num] : ( ord_less_eq_num @ one @ N2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_423_semiring__norm_I68_J) ).

thf(9816,axiom,
    ! [M: num,N2: num] :
      ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
      = ( ord_less_eq_num @ M @ N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_422_semiring__norm_I71_J) ).

thf(9817,axiom,
    ! [N2: num] :
      ( ( times_times_num @ one @ N2 )
      = N2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_421_semiring__norm_I12_J) ).

thf(9818,axiom,
    ! [M: num] :
      ( ( times_times_num @ M @ one )
      = M ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_420_semiring__norm_I11_J) ).

thf(9819,axiom,
    ! [M: num,N2: num] :
      ( ( times_times_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
      = ( bit0 @ ( bit0 @ ( times_times_num @ M @ N2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_419_semiring__norm_I13_J) ).

thf(9820,axiom,
    ! [M: num,N2: num] :
      ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
      = ( bit0 @ ( plus_plus_num @ M @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_418_semiring__norm_I6_J) ).

thf(9824,axiom,
    ! [A: nat] :
      ( ( power_power_nat @ A @ one_one_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_414_power__one__right) ).

thf(9828,axiom,
    ! [N2: nat] :
      ( ( power_power_nat @ one_one_nat @ N2 )
      = one_one_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_410_power__one) ).

thf(9831,axiom,
    ! [A: nat] :
      ( ( divide_divide_nat @ A @ one_one_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_407_bits__div__by__1) ).

thf(9832,axiom,
    ! [M: num] :
      ( ( bit0 @ M )
     != one ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_406_semiring__norm_I85_J) ).

thf(9833,axiom,
    ! [N2: num] :
      ( one
     != ( bit0 @ N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_405_semiring__norm_I83_J) ).

thf(9834,axiom,
    ! [M: num,N2: num] :
      ( ( ( bit0 @ M )
        = ( bit0 @ N2 ) )
      = ( M = N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_404_semiring__norm_I87_J) ).

thf(9836,axiom,
    ! [M: num,N2: num] :
      ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
      = ( ord_less_num @ M @ N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_402_semiring__norm_I78_J) ).

thf(9837,axiom,
    ! [M: num] :
      ~ ( ord_less_num @ M @ one ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_401_semiring__norm_I75_J) ).

thf(9839,axiom,
    ( ( plus_plus_num @ one @ one )
    = ( bit0 @ one ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_399_semiring__norm_I2_J) ).

thf(9843,axiom,
    ! [N2: num] : ( ord_less_num @ one @ ( bit0 @ N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_395_semiring__norm_I76_J) ).

thf(9871,axiom,
    ! [Option: option_nat,Option2: option_nat] :
      ( ( ( Option = none_nat )
        = ( Option2 = none_nat ) )
     => ( ( ( Option != none_nat )
         => ( ( Option2 != none_nat )
           => ( ( the_nat @ Option )
              = ( the_nat @ Option2 ) ) ) )
       => ( Option = Option2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_367_option_Oexpand) ).

thf(9874,axiom,
    ! [X22: nat] :
      ( ( the_nat @ ( some_nat @ X22 ) )
      = X22 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_364_option_Osel) ).

thf(9902,axiom,
    ! [M: nat,N2: nat] :
      ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N2 )
     => ( ord_less_eq_nat @ M @ N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_power2__nat__le__imp__le) ).

thf(9903,axiom,
    ! [M: nat,N2: nat] :
      ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
      = ( ord_less_eq_nat @ M @ N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_power2__nat__le__eq__le) ).

thf(9904,axiom,
    ! [K: nat,M: nat] :
      ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
     => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_self__le__ge2__pow) ).

thf(9905,axiom,
    ! [I2: nat,I5: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT,X6: vEBT_VEBT] :
      ( ( I2 != I5 )
     => ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ X ) @ I5 @ X6 )
        = ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I5 @ X6 ) @ I2 @ X ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_list__update__swap) ).

thf(9912,axiom,
    ! [N2: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N2 @ ( divide_divide_nat @ M @ N2 ) ) @ M ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_times__div__less__eq__dividend) ).

thf(9913,axiom,
    ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N2 ) @ N2 ) @ M ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_div__times__less__eq__dividend) ).

thf(9948,axiom,
    ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N2 ) @ M ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_div__le__dividend) ).

thf(9949,axiom,
    ! [M: nat,N2: nat,K: nat] :
      ( ( ord_less_eq_nat @ M @ N2 )
     => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N2 @ K ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_div__le__mono) ).

thf(9972,axiom,
    vEBT_invar_vebt @ ( nth_VEBT_VEBT @ treeList @ maxs ) @ na,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266__092_060open_062invar__vebt_A_ItreeList_A_B_Amaxs_J_An_092_060close_062) ).

thf(9974,axiom,
    vEBT_invar_vebt @ ( nth_VEBT_VEBT @ treeList @ summin ) @ na,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264__092_060open_062invar__vebt_A_ItreeList_A_B_Asummin_J_An_092_060close_062) ).

thf(9977,axiom,
    ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_dp) ).

thf(9980,axiom,
    ! [Xs: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT,Y: vEBT_VEBT] :
      ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ X ) @ I2 @ Y )
      = ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_list__update__overwrite) ).

thf(10005,axiom,
    ! [Xs: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT] :
      ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ X ) )
      = ( size_s6755466524823107622T_VEBT @ Xs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_length__list__update) ).

thf(10006,axiom,
    ! [Xs: list_VEBT_VEBT,I2: nat] :
      ( ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ ( nth_VEBT_VEBT @ Xs @ I2 ) )
      = Xs ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_list__update__id) ).

thf(10008,axiom,
    ! [I2: nat,J: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
      ( ( I2 != J )
     => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ X ) @ J )
        = ( nth_VEBT_VEBT @ Xs @ J ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_nth__list__update__neq) ).

thf(10023,axiom,
    ! [A: complex,N2: nat] :
      ( ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
      = ( power_power_complex @ ( power_power_complex @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_power__even__eq) ).

thf(10024,axiom,
    ! [A: int,N2: nat] :
      ( ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
      = ( power_power_int @ ( power_power_int @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_power__even__eq) ).

thf(10025,axiom,
    ! [A: real,N2: nat] :
      ( ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
      = ( power_power_real @ ( power_power_real @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_power__even__eq) ).

thf(10026,axiom,
    ! [A: nat,N2: nat] :
      ( ( power_power_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
      = ( power_power_nat @ ( power_power_nat @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_power__even__eq) ).

thf(10028,axiom,
    ! [X: nat] :
      ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
      = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X @ X ) @ X ) @ X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_power4__eq__xxxx) ).

thf(10033,axiom,
    ! [A: nat] :
      ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
      = ( times_times_nat @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_power2__eq__square) ).

thf(10038,axiom,
    ! [Z: nat] :
      ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
      = ( plus_plus_nat @ Z @ Z ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_mult__2) ).

thf(10043,axiom,
    ! [Z: nat] :
      ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
      = ( plus_plus_nat @ Z @ Z ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_mult__2__right) ).

thf(10048,axiom,
    ! [A: nat,B: nat] :
      ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
      = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_left__add__twice) ).

thf(10053,axiom,
    ! [N2: num] :
      ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
      = ( numeral_numeral_nat @ N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_numeral__Bit0__div__2) ).

thf(10055,axiom,
    ! [A: nat,M: nat,N2: nat] :
      ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N2 ) )
      = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_power__add) ).

thf(10063,axiom,
    ! [N2: num] :
      ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
      = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_numeral__Bit0) ).

thf(10068,axiom,
    ! [A: nat] :
      ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_mult__numeral__1) ).

thf(10073,axiom,
    ! [A: nat] :
      ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_mult__numeral__1__right) ).

thf(10077,axiom,
    ! [M: nat,N2: nat,Q2: nat] :
      ( ( divide_divide_nat @ M @ ( times_times_nat @ N2 @ Q2 ) )
      = ( divide_divide_nat @ ( divide_divide_nat @ M @ N2 ) @ Q2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_div__mult2__eq) ).

thf(10078,axiom,
    ! [A: complex,M: nat,N2: nat] :
      ( ( power_power_complex @ A @ ( times_times_nat @ M @ N2 ) )
      = ( power_power_complex @ ( power_power_complex @ A @ M ) @ N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_power__mult) ).

thf(10079,axiom,
    ! [A: int,M: nat,N2: nat] :
      ( ( power_power_int @ A @ ( times_times_nat @ M @ N2 ) )
      = ( power_power_int @ ( power_power_int @ A @ M ) @ N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_power__mult) ).

thf(10080,axiom,
    ! [A: real,M: nat,N2: nat] :
      ( ( power_power_real @ A @ ( times_times_nat @ M @ N2 ) )
      = ( power_power_real @ ( power_power_real @ A @ M ) @ N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_power__mult) ).

thf(10081,axiom,
    ! [A: nat,M: nat,N2: nat] :
      ( ( power_power_nat @ A @ ( times_times_nat @ M @ N2 ) )
      = ( power_power_nat @ ( power_power_nat @ A @ M ) @ N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_power__mult) ).

thf(10086,axiom,
    ! [A: nat,N2: nat] :
      ( ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ A )
      = ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_power__commutes) ).

thf(10091,axiom,
    ! [A: nat,B: nat,N2: nat] :
      ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N2 )
      = ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_power__mult__distrib) ).

thf(10096,axiom,
    ! [X: nat,Y: nat,N2: nat] :
      ( ( ( times_times_nat @ X @ Y )
        = ( times_times_nat @ Y @ X ) )
     => ( ( times_times_nat @ ( power_power_nat @ X @ N2 ) @ Y )
        = ( times_times_nat @ Y @ ( power_power_nat @ X @ N2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_power__commuting__commutes) ).

thf(10103,axiom,
    ! [N2: nat] : ( ord_less_nat @ N2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_less__exp) ).

thf(10104,axiom,
    ! [M: nat,I2: nat,N2: nat] :
      ( ( ord_less_nat @ M @ ( times_times_nat @ I2 @ N2 ) )
     => ( ord_less_nat @ ( divide_divide_nat @ M @ N2 ) @ I2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_less__mult__imp__div__less) ).

thf(10106,axiom,
    ! [A: nat,K: num,L2: num] :
      ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ L2 ) )
      = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ K @ L2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_div__mult2__numeral__eq) ).

thf(10107,axiom,
    ! [N2: num] :
      ( ( plus_plus_num @ one @ N2 )
      = ( plus_plus_num @ N2 @ one ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_add__One__commute) ).

thf(10121,axiom,
    ! [A: nat,M: num,N2: num] :
      ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N2 ) ) )
      = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_power__add__numeral) ).

thf(10126,axiom,
    ! [A: nat,M: num,N2: num,B: nat] :
      ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
      = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_power__add__numeral2) ).

thf(10135,axiom,
    ! [A: nat,M: num,N2: num] :
      ( ( power_power_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) )
      = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_power__mult__numeral) ).

thf(10136,axiom,
    ! [N2: num] :
      ( ( times_times_num @ ( bit0 @ one ) @ N2 )
      = ( bit0 @ N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_num__double) ).

thf(10138,axiom,
    ! [M: num,N2: num] :
      ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
      = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_numeral__plus__numeral) ).

thf(10143,axiom,
    ! [V: num,W: num,Z: nat] :
      ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
      = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_add__numeral__left) ).

thf(10148,axiom,
    ! [M: num,N2: num] :
      ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
      = ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_numeral__times__numeral) ).

thf(10153,axiom,
    ! [V: num,W: num,Z: nat] :
      ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
      = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_mult__numeral__left__semiring__numeral) ).

thf(10157,axiom,
    ! [X: nat,N2: nat,Y: nat] :
      ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
     => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ X ) @ N2 )
        = X ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_low__inv) ).

thf(10179,axiom,
    ! [X: nat,N2: nat,Y: nat] :
      ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
     => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ X ) @ N2 )
        = Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_high__inv) ).

thf(10182,axiom,
    ~ ! [Maxi: nat] :
        ( ( some_nat @ Maxi )
       != ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ maxs ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062maxi_O_ASome_Amaxi_A_061_Avebt__maxt_A_ItreeList_A_B_Amaxs_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).

thf(10183,axiom,
    ! [Ma: nat,N2: nat,M: nat] :
      ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) )
     => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_high__bound__aux) ).

thf(10187,axiom,
    ! [M: num,N2: num] :
      ( ( ( numeral_numeral_nat @ M )
        = ( numeral_numeral_nat @ N2 ) )
      = ( M = N2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_numeral__eq__iff) ).

thf(10196,axiom,
    ! [A: nat,M: nat,N2: nat] :
      ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
      = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_div__exp__eq) ).

thf(10197,axiom,
    vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ summin ) @ lx,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41__092_060open_062vebt__member_A_ItreeList_A_B_Asummin_J_Alx_092_060close_062) ).

thf(10198,axiom,
    ord_less_nat @ maxi @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40__092_060open_062maxi_A_060_A2_A_094_An_092_060close_062) ).

thf(10200,axiom,
    ! [X: nat,Y: nat] :
      ( ( power_power_nat @ ( plus_plus_nat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
      = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_power2__sum) ).

thf(10205,axiom,
    ! [A: nat,B: nat,V: num] :
      ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
      = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_distrib__right__numeral) ).

thf(10210,axiom,
    ! [V: num,B: nat,C: nat] :
      ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
      = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_distrib__left__numeral) ).

thf(10214,axiom,
    ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
   != mi ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_minxnrel) ).

thf(10215,axiom,
    ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23__092_060open_062summin_A_K_A2_A_094_An_A_L_Alx_A_060_A2_A_094_Adeg_092_060close_062) ).

thf(10216,axiom,
    ~ ! [Maxs: nat] :
        ( ( some_nat @ Maxs )
       != ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062maxs_O_ASome_Amaxs_A_061_Avebt__maxt_A_Ivebt__delete_Asummary_A_Ihigh_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_J_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062) ).

thf(10217,axiom,
    ! [M: nat] :
      ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
      = M ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_add__self__div__2) ).

thf(10218,axiom,
    ( ( size_s6755466524823107622T_VEBT @ treeList )
    = ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20__092_060open_062length_AtreeList_A_061_Alength_A_ItreeList_A_091high_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_A_058_061_Avebt__delete_A_ItreeList_A_B_Ahigh_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_J_A_Ilow_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_J_093_J_092_060close_062) ).

thf(10219,axiom,
    ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
    = ma ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_True) ).

thf(10220,axiom,
    ( ( some_nat @ maxs )
    = ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18__092_060open_062Some_Amaxs_A_061_Avebt__maxt_A_Ivebt__delete_Asummary_A_Ihigh_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_J_J_092_060close_062) ).

thf(10221,axiom,
    ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) )
   != none_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_False) ).

thf(10222,axiom,
    ( ( some_nat @ maxi )
    = ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ maxs ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16__092_060open_062Some_Amaxi_A_061_Avebt__maxt_A_ItreeList_A_B_Amaxs_J_092_060close_062) ).

thf(10223,axiom,
    vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ maxs,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15__092_060open_062both__member__options_A_Ivebt__delete_Asummary_A_Ihigh_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_J_J_Amaxs_092_060close_062) ).

thf(10224,axiom,
    ( ( vEBT_V8194947554948674370ptions @ summary @ maxs )
    & ( maxs
     != ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14__092_060open_062both__member__options_Asummary_Amaxs_A_092_060and_062_Amaxs_A_092_060noteq_062_Ahigh_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_092_060close_062) ).

thf(10225,axiom,
    ( ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) ) )
    = ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ maxs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13__092_060open_062the_A_Ivebt__maxt_A_ItreeList_A_091high_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_A_058_061_Avebt__delete_A_ItreeList_A_B_Ahigh_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_J_A_Ilow_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_J_093_A_B_Athe_A_Ivebt__maxt_A_Ivebt__delete_Asummary_A_Ihigh_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_J_J_J_J_J_A_061_Athe_A_Ivebt__maxt_A_ItreeList_A_B_Amaxs_J_J_092_060close_062) ).

thf(10226,axiom,
    ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) )
    = ( nth_VEBT_VEBT @ treeList @ maxs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12__092_060open_062treeList_A_091high_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_A_058_061_Avebt__delete_A_ItreeList_A_B_Ahigh_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_J_A_Ilow_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_J_093_A_B_Athe_A_Ivebt__maxt_A_Ivebt__delete_Asummary_A_Ihigh_A_Isummin_A_K_A2_A_094_An_A_L_Alx_J_An_J_J_J_A_061_AtreeList_A_B_Amaxs_092_060close_062) ).

thf(10227,axiom,
    ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) )
    = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_hprolist) ).

thf(10228,axiom,
    ( vEBT_VEBT_bit_concat
    = ( ^ [H: nat,L: nat,D2: nat] : ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D2 ) ) @ L ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_bit__concat__def) ).

thf(10229,axiom,
    ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ maxs ) @ X_1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9__092_060open_062_092_060exists_062z_O_Aboth__member__options_A_ItreeList_A_B_Amaxs_J_Az_092_060close_062) ).

thf(10230,axiom,
    ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ summin ) @ X_1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8__092_060open_062_092_060exists_062z_O_Aboth__member__options_A_ItreeList_A_B_Asummin_J_Az_092_060close_062) ).

thf(10231,axiom,
    ( deg
    = ( plus_plus_nat @ na @ m ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7__C4_Ohyps_C_I4_J) ).

thf(10232,axiom,
    ( ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
    = na ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__092_060open_062deg_Adiv_A2_A_061_An_092_060close_062) ).

thf(10233,axiom,
    ( vEBT_VEBT_high
    = ( ^ [X2: nat,N: nat] : ( divide_divide_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_high__def) ).

thf(10234,axiom,
    ! [A: nat,B: nat] :
      ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
      = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_pow__sum) ).

thf(10235,axiom,
    ! [X: nat,Y: nat] :
      ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ X ) @ Y )
      = ( ( X != Y )
        & ( vEBT_V8194947554948674370ptions @ summary @ Y ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__C4_OIH_C_I2_J) ).

thf(10236,axiom,
    ! [X: nat,D: nat] :
      ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X @ D ) @ ( vEBT_VEBT_low @ X @ D ) @ D )
      = X ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_bit__split__inv) ).

thf(10237,axiom,
    vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ maxs ) @ maxi,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062both__member__options_A_ItreeList_A_B_Amaxs_J_Amaxi_092_060close_062) ).

thf(10238,axiom,
    m = na,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__C4_Ohyps_C_I3_J) ).

thf(10239,conjecture,
    ( ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) ) ) )
    = ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) @ maxs ) @ maxi ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(10240,negated_conjecture,
    ( ( ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) ) ) )
      = ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) @ maxs ) @ maxi ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[10239]) ).

thf(10241,plain,
    ( ( ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) ) ) )
      = ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) @ maxs ) @ maxi ) )
    = $false ),
    inference(unfold_def,[status(thm)],[10240]) ).

thf(10242,plain,
    ( ( ! [P: $o] :
          ( ( P = $true )
          | ( P = $false ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3]) ).

thf(10243,plain,
    ( ( ! [K: nat,M: nat,N2: nat] :
          ( ( times_times_nat @ K @ ( gcd_gcd_nat @ M @ N2 ) )
          = ( gcd_gcd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[402]) ).

thf(10244,plain,
    ( ( ! [Q2: num] :
          ( ( num_of_nat @ ( numeral_numeral_nat @ Q2 ) )
          = Q2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[413]) ).

thf(10245,plain,
    ( ( bit_se8570568707652914677it_nat
      = ( ^ [N: nat,M6: nat] : ( divide_divide_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[466]) ).

thf(10246,plain,
    ( ( bit_se547839408752420682it_nat
      = ( ^ [N: nat,M6: nat] : ( times_times_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[692]) ).

thf(10247,plain,
    ( ( ! [N2: num] :
          ( ( bit_or_not_num_neg @ ( bit0 @ N2 ) @ one )
          = ( bit0 @ one ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[770]) ).

thf(10248,plain,
    ( ( ( bit_or_not_num_neg @ one @ one )
      = one )
    = $true ),
    inference(unfold_def,[status(thm)],[773]) ).

thf(10249,plain,
    ( ( ! [X: num] :
          ( ( pow @ X @ one )
          = X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[834]) ).

thf(10250,plain,
    ( ( ( inc @ one )
      = ( bit0 @ one ) )
    = $true ),
    inference(unfold_def,[status(thm)],[862]) ).

thf(10251,plain,
    ( ( ! [P: num > $o,X: num] :
          ( ( P @ one )
         => ( ! [X4: num] :
                ( ( P @ X4 )
               => ( P @ ( inc @ X4 ) ) )
           => ( P @ X ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[864]) ).

thf(10252,plain,
    ( ( ! [M: nat,N2: nat,X: real] :
          ( ( root @ ( times_times_nat @ M @ N2 ) @ X )
          = ( root @ M @ ( root @ N2 @ X ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[997]) ).

thf(10253,plain,
    ( ( ! [M: nat,R: nat,K: nat] :
          ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R ) @ K ) @ ( plus_plus_nat @ M @ K ) ) @ ( binomial @ ( plus_plus_nat @ M @ K ) @ K ) )
          = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M @ R ) @ M ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1289]) ).

thf(10254,plain,
    ( ( ! [F: nat > nat,A2: set_nat,N2: nat] :
          ( ( power_power_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ N2 )
          = ( groups708209901874060359at_nat
            @ ^ [X2: nat] : ( power_power_nat @ ( F @ X2 ) @ N2 )
            @ A2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1604]) ).

thf(10255,plain,
    ( ( ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
          ( ( groups708209901874060359at_nat
            @ ^ [X2: nat] : ( times_times_nat @ ( G @ X2 ) @ ( H2 @ X2 ) )
            @ A2 )
          = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ A2 ) @ ( groups708209901874060359at_nat @ H2 @ A2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1607]) ).

thf(10256,plain,
    ( ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
      = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2069]) ).

thf(10257,plain,
    ( ( ! [F: nat > nat,A: nat,G: nat > nat,B: nat] :
          ( ( sums_nat @ F @ A )
         => ( ( sums_nat @ G @ B )
           => ( sums_nat
              @ ^ [N: nat] : ( plus_plus_nat @ ( F @ N ) @ ( G @ N ) )
              @ ( plus_plus_nat @ A @ B ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2385]) ).

thf(10258,plain,
    ( ( ! [F: nat > complex,K: nat] :
          ( ( summable_complex @ F )
         => ( summable_complex
            @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2534]) ).

thf(10259,plain,
    ( ( ! [F: nat > real,K: nat] :
          ( ( summable_real @ F )
         => ( summable_real
            @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2535]) ).

thf(10260,plain,
    ( ( ! [F: nat > nat,G: nat > nat] :
          ( ( summable_nat @ F )
         => ( ( summable_nat @ G )
           => ( summable_nat
              @ ^ [N: nat] : ( plus_plus_nat @ ( F @ N ) @ ( G @ N ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2547]) ).

thf(10261,plain,
    ( ( ! [F: nat > complex,K: nat] :
          ( ( summable_complex
            @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
          = ( summable_complex @ F ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2558]) ).

thf(10262,plain,
    ( ( ! [F: nat > real,K: nat] :
          ( ( summable_real
            @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
          = ( summable_real @ F ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2559]) ).

thf(10263,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ M @ N2 ) )
          = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2949]) ).

thf(10264,plain,
    ( ( ! [A: nat,M: nat,N2: nat] :
          ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) )
          = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2963]) ).

thf(10265,plain,
    ( ( ( bitM @ one )
      = one )
    = $true ),
    inference(unfold_def,[status(thm)],[2978]) ).

thf(10266,plain,
    ( ( ! [X: nat,Y: nat] :
          ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X ) @ Y )
          = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[2981]) ).

thf(10267,plain,
    ( ( ! [Y: nat,X: num,N2: nat] :
          ( ( ( semiri1316708129612266289at_nat @ Y )
            = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) )
          = ( Y
            = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3125]) ).

thf(10268,plain,
    ( ( ! [X: num,N2: nat,Y: nat] :
          ( ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 )
            = ( semiri1316708129612266289at_nat @ Y ) )
          = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 )
            = Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3130]) ).

thf(10269,plain,
    ( ( ! [X: nat,B: nat,W: nat] :
          ( ( ( semiri1316708129612266289at_nat @ X )
            = ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
          = ( X
            = ( power_power_nat @ B @ W ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3239]) ).

thf(10270,plain,
    ( ( ! [B: nat,W: nat,X: nat] :
          ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W )
            = ( semiri1316708129612266289at_nat @ X ) )
          = ( ( power_power_nat @ B @ W )
            = X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3243]) ).

thf(10271,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ M @ N2 ) )
          = ( power_power_nat @ ( semiri1316708129612266289at_nat @ M ) @ N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3247]) ).

thf(10272,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N2 ) )
          = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3266]) ).

thf(10273,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N2 ) )
          = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3271]) ).

thf(10274,plain,
    ( ( ! [N2: num] :
          ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N2 ) )
          = ( numeral_numeral_nat @ N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3284]) ).

thf(10275,plain,
    ( ( ! [A: nat] :
          ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
          = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3495]) ).

thf(10276,plain,
    ( ( ! [N2: num] :
          ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( numeral_numeral_nat @ N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3506]) ).

thf(10277,plain,
    ( ( ! [Z: nat,W: num] :
          ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
          = ( times_times_nat @ ( times_times_nat @ Z @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3534]) ).

thf(10278,plain,
    ( ( ! [Y: num] :
          ( ( Y != one )
         => ( ! [X23: num] :
                ( Y
               != ( bit0 @ X23 ) )
           => ~ ! [X33: num] :
                  ( Y
                 != ( bit1 @ X33 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3646]) ).

thf(10279,plain,
    ( ( ! [X32: num] :
          ( one
         != ( bit1 @ X32 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3716]) ).

thf(10280,plain,
    ( ( ! [X22: num,X32: num] :
          ( ( bit0 @ X22 )
         != ( bit1 @ X32 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3717]) ).

thf(10281,plain,
    ( ( ! [N2: num] :
          ( one
         != ( bit1 @ N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3911]) ).

thf(10282,plain,
    ( ( ! [M: num] :
          ( ( bit1 @ M )
         != one ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3912]) ).

thf(10283,plain,
    ( ( ! [M: num,N2: num] :
          ( ( bit0 @ M )
         != ( bit1 @ N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3913]) ).

thf(10284,plain,
    ( ( ! [M: num,N2: num] :
          ( ( bit1 @ M )
         != ( bit0 @ N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3914]) ).

thf(10285,plain,
    ( ( ! [W: nat,Y: nat,X: nat,Z: nat] :
          ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y ) @ ( times_times_nat @ X @ Z ) )
            = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X @ Y ) ) )
          = ( ( W = X )
            | ( Y = Z ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3967]) ).

thf(10286,plain,
    ( ( ! [A: nat,B: nat,C: nat,D: nat] :
          ( ( ( A != B )
            & ( C != D ) )
          = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) )
           != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B @ C ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3971]) ).

thf(10287,plain,
    ( ( ! [B: nat,A: nat] :
          ( ( B
            = ( plus_plus_nat @ B @ A ) )
          = ( A = zero_zero_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[3975]) ).

thf(10288,plain,
    ( ( ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
          ( ( groups3542108847815614940at_nat
            @ ^ [X2: nat] : ( plus_plus_nat @ ( G @ X2 ) @ ( H2 @ X2 ) )
            @ A2 )
          = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ A2 ) @ ( groups3542108847815614940at_nat @ H2 @ A2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4626]) ).

thf(10289,plain,
    ( ( ! [R: nat,F: nat > nat,A2: set_nat] :
          ( ( times_times_nat @ R @ ( groups3542108847815614940at_nat @ F @ A2 ) )
          = ( groups3542108847815614940at_nat
            @ ^ [N: nat] : ( times_times_nat @ R @ ( F @ N ) )
            @ A2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4630]) ).

thf(10290,plain,
    ( ( ! [F: nat > nat,A2: set_nat,R: nat] :
          ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ R )
          = ( groups3542108847815614940at_nat
            @ ^ [N: nat] : ( times_times_nat @ ( F @ N ) @ R )
            @ A2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4634]) ).

thf(10291,plain,
    ( ( ! [F: nat > nat,A2: set_nat,G: nat > nat,B3: set_nat] :
          ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ B3 ) )
          = ( groups3542108847815614940at_nat
            @ ^ [I3: nat] :
                ( groups3542108847815614940at_nat
                @ ^ [J3: nat] : ( times_times_nat @ ( F @ I3 ) @ ( G @ J3 ) )
                @ B3 )
            @ A2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[4638]) ).

thf(10292,plain,
    ( ( ! [R: nat,A: nat,B: nat,C: nat,D: nat] :
          ( ( R != zero_zero_nat )
         => ( ( ( A = B )
              & ( C != D ) )
           => ( ( plus_plus_nat @ A @ ( times_times_nat @ R @ C ) )
             != ( plus_plus_nat @ B @ ( times_times_nat @ R @ D ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5158]) ).

thf(10293,plain,
    ( ( ! [P: nat > $o,A: nat] :
          ( ! [A3: nat] :
              ( ( ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                = A3 )
             => ( P @ A3 ) )
         => ( ! [A3: nat,B2: $o] :
                ( ( P @ A3 )
               => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                    = A3 )
                 => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
           => ( P @ A ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5181]) ).

thf(10294,plain,
    ( ( ! [P: $o,Q: $o] :
          ( ( zero_n2687167440665602831ol_nat
            @ ( P
              & Q ) )
          = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5233]) ).

thf(10295,plain,
    ( ( ! [A: nat] :
          ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
         => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
            = A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5652]) ).

thf(10296,plain,
    ( ( ( ^ [Y3: nat,Z2: nat] : ( Y3 = Z2 ) )
      = ( ^ [A5: nat,B5: nat] :
            ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 )
              = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B5 ) )
            & ( ( divide_divide_nat @ A5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
              = ( divide_divide_nat @ B5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5675]) ).

thf(10297,plain,
    ( ( ! [A: nat,B: nat] :
          ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
         => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
           => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5681]) ).

thf(10298,plain,
    ( ( ! [A: nat] :
          ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
         => ~ ! [B2: nat] :
                ( A
               != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[5693]) ).

thf(10299,plain,
    ( ( ! [N2: num] : ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6049]) ).

thf(10300,plain,
    ( ( ! [X: nat,Y: nat] :
          ( ( ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
            = ( divide_divide_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
         => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X )
              = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y ) )
           => ( X = Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6072]) ).

thf(10301,plain,
    ( ( ! [A: nat,B: nat] :
        ? [D4: nat,X4: nat,Y4: nat] :
          ( ( dvd_dvd_nat @ D4 @ A )
          & ( dvd_dvd_nat @ D4 @ B )
          & ( ( ( times_times_nat @ A @ X4 )
              = ( plus_plus_nat @ ( times_times_nat @ B @ Y4 ) @ D4 ) )
            | ( ( times_times_nat @ B @ X4 )
              = ( plus_plus_nat @ ( times_times_nat @ A @ Y4 ) @ D4 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6082]) ).

thf(10302,plain,
    ( ( ! [D: nat,A: nat,B: nat,X: nat,Y: nat] :
          ( ( dvd_dvd_nat @ D @ A )
         => ( ( dvd_dvd_nat @ D @ B )
           => ( ( ( ( times_times_nat @ A @ X )
                  = ( plus_plus_nat @ ( times_times_nat @ B @ Y ) @ D ) )
                | ( ( times_times_nat @ B @ X )
                  = ( plus_plus_nat @ ( times_times_nat @ A @ Y ) @ D ) ) )
             => ? [X4: nat,Y4: nat] :
                  ( ( dvd_dvd_nat @ D @ A )
                  & ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
                  & ( ( ( times_times_nat @ A @ X4 )
                      = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y4 ) @ D ) )
                    | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X4 )
                      = ( plus_plus_nat @ ( times_times_nat @ A @ Y4 ) @ D ) ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6083]) ).

thf(10303,plain,
    ( ( ! [B: nat,A: nat,N2: nat] :
          ( ( dvd_dvd_nat @ B @ A )
         => ( ( power_power_nat @ ( divide_divide_nat @ A @ B ) @ N2 )
            = ( divide_divide_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6108]) ).

thf(10304,plain,
    ( ( ! [C: nat,A: nat,B: nat] :
          ( ( dvd_dvd_nat @ C @ A )
         => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
            = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6120]) ).

thf(10305,plain,
    ( ( ! [C: nat,B: nat,A: nat] :
          ( ( dvd_dvd_nat @ C @ B )
         => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
            = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6123]) ).

thf(10306,plain,
    ( ( ! [C: nat,B: nat,A: nat] :
          ( ( dvd_dvd_nat @ C @ B )
         => ( ( times_times_nat @ ( divide_divide_nat @ B @ C ) @ A )
            = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6126]) ).

thf(10307,plain,
    ( ( ! [C: nat,B: nat,A: nat] :
          ( ( dvd_dvd_nat @ C @ B )
         => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
            = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6129]) ).

thf(10308,plain,
    ( ( ! [C: nat,B: nat,A: nat] :
          ( ( dvd_dvd_nat @ C @ B )
         => ( ( dvd_dvd_nat @ B @ A )
           => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C ) )
              = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6132]) ).

thf(10309,plain,
    ( ( ! [B: nat,C: nat,A: nat] :
          ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C ) @ A )
         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
            = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6135]) ).

thf(10310,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B )
         => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6138]) ).

thf(10311,plain,
    ( ( ! [B: nat,A: nat,D: nat,C: nat] :
          ( ( dvd_dvd_nat @ B @ A )
         => ( ( dvd_dvd_nat @ D @ C )
           => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C @ D ) )
              = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6141]) ).

thf(10312,plain,
    ( ( ! [N2: nat,K: int,M: nat,L2: int,R: int] :
          ( ( bit_concat_bit @ N2 @ K @ ( bit_concat_bit @ M @ L2 @ R ) )
          = ( bit_concat_bit @ ( plus_plus_nat @ M @ N2 ) @ ( bit_concat_bit @ N2 @ K @ L2 ) @ R ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6197]) ).

thf(10313,plain,
    ( ( ! [X: nat,Y: nat,N2: nat] :
          ( ( dvd_dvd_nat @ X @ Y )
         => ( dvd_dvd_nat @ ( power_power_nat @ X @ N2 ) @ ( power_power_nat @ Y @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6213]) ).

thf(10314,plain,
    ( ( ! [C: nat,A: nat,B: nat] :
          ( ( dvd_dvd_nat @ C @ A )
         => ( ( dvd_dvd_nat @ C @ B )
           => ( ( ( divide_divide_nat @ A @ C )
                = ( divide_divide_nat @ B @ C ) )
              = ( A = B ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6216]) ).

thf(10315,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( ( divide_divide_nat @ A @ C )
            = ( divide_divide_nat @ B @ C ) )
         => ( ( dvd_dvd_nat @ C @ A )
           => ( ( dvd_dvd_nat @ C @ B )
             => ( A = B ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6222]) ).

thf(10316,plain,
    ( ( ! [D: nat,B: nat,A: nat] :
          ( ( dvd_dvd_nat @ D @ B )
         => ( ( dvd_dvd_nat @ B @ A )
           => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D ) @ ( divide_divide_nat @ B @ D ) )
              = ( divide_divide_nat @ A @ B ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6228]) ).

thf(10317,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( dvd_dvd_nat @ A @ B )
         => ( ( dvd_dvd_nat @ A @ C )
           => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6249]) ).

thf(10318,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( dvd_dvd_nat @ A @ C )
         => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
            = ( dvd_dvd_nat @ A @ B ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6254]) ).

thf(10319,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( dvd_dvd_nat @ A @ B )
         => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
            = ( dvd_dvd_nat @ A @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6259]) ).

thf(10320,plain,
    ( ( ! [P4: nat,A: nat,B: nat] :
          ( ( dvd_dvd_nat @ P4 @ ( times_times_nat @ A @ B ) )
         => ~ ! [X4: nat,Y4: nat] :
                ( ( P4
                  = ( times_times_nat @ X4 @ Y4 ) )
               => ( ( dvd_dvd_nat @ X4 @ A )
                 => ~ ( dvd_dvd_nat @ Y4 @ B ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6264]) ).

thf(10321,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
         => ? [B8: nat,C5: nat] :
              ( ( A
                = ( times_times_nat @ B8 @ C5 ) )
              & ( dvd_dvd_nat @ B8 @ B )
              & ( dvd_dvd_nat @ C5 @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6266]) ).

thf(10322,plain,
    ( ( ! [B: nat,A: nat] :
          ( ( dvd_dvd_nat @ B @ A )
         => ~ ! [K2: nat] :
                ( A
               != ( times_times_nat @ B @ K2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6268]) ).

thf(10323,plain,
    ( ( ! [A: nat,B: nat,K: nat] :
          ( ( A
            = ( times_times_nat @ B @ K ) )
         => ( dvd_dvd_nat @ B @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6273]) ).

thf(10324,plain,
    ( ( dvd_dvd_nat
      = ( ^ [B5: nat,A5: nat] :
          ? [K3: nat] :
            ( A5
            = ( times_times_nat @ B5 @ K3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6278]) ).

thf(10325,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( dvd_dvd_nat @ A @ C )
         => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6283]) ).

thf(10326,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( dvd_dvd_nat @ A @ B )
         => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6288]) ).

thf(10327,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
         => ( dvd_dvd_nat @ A @ C ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6293]) ).

thf(10328,plain,
    ( ( ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6298]) ).

thf(10329,plain,
    ( ( ! [A: nat,B: nat,C: nat,D: nat] :
          ( ( dvd_dvd_nat @ A @ B )
         => ( ( dvd_dvd_nat @ C @ D )
           => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6303]) ).

thf(10330,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
         => ( dvd_dvd_nat @ B @ C ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6308]) ).

thf(10331,plain,
    ( ( ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6313]) ).

thf(10332,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) )
          = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
           != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6364]) ).

thf(10333,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) )
          = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
            = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6367]) ).

thf(10334,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
          = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
            | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6370]) ).

thf(10335,plain,
    ( ( ! [C: nat,A: nat,B: nat] :
          ( ( dvd_dvd_nat @ C @ A )
         => ( ( dvd_dvd_nat @ C @ B )
           => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
              = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6400]) ).

thf(10336,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( dvd_dvd_nat @ A @ B )
         => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
            = B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6403]) ).

thf(10337,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( dvd_dvd_nat @ A @ B )
         => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
            = B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6406]) ).

thf(10338,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
          = ( dvd_dvd_nat @ A @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6412]) ).

thf(10339,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
          = ( dvd_dvd_nat @ A @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6417]) ).

thf(10340,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( dvd_dvd_nat @ A @ B )
         => ( ( dvd_dvd_nat @ A @ C )
           => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B @ A ) @ ( divide_divide_nat @ C @ A ) )
              = ( dvd_dvd_nat @ B @ C ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6444]) ).

thf(10341,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
          = ( dvd_dvd_nat @ A @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6449]) ).

thf(10342,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
          = ( dvd_dvd_nat @ A @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6454]) ).

thf(10343,plain,
    ( ( ! [P: nat > nat > $o,A: nat,B: nat] :
          ( ! [A3: nat,B2: nat] :
              ( ( P @ A3 @ B2 )
              = ( P @ B2 @ A3 ) )
         => ( ! [A3: nat] : ( P @ A3 @ zero_zero_nat )
           => ( ! [A3: nat,B2: nat] :
                  ( ( P @ A3 @ B2 )
                 => ( P @ A3 @ ( plus_plus_nat @ A3 @ B2 ) ) )
             => ( P @ A @ B ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6480]) ).

thf(10344,plain,
    ( ( ! [X22: num] :
          ( one
         != ( bit0 @ X22 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6909]) ).

thf(10345,plain,
    ( ( ! [A: nat] :
          ( ( plus_plus_nat @ A @ zero_zero_nat )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6911]) ).

thf(10346,plain,
    ( ( ! [X22: num,Y22: num] :
          ( ( ( bit0 @ X22 )
            = ( bit0 @ Y22 ) )
          = ( X22 = Y22 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6985]) ).

thf(10347,plain,
    ( ( ! [A2: nat,N2: nat] :
          ( A2
          = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ N2 ) @ N2 ) @ ( modulo_modulo_nat @ A2 @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[6989]) ).

thf(10348,plain,
    ( ( ! [A: nat,N2: nat,M: nat] :
          ( ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
          = ( divide_divide_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7049]) ).

thf(10349,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
           != zero_zero_nat )
         => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
           != zero_zero_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7070]) ).

thf(10350,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
           != zero_zero_nat )
         => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
           != zero_zero_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7072]) ).

thf(10351,plain,
    ( ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
      = zero_zero_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[7140]) ).

thf(10352,plain,
    ( ( ! [M: nat,N2: nat,Q2: nat] :
          ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N2 @ Q2 ) )
          = ( plus_plus_nat @ ( times_times_nat @ N2 @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N2 ) @ Q2 ) ) @ ( modulo_modulo_nat @ M @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7465]) ).

thf(10353,plain,
    ( ( ! [B: nat,A: nat,C: nat] :
          ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
          = ( plus_plus_nat @ A @ C ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7480]) ).

thf(10354,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
          = ( plus_plus_nat @ A @ C ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7483]) ).

thf(10355,plain,
    ( ( ! [A: nat,B: nat] :
          ( A
          = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7486]) ).

thf(10356,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7489]) ).

thf(10357,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7492]) ).

thf(10358,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7495]) ).

thf(10359,plain,
    ( ( ! [B: nat,A: nat] :
          ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7498]) ).

thf(10360,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
          = ( plus_plus_nat @ ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7501]) ).

thf(10361,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
          = ( plus_plus_nat @ ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7862]) ).

thf(10362,plain,
    ( ( ! [M: num,Q2: num] :
          ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
         != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7867]) ).

thf(10363,plain,
    ( ( ! [Q2: num,N2: num] :
          ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
         != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7870]) ).

thf(10364,plain,
    ( ( ( ^ [H: nat] : zero_zero_nat )
      = ( times_times_nat @ zero_zero_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7882]) ).

thf(10365,plain,
    ( ( ! [X: nat,N2: nat,Y: nat] :
          ( ( ( modulo_modulo_nat @ X @ N2 )
            = ( modulo_modulo_nat @ Y @ N2 ) )
          = ( ? [Q1: nat,Q22: nat] :
                ( ( plus_plus_nat @ X @ ( times_times_nat @ N2 @ Q1 ) )
                = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q22 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7898]) ).

thf(10366,plain,
    ( ( ! [K: nat,M: nat,N2: nat] :
          ( ( ( times_times_nat @ K @ M )
            = ( times_times_nat @ K @ N2 ) )
          = ( ( K = zero_zero_nat )
            | ( M = N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7902]) ).

thf(10367,plain,
    ( ( ! [N2: nat] :
          ( ( times_times_nat @ zero_zero_nat @ N2 )
          = zero_zero_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7903]) ).

thf(10368,plain,
    ( ( ! [N2: nat] :
          ( ( plus_plus_nat @ zero_zero_nat @ N2 )
          = N2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7904]) ).

thf(10369,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( ( plus_plus_nat @ M @ N2 )
            = M )
         => ( N2 = zero_zero_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7905]) ).

thf(10370,plain,
    ( ( ! [A: nat,N2: nat] :
          ( ( A != zero_zero_nat )
         => ( ( power_power_nat @ A @ N2 )
           != zero_zero_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7937]) ).

thf(10371,plain,
    ( ( ! [A: nat] :
          ( ( plus_plus_nat @ zero_zero_nat @ A )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7950]) ).

thf(10372,plain,
    ( ( ! [A: nat] :
          ( ( plus_plus_nat @ A @ zero_zero_nat )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7955]) ).

thf(10373,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( ( times_times_nat @ A @ B )
           != zero_zero_nat )
         => ( ( A != zero_zero_nat )
            & ( B != zero_zero_nat ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7964]) ).

thf(10374,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( ( times_times_nat @ A @ B )
            = zero_zero_nat )
         => ( ( A = zero_zero_nat )
            | ( B = zero_zero_nat ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7969]) ).

thf(10375,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( A != zero_zero_nat )
         => ( ( B != zero_zero_nat )
           => ( ( times_times_nat @ A @ B )
             != zero_zero_nat ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7974]) ).

thf(10376,plain,
    ( ( ! [C: nat,A: nat,B: nat] :
          ( ( C != zero_zero_nat )
         => ( ( ( times_times_nat @ C @ A )
              = ( times_times_nat @ C @ B ) )
            = ( A = B ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7979]) ).

thf(10377,plain,
    ( ( ! [C: nat,A: nat,B: nat] :
          ( ( C != zero_zero_nat )
         => ( ( ( times_times_nat @ A @ C )
              = ( times_times_nat @ B @ C ) )
            = ( A = B ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7984]) ).

thf(10378,plain,
    ( ( ! [M: num,N2: num] :
          ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ one ) )
          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ one ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7990]) ).

thf(10379,plain,
    ( ( ! [M: num,Q2: num,N2: num] :
          ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
            = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
          = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
            = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7993]) ).

thf(10380,plain,
    ( ( ! [N2: num] :
          ( zero_zero_nat
         != ( numeral_numeral_nat @ N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[7995]) ).

thf(10381,plain,
    ( ( ! [A: nat,B: nat,N2: nat] :
          ( ( modulo_modulo_nat @ ( power_power_nat @ ( modulo_modulo_nat @ A @ B ) @ N2 ) @ B )
          = ( modulo_modulo_nat @ ( power_power_nat @ A @ N2 ) @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8025]) ).

thf(10382,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
          = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8036]) ).

thf(10383,plain,
    ( ( ! [A: nat,C: nat,A6: nat,B: nat,B6: nat] :
          ( ( ( modulo_modulo_nat @ A @ C )
            = ( modulo_modulo_nat @ A6 @ C ) )
         => ( ( ( modulo_modulo_nat @ B @ C )
              = ( modulo_modulo_nat @ B6 @ C ) )
           => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C )
              = ( modulo_modulo_nat @ ( plus_plus_nat @ A6 @ B6 ) @ C ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8039]) ).

thf(10384,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
          = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8042]) ).

thf(10385,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
          = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8045]) ).

thf(10386,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
          = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8048]) ).

thf(10387,plain,
    ( ( ! [A: nat,C: nat,A6: nat,B: nat,B6: nat] :
          ( ( ( modulo_modulo_nat @ A @ C )
            = ( modulo_modulo_nat @ A6 @ C ) )
         => ( ( ( modulo_modulo_nat @ B @ C )
              = ( modulo_modulo_nat @ B6 @ C ) )
           => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C )
              = ( modulo_modulo_nat @ ( times_times_nat @ A6 @ B6 ) @ C ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8051]) ).

thf(10388,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
          = ( times_times_nat @ ( modulo_modulo_nat @ A @ B ) @ C ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8054]) ).

thf(10389,plain,
    ( ( ! [C: nat,A: nat,B: nat] :
          ( ( times_times_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
          = ( modulo_modulo_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8057]) ).

thf(10390,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
          = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8060]) ).

thf(10391,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
          = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8063]) ).

thf(10392,plain,
    ( ( ! [A: nat] :
          ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
            = zero_zero_nat )
          = ( A = zero_zero_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8161]) ).

thf(10393,plain,
    ( ( ! [B: nat,A: nat,C: nat] :
          ( ( B != zero_zero_nat )
         => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
            = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8197]) ).

thf(10394,plain,
    ( ( ! [B: nat,A: nat,C: nat] :
          ( ( B != zero_zero_nat )
         => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
            = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8199]) ).

thf(10395,plain,
    ( ( ! [B: nat,C: nat,A: nat] :
          ( ( B != zero_zero_nat )
         => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
            = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8201]) ).

thf(10396,plain,
    ( ( ! [B: nat,C: nat,A: nat] :
          ( ( B != zero_zero_nat )
         => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
            = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8203]) ).

thf(10397,plain,
    ( ( ! [K: nat,M: nat,N2: nat] :
          ( ( ( K = zero_zero_nat )
           => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
              = zero_zero_nat ) )
          & ( ( K != zero_zero_nat )
           => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
              = ( divide_divide_nat @ M @ N2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8227]) ).

thf(10398,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
          = ( modulo_modulo_nat @ A @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8263]) ).

thf(10399,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
          = ( modulo_modulo_nat @ A @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8266]) ).

thf(10400,plain,
    ( ( ! [C: nat,B: nat,A: nat] :
          ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
          = ( modulo_modulo_nat @ A @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8269]) ).

thf(10401,plain,
    ( ( ! [B: nat,C: nat,A: nat] :
          ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
          = ( modulo_modulo_nat @ A @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8272]) ).

thf(10402,plain,
    ( ( ! [K: num] :
          ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
          = zero_zero_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8298]) ).

thf(10403,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( A != zero_zero_nat )
         => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
            = B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8351]) ).

thf(10404,plain,
    ( ( ! [B: nat,A: nat] :
          ( ( B != zero_zero_nat )
         => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
            = A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8356]) ).

thf(10405,plain,
    ( ( ! [C: nat,A: nat,B: nat] :
          ( ( C != zero_zero_nat )
         => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
            = ( divide_divide_nat @ A @ B ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8361]) ).

thf(10406,plain,
    ( ( ! [C: nat,A: nat,B: nat] :
          ( ( C != zero_zero_nat )
         => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
            = ( divide_divide_nat @ A @ B ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8363]) ).

thf(10407,plain,
    ( ( ! [C: nat,A: nat,B: nat] :
          ( ( ( C = zero_zero_nat )
           => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
              = zero_zero_nat ) )
          & ( ( C != zero_zero_nat )
           => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
              = ( divide_divide_nat @ A @ B ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8365]) ).

thf(10408,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( ( times_times_nat @ M @ N2 )
            = zero_zero_nat )
          = ( ( M = zero_zero_nat )
            | ( N2 = zero_zero_nat ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8444]) ).

thf(10409,plain,
    ( ( ! [M: nat] :
          ( ( times_times_nat @ M @ zero_zero_nat )
          = zero_zero_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8445]) ).

thf(10410,plain,
    ( ( ! [K: nat,M: nat,N2: nat] :
          ( ( ( times_times_nat @ K @ M )
            = ( times_times_nat @ K @ N2 ) )
          = ( ( M = N2 )
            | ( K = zero_zero_nat ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8446]) ).

thf(10411,plain,
    ( ( ! [M: nat,K: nat,N2: nat] :
          ( ( ( times_times_nat @ M @ K )
            = ( times_times_nat @ N2 @ K ) )
          = ( ( M = N2 )
            | ( K = zero_zero_nat ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8447]) ).

thf(10412,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( ( plus_plus_nat @ M @ N2 )
            = zero_zero_nat )
          = ( ( M = zero_zero_nat )
            & ( N2 = zero_zero_nat ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8450]) ).

thf(10413,plain,
    ( ( ! [M: nat] :
          ( ( plus_plus_nat @ M @ zero_zero_nat )
          = M ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8451]) ).

thf(10414,plain,
    ( ( ! [B: nat,A: nat] :
          ( ( modulo_modulo_nat @ ( plus_plus_nat @ B @ A ) @ B )
          = ( modulo_modulo_nat @ A @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8454]) ).

thf(10415,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ B )
          = ( modulo_modulo_nat @ A @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8457]) ).

thf(10416,plain,
    ( ( ! [A: nat] :
          ( ( divide_divide_nat @ zero_zero_nat @ A )
          = zero_zero_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8479]) ).

thf(10417,plain,
    ( ( ! [A: nat] :
          ( ( divide_divide_nat @ A @ zero_zero_nat )
          = zero_zero_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8484]) ).

thf(10418,plain,
    ( ( ! [A: nat] :
          ( ( divide_divide_nat @ zero_zero_nat @ A )
          = zero_zero_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8489]) ).

thf(10419,plain,
    ( ( ! [A: nat] :
          ( ( divide_divide_nat @ A @ zero_zero_nat )
          = zero_zero_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8491]) ).

thf(10420,plain,
    ( ( ! [A: nat] :
          ( ( plus_plus_nat @ A @ zero_zero_nat )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8512]) ).

thf(10421,plain,
    ( ( ! [B: nat,A: nat] :
          ( ( ( plus_plus_nat @ B @ A )
            = A )
          = ( B = zero_zero_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8520]) ).

thf(10422,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( ( plus_plus_nat @ A @ B )
            = A )
          = ( B = zero_zero_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8525]) ).

thf(10423,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( A
            = ( plus_plus_nat @ B @ A ) )
          = ( B = zero_zero_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8530]) ).

thf(10424,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( A
            = ( plus_plus_nat @ A @ B ) )
          = ( B = zero_zero_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8535]) ).

thf(10425,plain,
    ( ( ! [X: nat,Y: nat] :
          ( ( ( plus_plus_nat @ X @ Y )
            = zero_zero_nat )
          = ( ( X = zero_zero_nat )
            & ( Y = zero_zero_nat ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8539]) ).

thf(10426,plain,
    ( ( ! [X: nat,Y: nat] :
          ( ( zero_zero_nat
            = ( plus_plus_nat @ X @ Y ) )
          = ( ( X = zero_zero_nat )
            & ( Y = zero_zero_nat ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8540]) ).

thf(10427,plain,
    ( ( ! [A: nat] :
          ( ( plus_plus_nat @ zero_zero_nat @ A )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8542]) ).

thf(10428,plain,
    ( ( ! [A: nat] :
          ( ( times_times_nat @ zero_zero_nat @ A )
          = zero_zero_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8547]) ).

thf(10429,plain,
    ( ( ! [A: nat] :
          ( ( times_times_nat @ A @ zero_zero_nat )
          = zero_zero_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8552]) ).

thf(10430,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( ( times_times_nat @ A @ B )
            = zero_zero_nat )
          = ( ( A = zero_zero_nat )
            | ( B = zero_zero_nat ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8557]) ).

thf(10431,plain,
    ( ( ! [C: nat,A: nat,B: nat] :
          ( ( ( times_times_nat @ C @ A )
            = ( times_times_nat @ C @ B ) )
          = ( ( C = zero_zero_nat )
            | ( A = B ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8562]) ).

thf(10432,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( ( times_times_nat @ A @ C )
            = ( times_times_nat @ B @ C ) )
          = ( ( C = zero_zero_nat )
            | ( A = B ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8567]) ).

thf(10433,plain,
    ( ( vEBT_VEBT_low
      = ( ^ [X2: nat,N: nat] : ( modulo_modulo_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8589]) ).

thf(10434,plain,
    ( ( ! [X: nat,Y: nat,Z: nat] :
          ( ( plus_plus_nat @ X @ ( ord_max_nat @ Y @ Z ) )
          = ( ord_max_nat @ ( plus_plus_nat @ X @ Y ) @ ( plus_plus_nat @ X @ Z ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8648]) ).

thf(10435,plain,
    ( ( ! [X: nat,Y: nat,Z: nat] :
          ( ( plus_plus_nat @ ( ord_max_nat @ X @ Y ) @ Z )
          = ( ord_max_nat @ ( plus_plus_nat @ X @ Z ) @ ( plus_plus_nat @ Y @ Z ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8652]) ).

thf(10436,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
          = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8662]) ).

thf(10437,plain,
    ( ( ! [C: nat,B: nat,A: nat] :
          ( ( ( plus_plus_nat @ C @ B )
            = A )
         => ( C
            = ( minus_minus_nat @ A @ B ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8666]) ).

thf(10438,plain,
    ( ( ! [A: nat] :
          ( ( times_times_nat @ A @ one_one_nat )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8700]) ).

thf(10439,plain,
    ( ( ! [A: nat] :
          ( ( times_times_nat @ one_one_nat @ A )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8705]) ).

thf(10440,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
         => ( ord_less_nat @ A @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8734]) ).

thf(10441,plain,
    ( ( ! [C: nat,A: nat,B: nat] :
          ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
         => ( ord_less_nat @ A @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8738]) ).

thf(10442,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( ord_less_nat @ A @ B )
         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8742]) ).

thf(10443,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( ord_less_nat @ A @ B )
         => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8746]) ).

thf(10444,plain,
    ( ( ! [A: nat,B: nat,C: nat,D: nat] :
          ( ( ord_less_nat @ A @ B )
         => ( ( ord_less_nat @ C @ D )
           => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8750]) ).

thf(10445,plain,
    ( ( ! [I2: nat,J: nat,K: nat,L2: nat] :
          ( ( ( ord_less_nat @ I2 @ J )
            & ( K = L2 ) )
         => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8754]) ).

thf(10446,plain,
    ( ( ! [I2: nat,J: nat,K: nat,L2: nat] :
          ( ( ( I2 = J )
            & ( ord_less_nat @ K @ L2 ) )
         => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8758]) ).

thf(10447,plain,
    ( ( ! [I2: nat,J: nat,K: nat,L2: nat] :
          ( ( ( ord_less_nat @ I2 @ J )
            & ( ord_less_nat @ K @ L2 ) )
         => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8762]) ).

thf(10448,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
         => ( ord_less_eq_nat @ A @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8766]) ).

thf(10449,plain,
    ( ( ! [C: nat,A: nat,B: nat] :
          ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
         => ( ord_less_eq_nat @ A @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8770]) ).

thf(10450,plain,
    ( ( ord_less_eq_nat
      = ( ^ [A5: nat,B5: nat] :
          ? [C4: nat] :
            ( B5
            = ( plus_plus_nat @ A5 @ C4 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8773]) ).

thf(10451,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( ord_less_eq_nat @ A @ B )
         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8775]) ).

thf(10452,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( ord_less_eq_nat @ A @ B )
         => ~ ! [C3: nat] :
                ( B
               != ( plus_plus_nat @ A @ C3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8778]) ).

thf(10453,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( ord_less_eq_nat @ A @ B )
         => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8780]) ).

thf(10454,plain,
    ( ( ! [A: nat,B: nat,C: nat,D: nat] :
          ( ( ord_less_eq_nat @ A @ B )
         => ( ( ord_less_eq_nat @ C @ D )
           => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8784]) ).

thf(10455,plain,
    ( ( ! [I2: nat,J: nat,K: nat,L2: nat] :
          ( ( ( ord_less_eq_nat @ I2 @ J )
            & ( ord_less_eq_nat @ K @ L2 ) )
         => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8788]) ).

thf(10456,plain,
    ( ( ! [I2: nat,J: nat,K: nat,L2: nat] :
          ( ( ( I2 = J )
            & ( ord_less_eq_nat @ K @ L2 ) )
         => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8792]) ).

thf(10457,plain,
    ( ( ! [I2: nat,J: nat,K: nat,L2: nat] :
          ( ( ( ord_less_eq_nat @ I2 @ J )
            & ( K = L2 ) )
         => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8796]) ).

thf(10458,plain,
    ( ( ! [B: nat,A: nat,C: nat] :
          ( ( ( plus_plus_nat @ B @ A )
            = ( plus_plus_nat @ C @ A ) )
         => ( B = C ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8812]) ).

thf(10459,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( ( plus_plus_nat @ A @ B )
            = ( plus_plus_nat @ A @ C ) )
         => ( B = C ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8816]) ).

thf(10460,plain,
    ( ( ! [B: nat,A: nat,C: nat] :
          ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
          = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8820]) ).

thf(10461,plain,
    ( ( plus_plus_nat
      = ( ^ [A5: nat,B5: nat] : ( plus_plus_nat @ B5 @ A5 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8824]) ).

thf(10462,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
          = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8834]) ).

thf(10463,plain,
    ( ( ! [B3: nat,K: nat,B: nat,A: nat] :
          ( ( B3
            = ( plus_plus_nat @ K @ B ) )
         => ( ( plus_plus_nat @ A @ B3 )
            = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8838]) ).

thf(10464,plain,
    ( ( ! [A2: nat,K: nat,A: nat,B: nat] :
          ( ( A2
            = ( plus_plus_nat @ K @ A ) )
         => ( ( plus_plus_nat @ A2 @ B )
            = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8842]) ).

thf(10465,plain,
    ( ( ! [I2: nat,J: nat,K: nat,L2: nat] :
          ( ( ( I2 = J )
            & ( K = L2 ) )
         => ( ( plus_plus_nat @ I2 @ K )
            = ( plus_plus_nat @ J @ L2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8846]) ).

thf(10466,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
          = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8850]) ).

thf(10467,plain,
    ( ( ! [B: nat,A: nat,C: nat] :
          ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
          = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8854]) ).

thf(10468,plain,
    ( ( times_times_nat
      = ( ^ [A5: nat,B5: nat] : ( times_times_nat @ B5 @ A5 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8858]) ).

thf(10469,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
          = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8862]) ).

thf(10470,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
          = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8866]) ).

thf(10471,plain,
    ( ( ! [A: nat] :
          ( ( times_times_nat @ one_one_nat @ A )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8890]) ).

thf(10472,plain,
    ( ( ! [A: nat] :
          ( ( times_times_nat @ A @ one_one_nat )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8895]) ).

thf(10473,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
          = ( ord_less_nat @ A @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8900]) ).

thf(10474,plain,
    ( ( ! [C: nat,A: nat,B: nat] :
          ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
          = ( ord_less_nat @ A @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8904]) ).

thf(10475,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
          = ( ord_less_eq_nat @ A @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8908]) ).

thf(10476,plain,
    ( ( ! [C: nat,A: nat,B: nat] :
          ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
          = ( ord_less_eq_nat @ A @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8912]) ).

thf(10477,plain,
    ( ( ! [B: nat,A: nat,C: nat] :
          ( ( ( plus_plus_nat @ B @ A )
            = ( plus_plus_nat @ C @ A ) )
          = ( B = C ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8916]) ).

thf(10478,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( ( plus_plus_nat @ A @ B )
            = ( plus_plus_nat @ A @ C ) )
          = ( B = C ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8920]) ).

thf(10479,plain,
    ( ( ! [C: nat,A: nat,B: nat] :
          ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
          = ( minus_minus_nat @ A @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8936]) ).

thf(10480,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
          = B ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8940]) ).

thf(10481,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
          = ( minus_minus_nat @ A @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8944]) ).

thf(10482,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8948]) ).

thf(10483,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
         != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8951]) ).

thf(10484,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
         != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[8952]) ).

thf(10485,plain,
    ( ( ! [C: nat] :
          ( ( ^ [X2: nat] : ( times_times_nat @ X2 @ C ) )
          = ( times_times_nat @ C ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9048]) ).

thf(10486,plain,
    ( ( ( ^ [X2: nat] : X2 )
      = ( times_times_nat @ one_one_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9257]) ).

thf(10487,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
          = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9262]) ).

thf(10488,plain,
    ( ( ! [B: nat,C: nat,A: nat] :
          ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
          = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9266]) ).

thf(10489,plain,
    ( ( ! [A: nat,E: nat,B: nat,C: nat] :
          ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C ) )
          = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9276]) ).

thf(10490,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
          = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9280]) ).

thf(10491,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
          = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9284]) ).

thf(10492,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
          = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9288]) ).

thf(10493,plain,
    ( ( ! [M: nat,N2: nat,Q2: nat] :
          ( ( times_times_nat @ M @ ( ord_max_nat @ N2 @ Q2 ) )
          = ( ord_max_nat @ ( times_times_nat @ M @ N2 ) @ ( times_times_nat @ M @ Q2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9301]) ).

thf(10494,plain,
    ( ( ! [M: nat,N2: nat,Q2: nat] :
          ( ( times_times_nat @ ( ord_max_nat @ M @ N2 ) @ Q2 )
          = ( ord_max_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N2 @ Q2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9302]) ).

thf(10495,plain,
    ( ( ! [M: nat,N2: nat,Q2: nat] :
          ( ( plus_plus_nat @ M @ ( ord_max_nat @ N2 @ Q2 ) )
          = ( ord_max_nat @ ( plus_plus_nat @ M @ N2 ) @ ( plus_plus_nat @ M @ Q2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9303]) ).

thf(10496,plain,
    ( ( ! [M: nat,N2: nat,Q2: nat] :
          ( ( plus_plus_nat @ ( ord_max_nat @ M @ N2 ) @ Q2 )
          = ( ord_max_nat @ ( plus_plus_nat @ M @ Q2 ) @ ( plus_plus_nat @ N2 @ Q2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9304]) ).

thf(10497,plain,
    ( ( ! [A: nat] :
          ( ( divide_divide_nat @ A @ one_one_nat )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9321]) ).

thf(10498,plain,
    ( ( ! [N2: nat] :
          ( ( times_times_nat @ one_one_nat @ N2 )
          = N2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9361]) ).

thf(10499,plain,
    ( ( ! [N2: nat] :
          ( ( times_times_nat @ N2 @ one_one_nat )
          = N2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9362]) ).

thf(10500,plain,
    ( ( ! [M: nat,N2: nat,K: nat] :
          ( ( times_times_nat @ ( plus_plus_nat @ M @ N2 ) @ K )
          = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9363]) ).

thf(10501,plain,
    ( ( ! [K: nat,M: nat,N2: nat] :
          ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N2 ) )
          = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9364]) ).

thf(10502,plain,
    ( ( ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9365]) ).

thf(10503,plain,
    ( ( ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9366]) ).

thf(10504,plain,
    ( ( ! [I2: nat,J: nat,K: nat,L2: nat] :
          ( ( ord_less_eq_nat @ I2 @ J )
         => ( ( ord_less_eq_nat @ K @ L2 )
           => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ L2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9367]) ).

thf(10505,plain,
    ( ( ! [I2: nat,J: nat,K: nat] :
          ( ( ord_less_eq_nat @ I2 @ J )
         => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ K ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9368]) ).

thf(10506,plain,
    ( ( ! [I2: nat,J: nat,K: nat] :
          ( ( ord_less_eq_nat @ I2 @ J )
         => ( ord_less_eq_nat @ ( times_times_nat @ K @ I2 ) @ ( times_times_nat @ K @ J ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9369]) ).

thf(10507,plain,
    ( ( ! [M: nat,K: nat,N2: nat] :
          ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
         => ~ ( ( ord_less_eq_nat @ M @ N2 )
             => ~ ( ord_less_eq_nat @ K @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9370]) ).

thf(10508,plain,
    ( ( ! [N2: nat,M: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ N2 @ M ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9371]) ).

thf(10509,plain,
    ( ( ! [N2: nat,M: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ M @ N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9372]) ).

thf(10510,plain,
    ( ( ! [M: nat,K: nat,N2: nat] :
          ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
         => ( ord_less_eq_nat @ M @ N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9373]) ).

thf(10511,plain,
    ( ( ! [M: nat,K: nat,N2: nat] :
          ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
         => ( ord_less_eq_nat @ K @ N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9374]) ).

thf(10512,plain,
    ( ( ! [K: nat,L2: nat] :
          ( ( ord_less_eq_nat @ K @ L2 )
         => ? [N4: nat] :
              ( L2
              = ( plus_plus_nat @ K @ N4 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9375]) ).

thf(10513,plain,
    ( ( ! [I2: nat,J: nat,K: nat,L2: nat] :
          ( ( ord_less_eq_nat @ I2 @ J )
         => ( ( ord_less_eq_nat @ K @ L2 )
           => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9376]) ).

thf(10514,plain,
    ( ( ! [I2: nat,J: nat,K: nat] :
          ( ( ord_less_eq_nat @ I2 @ J )
         => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9377]) ).

thf(10515,plain,
    ( ( ! [I2: nat,J: nat,M: nat] :
          ( ( ord_less_eq_nat @ I2 @ J )
         => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9378]) ).

thf(10516,plain,
    ( ( ! [I2: nat,J: nat,M: nat] :
          ( ( ord_less_eq_nat @ I2 @ J )
         => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9379]) ).

thf(10517,plain,
    ( ( ord_less_eq_nat
      = ( ^ [M6: nat,N: nat] :
          ? [K3: nat] :
            ( N
            = ( plus_plus_nat @ M6 @ K3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9380]) ).

thf(10518,plain,
    ( ( ! [I2: nat,J: nat,K: nat] :
          ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ K )
         => ( ord_less_nat @ I2 @ K ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9381]) ).

thf(10519,plain,
    ( ( ! [I2: nat,J: nat,K: nat,L2: nat] :
          ( ( ord_less_nat @ I2 @ J )
         => ( ( ord_less_nat @ K @ L2 )
           => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9382]) ).

thf(10520,plain,
    ( ( ! [I2: nat,J: nat] :
          ~ ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ I2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9383]) ).

thf(10521,plain,
    ( ( ! [J: nat,I2: nat] :
          ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I2 ) @ I2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9384]) ).

thf(10522,plain,
    ( ( ! [I2: nat,J: nat,K: nat] :
          ( ( ord_less_nat @ I2 @ J )
         => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9385]) ).

thf(10523,plain,
    ( ( ! [I2: nat,J: nat,M: nat] :
          ( ( ord_less_nat @ I2 @ J )
         => ( ord_less_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9386]) ).

thf(10524,plain,
    ( ( ! [I2: nat,J: nat,M: nat] :
          ( ( ord_less_nat @ I2 @ J )
         => ( ord_less_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9387]) ).

thf(10525,plain,
    ( ( ! [K: nat,L2: nat,M: nat,N2: nat] :
          ( ( ord_less_nat @ K @ L2 )
         => ( ( ( plus_plus_nat @ M @ L2 )
              = ( plus_plus_nat @ K @ N2 ) )
           => ( ord_less_nat @ M @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9388]) ).

thf(10526,plain,
    ( ( ! [A: nat,N2: nat] :
          ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
          = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9400]) ).

thf(10527,plain,
    ( ( ! [A: nat,N2: nat] :
          ( ( power_power_nat @ A @ ( suc @ N2 ) )
          = ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9445]) ).

thf(10528,plain,
    ( ( ! [A: nat,N2: nat] :
          ( ( power_power_nat @ A @ ( suc @ N2 ) )
          = ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9450]) ).

thf(10529,plain,
    ( ( ! [Z: nat,W: num] :
          ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
          = ( times_times_nat @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9459]) ).

thf(10530,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( times_times_nat @ ( suc @ M ) @ N2 )
          = ( plus_plus_nat @ N2 @ ( times_times_nat @ M @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9466]) ).

thf(10531,plain,
    ( ( ! [N2: num] :
          ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
          = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9513]) ).

thf(10532,plain,
    ( ( ! [K: nat,M: nat,N2: nat] :
          ( ( ( times_times_nat @ ( suc @ K ) @ M )
            = ( times_times_nat @ ( suc @ K ) @ N2 ) )
          = ( M = N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9521]) ).

thf(10533,plain,
    ( ( ! [M: nat,N2: nat,K: nat] :
          ( ( times_times_nat @ ( minus_minus_nat @ M @ N2 ) @ K )
          = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9522]) ).

thf(10534,plain,
    ( ( ! [K: nat,M: nat,N2: nat] :
          ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
          = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9523]) ).

thf(10535,plain,
    ( ( ! [A2: nat,K: nat,A: nat] :
          ( ( A2
            = ( plus_plus_nat @ K @ A ) )
         => ( ( suc @ A2 )
            = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9524]) ).

thf(10536,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( plus_plus_nat @ ( suc @ M ) @ N2 )
          = ( suc @ ( plus_plus_nat @ M @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9525]) ).

thf(10537,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( plus_plus_nat @ ( suc @ M ) @ N2 )
          = ( plus_plus_nat @ M @ ( suc @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9526]) ).

thf(10538,plain,
    ( ( ! [K: nat,M: nat,N2: nat] :
          ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
          = ( minus_minus_nat @ M @ N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9537]) ).

thf(10539,plain,
    ( ( ! [M: nat,K: nat,N2: nat] :
          ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) )
          = ( minus_minus_nat @ M @ N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9538]) ).

thf(10540,plain,
    ( ( ! [N2: nat,M: nat] :
          ( ( minus_minus_nat @ ( plus_plus_nat @ N2 @ M ) @ N2 )
          = M ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9539]) ).

thf(10541,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ N2 )
          = M ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9540]) ).

thf(10542,plain,
    ( ( ! [M: nat] :
          ( ( divide_divide_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( suc @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9590]) ).

thf(10543,plain,
    ( ( ! [N2: nat] :
          ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
          = ( suc @ ( suc @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9591]) ).

thf(10544,plain,
    ( ( ! [N2: nat] :
          ( ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( suc @ ( suc @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9592]) ).

thf(10545,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( times_times_nat @ M @ ( suc @ N2 ) )
          = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9602]) ).

thf(10546,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( ( times_times_nat @ M @ N2 )
            = one_one_nat )
          = ( ( M = one_one_nat )
            & ( N2 = one_one_nat ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9611]) ).

thf(10547,plain,
    ( ( ! [I2: nat,J: nat,K: nat] :
          ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
          = ( minus_minus_nat @ I2 @ ( plus_plus_nat @ J @ K ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9612]) ).

thf(10548,plain,
    ( ( ! [K: nat,M: nat,N2: nat] :
          ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
          = ( ord_less_eq_nat @ M @ N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9614]) ).

thf(10549,plain,
    ( ( ! [K: nat,M: nat,N2: nat] :
          ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
          = ( ord_less_nat @ M @ N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9617]) ).

thf(10550,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( plus_plus_nat @ M @ ( suc @ N2 ) )
          = ( suc @ ( plus_plus_nat @ M @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9618]) ).

thf(10551,plain,
    ( ( ! [X: nat] :
          ( ! [N4: nat] :
              ( X
             != ( plus_plus_nat @ N4 @ N4 ) )
         => ~ ! [N4: nat] :
                ( X
               != ( plus_plus_nat @ N4 @ ( suc @ N4 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9634]) ).

thf(10552,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( one_one_nat
            = ( times_times_nat @ M @ N2 ) )
          = ( ( M = one_one_nat )
            & ( N2 = one_one_nat ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9635]) ).

thf(10553,plain,
    ( ( ! [I2: nat,U: nat,J: nat,K: nat] :
          ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
          = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I2 @ J ) @ U ) @ K ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9682]) ).

thf(10554,plain,
    ( ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
      = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9683]) ).

thf(10555,plain,
    ( ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
      = one_one_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[9687]) ).

thf(10556,plain,
    ( ( ( numeral_numeral_nat @ one )
      = one_one_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[9719]) ).

thf(10557,plain,
    ( ( ! [X: nat,Y: nat,N2: nat] :
          ( ( ( times_times_nat @ X @ Y )
            = one_one_nat )
         => ( ( times_times_nat @ ( power_power_nat @ X @ N2 ) @ ( power_power_nat @ Y @ N2 ) )
            = one_one_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9724]) ).

thf(10558,plain,
    ( ( ( numeral_numeral_nat @ one )
      = one_one_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[9733]) ).

thf(10559,plain,
    ( ( ! [X: num] :
          ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
          = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9738]) ).

thf(10560,plain,
    ( ( ! [X: num] :
          ( ( ord_less_eq_num @ X @ one )
          = ( X = one ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9766]) ).

thf(10561,plain,
    ( ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
      = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9792]) ).

thf(10562,plain,
    ( ( ! [M: num] :
          ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9800]) ).

thf(10563,plain,
    ( ( ! [N2: num] :
          ( ( ( numeral_numeral_nat @ N2 )
            = one_one_nat )
          = ( N2 = one ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9806]) ).

thf(10564,plain,
    ( ( ! [N2: num] :
          ( ( one_one_nat
            = ( numeral_numeral_nat @ N2 ) )
          = ( one = N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9811]) ).

thf(10565,plain,
    ( ( ! [N2: num] : ( ord_less_eq_num @ one @ N2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9815]) ).

thf(10566,plain,
    ( ( ! [M: num,N2: num] :
          ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
          = ( ord_less_eq_num @ M @ N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9816]) ).

thf(10567,plain,
    ( ( ! [N2: num] :
          ( ( times_times_num @ one @ N2 )
          = N2 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9817]) ).

thf(10568,plain,
    ( ( ! [M: num] :
          ( ( times_times_num @ M @ one )
          = M ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9818]) ).

thf(10569,plain,
    ( ( ! [M: num,N2: num] :
          ( ( times_times_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
          = ( bit0 @ ( bit0 @ ( times_times_num @ M @ N2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9819]) ).

thf(10570,plain,
    ( ( ! [M: num,N2: num] :
          ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
          = ( bit0 @ ( plus_plus_num @ M @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9820]) ).

thf(10571,plain,
    ( ( ! [A: nat] :
          ( ( power_power_nat @ A @ one_one_nat )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9824]) ).

thf(10572,plain,
    ( ( ! [N2: nat] :
          ( ( power_power_nat @ one_one_nat @ N2 )
          = one_one_nat ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9828]) ).

thf(10573,plain,
    ( ( ! [A: nat] :
          ( ( divide_divide_nat @ A @ one_one_nat )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9831]) ).

thf(10574,plain,
    ( ( ! [M: num] :
          ( ( bit0 @ M )
         != one ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9832]) ).

thf(10575,plain,
    ( ( ! [N2: num] :
          ( one
         != ( bit0 @ N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9833]) ).

thf(10576,plain,
    ( ( ! [M: num,N2: num] :
          ( ( ( bit0 @ M )
            = ( bit0 @ N2 ) )
          = ( M = N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9834]) ).

thf(10577,plain,
    ( ( ! [M: num,N2: num] :
          ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
          = ( ord_less_num @ M @ N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9836]) ).

thf(10578,plain,
    ( ( ! [M: num] :
          ~ ( ord_less_num @ M @ one ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9837]) ).

thf(10579,plain,
    ( ( ( plus_plus_num @ one @ one )
      = ( bit0 @ one ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9839]) ).

thf(10580,plain,
    ( ( ! [N2: num] : ( ord_less_num @ one @ ( bit0 @ N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9843]) ).

thf(10581,plain,
    ( ( ! [Option: option_nat,Option2: option_nat] :
          ( ( ( Option = none_nat )
            = ( Option2 = none_nat ) )
         => ( ( ( Option != none_nat )
             => ( ( Option2 != none_nat )
               => ( ( the_nat @ Option )
                  = ( the_nat @ Option2 ) ) ) )
           => ( Option = Option2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9871]) ).

thf(10582,plain,
    ( ( ! [X22: nat] :
          ( ( the_nat @ ( some_nat @ X22 ) )
          = X22 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9874]) ).

thf(10583,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N2 )
         => ( ord_less_eq_nat @ M @ N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9902]) ).

thf(10584,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
          = ( ord_less_eq_nat @ M @ N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9903]) ).

thf(10585,plain,
    ( ( ! [K: nat,M: nat] :
          ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
         => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9904]) ).

thf(10586,plain,
    ( ( ! [I2: nat,I5: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT,X6: vEBT_VEBT] :
          ( ( I2 != I5 )
         => ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ X ) @ I5 @ X6 )
            = ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I5 @ X6 ) @ I2 @ X ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9905]) ).

thf(10587,plain,
    ( ( ! [N2: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N2 @ ( divide_divide_nat @ M @ N2 ) ) @ M ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9912]) ).

thf(10588,plain,
    ( ( ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N2 ) @ N2 ) @ M ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9913]) ).

thf(10589,plain,
    ( ( ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N2 ) @ M ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9948]) ).

thf(10590,plain,
    ( ( ! [M: nat,N2: nat,K: nat] :
          ( ( ord_less_eq_nat @ M @ N2 )
         => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N2 @ K ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9949]) ).

thf(10591,plain,
    ( ( vEBT_invar_vebt @ ( nth_VEBT_VEBT @ treeList @ maxs ) @ na )
    = $true ),
    inference(unfold_def,[status(thm)],[9972]) ).

thf(10592,plain,
    ( ( vEBT_invar_vebt @ ( nth_VEBT_VEBT @ treeList @ summin ) @ na )
    = $true ),
    inference(unfold_def,[status(thm)],[9974]) ).

thf(10593,plain,
    ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg )
    = $true ),
    inference(unfold_def,[status(thm)],[9977]) ).

thf(10594,plain,
    ( ( ! [Xs: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT,Y: vEBT_VEBT] :
          ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ X ) @ I2 @ Y )
          = ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[9980]) ).

thf(10595,plain,
    ( ( ! [Xs: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT] :
          ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ X ) )
          = ( size_s6755466524823107622T_VEBT @ Xs ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10005]) ).

thf(10596,plain,
    ( ( ! [Xs: list_VEBT_VEBT,I2: nat] :
          ( ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ ( nth_VEBT_VEBT @ Xs @ I2 ) )
          = Xs ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10006]) ).

thf(10597,plain,
    ( ( ! [I2: nat,J: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
          ( ( I2 != J )
         => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ X ) @ J )
            = ( nth_VEBT_VEBT @ Xs @ J ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10008]) ).

thf(10598,plain,
    ( ( ! [A: complex,N2: nat] :
          ( ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
          = ( power_power_complex @ ( power_power_complex @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10023]) ).

thf(10599,plain,
    ( ( ! [A: int,N2: nat] :
          ( ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
          = ( power_power_int @ ( power_power_int @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10024]) ).

thf(10600,plain,
    ( ( ! [A: real,N2: nat] :
          ( ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
          = ( power_power_real @ ( power_power_real @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10025]) ).

thf(10601,plain,
    ( ( ! [A: nat,N2: nat] :
          ( ( power_power_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
          = ( power_power_nat @ ( power_power_nat @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10026]) ).

thf(10602,plain,
    ( ( ! [X: nat] :
          ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
          = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X @ X ) @ X ) @ X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10028]) ).

thf(10603,plain,
    ( ( ! [A: nat] :
          ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( times_times_nat @ A @ A ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10033]) ).

thf(10604,plain,
    ( ( ! [Z: nat] :
          ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
          = ( plus_plus_nat @ Z @ Z ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10038]) ).

thf(10605,plain,
    ( ( ! [Z: nat] :
          ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( plus_plus_nat @ Z @ Z ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10043]) ).

thf(10606,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
          = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10048]) ).

thf(10607,plain,
    ( ( ! [N2: num] :
          ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( numeral_numeral_nat @ N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10053]) ).

thf(10608,plain,
    ( ( ! [A: nat,M: nat,N2: nat] :
          ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N2 ) )
          = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10055]) ).

thf(10609,plain,
    ( ( ! [N2: num] :
          ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
          = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10063]) ).

thf(10610,plain,
    ( ( ! [A: nat] :
          ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10068]) ).

thf(10611,plain,
    ( ( ! [A: nat] :
          ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
          = A ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10073]) ).

thf(10612,plain,
    ( ( ! [M: nat,N2: nat,Q2: nat] :
          ( ( divide_divide_nat @ M @ ( times_times_nat @ N2 @ Q2 ) )
          = ( divide_divide_nat @ ( divide_divide_nat @ M @ N2 ) @ Q2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10077]) ).

thf(10613,plain,
    ( ( ! [A: complex,M: nat,N2: nat] :
          ( ( power_power_complex @ A @ ( times_times_nat @ M @ N2 ) )
          = ( power_power_complex @ ( power_power_complex @ A @ M ) @ N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10078]) ).

thf(10614,plain,
    ( ( ! [A: int,M: nat,N2: nat] :
          ( ( power_power_int @ A @ ( times_times_nat @ M @ N2 ) )
          = ( power_power_int @ ( power_power_int @ A @ M ) @ N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10079]) ).

thf(10615,plain,
    ( ( ! [A: real,M: nat,N2: nat] :
          ( ( power_power_real @ A @ ( times_times_nat @ M @ N2 ) )
          = ( power_power_real @ ( power_power_real @ A @ M ) @ N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10080]) ).

thf(10616,plain,
    ( ( ! [A: nat,M: nat,N2: nat] :
          ( ( power_power_nat @ A @ ( times_times_nat @ M @ N2 ) )
          = ( power_power_nat @ ( power_power_nat @ A @ M ) @ N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10081]) ).

thf(10617,plain,
    ( ( ! [A: nat,N2: nat] :
          ( ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ A )
          = ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10086]) ).

thf(10618,plain,
    ( ( ! [A: nat,B: nat,N2: nat] :
          ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N2 )
          = ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10091]) ).

thf(10619,plain,
    ( ( ! [X: nat,Y: nat,N2: nat] :
          ( ( ( times_times_nat @ X @ Y )
            = ( times_times_nat @ Y @ X ) )
         => ( ( times_times_nat @ ( power_power_nat @ X @ N2 ) @ Y )
            = ( times_times_nat @ Y @ ( power_power_nat @ X @ N2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10096]) ).

thf(10620,plain,
    ( ( ! [N2: nat] : ( ord_less_nat @ N2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10103]) ).

thf(10621,plain,
    ( ( ! [M: nat,I2: nat,N2: nat] :
          ( ( ord_less_nat @ M @ ( times_times_nat @ I2 @ N2 ) )
         => ( ord_less_nat @ ( divide_divide_nat @ M @ N2 ) @ I2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10104]) ).

thf(10622,plain,
    ( ( ! [A: nat,K: num,L2: num] :
          ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ L2 ) )
          = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ K @ L2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10106]) ).

thf(10623,plain,
    ( ( ! [N2: num] :
          ( ( plus_plus_num @ one @ N2 )
          = ( plus_plus_num @ N2 @ one ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10107]) ).

thf(10624,plain,
    ( ( ! [A: nat,M: num,N2: num] :
          ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N2 ) ) )
          = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10121]) ).

thf(10625,plain,
    ( ( ! [A: nat,M: num,N2: num,B: nat] :
          ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
          = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10126]) ).

thf(10626,plain,
    ( ( ! [A: nat,M: num,N2: num] :
          ( ( power_power_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) )
          = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10135]) ).

thf(10627,plain,
    ( ( ! [N2: num] :
          ( ( times_times_num @ ( bit0 @ one ) @ N2 )
          = ( bit0 @ N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10136]) ).

thf(10628,plain,
    ( ( ! [M: num,N2: num] :
          ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
          = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10138]) ).

thf(10629,plain,
    ( ( ! [V: num,W: num,Z: nat] :
          ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
          = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10143]) ).

thf(10630,plain,
    ( ( ! [M: num,N2: num] :
          ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
          = ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10148]) ).

thf(10631,plain,
    ( ( ! [V: num,W: num,Z: nat] :
          ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
          = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10153]) ).

thf(10632,plain,
    ( ( ! [X: nat,N2: nat,Y: nat] :
          ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
         => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ X ) @ N2 )
            = X ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10157]) ).

thf(10633,plain,
    ( ( ! [X: nat,N2: nat,Y: nat] :
          ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
         => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ X ) @ N2 )
            = Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10179]) ).

thf(10634,plain,
    ( ( ~ ! [Maxi: nat] :
            ( ( some_nat @ Maxi )
           != ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ maxs ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10182]) ).

thf(10635,plain,
    ( ( ! [Ma: nat,N2: nat,M: nat] :
          ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) )
         => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10183]) ).

thf(10636,plain,
    ( ( ! [M: num,N2: num] :
          ( ( ( numeral_numeral_nat @ M )
            = ( numeral_numeral_nat @ N2 ) )
          = ( M = N2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10187]) ).

thf(10637,plain,
    ( ( ! [A: nat,M: nat,N2: nat] :
          ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
          = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10196]) ).

thf(10638,plain,
    ( ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ summin ) @ lx )
    = $true ),
    inference(unfold_def,[status(thm)],[10197]) ).

thf(10639,plain,
    ( ( ord_less_nat @ maxi @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10198]) ).

thf(10640,plain,
    ( ( ! [X: nat,Y: nat] :
          ( ( power_power_nat @ ( plus_plus_nat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10200]) ).

thf(10641,plain,
    ( ( ! [A: nat,B: nat,V: num] :
          ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
          = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10205]) ).

thf(10642,plain,
    ( ( ! [V: num,B: nat,C: nat] :
          ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
          = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10210]) ).

thf(10643,plain,
    ( ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
     != mi )
    = $true ),
    inference(unfold_def,[status(thm)],[10214]) ).

thf(10644,plain,
    ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10215]) ).

thf(10645,plain,
    ( ( ~ ! [Maxs: nat] :
            ( ( some_nat @ Maxs )
           != ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10216]) ).

thf(10646,plain,
    ( ( ! [M: nat] :
          ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = M ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10217]) ).

thf(10647,plain,
    ( ( ( size_s6755466524823107622T_VEBT @ treeList )
      = ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10218]) ).

thf(10648,plain,
    ( ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
      = ma )
    = $true ),
    inference(unfold_def,[status(thm)],[10219]) ).

thf(10649,plain,
    ( ( ( some_nat @ maxs )
      = ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10220]) ).

thf(10650,plain,
    ( ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) )
     != none_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[10221]) ).

thf(10651,plain,
    ( ( ( some_nat @ maxi )
      = ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ maxs ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10222]) ).

thf(10652,plain,
    ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ maxs )
    = $true ),
    inference(unfold_def,[status(thm)],[10223]) ).

thf(10653,plain,
    ( ( ( vEBT_V8194947554948674370ptions @ summary @ maxs )
      & ( maxs
       != ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10224]) ).

thf(10654,plain,
    ( ( ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) ) )
      = ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ maxs ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10225]) ).

thf(10655,plain,
    ( ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) )
      = ( nth_VEBT_VEBT @ treeList @ maxs ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10226]) ).

thf(10656,plain,
    ( ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) )
      = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10227]) ).

thf(10657,plain,
    ( ( vEBT_VEBT_bit_concat
      = ( ^ [H: nat,L: nat,D2: nat] : ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D2 ) ) @ L ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10228]) ).

thf(10658,plain,
    ( ( ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ maxs ) @ X_1 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10229]) ).

thf(10659,plain,
    ( ( ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ summin ) @ X_1 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10230]) ).

thf(10660,plain,
    ( ( deg
      = ( plus_plus_nat @ na @ m ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10231]) ).

thf(10661,plain,
    ( ( ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
      = na )
    = $true ),
    inference(unfold_def,[status(thm)],[10232]) ).

thf(10662,plain,
    ( ( vEBT_VEBT_high
      = ( ^ [X2: nat,N: nat] : ( divide_divide_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10233]) ).

thf(10663,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10234]) ).

thf(10664,plain,
    ( ( ! [X: nat,Y: nat] :
          ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ X ) @ Y )
          = ( ( X != Y )
            & ( vEBT_V8194947554948674370ptions @ summary @ Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10235]) ).

thf(10665,plain,
    ( ( ! [X: nat,D: nat] :
          ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X @ D ) @ ( vEBT_VEBT_low @ X @ D ) @ D )
          = X ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10236]) ).

thf(10666,plain,
    ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ maxs ) @ maxi )
    = $true ),
    inference(unfold_def,[status(thm)],[10237]) ).

thf(10667,plain,
    ( ( m = na )
    = $true ),
    inference(unfold_def,[status(thm)],[10238]) ).

thf(10668,plain,
    ( ( ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) ) ) )
     != ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) @ maxs ) @ maxi ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[10241]) ).

thf(10669,plain,
    ( ( m = na )
    = $true ),
    inference(copy,[status(thm)],[10667]) ).

thf(10670,plain,
    ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ maxs ) @ maxi )
    = $true ),
    inference(copy,[status(thm)],[10666]) ).

thf(10671,plain,
    ( ( ! [X: nat,D: nat] :
          ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X @ D ) @ ( vEBT_VEBT_low @ X @ D ) @ D )
          = X ) )
    = $true ),
    inference(copy,[status(thm)],[10665]) ).

thf(10672,plain,
    ( ( ! [X: nat,Y: nat] :
          ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ X ) @ Y )
          = ( ( X != Y )
            & ( vEBT_V8194947554948674370ptions @ summary @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10664]) ).

thf(10673,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
          = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[10663]) ).

thf(10674,plain,
    ( ( vEBT_VEBT_high
      = ( ^ [X2: nat,N: nat] : ( divide_divide_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10662]) ).

thf(10675,plain,
    ( ( ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
      = na )
    = $true ),
    inference(copy,[status(thm)],[10661]) ).

thf(10676,plain,
    ( ( deg
      = ( plus_plus_nat @ na @ m ) )
    = $true ),
    inference(copy,[status(thm)],[10660]) ).

thf(10677,plain,
    ( ( ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ summin ) @ X_1 ) )
    = $true ),
    inference(copy,[status(thm)],[10659]) ).

thf(10678,plain,
    ( ( ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ maxs ) @ X_1 ) )
    = $true ),
    inference(copy,[status(thm)],[10658]) ).

thf(10679,plain,
    ( ( vEBT_VEBT_bit_concat
      = ( ^ [H: nat,L: nat,D2: nat] : ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D2 ) ) @ L ) ) )
    = $true ),
    inference(copy,[status(thm)],[10657]) ).

thf(10680,plain,
    ( ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) )
      = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) )
    = $true ),
    inference(copy,[status(thm)],[10656]) ).

thf(10681,plain,
    ( ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) )
      = ( nth_VEBT_VEBT @ treeList @ maxs ) )
    = $true ),
    inference(copy,[status(thm)],[10655]) ).

thf(10682,plain,
    ( ( ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) ) )
      = ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ maxs ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10654]) ).

thf(10683,plain,
    ( ( ( vEBT_V8194947554948674370ptions @ summary @ maxs )
      & ( maxs
       != ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) )
    = $true ),
    inference(copy,[status(thm)],[10653]) ).

thf(10684,plain,
    ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ maxs )
    = $true ),
    inference(copy,[status(thm)],[10652]) ).

thf(10685,plain,
    ( ( ( some_nat @ maxi )
      = ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ maxs ) ) )
    = $true ),
    inference(copy,[status(thm)],[10651]) ).

thf(10686,plain,
    ( ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) )
     != none_nat )
    = $true ),
    inference(copy,[status(thm)],[10650]) ).

thf(10687,plain,
    ( ( ( some_nat @ maxs )
      = ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10649]) ).

thf(10688,plain,
    ( ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
      = ma )
    = $true ),
    inference(copy,[status(thm)],[10648]) ).

thf(10689,plain,
    ( ( ( size_s6755466524823107622T_VEBT @ treeList )
      = ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10647]) ).

thf(10690,plain,
    ( ( ! [M: nat] :
          ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = M ) )
    = $true ),
    inference(copy,[status(thm)],[10646]) ).

thf(10691,plain,
    ( ( ~ ! [Maxs: nat] :
            ( ( some_nat @ Maxs )
           != ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10645]) ).

thf(10692,plain,
    ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) )
    = $true ),
    inference(copy,[status(thm)],[10644]) ).

thf(10693,plain,
    ( ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
     != mi )
    = $true ),
    inference(copy,[status(thm)],[10643]) ).

thf(10694,plain,
    ( ( ! [V: num,B: nat,C: nat] :
          ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
          = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10642]) ).

thf(10695,plain,
    ( ( ! [A: nat,B: nat,V: num] :
          ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
          = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10641]) ).

thf(10696,plain,
    ( ( ! [X: nat,Y: nat] :
          ( ( power_power_nat @ ( plus_plus_nat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10640]) ).

thf(10697,plain,
    ( ( ord_less_nat @ maxi @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) )
    = $true ),
    inference(copy,[status(thm)],[10639]) ).

thf(10698,plain,
    ( ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ summin ) @ lx )
    = $true ),
    inference(copy,[status(thm)],[10638]) ).

thf(10699,plain,
    ( ( ! [A: nat,M: nat,N2: nat] :
          ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
          = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10637]) ).

thf(10700,plain,
    ( ( ! [M: num,N2: num] :
          ( ( ( numeral_numeral_nat @ M )
            = ( numeral_numeral_nat @ N2 ) )
          = ( M = N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10636]) ).

thf(10701,plain,
    ( ( ! [Ma: nat,N2: nat,M: nat] :
          ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) )
         => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10635]) ).

thf(10702,plain,
    ( ( ~ ! [Maxi: nat] :
            ( ( some_nat @ Maxi )
           != ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ maxs ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10634]) ).

thf(10703,plain,
    ( ( ! [X: nat,N2: nat,Y: nat] :
          ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
         => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ X ) @ N2 )
            = Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[10633]) ).

thf(10704,plain,
    ( ( ! [X: nat,N2: nat,Y: nat] :
          ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
         => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ X ) @ N2 )
            = X ) ) )
    = $true ),
    inference(copy,[status(thm)],[10632]) ).

thf(10705,plain,
    ( ( ! [V: num,W: num,Z: nat] :
          ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
          = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z ) ) )
    = $true ),
    inference(copy,[status(thm)],[10631]) ).

thf(10706,plain,
    ( ( ! [M: num,N2: num] :
          ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
          = ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10630]) ).

thf(10707,plain,
    ( ( ! [V: num,W: num,Z: nat] :
          ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
          = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) )
    = $true ),
    inference(copy,[status(thm)],[10629]) ).

thf(10708,plain,
    ( ( ! [M: num,N2: num] :
          ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
          = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10628]) ).

thf(10709,plain,
    ( ( ! [N2: num] :
          ( ( times_times_num @ ( bit0 @ one ) @ N2 )
          = ( bit0 @ N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10627]) ).

thf(10710,plain,
    ( ( ! [A: nat,M: num,N2: num] :
          ( ( power_power_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) )
          = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10626]) ).

thf(10711,plain,
    ( ( ! [A: nat,M: num,N2: num,B: nat] :
          ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
          = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[10625]) ).

thf(10712,plain,
    ( ( ! [A: nat,M: num,N2: num] :
          ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N2 ) ) )
          = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10624]) ).

thf(10713,plain,
    ( ( ! [N2: num] :
          ( ( plus_plus_num @ one @ N2 )
          = ( plus_plus_num @ N2 @ one ) ) )
    = $true ),
    inference(copy,[status(thm)],[10623]) ).

thf(10714,plain,
    ( ( ! [A: nat,K: num,L2: num] :
          ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ L2 ) )
          = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ K @ L2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10622]) ).

thf(10715,plain,
    ( ( ! [M: nat,I2: nat,N2: nat] :
          ( ( ord_less_nat @ M @ ( times_times_nat @ I2 @ N2 ) )
         => ( ord_less_nat @ ( divide_divide_nat @ M @ N2 ) @ I2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10621]) ).

thf(10716,plain,
    ( ( ! [N2: nat] : ( ord_less_nat @ N2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10620]) ).

thf(10717,plain,
    ( ( ! [X: nat,Y: nat,N2: nat] :
          ( ( ( times_times_nat @ X @ Y )
            = ( times_times_nat @ Y @ X ) )
         => ( ( times_times_nat @ ( power_power_nat @ X @ N2 ) @ Y )
            = ( times_times_nat @ Y @ ( power_power_nat @ X @ N2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10619]) ).

thf(10718,plain,
    ( ( ! [A: nat,B: nat,N2: nat] :
          ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N2 )
          = ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10618]) ).

thf(10719,plain,
    ( ( ! [A: nat,N2: nat] :
          ( ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ A )
          = ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10617]) ).

thf(10720,plain,
    ( ( ! [A: nat,M: nat,N2: nat] :
          ( ( power_power_nat @ A @ ( times_times_nat @ M @ N2 ) )
          = ( power_power_nat @ ( power_power_nat @ A @ M ) @ N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10616]) ).

thf(10721,plain,
    ( ( ! [A: real,M: nat,N2: nat] :
          ( ( power_power_real @ A @ ( times_times_nat @ M @ N2 ) )
          = ( power_power_real @ ( power_power_real @ A @ M ) @ N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10615]) ).

thf(10722,plain,
    ( ( ! [A: int,M: nat,N2: nat] :
          ( ( power_power_int @ A @ ( times_times_nat @ M @ N2 ) )
          = ( power_power_int @ ( power_power_int @ A @ M ) @ N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10614]) ).

thf(10723,plain,
    ( ( ! [A: complex,M: nat,N2: nat] :
          ( ( power_power_complex @ A @ ( times_times_nat @ M @ N2 ) )
          = ( power_power_complex @ ( power_power_complex @ A @ M ) @ N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10613]) ).

thf(10724,plain,
    ( ( ! [M: nat,N2: nat,Q2: nat] :
          ( ( divide_divide_nat @ M @ ( times_times_nat @ N2 @ Q2 ) )
          = ( divide_divide_nat @ ( divide_divide_nat @ M @ N2 ) @ Q2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10612]) ).

thf(10725,plain,
    ( ( ! [A: nat] :
          ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[10611]) ).

thf(10726,plain,
    ( ( ! [A: nat] :
          ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[10610]) ).

thf(10727,plain,
    ( ( ! [N2: num] :
          ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
          = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10609]) ).

thf(10728,plain,
    ( ( ! [A: nat,M: nat,N2: nat] :
          ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N2 ) )
          = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10608]) ).

thf(10729,plain,
    ( ( ! [N2: num] :
          ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( numeral_numeral_nat @ N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10607]) ).

thf(10730,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
          = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[10606]) ).

thf(10731,plain,
    ( ( ! [Z: nat] :
          ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( plus_plus_nat @ Z @ Z ) ) )
    = $true ),
    inference(copy,[status(thm)],[10605]) ).

thf(10732,plain,
    ( ( ! [Z: nat] :
          ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
          = ( plus_plus_nat @ Z @ Z ) ) )
    = $true ),
    inference(copy,[status(thm)],[10604]) ).

thf(10733,plain,
    ( ( ! [A: nat] :
          ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( times_times_nat @ A @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[10603]) ).

thf(10734,plain,
    ( ( ! [X: nat] :
          ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
          = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X @ X ) @ X ) @ X ) ) )
    = $true ),
    inference(copy,[status(thm)],[10602]) ).

thf(10735,plain,
    ( ( ! [A: nat,N2: nat] :
          ( ( power_power_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
          = ( power_power_nat @ ( power_power_nat @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10601]) ).

thf(10736,plain,
    ( ( ! [A: real,N2: nat] :
          ( ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
          = ( power_power_real @ ( power_power_real @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10600]) ).

thf(10737,plain,
    ( ( ! [A: int,N2: nat] :
          ( ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
          = ( power_power_int @ ( power_power_int @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10599]) ).

thf(10738,plain,
    ( ( ! [A: complex,N2: nat] :
          ( ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
          = ( power_power_complex @ ( power_power_complex @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10598]) ).

thf(10739,plain,
    ( ( ! [I2: nat,J: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
          ( ( I2 != J )
         => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ X ) @ J )
            = ( nth_VEBT_VEBT @ Xs @ J ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10597]) ).

thf(10740,plain,
    ( ( ! [Xs: list_VEBT_VEBT,I2: nat] :
          ( ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ ( nth_VEBT_VEBT @ Xs @ I2 ) )
          = Xs ) )
    = $true ),
    inference(copy,[status(thm)],[10596]) ).

thf(10741,plain,
    ( ( ! [Xs: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT] :
          ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ X ) )
          = ( size_s6755466524823107622T_VEBT @ Xs ) ) )
    = $true ),
    inference(copy,[status(thm)],[10595]) ).

thf(10742,plain,
    ( ( ! [Xs: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT,Y: vEBT_VEBT] :
          ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ X ) @ I2 @ Y )
          = ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[10594]) ).

thf(10743,plain,
    ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg )
    = $true ),
    inference(copy,[status(thm)],[10593]) ).

thf(10744,plain,
    ( ( vEBT_invar_vebt @ ( nth_VEBT_VEBT @ treeList @ summin ) @ na )
    = $true ),
    inference(copy,[status(thm)],[10592]) ).

thf(10745,plain,
    ( ( vEBT_invar_vebt @ ( nth_VEBT_VEBT @ treeList @ maxs ) @ na )
    = $true ),
    inference(copy,[status(thm)],[10591]) ).

thf(10746,plain,
    ( ( ! [M: nat,N2: nat,K: nat] :
          ( ( ord_less_eq_nat @ M @ N2 )
         => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N2 @ K ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10590]) ).

thf(10747,plain,
    ( ( ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N2 ) @ M ) )
    = $true ),
    inference(copy,[status(thm)],[10589]) ).

thf(10748,plain,
    ( ( ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N2 ) @ N2 ) @ M ) )
    = $true ),
    inference(copy,[status(thm)],[10588]) ).

thf(10749,plain,
    ( ( ! [N2: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N2 @ ( divide_divide_nat @ M @ N2 ) ) @ M ) )
    = $true ),
    inference(copy,[status(thm)],[10587]) ).

thf(10750,plain,
    ( ( ! [I2: nat,I5: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT,X6: vEBT_VEBT] :
          ( ( I2 != I5 )
         => ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I2 @ X ) @ I5 @ X6 )
            = ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I5 @ X6 ) @ I2 @ X ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10586]) ).

thf(10751,plain,
    ( ( ! [K: nat,M: nat] :
          ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
         => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10585]) ).

thf(10752,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
          = ( ord_less_eq_nat @ M @ N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10584]) ).

thf(10753,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N2 )
         => ( ord_less_eq_nat @ M @ N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10583]) ).

thf(10754,plain,
    ( ( ! [X22: nat] :
          ( ( the_nat @ ( some_nat @ X22 ) )
          = X22 ) )
    = $true ),
    inference(copy,[status(thm)],[10582]) ).

thf(10755,plain,
    ( ( ! [Option: option_nat,Option2: option_nat] :
          ( ( ( Option = none_nat )
            = ( Option2 = none_nat ) )
         => ( ( ( Option != none_nat )
             => ( ( Option2 != none_nat )
               => ( ( the_nat @ Option )
                  = ( the_nat @ Option2 ) ) ) )
           => ( Option = Option2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10581]) ).

thf(10756,plain,
    ( ( ! [N2: num] : ( ord_less_num @ one @ ( bit0 @ N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10580]) ).

thf(10757,plain,
    ( ( ( plus_plus_num @ one @ one )
      = ( bit0 @ one ) )
    = $true ),
    inference(copy,[status(thm)],[10579]) ).

thf(10758,plain,
    ( ( ! [M: num] :
          ~ ( ord_less_num @ M @ one ) )
    = $true ),
    inference(copy,[status(thm)],[10578]) ).

thf(10759,plain,
    ( ( ! [M: num,N2: num] :
          ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
          = ( ord_less_num @ M @ N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10577]) ).

thf(10760,plain,
    ( ( ! [M: num,N2: num] :
          ( ( ( bit0 @ M )
            = ( bit0 @ N2 ) )
          = ( M = N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10576]) ).

thf(10761,plain,
    ( ( ! [N2: num] :
          ( one
         != ( bit0 @ N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10575]) ).

thf(10762,plain,
    ( ( ! [M: num] :
          ( ( bit0 @ M )
         != one ) )
    = $true ),
    inference(copy,[status(thm)],[10574]) ).

thf(10763,plain,
    ( ( ! [A: nat] :
          ( ( divide_divide_nat @ A @ one_one_nat )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[10573]) ).

thf(10764,plain,
    ( ( ! [N2: nat] :
          ( ( power_power_nat @ one_one_nat @ N2 )
          = one_one_nat ) )
    = $true ),
    inference(copy,[status(thm)],[10572]) ).

thf(10765,plain,
    ( ( ! [A: nat] :
          ( ( power_power_nat @ A @ one_one_nat )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[10571]) ).

thf(10766,plain,
    ( ( ! [M: num,N2: num] :
          ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
          = ( bit0 @ ( plus_plus_num @ M @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10570]) ).

thf(10767,plain,
    ( ( ! [M: num,N2: num] :
          ( ( times_times_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
          = ( bit0 @ ( bit0 @ ( times_times_num @ M @ N2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10569]) ).

thf(10768,plain,
    ( ( ! [M: num] :
          ( ( times_times_num @ M @ one )
          = M ) )
    = $true ),
    inference(copy,[status(thm)],[10568]) ).

thf(10769,plain,
    ( ( ! [N2: num] :
          ( ( times_times_num @ one @ N2 )
          = N2 ) )
    = $true ),
    inference(copy,[status(thm)],[10567]) ).

thf(10770,plain,
    ( ( ! [M: num,N2: num] :
          ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
          = ( ord_less_eq_num @ M @ N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10566]) ).

thf(10771,plain,
    ( ( ! [N2: num] : ( ord_less_eq_num @ one @ N2 ) )
    = $true ),
    inference(copy,[status(thm)],[10565]) ).

thf(10772,plain,
    ( ( ! [N2: num] :
          ( ( one_one_nat
            = ( numeral_numeral_nat @ N2 ) )
          = ( one = N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10564]) ).

thf(10773,plain,
    ( ( ! [N2: num] :
          ( ( ( numeral_numeral_nat @ N2 )
            = one_one_nat )
          = ( N2 = one ) ) )
    = $true ),
    inference(copy,[status(thm)],[10563]) ).

thf(10774,plain,
    ( ( ! [M: num] :
          ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) )
    = $true ),
    inference(copy,[status(thm)],[10562]) ).

thf(10775,plain,
    ( ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
      = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
    = $true ),
    inference(copy,[status(thm)],[10561]) ).

thf(10776,plain,
    ( ( ! [X: num] :
          ( ( ord_less_eq_num @ X @ one )
          = ( X = one ) ) )
    = $true ),
    inference(copy,[status(thm)],[10560]) ).

thf(10777,plain,
    ( ( ! [X: num] :
          ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
          = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[10559]) ).

thf(10778,plain,
    ( ( ( numeral_numeral_nat @ one )
      = one_one_nat )
    = $true ),
    inference(copy,[status(thm)],[10558]) ).

thf(10779,plain,
    ( ( ! [X: nat,Y: nat,N2: nat] :
          ( ( ( times_times_nat @ X @ Y )
            = one_one_nat )
         => ( ( times_times_nat @ ( power_power_nat @ X @ N2 ) @ ( power_power_nat @ Y @ N2 ) )
            = one_one_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[10557]) ).

thf(10780,plain,
    ( ( ( numeral_numeral_nat @ one )
      = one_one_nat )
    = $true ),
    inference(copy,[status(thm)],[10556]) ).

thf(10781,plain,
    ( ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
      = one_one_nat )
    = $true ),
    inference(copy,[status(thm)],[10555]) ).

thf(10782,plain,
    ( ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
      = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
    = $true ),
    inference(copy,[status(thm)],[10554]) ).

thf(10783,plain,
    ( ( ! [I2: nat,U: nat,J: nat,K: nat] :
          ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
          = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I2 @ J ) @ U ) @ K ) ) )
    = $true ),
    inference(copy,[status(thm)],[10553]) ).

thf(10784,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( one_one_nat
            = ( times_times_nat @ M @ N2 ) )
          = ( ( M = one_one_nat )
            & ( N2 = one_one_nat ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10552]) ).

thf(10785,plain,
    ( ( ! [X: nat] :
          ( ! [N4: nat] :
              ( X
             != ( plus_plus_nat @ N4 @ N4 ) )
         => ~ ! [N4: nat] :
                ( X
               != ( plus_plus_nat @ N4 @ ( suc @ N4 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10551]) ).

thf(10786,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( plus_plus_nat @ M @ ( suc @ N2 ) )
          = ( suc @ ( plus_plus_nat @ M @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10550]) ).

thf(10787,plain,
    ( ( ! [K: nat,M: nat,N2: nat] :
          ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
          = ( ord_less_nat @ M @ N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10549]) ).

thf(10788,plain,
    ( ( ! [K: nat,M: nat,N2: nat] :
          ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
          = ( ord_less_eq_nat @ M @ N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10548]) ).

thf(10789,plain,
    ( ( ! [I2: nat,J: nat,K: nat] :
          ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
          = ( minus_minus_nat @ I2 @ ( plus_plus_nat @ J @ K ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10547]) ).

thf(10790,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( ( times_times_nat @ M @ N2 )
            = one_one_nat )
          = ( ( M = one_one_nat )
            & ( N2 = one_one_nat ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10546]) ).

thf(10791,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( times_times_nat @ M @ ( suc @ N2 ) )
          = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10545]) ).

thf(10792,plain,
    ( ( ! [N2: nat] :
          ( ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( suc @ ( suc @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10544]) ).

thf(10793,plain,
    ( ( ! [N2: nat] :
          ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
          = ( suc @ ( suc @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10543]) ).

thf(10794,plain,
    ( ( ! [M: nat] :
          ( ( divide_divide_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( suc @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10542]) ).

thf(10795,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ N2 )
          = M ) )
    = $true ),
    inference(copy,[status(thm)],[10541]) ).

thf(10796,plain,
    ( ( ! [N2: nat,M: nat] :
          ( ( minus_minus_nat @ ( plus_plus_nat @ N2 @ M ) @ N2 )
          = M ) )
    = $true ),
    inference(copy,[status(thm)],[10540]) ).

thf(10797,plain,
    ( ( ! [M: nat,K: nat,N2: nat] :
          ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) )
          = ( minus_minus_nat @ M @ N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10539]) ).

thf(10798,plain,
    ( ( ! [K: nat,M: nat,N2: nat] :
          ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
          = ( minus_minus_nat @ M @ N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10538]) ).

thf(10799,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( plus_plus_nat @ ( suc @ M ) @ N2 )
          = ( plus_plus_nat @ M @ ( suc @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10537]) ).

thf(10800,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( plus_plus_nat @ ( suc @ M ) @ N2 )
          = ( suc @ ( plus_plus_nat @ M @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10536]) ).

thf(10801,plain,
    ( ( ! [A2: nat,K: nat,A: nat] :
          ( ( A2
            = ( plus_plus_nat @ K @ A ) )
         => ( ( suc @ A2 )
            = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10535]) ).

thf(10802,plain,
    ( ( ! [K: nat,M: nat,N2: nat] :
          ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
          = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10534]) ).

thf(10803,plain,
    ( ( ! [M: nat,N2: nat,K: nat] :
          ( ( times_times_nat @ ( minus_minus_nat @ M @ N2 ) @ K )
          = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10533]) ).

thf(10804,plain,
    ( ( ! [K: nat,M: nat,N2: nat] :
          ( ( ( times_times_nat @ ( suc @ K ) @ M )
            = ( times_times_nat @ ( suc @ K ) @ N2 ) )
          = ( M = N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10532]) ).

thf(10805,plain,
    ( ( ! [N2: num] :
          ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
          = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10531]) ).

thf(10806,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( times_times_nat @ ( suc @ M ) @ N2 )
          = ( plus_plus_nat @ N2 @ ( times_times_nat @ M @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10530]) ).

thf(10807,plain,
    ( ( ! [Z: nat,W: num] :
          ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
          = ( times_times_nat @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10529]) ).

thf(10808,plain,
    ( ( ! [A: nat,N2: nat] :
          ( ( power_power_nat @ A @ ( suc @ N2 ) )
          = ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[10528]) ).

thf(10809,plain,
    ( ( ! [A: nat,N2: nat] :
          ( ( power_power_nat @ A @ ( suc @ N2 ) )
          = ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10527]) ).

thf(10810,plain,
    ( ( ! [A: nat,N2: nat] :
          ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
          = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10526]) ).

thf(10811,plain,
    ( ( ! [K: nat,L2: nat,M: nat,N2: nat] :
          ( ( ord_less_nat @ K @ L2 )
         => ( ( ( plus_plus_nat @ M @ L2 )
              = ( plus_plus_nat @ K @ N2 ) )
           => ( ord_less_nat @ M @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10525]) ).

thf(10812,plain,
    ( ( ! [I2: nat,J: nat,M: nat] :
          ( ( ord_less_nat @ I2 @ J )
         => ( ord_less_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10524]) ).

thf(10813,plain,
    ( ( ! [I2: nat,J: nat,M: nat] :
          ( ( ord_less_nat @ I2 @ J )
         => ( ord_less_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10523]) ).

thf(10814,plain,
    ( ( ! [I2: nat,J: nat,K: nat] :
          ( ( ord_less_nat @ I2 @ J )
         => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10522]) ).

thf(10815,plain,
    ( ( ! [J: nat,I2: nat] :
          ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I2 ) @ I2 ) )
    = $true ),
    inference(copy,[status(thm)],[10521]) ).

thf(10816,plain,
    ( ( ! [I2: nat,J: nat] :
          ~ ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ I2 ) )
    = $true ),
    inference(copy,[status(thm)],[10520]) ).

thf(10817,plain,
    ( ( ! [I2: nat,J: nat,K: nat,L2: nat] :
          ( ( ord_less_nat @ I2 @ J )
         => ( ( ord_less_nat @ K @ L2 )
           => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10519]) ).

thf(10818,plain,
    ( ( ! [I2: nat,J: nat,K: nat] :
          ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ K )
         => ( ord_less_nat @ I2 @ K ) ) )
    = $true ),
    inference(copy,[status(thm)],[10518]) ).

thf(10819,plain,
    ( ( ord_less_eq_nat
      = ( ^ [M6: nat,N: nat] :
          ? [K3: nat] :
            ( N
            = ( plus_plus_nat @ M6 @ K3 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10517]) ).

thf(10820,plain,
    ( ( ! [I2: nat,J: nat,M: nat] :
          ( ( ord_less_eq_nat @ I2 @ J )
         => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10516]) ).

thf(10821,plain,
    ( ( ! [I2: nat,J: nat,M: nat] :
          ( ( ord_less_eq_nat @ I2 @ J )
         => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10515]) ).

thf(10822,plain,
    ( ( ! [I2: nat,J: nat,K: nat] :
          ( ( ord_less_eq_nat @ I2 @ J )
         => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10514]) ).

thf(10823,plain,
    ( ( ! [I2: nat,J: nat,K: nat,L2: nat] :
          ( ( ord_less_eq_nat @ I2 @ J )
         => ( ( ord_less_eq_nat @ K @ L2 )
           => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10513]) ).

thf(10824,plain,
    ( ( ! [K: nat,L2: nat] :
          ( ( ord_less_eq_nat @ K @ L2 )
         => ? [N4: nat] :
              ( L2
              = ( plus_plus_nat @ K @ N4 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10512]) ).

thf(10825,plain,
    ( ( ! [M: nat,K: nat,N2: nat] :
          ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
         => ( ord_less_eq_nat @ K @ N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10511]) ).

thf(10826,plain,
    ( ( ! [M: nat,K: nat,N2: nat] :
          ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
         => ( ord_less_eq_nat @ M @ N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10510]) ).

thf(10827,plain,
    ( ( ! [N2: nat,M: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ M @ N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10509]) ).

thf(10828,plain,
    ( ( ! [N2: nat,M: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ N2 @ M ) ) )
    = $true ),
    inference(copy,[status(thm)],[10508]) ).

thf(10829,plain,
    ( ( ! [M: nat,K: nat,N2: nat] :
          ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
         => ~ ( ( ord_less_eq_nat @ M @ N2 )
             => ~ ( ord_less_eq_nat @ K @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10507]) ).

thf(10830,plain,
    ( ( ! [I2: nat,J: nat,K: nat] :
          ( ( ord_less_eq_nat @ I2 @ J )
         => ( ord_less_eq_nat @ ( times_times_nat @ K @ I2 ) @ ( times_times_nat @ K @ J ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10506]) ).

thf(10831,plain,
    ( ( ! [I2: nat,J: nat,K: nat] :
          ( ( ord_less_eq_nat @ I2 @ J )
         => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ K ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10505]) ).

thf(10832,plain,
    ( ( ! [I2: nat,J: nat,K: nat,L2: nat] :
          ( ( ord_less_eq_nat @ I2 @ J )
         => ( ( ord_less_eq_nat @ K @ L2 )
           => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ L2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10504]) ).

thf(10833,plain,
    ( ( ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) )
    = $true ),
    inference(copy,[status(thm)],[10503]) ).

thf(10834,plain,
    ( ( ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10502]) ).

thf(10835,plain,
    ( ( ! [K: nat,M: nat,N2: nat] :
          ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N2 ) )
          = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10501]) ).

thf(10836,plain,
    ( ( ! [M: nat,N2: nat,K: nat] :
          ( ( times_times_nat @ ( plus_plus_nat @ M @ N2 ) @ K )
          = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10500]) ).

thf(10837,plain,
    ( ( ! [N2: nat] :
          ( ( times_times_nat @ N2 @ one_one_nat )
          = N2 ) )
    = $true ),
    inference(copy,[status(thm)],[10499]) ).

thf(10838,plain,
    ( ( ! [N2: nat] :
          ( ( times_times_nat @ one_one_nat @ N2 )
          = N2 ) )
    = $true ),
    inference(copy,[status(thm)],[10498]) ).

thf(10839,plain,
    ( ( ! [A: nat] :
          ( ( divide_divide_nat @ A @ one_one_nat )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[10497]) ).

thf(10840,plain,
    ( ( ! [M: nat,N2: nat,Q2: nat] :
          ( ( plus_plus_nat @ ( ord_max_nat @ M @ N2 ) @ Q2 )
          = ( ord_max_nat @ ( plus_plus_nat @ M @ Q2 ) @ ( plus_plus_nat @ N2 @ Q2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10496]) ).

thf(10841,plain,
    ( ( ! [M: nat,N2: nat,Q2: nat] :
          ( ( plus_plus_nat @ M @ ( ord_max_nat @ N2 @ Q2 ) )
          = ( ord_max_nat @ ( plus_plus_nat @ M @ N2 ) @ ( plus_plus_nat @ M @ Q2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10495]) ).

thf(10842,plain,
    ( ( ! [M: nat,N2: nat,Q2: nat] :
          ( ( times_times_nat @ ( ord_max_nat @ M @ N2 ) @ Q2 )
          = ( ord_max_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N2 @ Q2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10494]) ).

thf(10843,plain,
    ( ( ! [M: nat,N2: nat,Q2: nat] :
          ( ( times_times_nat @ M @ ( ord_max_nat @ N2 @ Q2 ) )
          = ( ord_max_nat @ ( times_times_nat @ M @ N2 ) @ ( times_times_nat @ M @ Q2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10493]) ).

thf(10844,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
          = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10492]) ).

thf(10845,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
          = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10491]) ).

thf(10846,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
          = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10490]) ).

thf(10847,plain,
    ( ( ! [A: nat,E: nat,B: nat,C: nat] :
          ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C ) )
          = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C ) ) )
    = $true ),
    inference(copy,[status(thm)],[10489]) ).

thf(10848,plain,
    ( ( ! [B: nat,C: nat,A: nat] :
          ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
          = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10488]) ).

thf(10849,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
          = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10487]) ).

thf(10850,plain,
    ( ( ( ^ [X2: nat] : X2 )
      = ( times_times_nat @ one_one_nat ) )
    = $true ),
    inference(copy,[status(thm)],[10486]) ).

thf(10851,plain,
    ( ( ! [C: nat] :
          ( ( ^ [X2: nat] : ( times_times_nat @ X2 @ C ) )
          = ( times_times_nat @ C ) ) )
    = $true ),
    inference(copy,[status(thm)],[10485]) ).

thf(10852,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
         != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10484]) ).

thf(10853,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
         != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10483]) ).

thf(10854,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[10482]) ).

thf(10855,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
          = ( minus_minus_nat @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[10481]) ).

thf(10856,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
          = B ) )
    = $true ),
    inference(copy,[status(thm)],[10480]) ).

thf(10857,plain,
    ( ( ! [C: nat,A: nat,B: nat] :
          ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
          = ( minus_minus_nat @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[10479]) ).

thf(10858,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( ( plus_plus_nat @ A @ B )
            = ( plus_plus_nat @ A @ C ) )
          = ( B = C ) ) )
    = $true ),
    inference(copy,[status(thm)],[10478]) ).

thf(10859,plain,
    ( ( ! [B: nat,A: nat,C: nat] :
          ( ( ( plus_plus_nat @ B @ A )
            = ( plus_plus_nat @ C @ A ) )
          = ( B = C ) ) )
    = $true ),
    inference(copy,[status(thm)],[10477]) ).

thf(10860,plain,
    ( ( ! [C: nat,A: nat,B: nat] :
          ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
          = ( ord_less_eq_nat @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[10476]) ).

thf(10861,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
          = ( ord_less_eq_nat @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[10475]) ).

thf(10862,plain,
    ( ( ! [C: nat,A: nat,B: nat] :
          ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
          = ( ord_less_nat @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[10474]) ).

thf(10863,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
          = ( ord_less_nat @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[10473]) ).

thf(10864,plain,
    ( ( ! [A: nat] :
          ( ( times_times_nat @ A @ one_one_nat )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[10472]) ).

thf(10865,plain,
    ( ( ! [A: nat] :
          ( ( times_times_nat @ one_one_nat @ A )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[10471]) ).

thf(10866,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
          = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10470]) ).

thf(10867,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
          = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10469]) ).

thf(10868,plain,
    ( ( times_times_nat
      = ( ^ [A5: nat,B5: nat] : ( times_times_nat @ B5 @ A5 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10468]) ).

thf(10869,plain,
    ( ( ! [B: nat,A: nat,C: nat] :
          ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
          = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10467]) ).

thf(10870,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
          = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10466]) ).

thf(10871,plain,
    ( ( ! [I2: nat,J: nat,K: nat,L2: nat] :
          ( ( ( I2 = J )
            & ( K = L2 ) )
         => ( ( plus_plus_nat @ I2 @ K )
            = ( plus_plus_nat @ J @ L2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10465]) ).

thf(10872,plain,
    ( ( ! [A2: nat,K: nat,A: nat,B: nat] :
          ( ( A2
            = ( plus_plus_nat @ K @ A ) )
         => ( ( plus_plus_nat @ A2 @ B )
            = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10464]) ).

thf(10873,plain,
    ( ( ! [B3: nat,K: nat,B: nat,A: nat] :
          ( ( B3
            = ( plus_plus_nat @ K @ B ) )
         => ( ( plus_plus_nat @ A @ B3 )
            = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10463]) ).

thf(10874,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
          = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10462]) ).

thf(10875,plain,
    ( ( plus_plus_nat
      = ( ^ [A5: nat,B5: nat] : ( plus_plus_nat @ B5 @ A5 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10461]) ).

thf(10876,plain,
    ( ( ! [B: nat,A: nat,C: nat] :
          ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
          = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10460]) ).

thf(10877,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( ( plus_plus_nat @ A @ B )
            = ( plus_plus_nat @ A @ C ) )
         => ( B = C ) ) )
    = $true ),
    inference(copy,[status(thm)],[10459]) ).

thf(10878,plain,
    ( ( ! [B: nat,A: nat,C: nat] :
          ( ( ( plus_plus_nat @ B @ A )
            = ( plus_plus_nat @ C @ A ) )
         => ( B = C ) ) )
    = $true ),
    inference(copy,[status(thm)],[10458]) ).

thf(10879,plain,
    ( ( ! [I2: nat,J: nat,K: nat,L2: nat] :
          ( ( ( ord_less_eq_nat @ I2 @ J )
            & ( K = L2 ) )
         => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10457]) ).

thf(10880,plain,
    ( ( ! [I2: nat,J: nat,K: nat,L2: nat] :
          ( ( ( I2 = J )
            & ( ord_less_eq_nat @ K @ L2 ) )
         => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10456]) ).

thf(10881,plain,
    ( ( ! [I2: nat,J: nat,K: nat,L2: nat] :
          ( ( ( ord_less_eq_nat @ I2 @ J )
            & ( ord_less_eq_nat @ K @ L2 ) )
         => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10455]) ).

thf(10882,plain,
    ( ( ! [A: nat,B: nat,C: nat,D: nat] :
          ( ( ord_less_eq_nat @ A @ B )
         => ( ( ord_less_eq_nat @ C @ D )
           => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10454]) ).

thf(10883,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( ord_less_eq_nat @ A @ B )
         => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10453]) ).

thf(10884,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( ord_less_eq_nat @ A @ B )
         => ~ ! [C3: nat] :
                ( B
               != ( plus_plus_nat @ A @ C3 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10452]) ).

thf(10885,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( ord_less_eq_nat @ A @ B )
         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10451]) ).

thf(10886,plain,
    ( ( ord_less_eq_nat
      = ( ^ [A5: nat,B5: nat] :
          ? [C4: nat] :
            ( B5
            = ( plus_plus_nat @ A5 @ C4 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10450]) ).

thf(10887,plain,
    ( ( ! [C: nat,A: nat,B: nat] :
          ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
         => ( ord_less_eq_nat @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[10449]) ).

thf(10888,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
         => ( ord_less_eq_nat @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[10448]) ).

thf(10889,plain,
    ( ( ! [I2: nat,J: nat,K: nat,L2: nat] :
          ( ( ( ord_less_nat @ I2 @ J )
            & ( ord_less_nat @ K @ L2 ) )
         => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10447]) ).

thf(10890,plain,
    ( ( ! [I2: nat,J: nat,K: nat,L2: nat] :
          ( ( ( I2 = J )
            & ( ord_less_nat @ K @ L2 ) )
         => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10446]) ).

thf(10891,plain,
    ( ( ! [I2: nat,J: nat,K: nat,L2: nat] :
          ( ( ( ord_less_nat @ I2 @ J )
            & ( K = L2 ) )
         => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10445]) ).

thf(10892,plain,
    ( ( ! [A: nat,B: nat,C: nat,D: nat] :
          ( ( ord_less_nat @ A @ B )
         => ( ( ord_less_nat @ C @ D )
           => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10444]) ).

thf(10893,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( ord_less_nat @ A @ B )
         => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10443]) ).

thf(10894,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( ord_less_nat @ A @ B )
         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10442]) ).

thf(10895,plain,
    ( ( ! [C: nat,A: nat,B: nat] :
          ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
         => ( ord_less_nat @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[10441]) ).

thf(10896,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
         => ( ord_less_nat @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[10440]) ).

thf(10897,plain,
    ( ( ! [A: nat] :
          ( ( times_times_nat @ one_one_nat @ A )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[10439]) ).

thf(10898,plain,
    ( ( ! [A: nat] :
          ( ( times_times_nat @ A @ one_one_nat )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[10438]) ).

thf(10899,plain,
    ( ( ! [C: nat,B: nat,A: nat] :
          ( ( ( plus_plus_nat @ C @ B )
            = A )
         => ( C
            = ( minus_minus_nat @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10437]) ).

thf(10900,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
          = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10436]) ).

thf(10901,plain,
    ( ( ! [X: nat,Y: nat,Z: nat] :
          ( ( plus_plus_nat @ ( ord_max_nat @ X @ Y ) @ Z )
          = ( ord_max_nat @ ( plus_plus_nat @ X @ Z ) @ ( plus_plus_nat @ Y @ Z ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10435]) ).

thf(10902,plain,
    ( ( ! [X: nat,Y: nat,Z: nat] :
          ( ( plus_plus_nat @ X @ ( ord_max_nat @ Y @ Z ) )
          = ( ord_max_nat @ ( plus_plus_nat @ X @ Y ) @ ( plus_plus_nat @ X @ Z ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10434]) ).

thf(10903,plain,
    ( ( vEBT_VEBT_low
      = ( ^ [X2: nat,N: nat] : ( modulo_modulo_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10433]) ).

thf(10904,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( ( times_times_nat @ A @ C )
            = ( times_times_nat @ B @ C ) )
          = ( ( C = zero_zero_nat )
            | ( A = B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10432]) ).

thf(10905,plain,
    ( ( ! [C: nat,A: nat,B: nat] :
          ( ( ( times_times_nat @ C @ A )
            = ( times_times_nat @ C @ B ) )
          = ( ( C = zero_zero_nat )
            | ( A = B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10431]) ).

thf(10906,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( ( times_times_nat @ A @ B )
            = zero_zero_nat )
          = ( ( A = zero_zero_nat )
            | ( B = zero_zero_nat ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10430]) ).

thf(10907,plain,
    ( ( ! [A: nat] :
          ( ( times_times_nat @ A @ zero_zero_nat )
          = zero_zero_nat ) )
    = $true ),
    inference(copy,[status(thm)],[10429]) ).

thf(10908,plain,
    ( ( ! [A: nat] :
          ( ( times_times_nat @ zero_zero_nat @ A )
          = zero_zero_nat ) )
    = $true ),
    inference(copy,[status(thm)],[10428]) ).

thf(10909,plain,
    ( ( ! [A: nat] :
          ( ( plus_plus_nat @ zero_zero_nat @ A )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[10427]) ).

thf(10910,plain,
    ( ( ! [X: nat,Y: nat] :
          ( ( zero_zero_nat
            = ( plus_plus_nat @ X @ Y ) )
          = ( ( X = zero_zero_nat )
            & ( Y = zero_zero_nat ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10426]) ).

thf(10911,plain,
    ( ( ! [X: nat,Y: nat] :
          ( ( ( plus_plus_nat @ X @ Y )
            = zero_zero_nat )
          = ( ( X = zero_zero_nat )
            & ( Y = zero_zero_nat ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10425]) ).

thf(10912,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( A
            = ( plus_plus_nat @ A @ B ) )
          = ( B = zero_zero_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[10424]) ).

thf(10913,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( A
            = ( plus_plus_nat @ B @ A ) )
          = ( B = zero_zero_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[10423]) ).

thf(10914,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( ( plus_plus_nat @ A @ B )
            = A )
          = ( B = zero_zero_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[10422]) ).

thf(10915,plain,
    ( ( ! [B: nat,A: nat] :
          ( ( ( plus_plus_nat @ B @ A )
            = A )
          = ( B = zero_zero_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[10421]) ).

thf(10916,plain,
    ( ( ! [A: nat] :
          ( ( plus_plus_nat @ A @ zero_zero_nat )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[10420]) ).

thf(10917,plain,
    ( ( ! [A: nat] :
          ( ( divide_divide_nat @ A @ zero_zero_nat )
          = zero_zero_nat ) )
    = $true ),
    inference(copy,[status(thm)],[10419]) ).

thf(10918,plain,
    ( ( ! [A: nat] :
          ( ( divide_divide_nat @ zero_zero_nat @ A )
          = zero_zero_nat ) )
    = $true ),
    inference(copy,[status(thm)],[10418]) ).

thf(10919,plain,
    ( ( ! [A: nat] :
          ( ( divide_divide_nat @ A @ zero_zero_nat )
          = zero_zero_nat ) )
    = $true ),
    inference(copy,[status(thm)],[10417]) ).

thf(10920,plain,
    ( ( ! [A: nat] :
          ( ( divide_divide_nat @ zero_zero_nat @ A )
          = zero_zero_nat ) )
    = $true ),
    inference(copy,[status(thm)],[10416]) ).

thf(10921,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ B )
          = ( modulo_modulo_nat @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[10415]) ).

thf(10922,plain,
    ( ( ! [B: nat,A: nat] :
          ( ( modulo_modulo_nat @ ( plus_plus_nat @ B @ A ) @ B )
          = ( modulo_modulo_nat @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[10414]) ).

thf(10923,plain,
    ( ( ! [M: nat] :
          ( ( plus_plus_nat @ M @ zero_zero_nat )
          = M ) )
    = $true ),
    inference(copy,[status(thm)],[10413]) ).

thf(10924,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( ( plus_plus_nat @ M @ N2 )
            = zero_zero_nat )
          = ( ( M = zero_zero_nat )
            & ( N2 = zero_zero_nat ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10412]) ).

thf(10925,plain,
    ( ( ! [M: nat,K: nat,N2: nat] :
          ( ( ( times_times_nat @ M @ K )
            = ( times_times_nat @ N2 @ K ) )
          = ( ( M = N2 )
            | ( K = zero_zero_nat ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10411]) ).

thf(10926,plain,
    ( ( ! [K: nat,M: nat,N2: nat] :
          ( ( ( times_times_nat @ K @ M )
            = ( times_times_nat @ K @ N2 ) )
          = ( ( M = N2 )
            | ( K = zero_zero_nat ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10410]) ).

thf(10927,plain,
    ( ( ! [M: nat] :
          ( ( times_times_nat @ M @ zero_zero_nat )
          = zero_zero_nat ) )
    = $true ),
    inference(copy,[status(thm)],[10409]) ).

thf(10928,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( ( times_times_nat @ M @ N2 )
            = zero_zero_nat )
          = ( ( M = zero_zero_nat )
            | ( N2 = zero_zero_nat ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10408]) ).

thf(10929,plain,
    ( ( ! [C: nat,A: nat,B: nat] :
          ( ( ( C = zero_zero_nat )
           => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
              = zero_zero_nat ) )
          & ( ( C != zero_zero_nat )
           => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
              = ( divide_divide_nat @ A @ B ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10407]) ).

thf(10930,plain,
    ( ( ! [C: nat,A: nat,B: nat] :
          ( ( C != zero_zero_nat )
         => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
            = ( divide_divide_nat @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10406]) ).

thf(10931,plain,
    ( ( ! [C: nat,A: nat,B: nat] :
          ( ( C != zero_zero_nat )
         => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
            = ( divide_divide_nat @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10405]) ).

thf(10932,plain,
    ( ( ! [B: nat,A: nat] :
          ( ( B != zero_zero_nat )
         => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
            = A ) ) )
    = $true ),
    inference(copy,[status(thm)],[10404]) ).

thf(10933,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( A != zero_zero_nat )
         => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
            = B ) ) )
    = $true ),
    inference(copy,[status(thm)],[10403]) ).

thf(10934,plain,
    ( ( ! [K: num] :
          ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
          = zero_zero_nat ) )
    = $true ),
    inference(copy,[status(thm)],[10402]) ).

thf(10935,plain,
    ( ( ! [B: nat,C: nat,A: nat] :
          ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
          = ( modulo_modulo_nat @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[10401]) ).

thf(10936,plain,
    ( ( ! [C: nat,B: nat,A: nat] :
          ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
          = ( modulo_modulo_nat @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[10400]) ).

thf(10937,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
          = ( modulo_modulo_nat @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[10399]) ).

thf(10938,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
          = ( modulo_modulo_nat @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[10398]) ).

thf(10939,plain,
    ( ( ! [K: nat,M: nat,N2: nat] :
          ( ( ( K = zero_zero_nat )
           => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
              = zero_zero_nat ) )
          & ( ( K != zero_zero_nat )
           => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
              = ( divide_divide_nat @ M @ N2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10397]) ).

thf(10940,plain,
    ( ( ! [B: nat,C: nat,A: nat] :
          ( ( B != zero_zero_nat )
         => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
            = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10396]) ).

thf(10941,plain,
    ( ( ! [B: nat,C: nat,A: nat] :
          ( ( B != zero_zero_nat )
         => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
            = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10395]) ).

thf(10942,plain,
    ( ( ! [B: nat,A: nat,C: nat] :
          ( ( B != zero_zero_nat )
         => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
            = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10394]) ).

thf(10943,plain,
    ( ( ! [B: nat,A: nat,C: nat] :
          ( ( B != zero_zero_nat )
         => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
            = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10393]) ).

thf(10944,plain,
    ( ( ! [A: nat] :
          ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
            = zero_zero_nat )
          = ( A = zero_zero_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[10392]) ).

thf(10945,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
          = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) )
    = $true ),
    inference(copy,[status(thm)],[10391]) ).

thf(10946,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
          = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) )
    = $true ),
    inference(copy,[status(thm)],[10390]) ).

thf(10947,plain,
    ( ( ! [C: nat,A: nat,B: nat] :
          ( ( times_times_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
          = ( modulo_modulo_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10389]) ).

thf(10948,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
          = ( times_times_nat @ ( modulo_modulo_nat @ A @ B ) @ C ) ) )
    = $true ),
    inference(copy,[status(thm)],[10388]) ).

thf(10949,plain,
    ( ( ! [A: nat,C: nat,A6: nat,B: nat,B6: nat] :
          ( ( ( modulo_modulo_nat @ A @ C )
            = ( modulo_modulo_nat @ A6 @ C ) )
         => ( ( ( modulo_modulo_nat @ B @ C )
              = ( modulo_modulo_nat @ B6 @ C ) )
           => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C )
              = ( modulo_modulo_nat @ ( times_times_nat @ A6 @ B6 ) @ C ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10387]) ).

thf(10950,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
          = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) )
    = $true ),
    inference(copy,[status(thm)],[10386]) ).

thf(10951,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
          = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) )
    = $true ),
    inference(copy,[status(thm)],[10385]) ).

thf(10952,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
          = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) )
    = $true ),
    inference(copy,[status(thm)],[10384]) ).

thf(10953,plain,
    ( ( ! [A: nat,C: nat,A6: nat,B: nat,B6: nat] :
          ( ( ( modulo_modulo_nat @ A @ C )
            = ( modulo_modulo_nat @ A6 @ C ) )
         => ( ( ( modulo_modulo_nat @ B @ C )
              = ( modulo_modulo_nat @ B6 @ C ) )
           => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C )
              = ( modulo_modulo_nat @ ( plus_plus_nat @ A6 @ B6 ) @ C ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10383]) ).

thf(10954,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
          = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) )
    = $true ),
    inference(copy,[status(thm)],[10382]) ).

thf(10955,plain,
    ( ( ! [A: nat,B: nat,N2: nat] :
          ( ( modulo_modulo_nat @ ( power_power_nat @ ( modulo_modulo_nat @ A @ B ) @ N2 ) @ B )
          = ( modulo_modulo_nat @ ( power_power_nat @ A @ N2 ) @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[10381]) ).

thf(10956,plain,
    ( ( ! [N2: num] :
          ( zero_zero_nat
         != ( numeral_numeral_nat @ N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10380]) ).

thf(10957,plain,
    ( ( ! [M: num,Q2: num,N2: num] :
          ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
            = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
          = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
            = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10379]) ).

thf(10958,plain,
    ( ( ! [M: num,N2: num] :
          ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ one ) )
          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ one ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10378]) ).

thf(10959,plain,
    ( ( ! [C: nat,A: nat,B: nat] :
          ( ( C != zero_zero_nat )
         => ( ( ( times_times_nat @ A @ C )
              = ( times_times_nat @ B @ C ) )
            = ( A = B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10377]) ).

thf(10960,plain,
    ( ( ! [C: nat,A: nat,B: nat] :
          ( ( C != zero_zero_nat )
         => ( ( ( times_times_nat @ C @ A )
              = ( times_times_nat @ C @ B ) )
            = ( A = B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10376]) ).

thf(10961,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( A != zero_zero_nat )
         => ( ( B != zero_zero_nat )
           => ( ( times_times_nat @ A @ B )
             != zero_zero_nat ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10375]) ).

thf(10962,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( ( times_times_nat @ A @ B )
            = zero_zero_nat )
         => ( ( A = zero_zero_nat )
            | ( B = zero_zero_nat ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10374]) ).

thf(10963,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( ( times_times_nat @ A @ B )
           != zero_zero_nat )
         => ( ( A != zero_zero_nat )
            & ( B != zero_zero_nat ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10373]) ).

thf(10964,plain,
    ( ( ! [A: nat] :
          ( ( plus_plus_nat @ A @ zero_zero_nat )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[10372]) ).

thf(10965,plain,
    ( ( ! [A: nat] :
          ( ( plus_plus_nat @ zero_zero_nat @ A )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[10371]) ).

thf(10966,plain,
    ( ( ! [A: nat,N2: nat] :
          ( ( A != zero_zero_nat )
         => ( ( power_power_nat @ A @ N2 )
           != zero_zero_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[10370]) ).

thf(10967,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( ( plus_plus_nat @ M @ N2 )
            = M )
         => ( N2 = zero_zero_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[10369]) ).

thf(10968,plain,
    ( ( ! [N2: nat] :
          ( ( plus_plus_nat @ zero_zero_nat @ N2 )
          = N2 ) )
    = $true ),
    inference(copy,[status(thm)],[10368]) ).

thf(10969,plain,
    ( ( ! [N2: nat] :
          ( ( times_times_nat @ zero_zero_nat @ N2 )
          = zero_zero_nat ) )
    = $true ),
    inference(copy,[status(thm)],[10367]) ).

thf(10970,plain,
    ( ( ! [K: nat,M: nat,N2: nat] :
          ( ( ( times_times_nat @ K @ M )
            = ( times_times_nat @ K @ N2 ) )
          = ( ( K = zero_zero_nat )
            | ( M = N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10366]) ).

thf(10971,plain,
    ( ( ! [X: nat,N2: nat,Y: nat] :
          ( ( ( modulo_modulo_nat @ X @ N2 )
            = ( modulo_modulo_nat @ Y @ N2 ) )
          = ( ? [Q1: nat,Q22: nat] :
                ( ( plus_plus_nat @ X @ ( times_times_nat @ N2 @ Q1 ) )
                = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q22 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10365]) ).

thf(10972,plain,
    ( ( ( ^ [H: nat] : zero_zero_nat )
      = ( times_times_nat @ zero_zero_nat ) )
    = $true ),
    inference(copy,[status(thm)],[10364]) ).

thf(10973,plain,
    ( ( ! [Q2: num,N2: num] :
          ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
         != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10363]) ).

thf(10974,plain,
    ( ( ! [M: num,Q2: num] :
          ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
         != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10362]) ).

thf(10975,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
          = ( plus_plus_nat @ ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10361]) ).

thf(10976,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
          = ( plus_plus_nat @ ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10360]) ).

thf(10977,plain,
    ( ( ! [B: nat,A: nat] :
          ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[10359]) ).

thf(10978,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[10358]) ).

thf(10979,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[10357]) ).

thf(10980,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[10356]) ).

thf(10981,plain,
    ( ( ! [A: nat,B: nat] :
          ( A
          = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10355]) ).

thf(10982,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
          = ( plus_plus_nat @ A @ C ) ) )
    = $true ),
    inference(copy,[status(thm)],[10354]) ).

thf(10983,plain,
    ( ( ! [B: nat,A: nat,C: nat] :
          ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
          = ( plus_plus_nat @ A @ C ) ) )
    = $true ),
    inference(copy,[status(thm)],[10353]) ).

thf(10984,plain,
    ( ( ! [M: nat,N2: nat,Q2: nat] :
          ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N2 @ Q2 ) )
          = ( plus_plus_nat @ ( times_times_nat @ N2 @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N2 ) @ Q2 ) ) @ ( modulo_modulo_nat @ M @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10352]) ).

thf(10985,plain,
    ( ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
      = zero_zero_nat )
    = $true ),
    inference(copy,[status(thm)],[10351]) ).

thf(10986,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
           != zero_zero_nat )
         => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
           != zero_zero_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[10350]) ).

thf(10987,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
           != zero_zero_nat )
         => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
           != zero_zero_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[10349]) ).

thf(10988,plain,
    ( ( ! [A: nat,N2: nat,M: nat] :
          ( ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
          = ( divide_divide_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10348]) ).

thf(10989,plain,
    ( ( ! [A2: nat,N2: nat] :
          ( A2
          = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ N2 ) @ N2 ) @ ( modulo_modulo_nat @ A2 @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10347]) ).

thf(10990,plain,
    ( ( ! [X22: num,Y22: num] :
          ( ( ( bit0 @ X22 )
            = ( bit0 @ Y22 ) )
          = ( X22 = Y22 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10346]) ).

thf(10991,plain,
    ( ( ! [A: nat] :
          ( ( plus_plus_nat @ A @ zero_zero_nat )
          = A ) )
    = $true ),
    inference(copy,[status(thm)],[10345]) ).

thf(10992,plain,
    ( ( ! [X22: num] :
          ( one
         != ( bit0 @ X22 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10344]) ).

thf(10993,plain,
    ( ( ! [P: nat > nat > $o,A: nat,B: nat] :
          ( ! [A3: nat,B2: nat] :
              ( ( P @ A3 @ B2 )
              = ( P @ B2 @ A3 ) )
         => ( ! [A3: nat] : ( P @ A3 @ zero_zero_nat )
           => ( ! [A3: nat,B2: nat] :
                  ( ( P @ A3 @ B2 )
                 => ( P @ A3 @ ( plus_plus_nat @ A3 @ B2 ) ) )
             => ( P @ A @ B ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10343]) ).

thf(10994,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
          = ( dvd_dvd_nat @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[10342]) ).

thf(10995,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
          = ( dvd_dvd_nat @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[10341]) ).

thf(10996,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( dvd_dvd_nat @ A @ B )
         => ( ( dvd_dvd_nat @ A @ C )
           => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B @ A ) @ ( divide_divide_nat @ C @ A ) )
              = ( dvd_dvd_nat @ B @ C ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10340]) ).

thf(10997,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
          = ( dvd_dvd_nat @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[10339]) ).

thf(10998,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
          = ( dvd_dvd_nat @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[10338]) ).

thf(10999,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( dvd_dvd_nat @ A @ B )
         => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
            = B ) ) )
    = $true ),
    inference(copy,[status(thm)],[10337]) ).

thf(11000,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( dvd_dvd_nat @ A @ B )
         => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
            = B ) ) )
    = $true ),
    inference(copy,[status(thm)],[10336]) ).

thf(11001,plain,
    ( ( ! [C: nat,A: nat,B: nat] :
          ( ( dvd_dvd_nat @ C @ A )
         => ( ( dvd_dvd_nat @ C @ B )
           => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
              = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10335]) ).

thf(11002,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
          = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
            | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10334]) ).

thf(11003,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) )
          = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
            = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10333]) ).

thf(11004,plain,
    ( ( ! [A: nat,B: nat] :
          ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) )
          = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
           != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10332]) ).

thf(11005,plain,
    ( ( ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[10331]) ).

thf(11006,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
         => ( dvd_dvd_nat @ B @ C ) ) )
    = $true ),
    inference(copy,[status(thm)],[10330]) ).

thf(11007,plain,
    ( ( ! [A: nat,B: nat,C: nat,D: nat] :
          ( ( dvd_dvd_nat @ A @ B )
         => ( ( dvd_dvd_nat @ C @ D )
           => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10329]) ).

thf(11008,plain,
    ( ( ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) )
    = $true ),
    inference(copy,[status(thm)],[10328]) ).

thf(11009,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
         => ( dvd_dvd_nat @ A @ C ) ) )
    = $true ),
    inference(copy,[status(thm)],[10327]) ).

thf(11010,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( dvd_dvd_nat @ A @ B )
         => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10326]) ).

thf(11011,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( dvd_dvd_nat @ A @ C )
         => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10325]) ).

thf(11012,plain,
    ( ( dvd_dvd_nat
      = ( ^ [B5: nat,A5: nat] :
          ? [K3: nat] :
            ( A5
            = ( times_times_nat @ B5 @ K3 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10324]) ).

thf(11013,plain,
    ( ( ! [A: nat,B: nat,K: nat] :
          ( ( A
            = ( times_times_nat @ B @ K ) )
         => ( dvd_dvd_nat @ B @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[10323]) ).

thf(11014,plain,
    ( ( ! [B: nat,A: nat] :
          ( ( dvd_dvd_nat @ B @ A )
         => ~ ! [K2: nat] :
                ( A
               != ( times_times_nat @ B @ K2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10322]) ).

thf(11015,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
         => ? [B8: nat,C5: nat] :
              ( ( A
                = ( times_times_nat @ B8 @ C5 ) )
              & ( dvd_dvd_nat @ B8 @ B )
              & ( dvd_dvd_nat @ C5 @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10321]) ).

thf(11016,plain,
    ( ( ! [P4: nat,A: nat,B: nat] :
          ( ( dvd_dvd_nat @ P4 @ ( times_times_nat @ A @ B ) )
         => ~ ! [X4: nat,Y4: nat] :
                ( ( P4
                  = ( times_times_nat @ X4 @ Y4 ) )
               => ( ( dvd_dvd_nat @ X4 @ A )
                 => ~ ( dvd_dvd_nat @ Y4 @ B ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10320]) ).

thf(11017,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( dvd_dvd_nat @ A @ B )
         => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
            = ( dvd_dvd_nat @ A @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10319]) ).

thf(11018,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( dvd_dvd_nat @ A @ C )
         => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
            = ( dvd_dvd_nat @ A @ B ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10318]) ).

thf(11019,plain,
    ( ( ! [A: nat,B: nat,C: nat] :
          ( ( dvd_dvd_nat @ A @ B )
         => ( ( dvd_dvd_nat @ A @ C )
           => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10317]) ).

thf(11020,plain,
    ( ( ! [D: nat,B: nat,A: nat] :
          ( ( dvd_dvd_nat @ D @ B )
         => ( ( dvd_dvd_nat @ B @ A )
           => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D ) @ ( divide_divide_nat @ B @ D ) )
              = ( divide_divide_nat @ A @ B ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10316]) ).

thf(11021,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( ( divide_divide_nat @ A @ C )
            = ( divide_divide_nat @ B @ C ) )
         => ( ( dvd_dvd_nat @ C @ A )
           => ( ( dvd_dvd_nat @ C @ B )
             => ( A = B ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10315]) ).

thf(11022,plain,
    ( ( ! [C: nat,A: nat,B: nat] :
          ( ( dvd_dvd_nat @ C @ A )
         => ( ( dvd_dvd_nat @ C @ B )
           => ( ( ( divide_divide_nat @ A @ C )
                = ( divide_divide_nat @ B @ C ) )
              = ( A = B ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10314]) ).

thf(11023,plain,
    ( ( ! [X: nat,Y: nat,N2: nat] :
          ( ( dvd_dvd_nat @ X @ Y )
         => ( dvd_dvd_nat @ ( power_power_nat @ X @ N2 ) @ ( power_power_nat @ Y @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10313]) ).

thf(11024,plain,
    ( ( ! [N2: nat,K: int,M: nat,L2: int,R: int] :
          ( ( bit_concat_bit @ N2 @ K @ ( bit_concat_bit @ M @ L2 @ R ) )
          = ( bit_concat_bit @ ( plus_plus_nat @ M @ N2 ) @ ( bit_concat_bit @ N2 @ K @ L2 ) @ R ) ) )
    = $true ),
    inference(copy,[status(thm)],[10312]) ).

thf(11025,plain,
    ( ( ! [B: nat,A: nat,D: nat,C: nat] :
          ( ( dvd_dvd_nat @ B @ A )
         => ( ( dvd_dvd_nat @ D @ C )
           => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C @ D ) )
              = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10311]) ).

thf(11026,plain,
    ( ( ! [A: nat,C: nat,B: nat] :
          ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B )
         => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10310]) ).

thf(11027,plain,
    ( ( ! [B: nat,C: nat,A: nat] :
          ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C ) @ A )
         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
            = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10309]) ).

thf(11028,plain,
    ( ( ! [C: nat,B: nat,A: nat] :
          ( ( dvd_dvd_nat @ C @ B )
         => ( ( dvd_dvd_nat @ B @ A )
           => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C ) )
              = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10308]) ).

thf(11029,plain,
    ( ( ! [C: nat,B: nat,A: nat] :
          ( ( dvd_dvd_nat @ C @ B )
         => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
            = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10307]) ).

thf(11030,plain,
    ( ( ! [C: nat,B: nat,A: nat] :
          ( ( dvd_dvd_nat @ C @ B )
         => ( ( times_times_nat @ ( divide_divide_nat @ B @ C ) @ A )
            = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10306]) ).

thf(11031,plain,
    ( ( ! [C: nat,B: nat,A: nat] :
          ( ( dvd_dvd_nat @ C @ B )
         => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
            = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10305]) ).

thf(11032,plain,
    ( ( ! [C: nat,A: nat,B: nat] :
          ( ( dvd_dvd_nat @ C @ A )
         => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
            = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10304]) ).

thf(11033,plain,
    ( ( ! [B: nat,A: nat,N2: nat] :
          ( ( dvd_dvd_nat @ B @ A )
         => ( ( power_power_nat @ ( divide_divide_nat @ A @ B ) @ N2 )
            = ( divide_divide_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10303]) ).

thf(11034,plain,
    ( ( ! [D: nat,A: nat,B: nat,X: nat,Y: nat] :
          ( ( dvd_dvd_nat @ D @ A )
         => ( ( dvd_dvd_nat @ D @ B )
           => ( ( ( ( times_times_nat @ A @ X )
                  = ( plus_plus_nat @ ( times_times_nat @ B @ Y ) @ D ) )
                | ( ( times_times_nat @ B @ X )
                  = ( plus_plus_nat @ ( times_times_nat @ A @ Y ) @ D ) ) )
             => ? [X4: nat,Y4: nat] :
                  ( ( dvd_dvd_nat @ D @ A )
                  & ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
                  & ( ( ( times_times_nat @ A @ X4 )
                      = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y4 ) @ D ) )
                    | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X4 )
                      = ( plus_plus_nat @ ( times_times_nat @ A @ Y4 ) @ D ) ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10302]) ).

thf(11035,plain,
    ( ( ! [A: nat,B: nat] :
        ? [D4: nat,X4: nat,Y4: nat] :
          ( ( dvd_dvd_nat @ D4 @ A )
          & ( dvd_dvd_nat @ D4 @ B )
          & ( ( ( times_times_nat @ A @ X4 )
              = ( plus_plus_nat @ ( times_times_nat @ B @ Y4 ) @ D4 ) )
            | ( ( times_times_nat @ B @ X4 )
              = ( plus_plus_nat @ ( times_times_nat @ A @ Y4 ) @ D4 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10301]) ).

thf(11036,plain,
    ( ( ! [X: nat,Y: nat] :
          ( ( ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
            = ( divide_divide_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
         => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X )
              = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y ) )
           => ( X = Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10300]) ).

thf(11037,plain,
    ( ( ! [N2: num] : ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10299]) ).

thf(11038,plain,
    ( ( ! [A: nat] :
          ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
         => ~ ! [B2: nat] :
                ( A
               != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10298]) ).

thf(11039,plain,
    ( ( ! [A: nat,B: nat] :
          ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
         => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
           => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10297]) ).

thf(11040,plain,
    ( ( ( ^ [Y3: nat,Z2: nat] : ( Y3 = Z2 ) )
      = ( ^ [A5: nat,B5: nat] :
            ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 )
              = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B5 ) )
            & ( ( divide_divide_nat @ A5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
              = ( divide_divide_nat @ B5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10296]) ).

thf(11041,plain,
    ( ( ! [A: nat] :
          ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
         => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
            = A ) ) )
    = $true ),
    inference(copy,[status(thm)],[10295]) ).

thf(11042,plain,
    ( ( ! [P: $o,Q: $o] :
          ( ( zero_n2687167440665602831ol_nat
            @ ( P
              & Q ) )
          = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10294]) ).

thf(11043,plain,
    ( ( ! [P: nat > $o,A: nat] :
          ( ! [A3: nat] :
              ( ( ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                = A3 )
             => ( P @ A3 ) )
         => ( ! [A3: nat,B2: $o] :
                ( ( P @ A3 )
               => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                    = A3 )
                 => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
           => ( P @ A ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10293]) ).

thf(11044,plain,
    ( ( ! [R: nat,A: nat,B: nat,C: nat,D: nat] :
          ( ( R != zero_zero_nat )
         => ( ( ( A = B )
              & ( C != D ) )
           => ( ( plus_plus_nat @ A @ ( times_times_nat @ R @ C ) )
             != ( plus_plus_nat @ B @ ( times_times_nat @ R @ D ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10292]) ).

thf(11045,plain,
    ( ( ! [F: nat > nat,A2: set_nat,G: nat > nat,B3: set_nat] :
          ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ B3 ) )
          = ( groups3542108847815614940at_nat
            @ ^ [I3: nat] :
                ( groups3542108847815614940at_nat
                @ ^ [J3: nat] : ( times_times_nat @ ( F @ I3 ) @ ( G @ J3 ) )
                @ B3 )
            @ A2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10291]) ).

thf(11046,plain,
    ( ( ! [F: nat > nat,A2: set_nat,R: nat] :
          ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ R )
          = ( groups3542108847815614940at_nat
            @ ^ [N: nat] : ( times_times_nat @ ( F @ N ) @ R )
            @ A2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10290]) ).

thf(11047,plain,
    ( ( ! [R: nat,F: nat > nat,A2: set_nat] :
          ( ( times_times_nat @ R @ ( groups3542108847815614940at_nat @ F @ A2 ) )
          = ( groups3542108847815614940at_nat
            @ ^ [N: nat] : ( times_times_nat @ R @ ( F @ N ) )
            @ A2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10289]) ).

thf(11048,plain,
    ( ( ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
          ( ( groups3542108847815614940at_nat
            @ ^ [X2: nat] : ( plus_plus_nat @ ( G @ X2 ) @ ( H2 @ X2 ) )
            @ A2 )
          = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ A2 ) @ ( groups3542108847815614940at_nat @ H2 @ A2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10288]) ).

thf(11049,plain,
    ( ( ! [B: nat,A: nat] :
          ( ( B
            = ( plus_plus_nat @ B @ A ) )
          = ( A = zero_zero_nat ) ) )
    = $true ),
    inference(copy,[status(thm)],[10287]) ).

thf(11050,plain,
    ( ( ! [A: nat,B: nat,C: nat,D: nat] :
          ( ( ( A != B )
            & ( C != D ) )
          = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) )
           != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B @ C ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10286]) ).

thf(11051,plain,
    ( ( ! [W: nat,Y: nat,X: nat,Z: nat] :
          ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y ) @ ( times_times_nat @ X @ Z ) )
            = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X @ Y ) ) )
          = ( ( W = X )
            | ( Y = Z ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10285]) ).

thf(11052,plain,
    ( ( ! [M: num,N2: num] :
          ( ( bit1 @ M )
         != ( bit0 @ N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10284]) ).

thf(11053,plain,
    ( ( ! [M: num,N2: num] :
          ( ( bit0 @ M )
         != ( bit1 @ N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10283]) ).

thf(11054,plain,
    ( ( ! [M: num] :
          ( ( bit1 @ M )
         != one ) )
    = $true ),
    inference(copy,[status(thm)],[10282]) ).

thf(11055,plain,
    ( ( ! [N2: num] :
          ( one
         != ( bit1 @ N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10281]) ).

thf(11056,plain,
    ( ( ! [X22: num,X32: num] :
          ( ( bit0 @ X22 )
         != ( bit1 @ X32 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10280]) ).

thf(11057,plain,
    ( ( ! [X32: num] :
          ( one
         != ( bit1 @ X32 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10279]) ).

thf(11058,plain,
    ( ( ! [Y: num] :
          ( ( Y != one )
         => ( ! [X23: num] :
                ( Y
               != ( bit0 @ X23 ) )
           => ~ ! [X33: num] :
                  ( Y
                 != ( bit1 @ X33 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10278]) ).

thf(11059,plain,
    ( ( ! [Z: nat,W: num] :
          ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
          = ( times_times_nat @ ( times_times_nat @ Z @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10277]) ).

thf(11060,plain,
    ( ( ! [N2: num] :
          ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( numeral_numeral_nat @ N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10276]) ).

thf(11061,plain,
    ( ( ! [A: nat] :
          ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
          = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) )
    = $true ),
    inference(copy,[status(thm)],[10275]) ).

thf(11062,plain,
    ( ( ! [N2: num] :
          ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N2 ) )
          = ( numeral_numeral_nat @ N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10274]) ).

thf(11063,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N2 ) )
          = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10273]) ).

thf(11064,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N2 ) )
          = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10272]) ).

thf(11065,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ M @ N2 ) )
          = ( power_power_nat @ ( semiri1316708129612266289at_nat @ M ) @ N2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10271]) ).

thf(11066,plain,
    ( ( ! [B: nat,W: nat,X: nat] :
          ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W )
            = ( semiri1316708129612266289at_nat @ X ) )
          = ( ( power_power_nat @ B @ W )
            = X ) ) )
    = $true ),
    inference(copy,[status(thm)],[10270]) ).

thf(11067,plain,
    ( ( ! [X: nat,B: nat,W: nat] :
          ( ( ( semiri1316708129612266289at_nat @ X )
            = ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
          = ( X
            = ( power_power_nat @ B @ W ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10269]) ).

thf(11068,plain,
    ( ( ! [X: num,N2: nat,Y: nat] :
          ( ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 )
            = ( semiri1316708129612266289at_nat @ Y ) )
          = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 )
            = Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[10268]) ).

thf(11069,plain,
    ( ( ! [Y: nat,X: num,N2: nat] :
          ( ( ( semiri1316708129612266289at_nat @ Y )
            = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) )
          = ( Y
            = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10267]) ).

thf(11070,plain,
    ( ( ! [X: nat,Y: nat] :
          ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X ) @ Y )
          = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10266]) ).

thf(11071,plain,
    ( ( ( bitM @ one )
      = one )
    = $true ),
    inference(copy,[status(thm)],[10265]) ).

thf(11072,plain,
    ( ( ! [A: nat,M: nat,N2: nat] :
          ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) )
          = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10264]) ).

thf(11073,plain,
    ( ( ! [M: nat,N2: nat] :
          ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ M @ N2 ) )
          = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10263]) ).

thf(11074,plain,
    ( ( ! [F: nat > real,K: nat] :
          ( ( summable_real
            @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
          = ( summable_real @ F ) ) )
    = $true ),
    inference(copy,[status(thm)],[10262]) ).

thf(11075,plain,
    ( ( ! [F: nat > complex,K: nat] :
          ( ( summable_complex
            @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
          = ( summable_complex @ F ) ) )
    = $true ),
    inference(copy,[status(thm)],[10261]) ).

thf(11076,plain,
    ( ( ! [F: nat > nat,G: nat > nat] :
          ( ( summable_nat @ F )
         => ( ( summable_nat @ G )
           => ( summable_nat
              @ ^ [N: nat] : ( plus_plus_nat @ ( F @ N ) @ ( G @ N ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10260]) ).

thf(11077,plain,
    ( ( ! [F: nat > real,K: nat] :
          ( ( summable_real @ F )
         => ( summable_real
            @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10259]) ).

thf(11078,plain,
    ( ( ! [F: nat > complex,K: nat] :
          ( ( summable_complex @ F )
         => ( summable_complex
            @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10258]) ).

thf(11079,plain,
    ( ( ! [F: nat > nat,A: nat,G: nat > nat,B: nat] :
          ( ( sums_nat @ F @ A )
         => ( ( sums_nat @ G @ B )
           => ( sums_nat
              @ ^ [N: nat] : ( plus_plus_nat @ ( F @ N ) @ ( G @ N ) )
              @ ( plus_plus_nat @ A @ B ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10257]) ).

thf(11080,plain,
    ( ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
      = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
    = $true ),
    inference(copy,[status(thm)],[10256]) ).

thf(11081,plain,
    ( ( ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
          ( ( groups708209901874060359at_nat
            @ ^ [X2: nat] : ( times_times_nat @ ( G @ X2 ) @ ( H2 @ X2 ) )
            @ A2 )
          = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ A2 ) @ ( groups708209901874060359at_nat @ H2 @ A2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10255]) ).

thf(11082,plain,
    ( ( ! [F: nat > nat,A2: set_nat,N2: nat] :
          ( ( power_power_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ N2 )
          = ( groups708209901874060359at_nat
            @ ^ [X2: nat] : ( power_power_nat @ ( F @ X2 ) @ N2 )
            @ A2 ) ) )
    = $true ),
    inference(copy,[status(thm)],[10254]) ).

thf(11083,plain,
    ( ( ! [M: nat,R: nat,K: nat] :
          ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R ) @ K ) @ ( plus_plus_nat @ M @ K ) ) @ ( binomial @ ( plus_plus_nat @ M @ K ) @ K ) )
          = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M @ R ) @ M ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10253]) ).

thf(11084,plain,
    ( ( ! [M: nat,N2: nat,X: real] :
          ( ( root @ ( times_times_nat @ M @ N2 ) @ X )
          = ( root @ M @ ( root @ N2 @ X ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10252]) ).

thf(11085,plain,
    ( ( ! [P: num > $o,X: num] :
          ( ( P @ one )
         => ( ! [X4: num] :
                ( ( P @ X4 )
               => ( P @ ( inc @ X4 ) ) )
           => ( P @ X ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10251]) ).

thf(11086,plain,
    ( ( ( inc @ one )
      = ( bit0 @ one ) )
    = $true ),
    inference(copy,[status(thm)],[10250]) ).

thf(11087,plain,
    ( ( ! [X: num] :
          ( ( pow @ X @ one )
          = X ) )
    = $true ),
    inference(copy,[status(thm)],[10249]) ).

thf(11088,plain,
    ( ( ( bit_or_not_num_neg @ one @ one )
      = one )
    = $true ),
    inference(copy,[status(thm)],[10248]) ).

thf(11089,plain,
    ( ( ! [N2: num] :
          ( ( bit_or_not_num_neg @ ( bit0 @ N2 ) @ one )
          = ( bit0 @ one ) ) )
    = $true ),
    inference(copy,[status(thm)],[10247]) ).

thf(11090,plain,
    ( ( bit_se547839408752420682it_nat
      = ( ^ [N: nat,M6: nat] : ( times_times_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10246]) ).

thf(11091,plain,
    ( ( bit_se8570568707652914677it_nat
      = ( ^ [N: nat,M6: nat] : ( divide_divide_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10245]) ).

thf(11092,plain,
    ( ( ! [Q2: num] :
          ( ( num_of_nat @ ( numeral_numeral_nat @ Q2 ) )
          = Q2 ) )
    = $true ),
    inference(copy,[status(thm)],[10244]) ).

thf(11093,plain,
    ( ( ! [K: nat,M: nat,N2: nat] :
          ( ( times_times_nat @ K @ ( gcd_gcd_nat @ M @ N2 ) )
          = ( gcd_gcd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[10243]) ).

thf(11094,plain,
    ( ( ! [P: $o] :
          ( ( P = $true )
          | ( P = $false ) ) )
    = $true ),
    inference(copy,[status(thm)],[10242]) ).

thf(11095,plain,
    ( ( ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) ) ) )
     != ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) @ maxs ) @ maxi ) )
    = $true ),
    inference(copy,[status(thm)],[10668]) ).

thf(11096,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ( SX0 != zero_zero_nat ) )
          | ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ SX0 @ SX1 ) @ SX2 ) @ SX0 )
            = ( plus_plus_nat @ SX1 @ ( divide_divide_nat @ SX2 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10940]) ).

thf(11097,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ord_less_nat @ SX0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SX1 ) )
          | ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ SX2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SX1 ) ) @ SX0 ) @ SX1 )
            = SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10704]) ).

thf(11098,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( dvd_dvd_nat @ SX0 @ SX1 )
          | ( ( divide_divide_nat @ ( plus_plus_nat @ SX1 @ SX2 ) @ SX0 )
            = ( plus_plus_nat @ ( divide_divide_nat @ SX1 @ SX0 ) @ ( divide_divide_nat @ SX2 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11032]) ).

thf(11099,plain,
    ( ( ~ ! [SX0: nat] :
            ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ maxs ) @ SX0 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10678]) ).

thf(11100,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ord_less_nat @ SX0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SX1 @ SX2 ) ) )
          | ( ord_less_nat @ ( vEBT_VEBT_high @ SX0 @ SX1 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10701]) ).

thf(11101,plain,
    ( ( ! [SX0: nat,SX1: nat] :
          ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SX0 ) )
         != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10853]) ).

thf(11102,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX1 ) @ SX2 )
          | ( ord_less_nat @ SX0 @ SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10818]) ).

thf(11103,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ( ( times_times_nat @ SX0 @ SX1 )
           != ( times_times_nat @ SX1 @ SX0 ) )
          | ( ( times_times_nat @ ( power_power_nat @ SX0 @ SX2 ) @ SX1 )
            = ( times_times_nat @ SX1 @ ( power_power_nat @ SX0 @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10717]) ).

thf(11104,plain,
    ( ( ! [SX0: nat,SX1: nat] :
          ( ( ( times_times_nat @ SX0 @ SX1 )
           != zero_zero_nat )
          | ( SX0 = zero_zero_nat )
          | ( SX1 = zero_zero_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10962]) ).

thf(11105,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ( SX0 != zero_zero_nat ) )
          | ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ SX1 @ SX0 ) @ SX2 ) @ SX0 )
            = ( plus_plus_nat @ SX1 @ ( divide_divide_nat @ SX2 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10941]) ).

thf(11106,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
          ( ~ ( ord_less_nat @ SX0 @ SX1 )
          | ( ( plus_plus_nat @ SX2 @ SX1 )
           != ( plus_plus_nat @ SX0 @ SX3 ) )
          | ( ord_less_nat @ SX2 @ SX3 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10811]) ).

thf(11107,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( dvd_dvd_nat @ ( times_times_nat @ SX0 @ SX1 ) @ SX2 )
          | ( dvd_dvd_nat @ SX0 @ ( divide_divide_nat @ SX2 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11026]) ).

thf(11108,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ~ ( ~ ( ( SX0 != zero_zero_nat )
                | ( ( divide_divide_nat @ ( times_times_nat @ SX0 @ SX1 ) @ ( times_times_nat @ SX0 @ SX2 ) )
                  = zero_zero_nat ) )
            | ~ ( ~ ( ( SX0 != zero_zero_nat ) )
                | ( ( divide_divide_nat @ ( times_times_nat @ SX0 @ SX1 ) @ ( times_times_nat @ SX0 @ SX2 ) )
                  = ( divide_divide_nat @ SX1 @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10929]) ).

thf(11109,plain,
    ( ( ! [SX0: nat,SX1: nat] :
          ( ~ ( ( SX0 != zero_zero_nat ) )
          | ( ( divide_divide_nat @ ( times_times_nat @ SX0 @ SX1 ) @ SX0 )
            = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10933]) ).

thf(11110,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ( SX0 != zero_zero_nat ) )
          | ( ( ( times_times_nat @ SX1 @ SX0 )
              = ( times_times_nat @ SX2 @ SX0 ) )
            = ( SX1 = SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10959]) ).

thf(11111,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( dvd_dvd_nat @ SX0 @ ( times_times_nat @ SX1 @ SX2 ) )
          | ~ ! [SX3: nat,SX4: nat] :
                ( ( SX0
                 != ( times_times_nat @ SX3 @ SX4 ) )
                | ~ ( dvd_dvd_nat @ SX3 @ SX1 )
                | ~ ( dvd_dvd_nat @ SX4 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11016]) ).

thf(11112,plain,
    ( ( ! [SX0: nat,SX1: nat] :
          ( ~ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SX0 @ SX1 ) )
               != zero_zero_nat ) )
          | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SX1 )
           != zero_zero_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10986]) ).

thf(11113,plain,
    ( ( ~ ( ~ ( vEBT_V8194947554948674370ptions @ summary @ maxs )
          | ~ ( ( maxs
               != ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10683]) ).

thf(11114,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
          ( ~ ~ ( ( SX0 != SX1 )
                | ( SX2 != SX3 ) )
          | ( ( plus_plus_nat @ SX0 @ SX2 )
            = ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10871]) ).

thf(11115,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( dvd_dvd_nat @ SX0 @ SX1 )
          | ~ ( dvd_dvd_nat @ SX0 @ SX2 )
          | ( ( divide_divide_nat @ ( plus_plus_nat @ SX1 @ SX2 ) @ SX0 )
            = ( plus_plus_nat @ ( divide_divide_nat @ SX1 @ SX0 ) @ ( divide_divide_nat @ SX2 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11001]) ).

thf(11116,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( dvd_dvd_nat @ SX0 @ SX1 )
          | ~ ( dvd_dvd_nat @ SX1 @ SX2 )
          | ( ( divide_divide_nat @ ( divide_divide_nat @ SX2 @ SX0 ) @ ( divide_divide_nat @ SX1 @ SX0 ) )
            = ( divide_divide_nat @ SX2 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11020]) ).

thf(11117,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
          ( ( SX0
           != ( plus_plus_nat @ SX1 @ SX2 ) )
          | ( ( plus_plus_nat @ SX0 @ SX3 )
            = ( plus_plus_nat @ SX1 @ ( plus_plus_nat @ SX2 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10872]) ).

thf(11118,plain,
    ( ( ! [SX0: nat > complex,SX1: nat] :
          ( ~ ( summable_complex @ SX0 )
          | ( summable_complex
            @ ^ [SX2: nat] : ( SX0 @ ( plus_plus_nat @ SX2 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11078]) ).

thf(11119,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
          | ( ord_less_eq_nat @ ( times_times_nat @ SX0 @ SX2 ) @ ( times_times_nat @ SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10831]) ).

thf(11120,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ( SX0 != zero_zero_nat ) )
          | ( ( divide_divide_nat @ ( times_times_nat @ SX1 @ SX0 ) @ ( times_times_nat @ SX2 @ SX0 ) )
            = ( divide_divide_nat @ SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10930]) ).

thf(11121,plain,
    ( ( ! [SX0: num] :
          ( one
         != ( bit1 @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11055]) ).

thf(11122,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX1 ) @ SX2 )
          | ~ ( ~ ( ord_less_eq_nat @ SX0 @ SX2 )
              | ~ ( ord_less_eq_nat @ SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10829]) ).

thf(11123,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ( SX0 != zero_zero_nat ) )
          | ( ( divide_divide_nat @ ( plus_plus_nat @ SX1 @ ( times_times_nat @ SX0 @ SX2 ) ) @ SX0 )
            = ( plus_plus_nat @ SX2 @ ( divide_divide_nat @ SX1 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10942]) ).

thf(11124,plain,
    ( ( ! [SX0: num] :
          ( one
         != ( bit0 @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10992]) ).

thf(11125,plain,
    ( ( ( ^ [SX0: nat,SX1: nat] : ( SX0 = SX1 ) )
      = ( ^ [SX0: nat,SX1: nat] :
            ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SX0 )
               != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SX1 ) )
              | ( ( divide_divide_nat @ SX0 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
               != ( divide_divide_nat @ SX1 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11040]) ).

thf(11126,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
          ( ~ ( dvd_dvd_nat @ SX0 @ SX1 )
          | ~ ( dvd_dvd_nat @ SX2 @ SX3 )
          | ( dvd_dvd_nat @ ( times_times_nat @ SX0 @ SX2 ) @ ( times_times_nat @ SX1 @ SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11007]) ).

thf(11127,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ( ( modulo_modulo_nat @ SX0 @ SX1 )
            = ( modulo_modulo_nat @ SX2 @ SX1 ) )
          = ( ~ ! [SX3: nat] :
                  ~ ~ ! [SX4: nat] :
                        ( ( plus_plus_nat @ SX0 @ ( times_times_nat @ SX1 @ SX3 ) )
                       != ( plus_plus_nat @ SX2 @ ( times_times_nat @ SX1 @ SX4 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10971]) ).

thf(11128,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ( ( plus_plus_nat @ SX0 @ SX1 )
           != ( plus_plus_nat @ SX2 @ SX1 ) )
          | ( SX0 = SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10878]) ).

thf(11129,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ( SX0 != zero_zero_nat ) )
          | ( ( divide_divide_nat @ ( plus_plus_nat @ SX1 @ ( times_times_nat @ SX2 @ SX0 ) ) @ SX0 )
            = ( plus_plus_nat @ SX2 @ ( divide_divide_nat @ SX1 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10943]) ).

thf(11130,plain,
    ( ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) )
     != none_nat )
    = $true ),
    inference(unfold_def,[status(thm)],[10686]) ).

thf(11131,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
          | ( ord_less_eq_nat @ ( times_times_nat @ SX2 @ SX0 ) @ ( times_times_nat @ SX2 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10830]) ).

thf(11132,plain,
    ( ( ! [SX0: nat] :
          ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SX0 )
          | ~ ! [SX1: nat] :
                ( SX0
               != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11038]) ).

thf(11133,plain,
    ( ( ! [SX0: num] :
          ( ( bit0 @ SX0 )
         != one ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10762]) ).

thf(11134,plain,
    ( ( ! [SX0: num] :
          ( ( bit1 @ SX0 )
         != one ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11054]) ).

thf(11135,plain,
    ( ( ! [SX0: nat,SX1: nat] :
          ( ~ ( ( ( times_times_nat @ SX0 @ SX1 )
               != zero_zero_nat ) )
          | ~ ( ~ ( ( SX0 != zero_zero_nat ) )
              | ~ ( ( SX1 != zero_zero_nat ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10963]) ).

thf(11136,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ord_less_nat @ SX0 @ ( times_times_nat @ SX1 @ SX2 ) )
          | ( ord_less_nat @ ( divide_divide_nat @ SX0 @ SX2 ) @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10715]) ).

thf(11137,plain,
    ( ( ~ ! [SX0: nat] :
            ( ( some_nat @ SX0 )
           != ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10691]) ).

thf(11138,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
          ( ( SX0
           != ( plus_plus_nat @ SX1 @ SX2 ) )
          | ( ( plus_plus_nat @ SX3 @ SX0 )
            = ( plus_plus_nat @ SX1 @ ( plus_plus_nat @ SX3 @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10873]) ).

thf(11139,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ( ( times_times_nat @ SX0 @ SX1 )
           != one_one_nat )
          | ( ( times_times_nat @ ( power_power_nat @ SX0 @ SX2 ) @ ( power_power_nat @ SX1 @ SX2 ) )
            = one_one_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10779]) ).

thf(11140,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
          ( ( ~ ( ~ ( ( SX0 != SX1 ) )
                | ~ ( ( SX2 != SX3 ) ) ) )
          = ( ( plus_plus_nat @ ( times_times_nat @ SX0 @ SX2 ) @ ( times_times_nat @ SX1 @ SX3 ) )
           != ( plus_plus_nat @ ( times_times_nat @ SX0 @ SX3 ) @ ( times_times_nat @ SX1 @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11050]) ).

thf(11141,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ( SX0 != zero_zero_nat ) )
          | ( ( ( times_times_nat @ SX0 @ SX1 )
              = ( times_times_nat @ SX0 @ SX2 ) )
            = ( SX1 = SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10960]) ).

thf(11142,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( dvd_dvd_nat @ SX0 @ SX1 )
          | ( ( times_times_nat @ ( divide_divide_nat @ SX1 @ SX0 ) @ SX2 )
            = ( divide_divide_nat @ ( times_times_nat @ SX1 @ SX2 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11030]) ).

thf(11143,plain,
    ( ( ! [SX0: nat,SX1: nat] :
          ( ~ ( ( SX0 != zero_zero_nat ) )
          | ~ ( ( SX1 != zero_zero_nat ) )
          | ( ( times_times_nat @ SX0 @ SX1 )
           != zero_zero_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10961]) ).

thf(11144,plain,
    ( ( ~ ! [SX0: nat] :
            ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ summin ) @ SX0 ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10677]) ).

thf(11145,plain,
    ( ( ! [SX0: nat,SX1: nat] :
          ( ( ( divide_divide_nat @ SX0 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
           != ( divide_divide_nat @ SX1 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SX0 )
           != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SX1 ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11036]) ).

thf(11146,plain,
    ( ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
     != mi )
    = $true ),
    inference(unfold_def,[status(thm)],[10693]) ).

thf(11147,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
          | ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10885]) ).

thf(11148,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
          ( ~ ~ ( ~ ( ord_less_nat @ SX0 @ SX1 )
                | ~ ( ord_less_nat @ SX2 @ SX3 ) )
          | ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10889]) ).

thf(11149,plain,
    ( ( ! [SX0: nat,SX1: nat] :
          ( ~ ( dvd_dvd_nat @ SX0 @ SX1 )
          | ( ( times_times_nat @ SX0 @ ( divide_divide_nat @ SX1 @ SX0 ) )
            = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10999]) ).

thf(11150,plain,
    ( ( ! [SX0: num,SX1: num] :
          ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SX0 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SX1 ) ) )
         != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10974]) ).

thf(11151,plain,
    ( ( ! [SX0: nat,SX1: nat] :
          ( ~ ( ( SX0 != zero_zero_nat ) )
          | ( ( divide_divide_nat @ ( times_times_nat @ SX1 @ SX0 ) @ SX0 )
            = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10932]) ).

thf(11152,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
          ( ~ ~ ( ( SX0 != SX1 )
                | ~ ( ord_less_nat @ SX2 @ SX3 ) )
          | ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10890]) ).

thf(11153,plain,
    ( ( ! [SX0: num,SX1: num] :
          ( ( bit1 @ SX0 )
         != ( bit0 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11052]) ).

thf(11154,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
          ( ~ ( ord_less_nat @ SX0 @ SX1 )
          | ~ ( ord_less_nat @ SX2 @ SX3 )
          | ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10892]) ).

thf(11155,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
          ( ~ ( dvd_dvd_nat @ SX0 @ SX1 )
          | ~ ( dvd_dvd_nat @ SX2 @ SX3 )
          | ( ( times_times_nat @ ( divide_divide_nat @ SX1 @ SX0 ) @ ( divide_divide_nat @ SX3 @ SX2 ) )
            = ( divide_divide_nat @ ( times_times_nat @ SX1 @ SX3 ) @ ( times_times_nat @ SX0 @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11025]) ).

thf(11156,plain,
    ( ( ! [SX0: nat,SX1: nat] :
          ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
          | ~ ! [SX2: nat] :
                ( SX1
               != ( plus_plus_nat @ SX0 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10884]) ).

thf(11157,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
          | ( ord_less_eq_nat @ SX0 @ ( plus_plus_nat @ SX2 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10820]) ).

thf(11158,plain,
    ( ( ! [SX0: nat,SX1: nat] :
          ( ( ( times_times_nat @ SX0 @ SX1 )
            = one_one_nat )
          = ( ~ ( ( SX0 != one_one_nat )
                | ( SX1 != one_one_nat ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10790]) ).

thf(11159,plain,
    ( ( ~ ! [SX0: nat] :
            ( ( some_nat @ SX0 )
           != ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ maxs ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10702]) ).

thf(11160,plain,
    ( ( dvd_dvd_nat
      = ( ^ [SX0: nat,SX1: nat] :
            ~ ! [SX2: nat] :
                ( SX1
               != ( times_times_nat @ SX0 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11012]) ).

thf(11161,plain,
    ( ( ! [SX0: nat > real,SX1: nat] :
          ( ~ ( summable_real @ SX0 )
          | ( summable_real
            @ ^ [SX2: nat] : ( SX0 @ ( plus_plus_nat @ SX2 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11077]) ).

thf(11162,plain,
    ( ( ! [SX0: nat,SX1: nat] :
          ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SX0 @ SX1 ) ) )
          = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SX0 ) )
           != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11004]) ).

thf(11163,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ord_less_nat @ SX0 @ SX1 )
          | ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10894]) ).

thf(11164,plain,
    ( ( ! [SX0: nat,SX1: nat] :
          ( ( ( plus_plus_nat @ SX0 @ SX1 )
            = zero_zero_nat )
          = ( ~ ( ( SX0 != zero_zero_nat )
                | ( SX1 != zero_zero_nat ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10911]) ).

thf(11165,plain,
    ( ( ! [SX0: num] :
          ( zero_zero_nat
         != ( numeral_numeral_nat @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10956]) ).

thf(11166,plain,
    ( ( ! [SX0: nat,SX1: nat] :
          ( ( ( plus_plus_nat @ SX0 @ SX1 )
           != SX0 )
          | ( SX1 = zero_zero_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10967]) ).

thf(11167,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
          | ( ord_less_eq_nat @ ( divide_divide_nat @ SX0 @ SX2 ) @ ( divide_divide_nat @ SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10746]) ).

thf(11168,plain,
    ( ( ! [SX0: nat,SX1: nat] :
          ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
          | ~ ! [SX2: nat] :
                ( SX1
               != ( plus_plus_nat @ SX0 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10824]) ).

thf(11169,plain,
    ( ( ! [SX0: nat,SX1: nat] :
          ( ( ( plus_plus_nat @ SX0 @ SX1 )
            = zero_zero_nat )
          = ( ~ ( ( SX0 != zero_zero_nat )
                | ( SX1 != zero_zero_nat ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10924]) ).

thf(11170,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( dvd_dvd_nat @ SX0 @ ( times_times_nat @ SX1 @ SX2 ) )
          | ~ ! [SX3: nat] :
                ~ ~ ! [SX4: nat] :
                      ~ ~ ( ~ ~ ( ( SX0
                                 != ( times_times_nat @ SX3 @ SX4 ) )
                                | ~ ( dvd_dvd_nat @ SX3 @ SX1 ) )
                          | ~ ( dvd_dvd_nat @ SX4 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11015]) ).

thf(11171,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat,SX4: nat] :
          ( ~ ( dvd_dvd_nat @ SX0 @ SX1 )
          | ~ ( dvd_dvd_nat @ SX0 @ SX2 )
          | ~ ( ( ( times_times_nat @ SX1 @ SX3 )
                = ( plus_plus_nat @ ( times_times_nat @ SX2 @ SX4 ) @ SX0 ) )
              | ( ( times_times_nat @ SX2 @ SX3 )
                = ( plus_plus_nat @ ( times_times_nat @ SX1 @ SX4 ) @ SX0 ) ) )
          | ~ ! [SX5: nat] :
                ~ ~ ! [SX6: nat] :
                      ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ SX0 @ SX1 )
                                | ~ ( dvd_dvd_nat @ SX0 @ ( plus_plus_nat @ SX1 @ SX2 ) ) )
                          | ~ ( ( ( times_times_nat @ SX1 @ SX5 )
                                = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SX1 @ SX2 ) @ SX6 ) @ SX0 ) )
                              | ( ( times_times_nat @ ( plus_plus_nat @ SX1 @ SX2 ) @ SX5 )
                                = ( plus_plus_nat @ ( times_times_nat @ SX1 @ SX6 ) @ SX0 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11034]) ).

thf(11172,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
          | ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10822]) ).

thf(11173,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( dvd_dvd_nat @ SX0 @ SX1 )
          | ~ ( dvd_dvd_nat @ SX1 @ SX2 )
          | ( ( divide_divide_nat @ SX2 @ ( divide_divide_nat @ SX1 @ SX0 ) )
            = ( times_times_nat @ ( divide_divide_nat @ SX2 @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11028]) ).

thf(11174,plain,
    ( ( ! [SX0: nat,SX1: nat] :
          ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SX0 )
         != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10852]) ).

thf(11175,plain,
    ( ( ! [SX0: num > $o,SX1: num] :
          ( ~ ( SX0 @ one )
          | ~ ! [SX2: num] :
                ( ~ ( SX0 @ SX2 )
                | ( SX0 @ ( inc @ SX2 ) ) )
          | ( SX0 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11085]) ).

thf(11176,plain,
    ( ( ! [SX0: nat,SX1: nat] :
          ( ~ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SX0 @ SX1 ) )
               != zero_zero_nat ) )
          | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SX0 )
           != zero_zero_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10987]) ).

thf(11177,plain,
    ( ( ! [SX0: num,SX1: num] :
          ( ( bit0 @ SX0 )
         != ( bit1 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11056]) ).

thf(11178,plain,
    ( ( ! [SX0: nat > nat > $o,SX1: nat,SX2: nat] :
          ( ~ ! [SX3: nat,SX4: nat] :
                ( ( SX0 @ SX3 @ SX4 )
                = ( SX0 @ SX4 @ SX3 ) )
          | ~ ! [SX3: nat] : ( SX0 @ SX3 @ zero_zero_nat )
          | ~ ! [SX3: nat,SX4: nat] :
                ( ~ ( SX0 @ SX3 @ SX4 )
                | ( SX0 @ SX3 @ ( plus_plus_nat @ SX3 @ SX4 ) ) )
          | ( SX0 @ SX1 @ SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10993]) ).

thf(11179,plain,
    ( ( ! [SX0: num,SX1: num] :
          ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ SX0 ) ) )
         != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SX1 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10973]) ).

thf(11180,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ord_less_nat @ SX0 @ SX1 )
          | ( ord_less_nat @ SX0 @ ( plus_plus_nat @ SX2 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10812]) ).

thf(11181,plain,
    ( ( ! [SX0: nat,SX1: nat] :
          ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SX0 ) @ SX1 )
          = ( ~ ( ~ ( ( SX0 != SX1 ) )
                | ~ ( vEBT_V8194947554948674370ptions @ summary @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10672]) ).

thf(11182,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat,SX4: nat] :
          ( ( ( modulo_modulo_nat @ SX0 @ SX1 )
           != ( modulo_modulo_nat @ SX2 @ SX1 ) )
          | ( ( modulo_modulo_nat @ SX3 @ SX1 )
           != ( modulo_modulo_nat @ SX4 @ SX1 ) )
          | ( ( modulo_modulo_nat @ ( times_times_nat @ SX0 @ SX3 ) @ SX1 )
            = ( modulo_modulo_nat @ ( times_times_nat @ SX2 @ SX4 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10949]) ).

thf(11183,plain,
    ( ( ord_less_eq_nat
      = ( ^ [SX0: nat,SX1: nat] :
            ~ ! [SX2: nat] :
                ( SX1
               != ( plus_plus_nat @ SX0 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10819]) ).

thf(11184,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( dvd_dvd_nat @ ( times_times_nat @ SX0 @ SX1 ) @ SX2 )
          | ( ( divide_divide_nat @ SX2 @ ( times_times_nat @ SX0 @ SX1 ) )
            = ( divide_divide_nat @ ( divide_divide_nat @ SX2 @ SX0 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11027]) ).

thf(11185,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( dvd_dvd_nat @ SX0 @ SX1 )
          | ( ( times_times_nat @ SX2 @ ( divide_divide_nat @ SX1 @ SX0 ) )
            = ( divide_divide_nat @ ( times_times_nat @ SX2 @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11029]) ).

thf(11186,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ord_less_nat @ SX0 @ SX1 )
          | ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10814]) ).

thf(11187,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
          ( ~ ~ ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
                | ( SX2 != SX3 ) )
          | ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10879]) ).

thf(11188,plain,
    ( ( ! [SX0: nat,SX1: nat] :
          ( ( zero_zero_nat
            = ( plus_plus_nat @ SX0 @ SX1 ) )
          = ( ~ ( ( SX0 != zero_zero_nat )
                | ( SX1 != zero_zero_nat ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10910]) ).

thf(11189,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( dvd_dvd_nat @ SX0 @ SX1 )
          | ( dvd_dvd_nat @ ( power_power_nat @ SX0 @ SX2 ) @ ( power_power_nat @ SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11023]) ).

thf(11190,plain,
    ( ( ! [SX0: nat,SX1: nat] :
          ( ~ ( ( SX0 != zero_zero_nat ) )
          | ( ( power_power_nat @ SX0 @ SX1 )
           != zero_zero_nat ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10966]) ).

thf(11191,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: list_VEBT_VEBT,SX3: vEBT_VEBT,SX4: vEBT_VEBT] :
          ( ~ ( ( SX0 != SX1 ) )
          | ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SX2 @ SX0 @ SX3 ) @ SX1 @ SX4 )
            = ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SX2 @ SX1 @ SX4 ) @ SX0 @ SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10750]) ).

thf(11192,plain,
    ( ( ! [SX0: $o,SX1: $o] :
          ( ( zero_n2687167440665602831ol_nat
            @ ~ ( ~ SX0
                | ~ SX1 ) )
          = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ SX0 ) @ ( zero_n2687167440665602831ol_nat @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11042]) ).

thf(11193,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX1 ) @ ( plus_plus_nat @ SX2 @ SX1 ) )
          | ( ord_less_nat @ SX0 @ SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10896]) ).

thf(11194,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
          ( ~ ~ ( ( SX0 != SX1 )
                | ~ ( ord_less_eq_nat @ SX2 @ SX3 ) )
          | ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10880]) ).

thf(11195,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( dvd_dvd_nat @ SX0 @ SX1 )
          | ( ( dvd_dvd_nat @ SX0 @ ( plus_plus_nat @ SX2 @ SX1 ) )
            = ( dvd_dvd_nat @ SX0 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11018]) ).

thf(11196,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ( SX0
           != ( plus_plus_nat @ SX1 @ SX2 ) )
          | ( ( suc @ SX0 )
            = ( plus_plus_nat @ SX1 @ ( suc @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10801]) ).

thf(11197,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( dvd_dvd_nat @ SX0 @ SX1 )
          | ~ ( dvd_dvd_nat @ SX0 @ SX2 )
          | ( dvd_dvd_nat @ SX0 @ ( plus_plus_nat @ SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11019]) ).

thf(11198,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ( ( plus_plus_nat @ SX0 @ SX1 )
           != ( plus_plus_nat @ SX0 @ SX2 ) )
          | ( SX1 = SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10877]) ).

thf(11199,plain,
    ( ( ! [SX0: nat] :
          ( ~ ! [SX1: nat] :
                ( SX0
               != ( plus_plus_nat @ SX1 @ SX1 ) )
          | ~ ! [SX1: nat] :
                ( SX0
               != ( plus_plus_nat @ SX1 @ ( suc @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10785]) ).

thf(11200,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
          ( ~ ~ ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
                | ~ ( ord_less_eq_nat @ SX2 @ SX3 ) )
          | ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10881]) ).

thf(11201,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ( SX0 != zero_zero_nat ) )
          | ( ( divide_divide_nat @ ( times_times_nat @ SX0 @ SX1 ) @ ( times_times_nat @ SX0 @ SX2 ) )
            = ( divide_divide_nat @ SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10931]) ).

thf(11202,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ord_less_nat @ SX0 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SX1 ) )
          | ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ SX2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SX1 ) ) @ SX0 ) @ SX1 )
            = SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10703]) ).

thf(11203,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( dvd_dvd_nat @ SX0 @ SX1 )
          | ( ( divide_divide_nat @ ( plus_plus_nat @ SX2 @ SX1 ) @ SX0 )
            = ( plus_plus_nat @ ( divide_divide_nat @ SX2 @ SX0 ) @ ( divide_divide_nat @ SX1 @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11031]) ).

thf(11204,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX1 ) @ SX2 )
          | ( ord_less_eq_nat @ SX1 @ SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10825]) ).

thf(11205,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( dvd_dvd_nat @ ( times_times_nat @ SX0 @ SX1 ) @ SX2 )
          | ( dvd_dvd_nat @ SX1 @ SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11006]) ).

thf(11206,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( dvd_dvd_nat @ SX0 @ SX1 )
          | ~ ( dvd_dvd_nat @ SX0 @ SX2 )
          | ( ( dvd_dvd_nat @ ( divide_divide_nat @ SX1 @ SX0 ) @ ( divide_divide_nat @ SX2 @ SX0 ) )
            = ( dvd_dvd_nat @ SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10996]) ).

thf(11207,plain,
    ( ( ! [SX0: nat] :
          ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SX0 )
          | ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ SX0 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
            = SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11041]) ).

thf(11208,plain,
    ( ( ! [SX0: nat,SX1: nat] :
          ~ ! [SX2: nat] :
              ~ ~ ! [SX3: nat] :
                    ~ ~ ! [SX4: nat] :
                          ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ SX2 @ SX0 )
                                    | ~ ( dvd_dvd_nat @ SX2 @ SX1 ) )
                              | ~ ( ( ( times_times_nat @ SX0 @ SX3 )
                                    = ( plus_plus_nat @ ( times_times_nat @ SX1 @ SX4 ) @ SX2 ) )
                                  | ( ( times_times_nat @ SX1 @ SX3 )
                                    = ( plus_plus_nat @ ( times_times_nat @ SX0 @ SX4 ) @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11035]) ).

thf(11209,plain,
    ( ( ! [SX0: nat,SX1: nat] :
          ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SX0 )
          | ( ord_less_eq_nat @ SX1 @ ( power_power_nat @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10751]) ).

thf(11210,plain,
    ( ( ! [SX0: nat,SX1: nat] :
          ( ( one_one_nat
            = ( times_times_nat @ SX0 @ SX1 ) )
          = ( ~ ( ( SX0 != one_one_nat )
                | ( SX1 != one_one_nat ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10784]) ).

thf(11211,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
          ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
          | ~ ( ord_less_eq_nat @ SX2 @ SX3 )
          | ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10882]) ).

thf(11212,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat,SX4: nat] :
          ( ~ ( ( SX0 != zero_zero_nat ) )
          | ~ ~ ( ( SX1 != SX2 )
                | ~ ( ( SX3 != SX4 ) ) )
          | ( ( plus_plus_nat @ SX1 @ ( times_times_nat @ SX0 @ SX3 ) )
           != ( plus_plus_nat @ SX2 @ ( times_times_nat @ SX0 @ SX4 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11044]) ).

thf(11213,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( dvd_dvd_nat @ SX0 @ SX1 )
          | ( ( dvd_dvd_nat @ SX0 @ ( plus_plus_nat @ SX1 @ SX2 ) )
            = ( dvd_dvd_nat @ SX0 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11017]) ).

thf(11214,plain,
    ( ( ! [SX0: nat > nat,SX1: nat > nat] :
          ( ~ ( summable_nat @ SX0 )
          | ~ ( summable_nat @ SX1 )
          | ( summable_nat
            @ ^ [SX2: nat] : ( plus_plus_nat @ ( SX0 @ SX2 ) @ ( SX1 @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11076]) ).

thf(11215,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ~ ( ~ ( ( SX0 != zero_zero_nat )
                | ( ( divide_divide_nat @ ( times_times_nat @ SX0 @ SX1 ) @ ( times_times_nat @ SX0 @ SX2 ) )
                  = zero_zero_nat ) )
            | ~ ( ~ ( ( SX0 != zero_zero_nat ) )
                | ( ( divide_divide_nat @ ( times_times_nat @ SX0 @ SX1 ) @ ( times_times_nat @ SX0 @ SX2 ) )
                  = ( divide_divide_nat @ SX1 @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10939]) ).

thf(11216,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX1 ) @ ( plus_plus_nat @ SX2 @ SX1 ) )
          | ( ord_less_eq_nat @ SX0 @ SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10888]) ).

thf(11217,plain,
    ( ( ! [SX0: num] :
          ( one
         != ( bit0 @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10761]) ).

thf(11218,plain,
    ( ( ! [SX0: nat,SX1: nat] :
          ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SX0 )
          | ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SX1 )
          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11039]) ).

thf(11219,plain,
    ( ( ! [SX0: nat,SX1: nat] :
          ( ~ ( dvd_dvd_nat @ SX0 @ SX1 )
          | ( ( times_times_nat @ ( divide_divide_nat @ SX1 @ SX0 ) @ SX0 )
            = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11000]) ).

thf(11220,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ( ( divide_divide_nat @ SX0 @ SX1 )
           != ( divide_divide_nat @ SX2 @ SX1 ) )
          | ~ ( dvd_dvd_nat @ SX1 @ SX0 )
          | ~ ( dvd_dvd_nat @ SX1 @ SX2 )
          | ( SX0 = SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11021]) ).

thf(11221,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( dvd_dvd_nat @ SX0 @ SX1 )
          | ~ ( dvd_dvd_nat @ SX0 @ SX2 )
          | ( ( ( divide_divide_nat @ SX1 @ SX0 )
              = ( divide_divide_nat @ SX2 @ SX0 ) )
            = ( SX1 = SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11022]) ).

thf(11222,plain,
    ( ( ! [SX0: nat,SX1: nat] :
          ( ~ ( dvd_dvd_nat @ SX0 @ SX1 )
          | ~ ! [SX2: nat] :
                ( SX1
               != ( times_times_nat @ SX0 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11014]) ).

thf(11223,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
          ( ~ ( ord_less_nat @ SX0 @ SX1 )
          | ~ ( ord_less_nat @ SX2 @ SX3 )
          | ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10817]) ).

thf(11224,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
          ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
          | ~ ( ord_less_eq_nat @ SX2 @ SX3 )
          | ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10823]) ).

thf(11225,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( dvd_dvd_nat @ ( times_times_nat @ SX0 @ SX1 ) @ SX2 )
          | ( dvd_dvd_nat @ SX0 @ SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11009]) ).

thf(11226,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ( SX0
           != ( times_times_nat @ SX1 @ SX2 ) )
          | ( dvd_dvd_nat @ SX1 @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11013]) ).

thf(11227,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
          | ( ord_less_eq_nat @ ( plus_plus_nat @ SX2 @ SX0 ) @ ( plus_plus_nat @ SX2 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10883]) ).

thf(11228,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ( ( plus_plus_nat @ SX0 @ SX1 )
           != SX2 )
          | ( SX0
            = ( minus_minus_nat @ SX2 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10899]) ).

thf(11229,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ord_less_nat @ SX0 @ SX1 )
          | ( ord_less_nat @ ( plus_plus_nat @ SX2 @ SX0 ) @ ( plus_plus_nat @ SX2 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10893]) ).

thf(11230,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( dvd_dvd_nat @ SX0 @ SX1 )
          | ( dvd_dvd_nat @ SX0 @ ( times_times_nat @ SX2 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11011]) ).

thf(11231,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( dvd_dvd_nat @ SX0 @ SX1 )
          | ( dvd_dvd_nat @ SX0 @ ( times_times_nat @ SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11010]) ).

thf(11232,plain,
    ( ( ! [SX0: option_nat,SX1: option_nat] :
          ( ( ( SX0 = none_nat )
           != ( SX1 = none_nat ) )
          | ~ ( ~ ( ( SX0 != none_nat ) )
              | ~ ( ( SX1 != none_nat ) )
              | ( ( the_nat @ SX0 )
                = ( the_nat @ SX1 ) ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10755]) ).

thf(11233,plain,
    ( ( ! [SX0: nat > $o,SX1: nat] :
          ( ~ ! [SX2: nat] :
                ( ( ( divide_divide_nat @ SX2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                 != SX2 )
                | ( SX0 @ SX2 ) )
          | ~ ! [SX2: nat,SX3: $o] :
                ( ~ ( SX0 @ SX2 )
                | ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ SX3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SX2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                 != SX2 )
                | ( SX0 @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ SX3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SX2 ) ) ) )
          | ( SX0 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11043]) ).

thf(11234,plain,
    ( ( ord_less_eq_nat
      = ( ^ [SX0: nat,SX1: nat] :
            ~ ! [SX2: nat] :
                ( SX1
               != ( plus_plus_nat @ SX0 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10886]) ).

thf(11235,plain,
    ( ( ! [SX0: num,SX1: num] :
          ( ( bit0 @ SX0 )
         != ( bit1 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11053]) ).

thf(11236,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( dvd_dvd_nat @ SX0 @ SX1 )
          | ( ( power_power_nat @ ( divide_divide_nat @ SX1 @ SX0 ) @ SX2 )
            = ( divide_divide_nat @ ( power_power_nat @ SX1 @ SX2 ) @ ( power_power_nat @ SX0 @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11033]) ).

thf(11237,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
          ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
          | ~ ( ord_less_eq_nat @ SX2 @ SX3 )
          | ( ord_less_eq_nat @ ( times_times_nat @ SX0 @ SX2 ) @ ( times_times_nat @ SX1 @ SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10832]) ).

thf(11238,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat] :
          ( ~ ~ ( ~ ( ord_less_nat @ SX0 @ SX1 )
                | ( SX2 != SX3 ) )
          | ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX2 ) @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10891]) ).

thf(11239,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX1 ) @ ( plus_plus_nat @ SX0 @ SX2 ) )
          | ( ord_less_eq_nat @ SX1 @ SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10887]) ).

thf(11240,plain,
    ( ( ! [SX0: nat,SX1: nat] :
          ( ~ ( ord_less_eq_nat @ ( power_power_nat @ SX0 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ SX1 )
          | ( ord_less_eq_nat @ SX0 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10753]) ).

thf(11241,plain,
    ( ( ! [SX0: num] :
          ( ~ ( ( SX0 != one ) )
          | ~ ! [SX1: num] :
                ( SX0
               != ( bit0 @ SX1 ) )
          | ~ ! [SX1: num] :
                ( SX0
               != ( bit1 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11058]) ).

thf(11242,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: list_VEBT_VEBT,SX3: vEBT_VEBT] :
          ( ~ ( ( SX0 != SX1 ) )
          | ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ SX2 @ SX0 @ SX3 ) @ SX1 )
            = ( nth_VEBT_VEBT @ SX2 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10739]) ).

thf(11243,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat,SX3: nat,SX4: nat] :
          ( ( ( modulo_modulo_nat @ SX0 @ SX1 )
           != ( modulo_modulo_nat @ SX2 @ SX1 ) )
          | ( ( modulo_modulo_nat @ SX3 @ SX1 )
           != ( modulo_modulo_nat @ SX4 @ SX1 ) )
          | ( ( modulo_modulo_nat @ ( plus_plus_nat @ SX0 @ SX3 ) @ SX1 )
            = ( modulo_modulo_nat @ ( plus_plus_nat @ SX2 @ SX4 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10953]) ).

thf(11244,plain,
    ( ( ! [SX0: num] :
          ( one
         != ( bit1 @ SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11057]) ).

thf(11245,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SX0 @ SX1 ) @ SX2 )
          | ( ord_less_eq_nat @ SX0 @ SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10826]) ).

thf(11246,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ord_less_nat @ ( plus_plus_nat @ SX0 @ SX1 ) @ ( plus_plus_nat @ SX0 @ SX2 ) )
          | ( ord_less_nat @ SX1 @ SX2 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10895]) ).

thf(11247,plain,
    ( ( ! [SX0: nat > nat,SX1: nat,SX2: nat > nat,SX3: nat] :
          ( ~ ( sums_nat @ SX0 @ SX1 )
          | ~ ( sums_nat @ SX2 @ SX3 )
          | ( sums_nat
            @ ^ [SX4: nat] : ( plus_plus_nat @ ( SX0 @ SX4 ) @ ( SX2 @ SX4 ) )
            @ ( plus_plus_nat @ SX1 @ SX3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[11079]) ).

thf(11248,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ord_less_nat @ SX0 @ SX1 )
          | ( ord_less_nat @ SX0 @ ( plus_plus_nat @ SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10813]) ).

thf(11249,plain,
    ( ( ! [SX0: nat,SX1: nat,SX2: nat] :
          ( ~ ( ord_less_eq_nat @ SX0 @ SX1 )
          | ( ord_less_eq_nat @ SX0 @ ( plus_plus_nat @ SX1 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[10821]) ).

thf(11250,plain,
    ! [SV1: nat] :
      ( ( ! [SY983: nat] :
            ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ SV1 @ SY983 ) @ ( vEBT_VEBT_low @ SV1 @ SY983 ) @ SY983 )
            = SV1 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10671]) ).

thf(11251,plain,
    ! [SV2: nat] :
      ( ( ! [SY984: nat] :
            ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV2 @ SY984 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV2 ) )
            = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY984 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10673]) ).

thf(11252,plain,
    ( ( ! [SV3: nat] :
          ( ( vEBT_VEBT_high @ SV3 )
          = ( ^ [SY985: nat] : ( divide_divide_nat @ SV3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY985 ) ) ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[10674]) ).

thf(11253,plain,
    ( ( vEBT_VEBT_high
      = ( ^ [X2: nat,N: nat] : ( divide_divide_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[10674]) ).

thf(11254,plain,
    ( ( ! [SV4: nat] :
          ( ( vEBT_VEBT_bit_concat @ SV4 )
          = ( ^ [SY986: nat,SY987: nat] : ( plus_plus_nat @ ( times_times_nat @ SV4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY987 ) ) @ SY986 ) ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[10679]) ).

thf(11255,plain,
    ( ( vEBT_VEBT_bit_concat
      = ( ^ [H: nat,L: nat,D2: nat] : ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D2 ) ) @ L ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[10679]) ).

thf(11256,plain,
    ! [SV5: nat] :
      ( ( ( divide_divide_nat @ ( plus_plus_nat @ SV5 @ SV5 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
        = SV5 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10690]) ).

thf(11257,plain,
    ! [SV6: num] :
      ( ( ! [SY988: nat,SY989: nat] :
            ( ( times_times_nat @ ( numeral_numeral_nat @ SV6 ) @ ( plus_plus_nat @ SY988 @ SY989 ) )
            = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ SV6 ) @ SY988 ) @ ( times_times_nat @ ( numeral_numeral_nat @ SV6 ) @ SY989 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10694]) ).

thf(11258,plain,
    ! [SV7: nat] :
      ( ( ! [SY990: nat,SY991: num] :
            ( ( times_times_nat @ ( plus_plus_nat @ SV7 @ SY990 ) @ ( numeral_numeral_nat @ SY991 ) )
            = ( plus_plus_nat @ ( times_times_nat @ SV7 @ ( numeral_numeral_nat @ SY991 ) ) @ ( times_times_nat @ SY990 @ ( numeral_numeral_nat @ SY991 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10695]) ).

thf(11259,plain,
    ! [SV8: nat] :
      ( ( ! [SY992: nat] :
            ( ( power_power_nat @ ( plus_plus_nat @ SV8 @ SY992 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
            = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ SV8 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ SY992 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV8 ) @ SY992 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10696]) ).

thf(11260,plain,
    ! [SV9: nat] :
      ( ( ! [SY993: nat,SY994: nat] :
            ( ( divide_divide_nat @ ( divide_divide_nat @ SV9 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY993 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY994 ) )
            = ( divide_divide_nat @ SV9 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SY993 @ SY994 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10699]) ).

thf(11261,plain,
    ! [SV10: num] :
      ( ( ! [SY995: num] :
            ( ( ( numeral_numeral_nat @ SV10 )
              = ( numeral_numeral_nat @ SY995 ) )
            = ( SV10 = SY995 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10700]) ).

thf(11262,plain,
    ! [SV11: num] :
      ( ( ! [SY996: num,SY997: nat] :
            ( ( times_times_nat @ ( numeral_numeral_nat @ SV11 ) @ ( times_times_nat @ ( numeral_numeral_nat @ SY996 ) @ SY997 ) )
            = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ SV11 @ SY996 ) ) @ SY997 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10705]) ).

thf(11263,plain,
    ! [SV12: num] :
      ( ( ! [SY998: num] :
            ( ( times_times_nat @ ( numeral_numeral_nat @ SV12 ) @ ( numeral_numeral_nat @ SY998 ) )
            = ( numeral_numeral_nat @ ( times_times_num @ SV12 @ SY998 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10706]) ).

thf(11264,plain,
    ! [SV13: num] :
      ( ( ! [SY999: num,SY1000: nat] :
            ( ( plus_plus_nat @ ( numeral_numeral_nat @ SV13 ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ SY999 ) @ SY1000 ) )
            = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ SV13 @ SY999 ) ) @ SY1000 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10707]) ).

thf(11265,plain,
    ! [SV14: num] :
      ( ( ! [SY1001: num] :
            ( ( plus_plus_nat @ ( numeral_numeral_nat @ SV14 ) @ ( numeral_numeral_nat @ SY1001 ) )
            = ( numeral_numeral_nat @ ( plus_plus_num @ SV14 @ SY1001 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10708]) ).

thf(11266,plain,
    ! [SV15: num] :
      ( ( ( times_times_num @ ( bit0 @ one ) @ SV15 )
        = ( bit0 @ SV15 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10709]) ).

thf(11267,plain,
    ! [SV16: nat] :
      ( ( ! [SY1002: num,SY1003: num] :
            ( ( power_power_nat @ ( power_power_nat @ SV16 @ ( numeral_numeral_nat @ SY1002 ) ) @ ( numeral_numeral_nat @ SY1003 ) )
            = ( power_power_nat @ SV16 @ ( numeral_numeral_nat @ ( times_times_num @ SY1002 @ SY1003 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10710]) ).

thf(11268,plain,
    ! [SV17: nat] :
      ( ( ! [SY1004: num,SY1005: num,SY1006: nat] :
            ( ( times_times_nat @ ( power_power_nat @ SV17 @ ( numeral_numeral_nat @ SY1004 ) ) @ ( times_times_nat @ ( power_power_nat @ SV17 @ ( numeral_numeral_nat @ SY1005 ) ) @ SY1006 ) )
            = ( times_times_nat @ ( power_power_nat @ SV17 @ ( numeral_numeral_nat @ ( plus_plus_num @ SY1004 @ SY1005 ) ) ) @ SY1006 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10711]) ).

thf(11269,plain,
    ! [SV18: nat] :
      ( ( ! [SY1007: num,SY1008: num] :
            ( ( times_times_nat @ ( power_power_nat @ SV18 @ ( numeral_numeral_nat @ SY1007 ) ) @ ( power_power_nat @ SV18 @ ( numeral_numeral_nat @ SY1008 ) ) )
            = ( power_power_nat @ SV18 @ ( numeral_numeral_nat @ ( plus_plus_num @ SY1007 @ SY1008 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10712]) ).

thf(11270,plain,
    ! [SV19: num] :
      ( ( ( plus_plus_num @ one @ SV19 )
        = ( plus_plus_num @ SV19 @ one ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10713]) ).

thf(11271,plain,
    ! [SV20: nat] :
      ( ( ! [SY1009: num,SY1010: num] :
            ( ( divide_divide_nat @ ( divide_divide_nat @ SV20 @ ( numeral_numeral_nat @ SY1009 ) ) @ ( numeral_numeral_nat @ SY1010 ) )
            = ( divide_divide_nat @ SV20 @ ( numeral_numeral_nat @ ( times_times_num @ SY1009 @ SY1010 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10714]) ).

thf(11272,plain,
    ! [SV21: nat] :
      ( ( ord_less_nat @ SV21 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV21 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10716]) ).

thf(11273,plain,
    ! [SV22: nat] :
      ( ( ! [SY1011: nat,SY1012: nat] :
            ( ( power_power_nat @ ( times_times_nat @ SV22 @ SY1011 ) @ SY1012 )
            = ( times_times_nat @ ( power_power_nat @ SV22 @ SY1012 ) @ ( power_power_nat @ SY1011 @ SY1012 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10718]) ).

thf(11274,plain,
    ! [SV23: nat] :
      ( ( ! [SY1013: nat] :
            ( ( times_times_nat @ ( power_power_nat @ SV23 @ SY1013 ) @ SV23 )
            = ( times_times_nat @ SV23 @ ( power_power_nat @ SV23 @ SY1013 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10719]) ).

thf(11275,plain,
    ! [SV24: nat] :
      ( ( ! [SY1014: nat,SY1015: nat] :
            ( ( power_power_nat @ SV24 @ ( times_times_nat @ SY1014 @ SY1015 ) )
            = ( power_power_nat @ ( power_power_nat @ SV24 @ SY1014 ) @ SY1015 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10720]) ).

thf(11276,plain,
    ! [SV25: real] :
      ( ( ! [SY1016: nat,SY1017: nat] :
            ( ( power_power_real @ SV25 @ ( times_times_nat @ SY1016 @ SY1017 ) )
            = ( power_power_real @ ( power_power_real @ SV25 @ SY1016 ) @ SY1017 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10721]) ).

thf(11277,plain,
    ! [SV26: int] :
      ( ( ! [SY1018: nat,SY1019: nat] :
            ( ( power_power_int @ SV26 @ ( times_times_nat @ SY1018 @ SY1019 ) )
            = ( power_power_int @ ( power_power_int @ SV26 @ SY1018 ) @ SY1019 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10722]) ).

thf(11278,plain,
    ! [SV27: complex] :
      ( ( ! [SY1020: nat,SY1021: nat] :
            ( ( power_power_complex @ SV27 @ ( times_times_nat @ SY1020 @ SY1021 ) )
            = ( power_power_complex @ ( power_power_complex @ SV27 @ SY1020 ) @ SY1021 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10723]) ).

thf(11279,plain,
    ! [SV28: nat] :
      ( ( ! [SY1022: nat,SY1023: nat] :
            ( ( divide_divide_nat @ SV28 @ ( times_times_nat @ SY1022 @ SY1023 ) )
            = ( divide_divide_nat @ ( divide_divide_nat @ SV28 @ SY1022 ) @ SY1023 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10724]) ).

thf(11280,plain,
    ! [SV29: nat] :
      ( ( ( times_times_nat @ SV29 @ ( numeral_numeral_nat @ one ) )
        = SV29 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10725]) ).

thf(11281,plain,
    ! [SV30: nat] :
      ( ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ SV30 )
        = SV30 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10726]) ).

thf(11282,plain,
    ! [SV31: num] :
      ( ( ( numeral_numeral_nat @ ( bit0 @ SV31 ) )
        = ( plus_plus_nat @ ( numeral_numeral_nat @ SV31 ) @ ( numeral_numeral_nat @ SV31 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10727]) ).

thf(11283,plain,
    ! [SV32: nat] :
      ( ( ! [SY1024: nat,SY1025: nat] :
            ( ( power_power_nat @ SV32 @ ( plus_plus_nat @ SY1024 @ SY1025 ) )
            = ( times_times_nat @ ( power_power_nat @ SV32 @ SY1024 ) @ ( power_power_nat @ SV32 @ SY1025 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10728]) ).

thf(11284,plain,
    ! [SV33: num] :
      ( ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit0 @ SV33 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
        = ( numeral_numeral_nat @ SV33 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10729]) ).

thf(11285,plain,
    ! [SV34: nat] :
      ( ( ! [SY1026: nat] :
            ( ( plus_plus_nat @ SV34 @ ( plus_plus_nat @ SV34 @ SY1026 ) )
            = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV34 ) @ SY1026 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10730]) ).

thf(11286,plain,
    ! [SV35: nat] :
      ( ( ( times_times_nat @ SV35 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
        = ( plus_plus_nat @ SV35 @ SV35 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10731]) ).

thf(11287,plain,
    ! [SV36: nat] :
      ( ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV36 )
        = ( plus_plus_nat @ SV36 @ SV36 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10732]) ).

thf(11288,plain,
    ! [SV37: nat] :
      ( ( ( power_power_nat @ SV37 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
        = ( times_times_nat @ SV37 @ SV37 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10733]) ).

thf(11289,plain,
    ! [SV38: nat] :
      ( ( ( power_power_nat @ SV38 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
        = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ SV38 @ SV38 ) @ SV38 ) @ SV38 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10734]) ).

thf(11290,plain,
    ! [SV39: nat] :
      ( ( ! [SY1027: nat] :
            ( ( power_power_nat @ SV39 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1027 ) )
            = ( power_power_nat @ ( power_power_nat @ SV39 @ SY1027 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10735]) ).

thf(11291,plain,
    ! [SV40: real] :
      ( ( ! [SY1028: nat] :
            ( ( power_power_real @ SV40 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1028 ) )
            = ( power_power_real @ ( power_power_real @ SV40 @ SY1028 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10736]) ).

thf(11292,plain,
    ! [SV41: int] :
      ( ( ! [SY1029: nat] :
            ( ( power_power_int @ SV41 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1029 ) )
            = ( power_power_int @ ( power_power_int @ SV41 @ SY1029 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10737]) ).

thf(11293,plain,
    ! [SV42: complex] :
      ( ( ! [SY1030: nat] :
            ( ( power_power_complex @ SV42 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1030 ) )
            = ( power_power_complex @ ( power_power_complex @ SV42 @ SY1030 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10738]) ).

thf(11294,plain,
    ! [SV43: list_VEBT_VEBT] :
      ( ( ! [SY1031: nat] :
            ( ( list_u1324408373059187874T_VEBT @ SV43 @ SY1031 @ ( nth_VEBT_VEBT @ SV43 @ SY1031 ) )
            = SV43 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10740]) ).

thf(11295,plain,
    ! [SV44: list_VEBT_VEBT] :
      ( ( ! [SY1032: nat,SY1033: vEBT_VEBT] :
            ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV44 @ SY1032 @ SY1033 ) )
            = ( size_s6755466524823107622T_VEBT @ SV44 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10741]) ).

thf(11296,plain,
    ! [SV45: list_VEBT_VEBT] :
      ( ( ! [SY1034: nat,SY1035: vEBT_VEBT,SY1036: vEBT_VEBT] :
            ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV45 @ SY1034 @ SY1035 ) @ SY1034 @ SY1036 )
            = ( list_u1324408373059187874T_VEBT @ SV45 @ SY1034 @ SY1036 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10742]) ).

thf(11297,plain,
    ! [SV46: nat] :
      ( ( ! [SY1037: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ SV46 @ SY1037 ) @ SV46 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10747]) ).

thf(11298,plain,
    ! [SV47: nat] :
      ( ( ! [SY1038: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ SV47 @ SY1038 ) @ SY1038 ) @ SV47 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10748]) ).

thf(11299,plain,
    ! [SV48: nat] :
      ( ( ! [SY1039: nat] : ( ord_less_eq_nat @ ( times_times_nat @ SV48 @ ( divide_divide_nat @ SY1039 @ SV48 ) ) @ SY1039 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10749]) ).

thf(11300,plain,
    ! [SV49: nat] :
      ( ( ! [SY1040: nat] :
            ( ( ord_less_eq_nat @ ( power_power_nat @ SV49 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ SY1040 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
            = ( ord_less_eq_nat @ SV49 @ SY1040 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10752]) ).

thf(11301,plain,
    ! [SV50: nat] :
      ( ( ( the_nat @ ( some_nat @ SV50 ) )
        = SV50 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10754]) ).

thf(11302,plain,
    ! [SV51: num] :
      ( ( ord_less_num @ one @ ( bit0 @ SV51 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10756]) ).

thf(11303,plain,
    ! [SV52: num] :
      ( ( ~ ( ord_less_num @ SV52 @ one ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10758]) ).

thf(11304,plain,
    ! [SV53: num] :
      ( ( ! [SY1041: num] :
            ( ( ord_less_num @ ( bit0 @ SV53 ) @ ( bit0 @ SY1041 ) )
            = ( ord_less_num @ SV53 @ SY1041 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10759]) ).

thf(11305,plain,
    ! [SV54: num] :
      ( ( ! [SY1042: num] :
            ( ( ( bit0 @ SV54 )
              = ( bit0 @ SY1042 ) )
            = ( SV54 = SY1042 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10760]) ).

thf(11306,plain,
    ! [SV55: nat] :
      ( ( ( divide_divide_nat @ SV55 @ one_one_nat )
        = SV55 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10763]) ).

thf(11307,plain,
    ! [SV56: nat] :
      ( ( ( power_power_nat @ one_one_nat @ SV56 )
        = one_one_nat )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10764]) ).

thf(11308,plain,
    ! [SV57: nat] :
      ( ( ( power_power_nat @ SV57 @ one_one_nat )
        = SV57 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10765]) ).

thf(11309,plain,
    ! [SV58: num] :
      ( ( ! [SY1043: num] :
            ( ( plus_plus_num @ ( bit0 @ SV58 ) @ ( bit0 @ SY1043 ) )
            = ( bit0 @ ( plus_plus_num @ SV58 @ SY1043 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10766]) ).

thf(11310,plain,
    ! [SV59: num] :
      ( ( ! [SY1044: num] :
            ( ( times_times_num @ ( bit0 @ SV59 ) @ ( bit0 @ SY1044 ) )
            = ( bit0 @ ( bit0 @ ( times_times_num @ SV59 @ SY1044 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10767]) ).

thf(11311,plain,
    ! [SV60: num] :
      ( ( ( times_times_num @ SV60 @ one )
        = SV60 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10768]) ).

thf(11312,plain,
    ! [SV61: num] :
      ( ( ( times_times_num @ one @ SV61 )
        = SV61 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10769]) ).

thf(11313,plain,
    ! [SV62: num] :
      ( ( ! [SY1045: num] :
            ( ( ord_less_eq_num @ ( bit0 @ SV62 ) @ ( bit0 @ SY1045 ) )
            = ( ord_less_eq_num @ SV62 @ SY1045 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10770]) ).

thf(11314,plain,
    ! [SV63: num] :
      ( ( ord_less_eq_num @ one @ SV63 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10771]) ).

thf(11315,plain,
    ! [SV64: num] :
      ( ( ( one_one_nat
          = ( numeral_numeral_nat @ SV64 ) )
        = ( one = SV64 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10772]) ).

thf(11316,plain,
    ! [SV65: num] :
      ( ( ( ( numeral_numeral_nat @ SV65 )
          = one_one_nat )
        = ( SV65 = one ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10773]) ).

thf(11317,plain,
    ! [SV66: num] :
      ( ( ~ ( ord_less_eq_num @ ( bit0 @ SV66 ) @ one ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10774]) ).

thf(11318,plain,
    ! [SV67: num] :
      ( ( ( ord_less_eq_num @ SV67 @ one )
        = ( SV67 = one ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10776]) ).

thf(11319,plain,
    ! [SV68: num] :
      ( ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ SV68 ) )
        = ( plus_plus_nat @ ( numeral_numeral_nat @ SV68 ) @ one_one_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10777]) ).

thf(11320,plain,
    ! [SV69: nat] :
      ( ( ! [SY1046: nat,SY1047: nat,SY1048: nat] :
            ( ( plus_plus_nat @ ( times_times_nat @ SV69 @ SY1046 ) @ ( plus_plus_nat @ ( times_times_nat @ SY1047 @ SY1046 ) @ SY1048 ) )
            = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV69 @ SY1047 ) @ SY1046 ) @ SY1048 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10783]) ).

thf(11321,plain,
    ! [SV70: nat] :
      ( ( ! [SY1049: nat] :
            ( ( plus_plus_nat @ SV70 @ ( suc @ SY1049 ) )
            = ( suc @ ( plus_plus_nat @ SV70 @ SY1049 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10786]) ).

thf(11322,plain,
    ! [SV71: nat] :
      ( ( ! [SY1050: nat,SY1051: nat] :
            ( ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SY1050 ) @ ( plus_plus_nat @ SV71 @ SY1051 ) )
            = ( ord_less_nat @ SY1050 @ SY1051 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10787]) ).

thf(11323,plain,
    ! [SV72: nat] :
      ( ( ! [SY1052: nat,SY1053: nat] :
            ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV72 @ SY1052 ) @ ( plus_plus_nat @ SV72 @ SY1053 ) )
            = ( ord_less_eq_nat @ SY1052 @ SY1053 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10788]) ).

thf(11324,plain,
    ! [SV73: nat] :
      ( ( ! [SY1054: nat,SY1055: nat] :
            ( ( minus_minus_nat @ ( minus_minus_nat @ SV73 @ SY1054 ) @ SY1055 )
            = ( minus_minus_nat @ SV73 @ ( plus_plus_nat @ SY1054 @ SY1055 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10789]) ).

thf(11325,plain,
    ! [SV74: nat] :
      ( ( ! [SY1056: nat] :
            ( ( times_times_nat @ SV74 @ ( suc @ SY1056 ) )
            = ( plus_plus_nat @ SV74 @ ( times_times_nat @ SV74 @ SY1056 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10791]) ).

thf(11326,plain,
    ! [SV75: nat] :
      ( ( ( plus_plus_nat @ SV75 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
        = ( suc @ ( suc @ SV75 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10792]) ).

thf(11327,plain,
    ! [SV76: nat] :
      ( ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV76 )
        = ( suc @ ( suc @ SV76 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10793]) ).

thf(11328,plain,
    ! [SV77: nat] :
      ( ( ( divide_divide_nat @ ( suc @ ( suc @ SV77 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
        = ( suc @ ( divide_divide_nat @ SV77 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10794]) ).

thf(11329,plain,
    ! [SV78: nat] :
      ( ( ! [SY1057: nat] :
            ( ( minus_minus_nat @ ( plus_plus_nat @ SV78 @ SY1057 ) @ SY1057 )
            = SV78 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10795]) ).

thf(11330,plain,
    ! [SV79: nat] :
      ( ( ! [SY1058: nat] :
            ( ( minus_minus_nat @ ( plus_plus_nat @ SV79 @ SY1058 ) @ SV79 )
            = SY1058 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10796]) ).

thf(11331,plain,
    ! [SV80: nat] :
      ( ( ! [SY1059: nat,SY1060: nat] :
            ( ( minus_minus_nat @ ( plus_plus_nat @ SV80 @ SY1059 ) @ ( plus_plus_nat @ SY1060 @ SY1059 ) )
            = ( minus_minus_nat @ SV80 @ SY1060 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10797]) ).

thf(11332,plain,
    ! [SV81: nat] :
      ( ( ! [SY1061: nat,SY1062: nat] :
            ( ( minus_minus_nat @ ( plus_plus_nat @ SV81 @ SY1061 ) @ ( plus_plus_nat @ SV81 @ SY1062 ) )
            = ( minus_minus_nat @ SY1061 @ SY1062 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10798]) ).

thf(11333,plain,
    ! [SV82: nat] :
      ( ( ! [SY1063: nat] :
            ( ( plus_plus_nat @ ( suc @ SV82 ) @ SY1063 )
            = ( plus_plus_nat @ SV82 @ ( suc @ SY1063 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10799]) ).

thf(11334,plain,
    ! [SV83: nat] :
      ( ( ! [SY1064: nat] :
            ( ( plus_plus_nat @ ( suc @ SV83 ) @ SY1064 )
            = ( suc @ ( plus_plus_nat @ SV83 @ SY1064 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10800]) ).

thf(11335,plain,
    ! [SV84: nat] :
      ( ( ! [SY1065: nat,SY1066: nat] :
            ( ( times_times_nat @ SV84 @ ( minus_minus_nat @ SY1065 @ SY1066 ) )
            = ( minus_minus_nat @ ( times_times_nat @ SV84 @ SY1065 ) @ ( times_times_nat @ SV84 @ SY1066 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10802]) ).

thf(11336,plain,
    ! [SV85: nat] :
      ( ( ! [SY1067: nat,SY1068: nat] :
            ( ( times_times_nat @ ( minus_minus_nat @ SV85 @ SY1067 ) @ SY1068 )
            = ( minus_minus_nat @ ( times_times_nat @ SV85 @ SY1068 ) @ ( times_times_nat @ SY1067 @ SY1068 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10803]) ).

thf(11337,plain,
    ! [SV86: nat] :
      ( ( ! [SY1069: nat,SY1070: nat] :
            ( ( ( times_times_nat @ ( suc @ SV86 ) @ SY1069 )
              = ( times_times_nat @ ( suc @ SV86 ) @ SY1070 ) )
            = ( SY1069 = SY1070 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10804]) ).

thf(11338,plain,
    ! [SV87: num] :
      ( ( ( numeral_numeral_nat @ ( bit0 @ SV87 ) )
        = ( plus_plus_nat @ ( numeral_numeral_nat @ SV87 ) @ ( numeral_numeral_nat @ SV87 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10805]) ).

thf(11339,plain,
    ! [SV88: nat] :
      ( ( ! [SY1071: nat] :
            ( ( times_times_nat @ ( suc @ SV88 ) @ SY1071 )
            = ( plus_plus_nat @ SY1071 @ ( times_times_nat @ SV88 @ SY1071 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10806]) ).

thf(11340,plain,
    ! [SV89: nat] :
      ( ( ! [SY1072: num] :
            ( ( power_power_nat @ SV89 @ ( numeral_numeral_nat @ ( bit0 @ SY1072 ) ) )
            = ( times_times_nat @ ( power_power_nat @ SV89 @ ( numeral_numeral_nat @ SY1072 ) ) @ ( power_power_nat @ SV89 @ ( numeral_numeral_nat @ SY1072 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10807]) ).

thf(11341,plain,
    ! [SV90: nat] :
      ( ( ! [SY1073: nat] :
            ( ( power_power_nat @ SV90 @ ( suc @ SY1073 ) )
            = ( times_times_nat @ ( power_power_nat @ SV90 @ SY1073 ) @ SV90 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10808]) ).

thf(11342,plain,
    ! [SV91: nat] :
      ( ( ! [SY1074: nat] :
            ( ( power_power_nat @ SV91 @ ( suc @ SY1074 ) )
            = ( times_times_nat @ SV91 @ ( power_power_nat @ SV91 @ SY1074 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10809]) ).

thf(11343,plain,
    ! [SV92: nat] :
      ( ( ! [SY1075: nat] :
            ( ( power_power_nat @ SV92 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1075 ) ) )
            = ( times_times_nat @ SV92 @ ( power_power_nat @ ( power_power_nat @ SV92 @ SY1075 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10810]) ).

thf(11344,plain,
    ! [SV93: nat] :
      ( ( ! [SY1076: nat] :
            ~ ( ord_less_nat @ ( plus_plus_nat @ SV93 @ SY1076 ) @ SY1076 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10815]) ).

thf(11345,plain,
    ! [SV94: nat] :
      ( ( ! [SY1077: nat] :
            ~ ( ord_less_nat @ ( plus_plus_nat @ SV94 @ SY1077 ) @ SV94 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10816]) ).

thf(11346,plain,
    ! [SV95: nat] :
      ( ( ! [SY1078: nat] : ( ord_less_eq_nat @ SV95 @ ( plus_plus_nat @ SY1078 @ SV95 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10827]) ).

thf(11347,plain,
    ! [SV96: nat] :
      ( ( ! [SY1079: nat] : ( ord_less_eq_nat @ SV96 @ ( plus_plus_nat @ SV96 @ SY1079 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10828]) ).

thf(11348,plain,
    ! [SV97: nat] :
      ( ( ord_less_eq_nat @ SV97 @ ( times_times_nat @ SV97 @ SV97 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10833]) ).

thf(11349,plain,
    ! [SV98: nat] :
      ( ( ord_less_eq_nat @ SV98 @ ( times_times_nat @ SV98 @ ( times_times_nat @ SV98 @ SV98 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10834]) ).

thf(11350,plain,
    ! [SV99: nat] :
      ( ( ! [SY1080: nat,SY1081: nat] :
            ( ( times_times_nat @ SV99 @ ( plus_plus_nat @ SY1080 @ SY1081 ) )
            = ( plus_plus_nat @ ( times_times_nat @ SV99 @ SY1080 ) @ ( times_times_nat @ SV99 @ SY1081 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10835]) ).

thf(11351,plain,
    ! [SV100: nat] :
      ( ( ! [SY1082: nat,SY1083: nat] :
            ( ( times_times_nat @ ( plus_plus_nat @ SV100 @ SY1082 ) @ SY1083 )
            = ( plus_plus_nat @ ( times_times_nat @ SV100 @ SY1083 ) @ ( times_times_nat @ SY1082 @ SY1083 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10836]) ).

thf(11352,plain,
    ! [SV101: nat] :
      ( ( ( times_times_nat @ SV101 @ one_one_nat )
        = SV101 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10837]) ).

thf(11353,plain,
    ! [SV102: nat] :
      ( ( ( times_times_nat @ one_one_nat @ SV102 )
        = SV102 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10838]) ).

thf(11354,plain,
    ! [SV103: nat] :
      ( ( ( divide_divide_nat @ SV103 @ one_one_nat )
        = SV103 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10839]) ).

thf(11355,plain,
    ! [SV104: nat] :
      ( ( ! [SY1084: nat,SY1085: nat] :
            ( ( plus_plus_nat @ ( ord_max_nat @ SV104 @ SY1084 ) @ SY1085 )
            = ( ord_max_nat @ ( plus_plus_nat @ SV104 @ SY1085 ) @ ( plus_plus_nat @ SY1084 @ SY1085 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10840]) ).

thf(11356,plain,
    ! [SV105: nat] :
      ( ( ! [SY1086: nat,SY1087: nat] :
            ( ( plus_plus_nat @ SV105 @ ( ord_max_nat @ SY1086 @ SY1087 ) )
            = ( ord_max_nat @ ( plus_plus_nat @ SV105 @ SY1086 ) @ ( plus_plus_nat @ SV105 @ SY1087 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10841]) ).

thf(11357,plain,
    ! [SV106: nat] :
      ( ( ! [SY1088: nat,SY1089: nat] :
            ( ( times_times_nat @ ( ord_max_nat @ SV106 @ SY1088 ) @ SY1089 )
            = ( ord_max_nat @ ( times_times_nat @ SV106 @ SY1089 ) @ ( times_times_nat @ SY1088 @ SY1089 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10842]) ).

thf(11358,plain,
    ! [SV107: nat] :
      ( ( ! [SY1090: nat,SY1091: nat] :
            ( ( times_times_nat @ SV107 @ ( ord_max_nat @ SY1090 @ SY1091 ) )
            = ( ord_max_nat @ ( times_times_nat @ SV107 @ SY1090 ) @ ( times_times_nat @ SV107 @ SY1091 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10843]) ).

thf(11359,plain,
    ! [SV108: nat] :
      ( ( ! [SY1092: nat,SY1093: nat] :
            ( ( times_times_nat @ ( plus_plus_nat @ SV108 @ SY1092 ) @ SY1093 )
            = ( plus_plus_nat @ ( times_times_nat @ SV108 @ SY1093 ) @ ( times_times_nat @ SY1092 @ SY1093 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10844]) ).

thf(11360,plain,
    ! [SV109: nat] :
      ( ( ! [SY1094: nat,SY1095: nat] :
            ( ( times_times_nat @ SV109 @ ( plus_plus_nat @ SY1094 @ SY1095 ) )
            = ( plus_plus_nat @ ( times_times_nat @ SV109 @ SY1094 ) @ ( times_times_nat @ SV109 @ SY1095 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10845]) ).

thf(11361,plain,
    ! [SV110: nat] :
      ( ( ! [SY1096: nat,SY1097: nat] :
            ( ( times_times_nat @ ( plus_plus_nat @ SV110 @ SY1096 ) @ SY1097 )
            = ( plus_plus_nat @ ( times_times_nat @ SV110 @ SY1097 ) @ ( times_times_nat @ SY1096 @ SY1097 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10846]) ).

thf(11362,plain,
    ! [SV111: nat] :
      ( ( ! [SY1098: nat,SY1099: nat,SY1100: nat] :
            ( ( plus_plus_nat @ ( times_times_nat @ SV111 @ SY1098 ) @ ( plus_plus_nat @ ( times_times_nat @ SY1099 @ SY1098 ) @ SY1100 ) )
            = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV111 @ SY1099 ) @ SY1098 ) @ SY1100 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10847]) ).

thf(11363,plain,
    ! [SV112: nat] :
      ( ( ! [SY1101: nat,SY1102: nat] :
            ( ( times_times_nat @ ( minus_minus_nat @ SV112 @ SY1101 ) @ SY1102 )
            = ( minus_minus_nat @ ( times_times_nat @ SV112 @ SY1102 ) @ ( times_times_nat @ SY1101 @ SY1102 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10848]) ).

thf(11364,plain,
    ! [SV113: nat] :
      ( ( ! [SY1103: nat,SY1104: nat] :
            ( ( times_times_nat @ SV113 @ ( minus_minus_nat @ SY1103 @ SY1104 ) )
            = ( minus_minus_nat @ ( times_times_nat @ SV113 @ SY1103 ) @ ( times_times_nat @ SV113 @ SY1104 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10849]) ).

thf(11365,plain,
    ( ( ! [SV114: nat] :
          ( SV114
          = ( times_times_nat @ one_one_nat @ SV114 ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[10850]) ).

thf(11366,plain,
    ( ( ( ^ [X2: nat] : X2 )
      = ( times_times_nat @ one_one_nat ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[10850]) ).

thf(11367,plain,
    ! [SV115: nat] :
      ( ( ( ^ [SY1105: nat] : ( times_times_nat @ SY1105 @ SV115 ) )
        = ( times_times_nat @ SV115 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10851]) ).

thf(11368,plain,
    ! [SV116: nat] :
      ( ( ! [SY1106: nat] :
            ( ( minus_minus_nat @ ( plus_plus_nat @ SV116 @ SY1106 ) @ SY1106 )
            = SV116 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10854]) ).

thf(11369,plain,
    ! [SV117: nat] :
      ( ( ! [SY1107: nat,SY1108: nat] :
            ( ( minus_minus_nat @ ( plus_plus_nat @ SV117 @ SY1107 ) @ ( plus_plus_nat @ SY1108 @ SY1107 ) )
            = ( minus_minus_nat @ SV117 @ SY1108 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10855]) ).

thf(11370,plain,
    ! [SV118: nat] :
      ( ( ! [SY1109: nat] :
            ( ( minus_minus_nat @ ( plus_plus_nat @ SV118 @ SY1109 ) @ SV118 )
            = SY1109 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10856]) ).

thf(11371,plain,
    ! [SV119: nat] :
      ( ( ! [SY1110: nat,SY1111: nat] :
            ( ( minus_minus_nat @ ( plus_plus_nat @ SV119 @ SY1110 ) @ ( plus_plus_nat @ SV119 @ SY1111 ) )
            = ( minus_minus_nat @ SY1110 @ SY1111 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10857]) ).

thf(11372,plain,
    ! [SV120: nat] :
      ( ( ! [SY1112: nat,SY1113: nat] :
            ( ( ( plus_plus_nat @ SV120 @ SY1112 )
              = ( plus_plus_nat @ SV120 @ SY1113 ) )
            = ( SY1112 = SY1113 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10858]) ).

thf(11373,plain,
    ! [SV121: nat] :
      ( ( ! [SY1114: nat,SY1115: nat] :
            ( ( ( plus_plus_nat @ SV121 @ SY1114 )
              = ( plus_plus_nat @ SY1115 @ SY1114 ) )
            = ( SV121 = SY1115 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10859]) ).

thf(11374,plain,
    ! [SV122: nat] :
      ( ( ! [SY1116: nat,SY1117: nat] :
            ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ SY1116 ) @ ( plus_plus_nat @ SV122 @ SY1117 ) )
            = ( ord_less_eq_nat @ SY1116 @ SY1117 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10860]) ).

thf(11375,plain,
    ! [SV123: nat] :
      ( ( ! [SY1118: nat,SY1119: nat] :
            ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV123 @ SY1118 ) @ ( plus_plus_nat @ SY1119 @ SY1118 ) )
            = ( ord_less_eq_nat @ SV123 @ SY1119 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10861]) ).

thf(11376,plain,
    ! [SV124: nat] :
      ( ( ! [SY1120: nat,SY1121: nat] :
            ( ( ord_less_nat @ ( plus_plus_nat @ SV124 @ SY1120 ) @ ( plus_plus_nat @ SV124 @ SY1121 ) )
            = ( ord_less_nat @ SY1120 @ SY1121 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10862]) ).

thf(11377,plain,
    ! [SV125: nat] :
      ( ( ! [SY1122: nat,SY1123: nat] :
            ( ( ord_less_nat @ ( plus_plus_nat @ SV125 @ SY1122 ) @ ( plus_plus_nat @ SY1123 @ SY1122 ) )
            = ( ord_less_nat @ SV125 @ SY1123 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10863]) ).

thf(11378,plain,
    ! [SV126: nat] :
      ( ( ( times_times_nat @ SV126 @ one_one_nat )
        = SV126 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10864]) ).

thf(11379,plain,
    ! [SV127: nat] :
      ( ( ( times_times_nat @ one_one_nat @ SV127 )
        = SV127 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10865]) ).

thf(11380,plain,
    ! [SV128: nat] :
      ( ( ! [SY1124: nat,SY1125: nat] :
            ( ( times_times_nat @ ( times_times_nat @ SV128 @ SY1124 ) @ SY1125 )
            = ( times_times_nat @ SV128 @ ( times_times_nat @ SY1124 @ SY1125 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10866]) ).

thf(11381,plain,
    ! [SV129: nat] :
      ( ( ! [SY1126: nat,SY1127: nat] :
            ( ( times_times_nat @ ( times_times_nat @ SV129 @ SY1126 ) @ SY1127 )
            = ( times_times_nat @ SV129 @ ( times_times_nat @ SY1126 @ SY1127 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10867]) ).

thf(11382,plain,
    ( ( ! [SV130: nat] :
          ( ( times_times_nat @ SV130 )
          = ( ^ [SY1128: nat] : ( times_times_nat @ SY1128 @ SV130 ) ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[10868]) ).

thf(11383,plain,
    ( ( times_times_nat
      = ( ^ [A5: nat,B5: nat] : ( times_times_nat @ B5 @ A5 ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[10868]) ).

thf(11384,plain,
    ! [SV131: nat] :
      ( ( ! [SY1129: nat,SY1130: nat] :
            ( ( times_times_nat @ SV131 @ ( times_times_nat @ SY1129 @ SY1130 ) )
            = ( times_times_nat @ SY1129 @ ( times_times_nat @ SV131 @ SY1130 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10869]) ).

thf(11385,plain,
    ! [SV132: nat] :
      ( ( ! [SY1131: nat,SY1132: nat] :
            ( ( plus_plus_nat @ ( plus_plus_nat @ SV132 @ SY1131 ) @ SY1132 )
            = ( plus_plus_nat @ SV132 @ ( plus_plus_nat @ SY1131 @ SY1132 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10870]) ).

thf(11386,plain,
    ! [SV133: nat] :
      ( ( ! [SY1133: nat,SY1134: nat] :
            ( ( plus_plus_nat @ ( plus_plus_nat @ SV133 @ SY1133 ) @ SY1134 )
            = ( plus_plus_nat @ SV133 @ ( plus_plus_nat @ SY1133 @ SY1134 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10874]) ).

thf(11387,plain,
    ( ( ! [SV134: nat] :
          ( ( plus_plus_nat @ SV134 )
          = ( ^ [SY1135: nat] : ( plus_plus_nat @ SY1135 @ SV134 ) ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[10875]) ).

thf(11388,plain,
    ( ( plus_plus_nat
      = ( ^ [A5: nat,B5: nat] : ( plus_plus_nat @ B5 @ A5 ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[10875]) ).

thf(11389,plain,
    ! [SV135: nat] :
      ( ( ! [SY1136: nat,SY1137: nat] :
            ( ( plus_plus_nat @ SV135 @ ( plus_plus_nat @ SY1136 @ SY1137 ) )
            = ( plus_plus_nat @ SY1136 @ ( plus_plus_nat @ SV135 @ SY1137 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10876]) ).

thf(11390,plain,
    ! [SV136: nat] :
      ( ( ( times_times_nat @ one_one_nat @ SV136 )
        = SV136 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10897]) ).

thf(11391,plain,
    ! [SV137: nat] :
      ( ( ( times_times_nat @ SV137 @ one_one_nat )
        = SV137 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10898]) ).

thf(11392,plain,
    ! [SV138: nat] :
      ( ( ! [SY1138: nat,SY1139: nat] :
            ( ( minus_minus_nat @ ( minus_minus_nat @ SV138 @ SY1138 ) @ SY1139 )
            = ( minus_minus_nat @ SV138 @ ( plus_plus_nat @ SY1138 @ SY1139 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10900]) ).

thf(11393,plain,
    ! [SV139: nat] :
      ( ( ! [SY1140: nat,SY1141: nat] :
            ( ( plus_plus_nat @ ( ord_max_nat @ SV139 @ SY1140 ) @ SY1141 )
            = ( ord_max_nat @ ( plus_plus_nat @ SV139 @ SY1141 ) @ ( plus_plus_nat @ SY1140 @ SY1141 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10901]) ).

thf(11394,plain,
    ! [SV140: nat] :
      ( ( ! [SY1142: nat,SY1143: nat] :
            ( ( plus_plus_nat @ SV140 @ ( ord_max_nat @ SY1142 @ SY1143 ) )
            = ( ord_max_nat @ ( plus_plus_nat @ SV140 @ SY1142 ) @ ( plus_plus_nat @ SV140 @ SY1143 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10902]) ).

thf(11395,plain,
    ( ( ! [SV141: nat] :
          ( ( vEBT_VEBT_low @ SV141 )
          = ( ^ [SY1144: nat] : ( modulo_modulo_nat @ SV141 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1144 ) ) ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[10903]) ).

thf(11396,plain,
    ( ( vEBT_VEBT_low
      = ( ^ [X2: nat,N: nat] : ( modulo_modulo_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[10903]) ).

thf(11397,plain,
    ! [SV142: nat] :
      ( ( ! [SY1145: nat,SY1146: nat] :
            ( ( ( times_times_nat @ SV142 @ SY1145 )
              = ( times_times_nat @ SY1146 @ SY1145 ) )
            = ( ( SY1145 = zero_zero_nat )
              | ( SV142 = SY1146 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10904]) ).

thf(11398,plain,
    ! [SV143: nat] :
      ( ( ! [SY1147: nat,SY1148: nat] :
            ( ( ( times_times_nat @ SV143 @ SY1147 )
              = ( times_times_nat @ SV143 @ SY1148 ) )
            = ( ( SV143 = zero_zero_nat )
              | ( SY1147 = SY1148 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10905]) ).

thf(11399,plain,
    ! [SV144: nat] :
      ( ( ! [SY1149: nat] :
            ( ( ( times_times_nat @ SV144 @ SY1149 )
              = zero_zero_nat )
            = ( ( SV144 = zero_zero_nat )
              | ( SY1149 = zero_zero_nat ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10906]) ).

thf(11400,plain,
    ! [SV145: nat] :
      ( ( ( times_times_nat @ SV145 @ zero_zero_nat )
        = zero_zero_nat )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10907]) ).

thf(11401,plain,
    ! [SV146: nat] :
      ( ( ( times_times_nat @ zero_zero_nat @ SV146 )
        = zero_zero_nat )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10908]) ).

thf(11402,plain,
    ! [SV147: nat] :
      ( ( ( plus_plus_nat @ zero_zero_nat @ SV147 )
        = SV147 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10909]) ).

thf(11403,plain,
    ! [SV148: nat] :
      ( ( ! [SY1150: nat] :
            ( ( SV148
              = ( plus_plus_nat @ SV148 @ SY1150 ) )
            = ( SY1150 = zero_zero_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10912]) ).

thf(11404,plain,
    ! [SV149: nat] :
      ( ( ! [SY1151: nat] :
            ( ( SV149
              = ( plus_plus_nat @ SY1151 @ SV149 ) )
            = ( SY1151 = zero_zero_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10913]) ).

thf(11405,plain,
    ! [SV150: nat] :
      ( ( ! [SY1152: nat] :
            ( ( ( plus_plus_nat @ SV150 @ SY1152 )
              = SV150 )
            = ( SY1152 = zero_zero_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10914]) ).

thf(11406,plain,
    ! [SV151: nat] :
      ( ( ! [SY1153: nat] :
            ( ( ( plus_plus_nat @ SV151 @ SY1153 )
              = SY1153 )
            = ( SV151 = zero_zero_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10915]) ).

thf(11407,plain,
    ! [SV152: nat] :
      ( ( ( plus_plus_nat @ SV152 @ zero_zero_nat )
        = SV152 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10916]) ).

thf(11408,plain,
    ! [SV153: nat] :
      ( ( ( divide_divide_nat @ SV153 @ zero_zero_nat )
        = zero_zero_nat )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10917]) ).

thf(11409,plain,
    ! [SV154: nat] :
      ( ( ( divide_divide_nat @ zero_zero_nat @ SV154 )
        = zero_zero_nat )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10918]) ).

thf(11410,plain,
    ! [SV155: nat] :
      ( ( ( divide_divide_nat @ SV155 @ zero_zero_nat )
        = zero_zero_nat )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10919]) ).

thf(11411,plain,
    ! [SV156: nat] :
      ( ( ( divide_divide_nat @ zero_zero_nat @ SV156 )
        = zero_zero_nat )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10920]) ).

thf(11412,plain,
    ! [SV157: nat] :
      ( ( ! [SY1154: nat] :
            ( ( modulo_modulo_nat @ ( plus_plus_nat @ SV157 @ SY1154 ) @ SY1154 )
            = ( modulo_modulo_nat @ SV157 @ SY1154 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10921]) ).

thf(11413,plain,
    ! [SV158: nat] :
      ( ( ! [SY1155: nat] :
            ( ( modulo_modulo_nat @ ( plus_plus_nat @ SV158 @ SY1155 ) @ SV158 )
            = ( modulo_modulo_nat @ SY1155 @ SV158 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10922]) ).

thf(11414,plain,
    ! [SV159: nat] :
      ( ( ( plus_plus_nat @ SV159 @ zero_zero_nat )
        = SV159 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10923]) ).

thf(11415,plain,
    ! [SV160: nat] :
      ( ( ! [SY1156: nat,SY1157: nat] :
            ( ( ( times_times_nat @ SV160 @ SY1156 )
              = ( times_times_nat @ SY1157 @ SY1156 ) )
            = ( ( SV160 = SY1157 )
              | ( SY1156 = zero_zero_nat ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10925]) ).

thf(11416,plain,
    ! [SV161: nat] :
      ( ( ! [SY1158: nat,SY1159: nat] :
            ( ( ( times_times_nat @ SV161 @ SY1158 )
              = ( times_times_nat @ SV161 @ SY1159 ) )
            = ( ( SY1158 = SY1159 )
              | ( SV161 = zero_zero_nat ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10926]) ).

thf(11417,plain,
    ! [SV162: nat] :
      ( ( ( times_times_nat @ SV162 @ zero_zero_nat )
        = zero_zero_nat )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10927]) ).

thf(11418,plain,
    ! [SV163: nat] :
      ( ( ! [SY1160: nat] :
            ( ( ( times_times_nat @ SV163 @ SY1160 )
              = zero_zero_nat )
            = ( ( SV163 = zero_zero_nat )
              | ( SY1160 = zero_zero_nat ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10928]) ).

thf(11419,plain,
    ! [SV164: num] :
      ( ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ SV164 ) )
        = zero_zero_nat )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10934]) ).

thf(11420,plain,
    ! [SV165: nat] :
      ( ( ! [SY1161: nat,SY1162: nat] :
            ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ SV165 @ SY1161 ) @ SY1162 ) @ SV165 )
            = ( modulo_modulo_nat @ SY1162 @ SV165 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10935]) ).

thf(11421,plain,
    ! [SV166: nat] :
      ( ( ! [SY1163: nat,SY1164: nat] :
            ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ SV166 @ SY1163 ) @ SY1164 ) @ SY1163 )
            = ( modulo_modulo_nat @ SY1164 @ SY1163 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10936]) ).

thf(11422,plain,
    ! [SV167: nat] :
      ( ( ! [SY1165: nat,SY1166: nat] :
            ( ( modulo_modulo_nat @ ( plus_plus_nat @ SV167 @ ( times_times_nat @ SY1165 @ SY1166 ) ) @ SY1165 )
            = ( modulo_modulo_nat @ SV167 @ SY1165 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10937]) ).

thf(11423,plain,
    ! [SV168: nat] :
      ( ( ! [SY1167: nat,SY1168: nat] :
            ( ( modulo_modulo_nat @ ( plus_plus_nat @ SV168 @ ( times_times_nat @ SY1167 @ SY1168 ) ) @ SY1168 )
            = ( modulo_modulo_nat @ SV168 @ SY1168 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10938]) ).

thf(11424,plain,
    ! [SV169: nat] :
      ( ( ( ( power_power_nat @ SV169 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = zero_zero_nat )
        = ( SV169 = zero_zero_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10944]) ).

thf(11425,plain,
    ! [SV170: nat] :
      ( ( ! [SY1169: nat,SY1170: nat] :
            ( ( modulo_modulo_nat @ ( times_times_nat @ SV170 @ ( modulo_modulo_nat @ SY1169 @ SY1170 ) ) @ SY1170 )
            = ( modulo_modulo_nat @ ( times_times_nat @ SV170 @ SY1169 ) @ SY1170 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10945]) ).

thf(11426,plain,
    ! [SV171: nat] :
      ( ( ! [SY1171: nat,SY1172: nat] :
            ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ SV171 @ SY1171 ) @ SY1172 ) @ SY1171 )
            = ( modulo_modulo_nat @ ( times_times_nat @ SV171 @ SY1172 ) @ SY1171 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10946]) ).

thf(11427,plain,
    ! [SV172: nat] :
      ( ( ! [SY1173: nat,SY1174: nat] :
            ( ( times_times_nat @ SV172 @ ( modulo_modulo_nat @ SY1173 @ SY1174 ) )
            = ( modulo_modulo_nat @ ( times_times_nat @ SV172 @ SY1173 ) @ ( times_times_nat @ SV172 @ SY1174 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10947]) ).

thf(11428,plain,
    ! [SV173: nat] :
      ( ( ! [SY1175: nat,SY1176: nat] :
            ( ( modulo_modulo_nat @ ( times_times_nat @ SV173 @ SY1175 ) @ ( times_times_nat @ SY1176 @ SY1175 ) )
            = ( times_times_nat @ ( modulo_modulo_nat @ SV173 @ SY1176 ) @ SY1175 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10948]) ).

thf(11429,plain,
    ! [SV174: nat] :
      ( ( ! [SY1177: nat,SY1178: nat] :
            ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ SV174 @ SY1177 ) @ ( modulo_modulo_nat @ SY1178 @ SY1177 ) ) @ SY1177 )
            = ( modulo_modulo_nat @ ( times_times_nat @ SV174 @ SY1178 ) @ SY1177 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10950]) ).

thf(11430,plain,
    ! [SV175: nat] :
      ( ( ! [SY1179: nat,SY1180: nat] :
            ( ( modulo_modulo_nat @ ( plus_plus_nat @ SV175 @ ( modulo_modulo_nat @ SY1179 @ SY1180 ) ) @ SY1180 )
            = ( modulo_modulo_nat @ ( plus_plus_nat @ SV175 @ SY1179 ) @ SY1180 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10951]) ).

thf(11431,plain,
    ! [SV176: nat] :
      ( ( ! [SY1181: nat,SY1182: nat] :
            ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ SV176 @ SY1181 ) @ SY1182 ) @ SY1181 )
            = ( modulo_modulo_nat @ ( plus_plus_nat @ SV176 @ SY1182 ) @ SY1181 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10952]) ).

thf(11432,plain,
    ! [SV177: nat] :
      ( ( ! [SY1183: nat,SY1184: nat] :
            ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ SV177 @ SY1183 ) @ ( modulo_modulo_nat @ SY1184 @ SY1183 ) ) @ SY1183 )
            = ( modulo_modulo_nat @ ( plus_plus_nat @ SV177 @ SY1184 ) @ SY1183 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10954]) ).

thf(11433,plain,
    ! [SV178: nat] :
      ( ( ! [SY1185: nat,SY1186: nat] :
            ( ( modulo_modulo_nat @ ( power_power_nat @ ( modulo_modulo_nat @ SV178 @ SY1185 ) @ SY1186 ) @ SY1185 )
            = ( modulo_modulo_nat @ ( power_power_nat @ SV178 @ SY1186 ) @ SY1185 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10955]) ).

thf(11434,plain,
    ! [SV179: num] :
      ( ( ! [SY1187: num,SY1188: num] :
            ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV179 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SY1187 ) ) )
              = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SY1188 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SY1187 ) ) ) )
            = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV179 ) @ ( numeral_numeral_nat @ SY1187 ) )
              = ( modulo_modulo_nat @ ( numeral_numeral_nat @ SY1188 ) @ ( numeral_numeral_nat @ SY1187 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10957]) ).

thf(11435,plain,
    ! [SV180: num] :
      ( ( ! [SY1189: num] :
            ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV180 ) @ ( numeral_numeral_nat @ one ) )
            = ( modulo_modulo_nat @ ( numeral_numeral_nat @ SY1189 ) @ ( numeral_numeral_nat @ one ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10958]) ).

thf(11436,plain,
    ! [SV181: nat] :
      ( ( ( plus_plus_nat @ SV181 @ zero_zero_nat )
        = SV181 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10964]) ).

thf(11437,plain,
    ! [SV182: nat] :
      ( ( ( plus_plus_nat @ zero_zero_nat @ SV182 )
        = SV182 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10965]) ).

thf(11438,plain,
    ! [SV183: nat] :
      ( ( ( plus_plus_nat @ zero_zero_nat @ SV183 )
        = SV183 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10968]) ).

thf(11439,plain,
    ! [SV184: nat] :
      ( ( ( times_times_nat @ zero_zero_nat @ SV184 )
        = zero_zero_nat )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10969]) ).

thf(11440,plain,
    ! [SV185: nat] :
      ( ( ! [SY1190: nat,SY1191: nat] :
            ( ( ( times_times_nat @ SV185 @ SY1190 )
              = ( times_times_nat @ SV185 @ SY1191 ) )
            = ( ( SV185 = zero_zero_nat )
              | ( SY1190 = SY1191 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10970]) ).

thf(11441,plain,
    ( ( ! [SV186: nat] :
          ( zero_zero_nat
          = ( times_times_nat @ zero_zero_nat @ SV186 ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[10972]) ).

thf(11442,plain,
    ( ( ( ^ [H: nat] : zero_zero_nat )
      = ( times_times_nat @ zero_zero_nat ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[10972]) ).

thf(11443,plain,
    ! [SV187: nat] :
      ( ( ! [SY1192: nat,SY1193: nat] :
            ( ( divide_divide_nat @ ( plus_plus_nat @ SV187 @ SY1192 ) @ SY1193 )
            = ( plus_plus_nat @ ( plus_plus_nat @ ( divide_divide_nat @ SV187 @ SY1193 ) @ ( divide_divide_nat @ SY1192 @ SY1193 ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ SV187 @ SY1193 ) @ ( modulo_modulo_nat @ SY1192 @ SY1193 ) ) @ SY1193 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10975]) ).

thf(11444,plain,
    ! [SV188: nat] :
      ( ( ! [SY1194: nat,SY1195: nat] :
            ( ( divide_divide_nat @ ( times_times_nat @ SV188 @ SY1194 ) @ SY1195 )
            = ( plus_plus_nat @ ( times_times_nat @ SV188 @ ( divide_divide_nat @ SY1194 @ SY1195 ) ) @ ( divide_divide_nat @ ( times_times_nat @ SV188 @ ( modulo_modulo_nat @ SY1194 @ SY1195 ) ) @ SY1195 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10976]) ).

thf(11445,plain,
    ! [SV189: nat] :
      ( ( ! [SY1196: nat] :
            ( ( plus_plus_nat @ ( times_times_nat @ SV189 @ ( divide_divide_nat @ SY1196 @ SV189 ) ) @ ( modulo_modulo_nat @ SY1196 @ SV189 ) )
            = SY1196 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10977]) ).

thf(11446,plain,
    ! [SV190: nat] :
      ( ( ! [SY1197: nat] :
            ( ( plus_plus_nat @ ( modulo_modulo_nat @ SV190 @ SY1197 ) @ ( times_times_nat @ SY1197 @ ( divide_divide_nat @ SV190 @ SY1197 ) ) )
            = SV190 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10978]) ).

thf(11447,plain,
    ! [SV191: nat] :
      ( ( ! [SY1198: nat] :
            ( ( plus_plus_nat @ ( modulo_modulo_nat @ SV191 @ SY1198 ) @ ( times_times_nat @ ( divide_divide_nat @ SV191 @ SY1198 ) @ SY1198 ) )
            = SV191 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10979]) ).

thf(11448,plain,
    ! [SV192: nat] :
      ( ( ! [SY1199: nat] :
            ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ SV192 @ SY1199 ) @ SY1199 ) @ ( modulo_modulo_nat @ SV192 @ SY1199 ) )
            = SV192 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10980]) ).

thf(11449,plain,
    ! [SV193: nat] :
      ( ( ! [SY1200: nat] :
            ( SV193
            = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ SV193 @ SY1200 ) @ SY1200 ) @ ( modulo_modulo_nat @ SV193 @ SY1200 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10981]) ).

thf(11450,plain,
    ! [SV194: nat] :
      ( ( ! [SY1201: nat,SY1202: nat] :
            ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ SV194 @ SY1201 ) @ SY1201 ) @ ( modulo_modulo_nat @ SV194 @ SY1201 ) ) @ SY1202 )
            = ( plus_plus_nat @ SV194 @ SY1202 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10982]) ).

thf(11451,plain,
    ! [SV195: nat] :
      ( ( ! [SY1203: nat,SY1204: nat] :
            ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ SV195 @ ( divide_divide_nat @ SY1203 @ SV195 ) ) @ ( modulo_modulo_nat @ SY1203 @ SV195 ) ) @ SY1204 )
            = ( plus_plus_nat @ SY1203 @ SY1204 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10983]) ).

thf(11452,plain,
    ! [SV196: nat] :
      ( ( ! [SY1205: nat,SY1206: nat] :
            ( ( modulo_modulo_nat @ SV196 @ ( times_times_nat @ SY1205 @ SY1206 ) )
            = ( plus_plus_nat @ ( times_times_nat @ SY1205 @ ( modulo_modulo_nat @ ( divide_divide_nat @ SV196 @ SY1205 ) @ SY1206 ) ) @ ( modulo_modulo_nat @ SV196 @ SY1205 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10984]) ).

thf(11453,plain,
    ! [SV197: nat] :
      ( ( ! [SY1207: nat,SY1208: nat] :
            ( ( modulo_modulo_nat @ ( divide_divide_nat @ SV197 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1207 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1208 ) )
            = ( divide_divide_nat @ ( modulo_modulo_nat @ SV197 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SY1207 @ SY1208 ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1207 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10988]) ).

thf(11454,plain,
    ! [SV198: nat] :
      ( ( ! [SY1209: nat] :
            ( SV198
            = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ SV198 @ SY1209 ) @ SY1209 ) @ ( modulo_modulo_nat @ SV198 @ SY1209 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10989]) ).

thf(11455,plain,
    ! [SV199: num] :
      ( ( ! [SY1210: num] :
            ( ( ( bit0 @ SV199 )
              = ( bit0 @ SY1210 ) )
            = ( SV199 = SY1210 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10990]) ).

thf(11456,plain,
    ! [SV200: nat] :
      ( ( ( plus_plus_nat @ SV200 @ zero_zero_nat )
        = SV200 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10991]) ).

thf(11457,plain,
    ! [SV201: nat] :
      ( ( ! [SY1211: nat] :
            ( ( dvd_dvd_nat @ SV201 @ ( plus_plus_nat @ SY1211 @ SV201 ) )
            = ( dvd_dvd_nat @ SV201 @ SY1211 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10994]) ).

thf(11458,plain,
    ! [SV202: nat] :
      ( ( ! [SY1212: nat] :
            ( ( dvd_dvd_nat @ SV202 @ ( plus_plus_nat @ SV202 @ SY1212 ) )
            = ( dvd_dvd_nat @ SV202 @ SY1212 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10995]) ).

thf(11459,plain,
    ! [SV203: nat] :
      ( ( ! [SY1213: nat,SY1214: nat] :
            ( ( dvd_dvd_nat @ SV203 @ ( plus_plus_nat @ SY1213 @ ( times_times_nat @ SY1214 @ SV203 ) ) )
            = ( dvd_dvd_nat @ SV203 @ SY1213 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10997]) ).

thf(11460,plain,
    ! [SV204: nat] :
      ( ( ! [SY1215: nat,SY1216: nat] :
            ( ( dvd_dvd_nat @ SV204 @ ( plus_plus_nat @ ( times_times_nat @ SY1215 @ SV204 ) @ SY1216 ) )
            = ( dvd_dvd_nat @ SV204 @ SY1216 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[10998]) ).

thf(11461,plain,
    ! [SV205: nat] :
      ( ( ! [SY1217: nat] :
            ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ SV205 @ SY1217 ) )
            = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
              | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1217 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11002]) ).

thf(11462,plain,
    ! [SV206: nat] :
      ( ( ! [SY1218: nat] :
            ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SY1218 ) )
            = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1218 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11003]) ).

thf(11463,plain,
    ! [SV207: nat] :
      ( ( ! [SY1219: nat] : ( dvd_dvd_nat @ SV207 @ ( times_times_nat @ SY1219 @ SV207 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11005]) ).

thf(11464,plain,
    ! [SV208: nat] :
      ( ( ! [SY1220: nat] : ( dvd_dvd_nat @ SV208 @ ( times_times_nat @ SV208 @ SY1220 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11008]) ).

thf(11465,plain,
    ! [SV209: nat] :
      ( ( ! [SY1221: int,SY1222: nat,SY1223: int,SY1224: int] :
            ( ( bit_concat_bit @ SV209 @ SY1221 @ ( bit_concat_bit @ SY1222 @ SY1223 @ SY1224 ) )
            = ( bit_concat_bit @ ( plus_plus_nat @ SY1222 @ SV209 ) @ ( bit_concat_bit @ SV209 @ SY1221 @ SY1223 ) @ SY1224 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11024]) ).

thf(11466,plain,
    ! [SV210: num] :
      ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV210 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11037]) ).

thf(11467,plain,
    ! [SV211: nat > nat] :
      ( ( ! [SY1225: set_nat,SY1226: nat > nat,SY1227: set_nat] :
            ( ( times_times_nat @ ( groups3542108847815614940at_nat @ SV211 @ SY1225 ) @ ( groups3542108847815614940at_nat @ SY1226 @ SY1227 ) )
            = ( groups3542108847815614940at_nat
              @ ^ [SY1228: nat] :
                  ( groups3542108847815614940at_nat
                  @ ^ [SY1229: nat] : ( times_times_nat @ ( SV211 @ SY1228 ) @ ( SY1226 @ SY1229 ) )
                  @ SY1227 )
              @ SY1225 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11045]) ).

thf(11468,plain,
    ! [SV212: nat > nat] :
      ( ( ! [SY1230: set_nat,SY1231: nat] :
            ( ( times_times_nat @ ( groups3542108847815614940at_nat @ SV212 @ SY1230 ) @ SY1231 )
            = ( groups3542108847815614940at_nat
              @ ^ [SY1232: nat] : ( times_times_nat @ ( SV212 @ SY1232 ) @ SY1231 )
              @ SY1230 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11046]) ).

thf(11469,plain,
    ! [SV213: nat] :
      ( ( ! [SY1233: nat > nat,SY1234: set_nat] :
            ( ( times_times_nat @ SV213 @ ( groups3542108847815614940at_nat @ SY1233 @ SY1234 ) )
            = ( groups3542108847815614940at_nat
              @ ^ [SY1235: nat] : ( times_times_nat @ SV213 @ ( SY1233 @ SY1235 ) )
              @ SY1234 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11047]) ).

thf(11470,plain,
    ! [SV214: nat > nat] :
      ( ( ! [SY1236: nat > nat,SY1237: set_nat] :
            ( ( groups3542108847815614940at_nat
              @ ^ [SY1238: nat] : ( plus_plus_nat @ ( SV214 @ SY1238 ) @ ( SY1236 @ SY1238 ) )
              @ SY1237 )
            = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ SV214 @ SY1237 ) @ ( groups3542108847815614940at_nat @ SY1236 @ SY1237 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11048]) ).

thf(11471,plain,
    ! [SV215: nat] :
      ( ( ! [SY1239: nat] :
            ( ( SV215
              = ( plus_plus_nat @ SV215 @ SY1239 ) )
            = ( SY1239 = zero_zero_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11049]) ).

thf(11472,plain,
    ! [SV216: nat] :
      ( ( ! [SY1240: nat,SY1241: nat,SY1242: nat] :
            ( ( ( plus_plus_nat @ ( times_times_nat @ SV216 @ SY1240 ) @ ( times_times_nat @ SY1241 @ SY1242 ) )
              = ( plus_plus_nat @ ( times_times_nat @ SV216 @ SY1242 ) @ ( times_times_nat @ SY1241 @ SY1240 ) ) )
            = ( ( SV216 = SY1241 )
              | ( SY1240 = SY1242 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11051]) ).

thf(11473,plain,
    ! [SV217: nat] :
      ( ( ! [SY1243: num] :
            ( ( power_power_nat @ SV217 @ ( numeral_numeral_nat @ ( bit1 @ SY1243 ) ) )
            = ( times_times_nat @ ( times_times_nat @ SV217 @ ( power_power_nat @ SV217 @ ( numeral_numeral_nat @ SY1243 ) ) ) @ ( power_power_nat @ SV217 @ ( numeral_numeral_nat @ SY1243 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11059]) ).

thf(11474,plain,
    ! [SV218: num] :
      ( ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit1 @ SV218 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
        = ( numeral_numeral_nat @ SV218 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11060]) ).

thf(11475,plain,
    ! [SV219: nat] :
      ( ( ( power_power_nat @ SV219 @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
        = ( times_times_nat @ ( times_times_nat @ SV219 @ SV219 ) @ SV219 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11061]) ).

thf(11476,plain,
    ! [SV220: num] :
      ( ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ SV220 ) )
        = ( numeral_numeral_nat @ SV220 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11062]) ).

thf(11477,plain,
    ! [SV221: nat] :
      ( ( ! [SY1244: nat] :
            ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ SV221 @ SY1244 ) )
            = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ SV221 ) @ ( semiri1316708129612266289at_nat @ SY1244 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11063]) ).

thf(11478,plain,
    ! [SV222: nat] :
      ( ( ! [SY1245: nat] :
            ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ SV222 @ SY1245 ) )
            = ( times_times_nat @ ( semiri1316708129612266289at_nat @ SV222 ) @ ( semiri1316708129612266289at_nat @ SY1245 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11064]) ).

thf(11479,plain,
    ! [SV223: nat] :
      ( ( ! [SY1246: nat] :
            ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ SV223 @ SY1246 ) )
            = ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV223 ) @ SY1246 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11065]) ).

thf(11480,plain,
    ! [SV224: nat] :
      ( ( ! [SY1247: nat,SY1248: nat] :
            ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV224 ) @ SY1247 )
              = ( semiri1316708129612266289at_nat @ SY1248 ) )
            = ( ( power_power_nat @ SV224 @ SY1247 )
              = SY1248 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11066]) ).

thf(11481,plain,
    ! [SV225: nat] :
      ( ( ! [SY1249: nat,SY1250: nat] :
            ( ( ( semiri1316708129612266289at_nat @ SV225 )
              = ( power_power_nat @ ( semiri1316708129612266289at_nat @ SY1249 ) @ SY1250 ) )
            = ( SV225
              = ( power_power_nat @ SY1249 @ SY1250 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11067]) ).

thf(11482,plain,
    ! [SV226: num] :
      ( ( ! [SY1251: nat,SY1252: nat] :
            ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SY1251 )
              = ( semiri1316708129612266289at_nat @ SY1252 ) )
            = ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SY1251 )
              = SY1252 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11068]) ).

thf(11483,plain,
    ! [SV227: nat] :
      ( ( ! [SY1253: num,SY1254: nat] :
            ( ( ( semiri1316708129612266289at_nat @ SV227 )
              = ( power_power_nat @ ( numeral_numeral_nat @ SY1253 ) @ SY1254 ) )
            = ( SV227
              = ( power_power_nat @ ( numeral_numeral_nat @ SY1253 ) @ SY1254 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11069]) ).

thf(11484,plain,
    ! [SV228: nat] :
      ( ( ! [SY1255: nat] :
            ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ SV228 ) @ SY1255 )
            = ( times_times_nat @ SY1255 @ ( semiri1316708129612266289at_nat @ SV228 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11070]) ).

thf(11485,plain,
    ! [SV229: nat] :
      ( ( ! [SY1256: nat,SY1257: nat] :
            ( ( divide_divide_nat @ SV229 @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ SY1256 ) @ ( semiri1316708129612266289at_nat @ SY1257 ) ) )
            = ( divide_divide_nat @ ( divide_divide_nat @ SV229 @ ( semiri1316708129612266289at_nat @ SY1256 ) ) @ ( semiri1316708129612266289at_nat @ SY1257 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11072]) ).

thf(11486,plain,
    ! [SV230: nat] :
      ( ( ! [SY1258: nat] :
            ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ SV230 @ SY1258 ) )
            = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ SV230 ) @ ( semiri1316708129612266289at_nat @ SY1258 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11073]) ).

thf(11487,plain,
    ! [SV231: nat > real] :
      ( ( ! [SY1259: nat] :
            ( ( summable_real
              @ ^ [SY1260: nat] : ( SV231 @ ( plus_plus_nat @ SY1260 @ SY1259 ) ) )
            = ( summable_real @ SV231 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11074]) ).

thf(11488,plain,
    ! [SV232: nat > complex] :
      ( ( ! [SY1261: nat] :
            ( ( summable_complex
              @ ^ [SY1262: nat] : ( SV232 @ ( plus_plus_nat @ SY1262 @ SY1261 ) ) )
            = ( summable_complex @ SV232 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11075]) ).

thf(11489,plain,
    ! [SV233: nat > nat] :
      ( ( ! [SY1263: nat > nat,SY1264: set_nat] :
            ( ( groups708209901874060359at_nat
              @ ^ [SY1265: nat] : ( times_times_nat @ ( SV233 @ SY1265 ) @ ( SY1263 @ SY1265 ) )
              @ SY1264 )
            = ( times_times_nat @ ( groups708209901874060359at_nat @ SV233 @ SY1264 ) @ ( groups708209901874060359at_nat @ SY1263 @ SY1264 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11081]) ).

thf(11490,plain,
    ! [SV234: nat > nat] :
      ( ( ! [SY1266: set_nat,SY1267: nat] :
            ( ( power_power_nat @ ( groups708209901874060359at_nat @ SV234 @ SY1266 ) @ SY1267 )
            = ( groups708209901874060359at_nat
              @ ^ [SY1268: nat] : ( power_power_nat @ ( SV234 @ SY1268 ) @ SY1267 )
              @ SY1266 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11082]) ).

thf(11491,plain,
    ! [SV235: nat] :
      ( ( ! [SY1269: nat,SY1270: nat] :
            ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ SV235 @ SY1269 ) @ SY1270 ) @ ( plus_plus_nat @ SV235 @ SY1270 ) ) @ ( binomial @ ( plus_plus_nat @ SV235 @ SY1270 ) @ SY1270 ) )
            = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ SV235 @ SY1269 ) @ SY1270 ) @ SY1270 ) @ ( binomial @ ( plus_plus_nat @ SV235 @ SY1269 ) @ SV235 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11083]) ).

thf(11492,plain,
    ! [SV236: nat] :
      ( ( ! [SY1271: nat,SY1272: real] :
            ( ( root @ ( times_times_nat @ SV236 @ SY1271 ) @ SY1272 )
            = ( root @ SV236 @ ( root @ SY1271 @ SY1272 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11084]) ).

thf(11493,plain,
    ! [SV237: num] :
      ( ( ( pow @ SV237 @ one )
        = SV237 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11087]) ).

thf(11494,plain,
    ! [SV238: num] :
      ( ( ( bit_or_not_num_neg @ ( bit0 @ SV238 ) @ one )
        = ( bit0 @ one ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11089]) ).

thf(11495,plain,
    ( ( ! [SV239: nat] :
          ( ( bit_se547839408752420682it_nat @ SV239 )
          = ( ^ [SY1273: nat] : ( times_times_nat @ SY1273 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV239 ) ) ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11090]) ).

thf(11496,plain,
    ( ( bit_se547839408752420682it_nat
      = ( ^ [N: nat,M6: nat] : ( times_times_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11090]) ).

thf(11497,plain,
    ( ( ! [SV240: nat] :
          ( ( bit_se8570568707652914677it_nat @ SV240 )
          = ( ^ [SY1274: nat] : ( divide_divide_nat @ SY1274 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV240 ) ) ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11091]) ).

thf(11498,plain,
    ( ( bit_se8570568707652914677it_nat
      = ( ^ [N: nat,M6: nat] : ( divide_divide_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11091]) ).

thf(11499,plain,
    ! [SV241: num] :
      ( ( ( num_of_nat @ ( numeral_numeral_nat @ SV241 ) )
        = SV241 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11092]) ).

thf(11500,plain,
    ! [SV242: nat] :
      ( ( ! [SY1275: nat,SY1276: nat] :
            ( ( times_times_nat @ SV242 @ ( gcd_gcd_nat @ SY1275 @ SY1276 ) )
            = ( gcd_gcd_nat @ ( times_times_nat @ SV242 @ SY1275 ) @ ( times_times_nat @ SV242 @ SY1276 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11093]) ).

thf(11501,plain,
    ! [SV243: $o] :
      ( ( ( SV243 = $true )
        | ( SV243 = $false ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[11094]) ).

thf(11502,plain,
    ( ( ( $true = $true )
      | ( $true = $false ) )
    = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[11094]) ).

thf(11503,plain,
    ( ( ( $false = $true )
      | ( $false = $false ) )
    = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[11094]) ).

thf(11504,plain,
    ( ( ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) ) ) ) )
      = ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) @ maxs ) @ maxi ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[11095]) ).

thf(11505,plain,
    ! [SV244: nat] :
      ( ( ! [SY1277: nat,SY1278: nat] :
            ( ~ ( ( SV244 != zero_zero_nat ) )
            | ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ SV244 @ SY1277 ) @ SY1278 ) @ SV244 )
              = ( plus_plus_nat @ SY1277 @ ( divide_divide_nat @ SY1278 @ SV244 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11096]) ).

thf(11506,plain,
    ! [SV245: nat] :
      ( ( ! [SY1279: nat,SY1280: nat] :
            ( ~ ( ord_less_nat @ SV245 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1279 ) )
            | ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ SY1280 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1279 ) ) @ SV245 ) @ SY1279 )
              = SV245 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11097]) ).

thf(11507,plain,
    ! [SV246: nat] :
      ( ( ! [SY1281: nat,SY1282: nat] :
            ( ~ ( dvd_dvd_nat @ SV246 @ SY1281 )
            | ( ( divide_divide_nat @ ( plus_plus_nat @ SY1281 @ SY1282 ) @ SV246 )
              = ( plus_plus_nat @ ( divide_divide_nat @ SY1281 @ SV246 ) @ ( divide_divide_nat @ SY1282 @ SV246 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11098]) ).

thf(11508,plain,
    ( ( ! [SX0: nat] :
          ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ maxs ) @ SX0 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[11099]) ).

thf(11509,plain,
    ! [SV247: nat] :
      ( ( ! [SY1283: nat,SY1284: nat] :
            ( ~ ( ord_less_nat @ SV247 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SY1283 @ SY1284 ) ) )
            | ( ord_less_nat @ ( vEBT_VEBT_high @ SV247 @ SY1283 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1284 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11100]) ).

thf(11510,plain,
    ! [SV248: nat] :
      ( ( ! [SY1285: nat] :
            ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV248 ) )
           != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1285 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11101]) ).

thf(11511,plain,
    ! [SV249: nat] :
      ( ( ! [SY1286: nat,SY1287: nat] :
            ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV249 @ SY1286 ) @ SY1287 )
            | ( ord_less_nat @ SV249 @ SY1287 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11102]) ).

thf(11512,plain,
    ! [SV250: nat] :
      ( ( ! [SY1288: nat,SY1289: nat] :
            ( ( ( times_times_nat @ SV250 @ SY1288 )
             != ( times_times_nat @ SY1288 @ SV250 ) )
            | ( ( times_times_nat @ ( power_power_nat @ SV250 @ SY1289 ) @ SY1288 )
              = ( times_times_nat @ SY1288 @ ( power_power_nat @ SV250 @ SY1289 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11103]) ).

thf(11513,plain,
    ! [SV251: nat] :
      ( ( ! [SY1290: nat] :
            ( ( ( times_times_nat @ SV251 @ SY1290 )
             != zero_zero_nat )
            | ( SV251 = zero_zero_nat )
            | ( SY1290 = zero_zero_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11104]) ).

thf(11514,plain,
    ! [SV252: nat] :
      ( ( ! [SY1291: nat,SY1292: nat] :
            ( ~ ( ( SV252 != zero_zero_nat ) )
            | ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ SY1291 @ SV252 ) @ SY1292 ) @ SV252 )
              = ( plus_plus_nat @ SY1291 @ ( divide_divide_nat @ SY1292 @ SV252 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11105]) ).

thf(11515,plain,
    ! [SV253: nat] :
      ( ( ! [SY1293: nat,SY1294: nat,SY1295: nat] :
            ( ~ ( ord_less_nat @ SV253 @ SY1293 )
            | ( ( plus_plus_nat @ SY1294 @ SY1293 )
             != ( plus_plus_nat @ SV253 @ SY1295 ) )
            | ( ord_less_nat @ SY1294 @ SY1295 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11106]) ).

thf(11516,plain,
    ! [SV254: nat] :
      ( ( ! [SY1296: nat,SY1297: nat] :
            ( ~ ( dvd_dvd_nat @ ( times_times_nat @ SV254 @ SY1296 ) @ SY1297 )
            | ( dvd_dvd_nat @ SV254 @ ( divide_divide_nat @ SY1297 @ SY1296 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11107]) ).

thf(11517,plain,
    ! [SV255: nat] :
      ( ( ! [SY1298: nat,SY1299: nat] :
            ~ ( ~ ( ( SV255 != zero_zero_nat )
                  | ( ( divide_divide_nat @ ( times_times_nat @ SV255 @ SY1298 ) @ ( times_times_nat @ SV255 @ SY1299 ) )
                    = zero_zero_nat ) )
              | ~ ( ~ ( ( SV255 != zero_zero_nat ) )
                  | ( ( divide_divide_nat @ ( times_times_nat @ SV255 @ SY1298 ) @ ( times_times_nat @ SV255 @ SY1299 ) )
                    = ( divide_divide_nat @ SY1298 @ SY1299 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11108]) ).

thf(11518,plain,
    ! [SV256: nat] :
      ( ( ! [SY1300: nat] :
            ( ~ ( ( SV256 != zero_zero_nat ) )
            | ( ( divide_divide_nat @ ( times_times_nat @ SV256 @ SY1300 ) @ SV256 )
              = SY1300 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11109]) ).

thf(11519,plain,
    ! [SV257: nat] :
      ( ( ! [SY1301: nat,SY1302: nat] :
            ( ~ ( ( SV257 != zero_zero_nat ) )
            | ( ( ( times_times_nat @ SY1301 @ SV257 )
                = ( times_times_nat @ SY1302 @ SV257 ) )
              = ( SY1301 = SY1302 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11110]) ).

thf(11520,plain,
    ! [SV258: nat] :
      ( ( ! [SY1303: nat,SY1304: nat] :
            ( ~ ( dvd_dvd_nat @ SV258 @ ( times_times_nat @ SY1303 @ SY1304 ) )
            | ~ ! [SY1305: nat,SY1306: nat] :
                  ( ( SV258
                   != ( times_times_nat @ SY1305 @ SY1306 ) )
                  | ~ ( dvd_dvd_nat @ SY1305 @ SY1303 )
                  | ~ ( dvd_dvd_nat @ SY1306 @ SY1304 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11111]) ).

thf(11521,plain,
    ! [SV259: nat] :
      ( ( ! [SY1307: nat] :
            ( ~ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV259 @ SY1307 ) )
                 != zero_zero_nat ) )
            | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1307 )
             != zero_zero_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11112]) ).

thf(11522,plain,
    ( ( ~ ( vEBT_V8194947554948674370ptions @ summary @ maxs )
      | ~ ( ( maxs
           != ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[11113]) ).

thf(11523,plain,
    ! [SV260: nat] :
      ( ( ! [SY1308: nat,SY1309: nat,SY1310: nat] :
            ( ~ ~ ( ( SV260 != SY1308 )
                  | ( SY1309 != SY1310 ) )
            | ( ( plus_plus_nat @ SV260 @ SY1309 )
              = ( plus_plus_nat @ SY1308 @ SY1310 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11114]) ).

thf(11524,plain,
    ! [SV261: nat] :
      ( ( ! [SY1311: nat,SY1312: nat] :
            ( ~ ( dvd_dvd_nat @ SV261 @ SY1311 )
            | ~ ( dvd_dvd_nat @ SV261 @ SY1312 )
            | ( ( divide_divide_nat @ ( plus_plus_nat @ SY1311 @ SY1312 ) @ SV261 )
              = ( plus_plus_nat @ ( divide_divide_nat @ SY1311 @ SV261 ) @ ( divide_divide_nat @ SY1312 @ SV261 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11115]) ).

thf(11525,plain,
    ! [SV262: nat] :
      ( ( ! [SY1313: nat,SY1314: nat] :
            ( ~ ( dvd_dvd_nat @ SV262 @ SY1313 )
            | ~ ( dvd_dvd_nat @ SY1313 @ SY1314 )
            | ( ( divide_divide_nat @ ( divide_divide_nat @ SY1314 @ SV262 ) @ ( divide_divide_nat @ SY1313 @ SV262 ) )
              = ( divide_divide_nat @ SY1314 @ SY1313 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11116]) ).

thf(11526,plain,
    ! [SV263: nat] :
      ( ( ! [SY1315: nat,SY1316: nat,SY1317: nat] :
            ( ( SV263
             != ( plus_plus_nat @ SY1315 @ SY1316 ) )
            | ( ( plus_plus_nat @ SV263 @ SY1317 )
              = ( plus_plus_nat @ SY1315 @ ( plus_plus_nat @ SY1316 @ SY1317 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11117]) ).

thf(11527,plain,
    ! [SV264: nat > complex] :
      ( ( ! [SY1318: nat] :
            ( ~ ( summable_complex @ SV264 )
            | ( summable_complex
              @ ^ [SY1319: nat] : ( SV264 @ ( plus_plus_nat @ SY1319 @ SY1318 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11118]) ).

thf(11528,plain,
    ! [SV265: nat] :
      ( ( ! [SY1320: nat,SY1321: nat] :
            ( ~ ( ord_less_eq_nat @ SV265 @ SY1320 )
            | ( ord_less_eq_nat @ ( times_times_nat @ SV265 @ SY1321 ) @ ( times_times_nat @ SY1320 @ SY1321 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11119]) ).

thf(11529,plain,
    ! [SV266: nat] :
      ( ( ! [SY1322: nat,SY1323: nat] :
            ( ~ ( ( SV266 != zero_zero_nat ) )
            | ( ( divide_divide_nat @ ( times_times_nat @ SY1322 @ SV266 ) @ ( times_times_nat @ SY1323 @ SV266 ) )
              = ( divide_divide_nat @ SY1322 @ SY1323 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11120]) ).

thf(11530,plain,
    ! [SV267: num] :
      ( ( one
       != ( bit1 @ SV267 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11121]) ).

thf(11531,plain,
    ! [SV268: nat] :
      ( ( ! [SY1324: nat,SY1325: nat] :
            ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV268 @ SY1324 ) @ SY1325 )
            | ~ ( ~ ( ord_less_eq_nat @ SV268 @ SY1325 )
                | ~ ( ord_less_eq_nat @ SY1324 @ SY1325 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11122]) ).

thf(11532,plain,
    ! [SV269: nat] :
      ( ( ! [SY1326: nat,SY1327: nat] :
            ( ~ ( ( SV269 != zero_zero_nat ) )
            | ( ( divide_divide_nat @ ( plus_plus_nat @ SY1326 @ ( times_times_nat @ SV269 @ SY1327 ) ) @ SV269 )
              = ( plus_plus_nat @ SY1327 @ ( divide_divide_nat @ SY1326 @ SV269 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11123]) ).

thf(11533,plain,
    ! [SV270: num] :
      ( ( one
       != ( bit0 @ SV270 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11124]) ).

thf(11534,plain,
    ( ( ! [SV271: nat] :
          ( ( ^ [SY1328: nat] : ( SV271 = SY1328 ) )
          = ( ^ [SY1329: nat] :
                ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV271 )
                   != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1329 ) )
                  | ( ( divide_divide_nat @ SV271 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                   != ( divide_divide_nat @ SY1329 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11125]) ).

thf(11535,plain,
    ( ( ( ^ [SX0: nat,SX1: nat] : ( SX0 = SX1 ) )
      = ( ^ [SX0: nat,SX1: nat] :
            ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SX0 )
               != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SX1 ) )
              | ( ( divide_divide_nat @ SX0 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
               != ( divide_divide_nat @ SX1 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11125]) ).

thf(11536,plain,
    ! [SV272: nat] :
      ( ( ! [SY1330: nat,SY1331: nat,SY1332: nat] :
            ( ~ ( dvd_dvd_nat @ SV272 @ SY1330 )
            | ~ ( dvd_dvd_nat @ SY1331 @ SY1332 )
            | ( dvd_dvd_nat @ ( times_times_nat @ SV272 @ SY1331 ) @ ( times_times_nat @ SY1330 @ SY1332 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11126]) ).

thf(11537,plain,
    ! [SV273: nat] :
      ( ( ! [SY1333: nat,SY1334: nat] :
            ( ( ( modulo_modulo_nat @ SV273 @ SY1333 )
              = ( modulo_modulo_nat @ SY1334 @ SY1333 ) )
            = ( ~ ! [SY1335: nat] :
                    ~ ~ ! [SY1336: nat] :
                          ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SY1333 @ SY1335 ) )
                         != ( plus_plus_nat @ SY1334 @ ( times_times_nat @ SY1333 @ SY1336 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11127]) ).

thf(11538,plain,
    ! [SV274: nat] :
      ( ( ! [SY1337: nat,SY1338: nat] :
            ( ( ( plus_plus_nat @ SV274 @ SY1337 )
             != ( plus_plus_nat @ SY1338 @ SY1337 ) )
            | ( SV274 = SY1338 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11128]) ).

thf(11539,plain,
    ! [SV275: nat] :
      ( ( ! [SY1339: nat,SY1340: nat] :
            ( ~ ( ( SV275 != zero_zero_nat ) )
            | ( ( divide_divide_nat @ ( plus_plus_nat @ SY1339 @ ( times_times_nat @ SY1340 @ SV275 ) ) @ SV275 )
              = ( plus_plus_nat @ SY1340 @ ( divide_divide_nat @ SY1339 @ SV275 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11129]) ).

thf(11540,plain,
    ( ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) )
      = none_nat )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[11130]) ).

thf(11541,plain,
    ! [SV276: nat] :
      ( ( ! [SY1341: nat,SY1342: nat] :
            ( ~ ( ord_less_eq_nat @ SV276 @ SY1341 )
            | ( ord_less_eq_nat @ ( times_times_nat @ SY1342 @ SV276 ) @ ( times_times_nat @ SY1342 @ SY1341 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11131]) ).

thf(11542,plain,
    ! [SV277: nat] :
      ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV277 )
        | ~ ! [SY1343: nat] :
              ( SV277
             != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1343 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11132]) ).

thf(11543,plain,
    ! [SV278: num] :
      ( ( ( bit0 @ SV278 )
       != one )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11133]) ).

thf(11544,plain,
    ! [SV279: num] :
      ( ( ( bit1 @ SV279 )
       != one )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11134]) ).

thf(11545,plain,
    ! [SV280: nat] :
      ( ( ! [SY1344: nat] :
            ( ~ ( ( ( times_times_nat @ SV280 @ SY1344 )
                 != zero_zero_nat ) )
            | ~ ( ~ ( ( SV280 != zero_zero_nat ) )
                | ~ ( ( SY1344 != zero_zero_nat ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11135]) ).

thf(11546,plain,
    ! [SV281: nat] :
      ( ( ! [SY1345: nat,SY1346: nat] :
            ( ~ ( ord_less_nat @ SV281 @ ( times_times_nat @ SY1345 @ SY1346 ) )
            | ( ord_less_nat @ ( divide_divide_nat @ SV281 @ SY1346 ) @ SY1345 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11136]) ).

thf(11547,plain,
    ( ( ! [SX0: nat] :
          ( ( some_nat @ SX0 )
         != ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[11137]) ).

thf(11548,plain,
    ! [SV282: nat] :
      ( ( ! [SY1347: nat,SY1348: nat,SY1349: nat] :
            ( ( SV282
             != ( plus_plus_nat @ SY1347 @ SY1348 ) )
            | ( ( plus_plus_nat @ SY1349 @ SV282 )
              = ( plus_plus_nat @ SY1347 @ ( plus_plus_nat @ SY1349 @ SY1348 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11138]) ).

thf(11549,plain,
    ! [SV283: nat] :
      ( ( ! [SY1350: nat,SY1351: nat] :
            ( ( ( times_times_nat @ SV283 @ SY1350 )
             != one_one_nat )
            | ( ( times_times_nat @ ( power_power_nat @ SV283 @ SY1351 ) @ ( power_power_nat @ SY1350 @ SY1351 ) )
              = one_one_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11139]) ).

thf(11550,plain,
    ! [SV284: nat] :
      ( ( ! [SY1352: nat,SY1353: nat,SY1354: nat] :
            ( ( ~ ( ~ ( ( SV284 != SY1352 ) )
                  | ~ ( ( SY1353 != SY1354 ) ) ) )
            = ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SY1353 ) @ ( times_times_nat @ SY1352 @ SY1354 ) )
             != ( plus_plus_nat @ ( times_times_nat @ SV284 @ SY1354 ) @ ( times_times_nat @ SY1352 @ SY1353 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11140]) ).

thf(11551,plain,
    ! [SV285: nat] :
      ( ( ! [SY1355: nat,SY1356: nat] :
            ( ~ ( ( SV285 != zero_zero_nat ) )
            | ( ( ( times_times_nat @ SV285 @ SY1355 )
                = ( times_times_nat @ SV285 @ SY1356 ) )
              = ( SY1355 = SY1356 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11141]) ).

thf(11552,plain,
    ! [SV286: nat] :
      ( ( ! [SY1357: nat,SY1358: nat] :
            ( ~ ( dvd_dvd_nat @ SV286 @ SY1357 )
            | ( ( times_times_nat @ ( divide_divide_nat @ SY1357 @ SV286 ) @ SY1358 )
              = ( divide_divide_nat @ ( times_times_nat @ SY1357 @ SY1358 ) @ SV286 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11142]) ).

thf(11553,plain,
    ! [SV287: nat] :
      ( ( ! [SY1359: nat] :
            ( ~ ( ( SV287 != zero_zero_nat ) )
            | ~ ( ( SY1359 != zero_zero_nat ) )
            | ( ( times_times_nat @ SV287 @ SY1359 )
             != zero_zero_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11143]) ).

thf(11554,plain,
    ( ( ! [SX0: nat] :
          ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ summin ) @ SX0 ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[11144]) ).

thf(11555,plain,
    ! [SV288: nat] :
      ( ( ! [SY1360: nat] :
            ( ( ( divide_divide_nat @ SV288 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
             != ( divide_divide_nat @ SY1360 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV288 )
             != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1360 ) )
            | ( SV288 = SY1360 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11145]) ).

thf(11556,plain,
    ( ( ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx )
      = mi )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[11146]) ).

thf(11557,plain,
    ! [SV289: nat] :
      ( ( ! [SY1361: nat,SY1362: nat] :
            ( ~ ( ord_less_eq_nat @ SV289 @ SY1361 )
            | ( ord_less_eq_nat @ ( plus_plus_nat @ SV289 @ SY1362 ) @ ( plus_plus_nat @ SY1361 @ SY1362 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11147]) ).

thf(11558,plain,
    ! [SV290: nat] :
      ( ( ! [SY1363: nat,SY1364: nat,SY1365: nat] :
            ( ~ ~ ( ~ ( ord_less_nat @ SV290 @ SY1363 )
                  | ~ ( ord_less_nat @ SY1364 @ SY1365 ) )
            | ( ord_less_nat @ ( plus_plus_nat @ SV290 @ SY1364 ) @ ( plus_plus_nat @ SY1363 @ SY1365 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11148]) ).

thf(11559,plain,
    ! [SV291: nat] :
      ( ( ! [SY1366: nat] :
            ( ~ ( dvd_dvd_nat @ SV291 @ SY1366 )
            | ( ( times_times_nat @ SV291 @ ( divide_divide_nat @ SY1366 @ SV291 ) )
              = SY1366 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11149]) ).

thf(11560,plain,
    ! [SV292: num] :
      ( ( ! [SY1367: num] :
            ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV292 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SY1367 ) ) )
           != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ SY1367 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11150]) ).

thf(11561,plain,
    ! [SV293: nat] :
      ( ( ! [SY1368: nat] :
            ( ~ ( ( SV293 != zero_zero_nat ) )
            | ( ( divide_divide_nat @ ( times_times_nat @ SY1368 @ SV293 ) @ SV293 )
              = SY1368 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11151]) ).

thf(11562,plain,
    ! [SV294: nat] :
      ( ( ! [SY1369: nat,SY1370: nat,SY1371: nat] :
            ( ~ ~ ( ( SV294 != SY1369 )
                  | ~ ( ord_less_nat @ SY1370 @ SY1371 ) )
            | ( ord_less_nat @ ( plus_plus_nat @ SV294 @ SY1370 ) @ ( plus_plus_nat @ SY1369 @ SY1371 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11152]) ).

thf(11563,plain,
    ! [SV295: num] :
      ( ( ! [SY1372: num] :
            ( ( bit1 @ SV295 )
           != ( bit0 @ SY1372 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11153]) ).

thf(11564,plain,
    ! [SV296: nat] :
      ( ( ! [SY1373: nat,SY1374: nat,SY1375: nat] :
            ( ~ ( ord_less_nat @ SV296 @ SY1373 )
            | ~ ( ord_less_nat @ SY1374 @ SY1375 )
            | ( ord_less_nat @ ( plus_plus_nat @ SV296 @ SY1374 ) @ ( plus_plus_nat @ SY1373 @ SY1375 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11154]) ).

thf(11565,plain,
    ! [SV297: nat] :
      ( ( ! [SY1376: nat,SY1377: nat,SY1378: nat] :
            ( ~ ( dvd_dvd_nat @ SV297 @ SY1376 )
            | ~ ( dvd_dvd_nat @ SY1377 @ SY1378 )
            | ( ( times_times_nat @ ( divide_divide_nat @ SY1376 @ SV297 ) @ ( divide_divide_nat @ SY1378 @ SY1377 ) )
              = ( divide_divide_nat @ ( times_times_nat @ SY1376 @ SY1378 ) @ ( times_times_nat @ SV297 @ SY1377 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11155]) ).

thf(11566,plain,
    ! [SV298: nat] :
      ( ( ! [SY1379: nat] :
            ( ~ ( ord_less_eq_nat @ SV298 @ SY1379 )
            | ~ ! [SY1380: nat] :
                  ( SY1379
                 != ( plus_plus_nat @ SV298 @ SY1380 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11156]) ).

thf(11567,plain,
    ! [SV299: nat] :
      ( ( ! [SY1381: nat,SY1382: nat] :
            ( ~ ( ord_less_eq_nat @ SV299 @ SY1381 )
            | ( ord_less_eq_nat @ SV299 @ ( plus_plus_nat @ SY1382 @ SY1381 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11157]) ).

thf(11568,plain,
    ! [SV300: nat] :
      ( ( ! [SY1383: nat] :
            ( ( ( times_times_nat @ SV300 @ SY1383 )
              = one_one_nat )
            = ( ~ ( ( SV300 != one_one_nat )
                  | ( SY1383 != one_one_nat ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11158]) ).

thf(11569,plain,
    ( ( ! [SX0: nat] :
          ( ( some_nat @ SX0 )
         != ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ maxs ) ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[11159]) ).

thf(11570,plain,
    ( ( ! [SV301: nat] :
          ( ( dvd_dvd_nat @ SV301 )
          = ( ^ [SY1384: nat] :
                ~ ! [SY1385: nat] :
                    ( SY1384
                   != ( times_times_nat @ SV301 @ SY1385 ) ) ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11160]) ).

thf(11571,plain,
    ( ( dvd_dvd_nat
      = ( ^ [SX0: nat,SX1: nat] :
            ~ ! [SX2: nat] :
                ( SX1
               != ( times_times_nat @ SX0 @ SX2 ) ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11160]) ).

thf(11572,plain,
    ! [SV302: nat > real] :
      ( ( ! [SY1386: nat] :
            ( ~ ( summable_real @ SV302 )
            | ( summable_real
              @ ^ [SY1387: nat] : ( SV302 @ ( plus_plus_nat @ SY1387 @ SY1386 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11161]) ).

thf(11573,plain,
    ! [SV303: nat] :
      ( ( ! [SY1388: nat] :
            ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SY1388 ) ) )
            = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
             != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1388 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11162]) ).

thf(11574,plain,
    ! [SV304: nat] :
      ( ( ! [SY1389: nat,SY1390: nat] :
            ( ~ ( ord_less_nat @ SV304 @ SY1389 )
            | ( ord_less_nat @ ( plus_plus_nat @ SV304 @ SY1390 ) @ ( plus_plus_nat @ SY1389 @ SY1390 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11163]) ).

thf(11575,plain,
    ! [SV305: nat] :
      ( ( ! [SY1391: nat] :
            ( ( ( plus_plus_nat @ SV305 @ SY1391 )
              = zero_zero_nat )
            = ( ~ ( ( SV305 != zero_zero_nat )
                  | ( SY1391 != zero_zero_nat ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11164]) ).

thf(11576,plain,
    ! [SV306: num] :
      ( ( zero_zero_nat
       != ( numeral_numeral_nat @ SV306 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11165]) ).

thf(11577,plain,
    ! [SV307: nat] :
      ( ( ! [SY1392: nat] :
            ( ( ( plus_plus_nat @ SV307 @ SY1392 )
             != SV307 )
            | ( SY1392 = zero_zero_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11166]) ).

thf(11578,plain,
    ! [SV308: nat] :
      ( ( ! [SY1393: nat,SY1394: nat] :
            ( ~ ( ord_less_eq_nat @ SV308 @ SY1393 )
            | ( ord_less_eq_nat @ ( divide_divide_nat @ SV308 @ SY1394 ) @ ( divide_divide_nat @ SY1393 @ SY1394 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11167]) ).

thf(11579,plain,
    ! [SV309: nat] :
      ( ( ! [SY1395: nat] :
            ( ~ ( ord_less_eq_nat @ SV309 @ SY1395 )
            | ~ ! [SY1396: nat] :
                  ( SY1395
                 != ( plus_plus_nat @ SV309 @ SY1396 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11168]) ).

thf(11580,plain,
    ! [SV310: nat] :
      ( ( ! [SY1397: nat] :
            ( ( ( plus_plus_nat @ SV310 @ SY1397 )
              = zero_zero_nat )
            = ( ~ ( ( SV310 != zero_zero_nat )
                  | ( SY1397 != zero_zero_nat ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11169]) ).

thf(11581,plain,
    ! [SV311: nat] :
      ( ( ! [SY1398: nat,SY1399: nat] :
            ( ~ ( dvd_dvd_nat @ SV311 @ ( times_times_nat @ SY1398 @ SY1399 ) )
            | ~ ! [SY1400: nat] :
                  ~ ~ ! [SY1401: nat] :
                        ~ ~ ( ~ ~ ( ( SV311
                                   != ( times_times_nat @ SY1400 @ SY1401 ) )
                                  | ~ ( dvd_dvd_nat @ SY1400 @ SY1398 ) )
                            | ~ ( dvd_dvd_nat @ SY1401 @ SY1399 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11170]) ).

thf(11582,plain,
    ! [SV312: nat] :
      ( ( ! [SY1402: nat,SY1403: nat,SY1404: nat,SY1405: nat] :
            ( ~ ( dvd_dvd_nat @ SV312 @ SY1402 )
            | ~ ( dvd_dvd_nat @ SV312 @ SY1403 )
            | ~ ( ( ( times_times_nat @ SY1402 @ SY1404 )
                  = ( plus_plus_nat @ ( times_times_nat @ SY1403 @ SY1405 ) @ SV312 ) )
                | ( ( times_times_nat @ SY1403 @ SY1404 )
                  = ( plus_plus_nat @ ( times_times_nat @ SY1402 @ SY1405 ) @ SV312 ) ) )
            | ~ ! [SY1406: nat] :
                  ~ ~ ! [SY1407: nat] :
                        ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ SV312 @ SY1402 )
                                  | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SY1402 @ SY1403 ) ) )
                            | ~ ( ( ( times_times_nat @ SY1402 @ SY1406 )
                                  = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SY1402 @ SY1403 ) @ SY1407 ) @ SV312 ) )
                                | ( ( times_times_nat @ ( plus_plus_nat @ SY1402 @ SY1403 ) @ SY1406 )
                                  = ( plus_plus_nat @ ( times_times_nat @ SY1402 @ SY1407 ) @ SV312 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11171]) ).

thf(11583,plain,
    ! [SV313: nat] :
      ( ( ! [SY1408: nat,SY1409: nat] :
            ( ~ ( ord_less_eq_nat @ SV313 @ SY1408 )
            | ( ord_less_eq_nat @ ( plus_plus_nat @ SV313 @ SY1409 ) @ ( plus_plus_nat @ SY1408 @ SY1409 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11172]) ).

thf(11584,plain,
    ! [SV314: nat] :
      ( ( ! [SY1410: nat,SY1411: nat] :
            ( ~ ( dvd_dvd_nat @ SV314 @ SY1410 )
            | ~ ( dvd_dvd_nat @ SY1410 @ SY1411 )
            | ( ( divide_divide_nat @ SY1411 @ ( divide_divide_nat @ SY1410 @ SV314 ) )
              = ( times_times_nat @ ( divide_divide_nat @ SY1411 @ SY1410 ) @ SV314 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11173]) ).

thf(11585,plain,
    ! [SV315: nat] :
      ( ( ! [SY1412: nat] :
            ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV315 )
           != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1412 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11174]) ).

thf(11586,plain,
    ! [SV316: num > $o] :
      ( ( ! [SY1413: num] :
            ( ~ ( SV316 @ one )
            | ~ ! [SY1414: num] :
                  ( ~ ( SV316 @ SY1414 )
                  | ( SV316 @ ( inc @ SY1414 ) ) )
            | ( SV316 @ SY1413 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11175]) ).

thf(11587,plain,
    ! [SV317: nat] :
      ( ( ! [SY1415: nat] :
            ( ~ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV317 @ SY1415 ) )
                 != zero_zero_nat ) )
            | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV317 )
             != zero_zero_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11176]) ).

thf(11588,plain,
    ! [SV318: num] :
      ( ( ! [SY1416: num] :
            ( ( bit0 @ SV318 )
           != ( bit1 @ SY1416 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11177]) ).

thf(11589,plain,
    ! [SV319: nat > nat > $o] :
      ( ( ! [SY1417: nat,SY1418: nat] :
            ( ~ ! [SY1419: nat,SY1420: nat] :
                  ( ( SV319 @ SY1419 @ SY1420 )
                  = ( SV319 @ SY1420 @ SY1419 ) )
            | ~ ! [SY1421: nat] : ( SV319 @ SY1421 @ zero_zero_nat )
            | ~ ! [SY1422: nat,SY1423: nat] :
                  ( ~ ( SV319 @ SY1422 @ SY1423 )
                  | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) )
            | ( SV319 @ SY1417 @ SY1418 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11178]) ).

thf(11590,plain,
    ! [SV320: num] :
      ( ( ! [SY1424: num] :
            ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ SV320 ) ) )
           != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SY1424 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV320 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11179]) ).

thf(11591,plain,
    ! [SV321: nat] :
      ( ( ! [SY1425: nat,SY1426: nat] :
            ( ~ ( ord_less_nat @ SV321 @ SY1425 )
            | ( ord_less_nat @ SV321 @ ( plus_plus_nat @ SY1426 @ SY1425 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11180]) ).

thf(11592,plain,
    ! [SV322: nat] :
      ( ( ! [SY1427: nat] :
            ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SY1427 )
            = ( ~ ( ~ ( ( SV322 != SY1427 ) )
                  | ~ ( vEBT_V8194947554948674370ptions @ summary @ SY1427 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11181]) ).

thf(11593,plain,
    ! [SV323: nat] :
      ( ( ! [SY1428: nat,SY1429: nat,SY1430: nat,SY1431: nat] :
            ( ( ( modulo_modulo_nat @ SV323 @ SY1428 )
             != ( modulo_modulo_nat @ SY1429 @ SY1428 ) )
            | ( ( modulo_modulo_nat @ SY1430 @ SY1428 )
             != ( modulo_modulo_nat @ SY1431 @ SY1428 ) )
            | ( ( modulo_modulo_nat @ ( times_times_nat @ SV323 @ SY1430 ) @ SY1428 )
              = ( modulo_modulo_nat @ ( times_times_nat @ SY1429 @ SY1431 ) @ SY1428 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11182]) ).

thf(11594,plain,
    ( ( ! [SV324: nat] :
          ( ( ord_less_eq_nat @ SV324 )
          = ( ^ [SY1432: nat] :
                ~ ! [SY1433: nat] :
                    ( SY1432
                   != ( plus_plus_nat @ SV324 @ SY1433 ) ) ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11183]) ).

thf(11595,plain,
    ( ( ord_less_eq_nat
      = ( ^ [SX0: nat,SX1: nat] :
            ~ ! [SX2: nat] :
                ( SX1
               != ( plus_plus_nat @ SX0 @ SX2 ) ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11183]) ).

thf(11596,plain,
    ! [SV325: nat] :
      ( ( ! [SY1434: nat,SY1435: nat] :
            ( ~ ( dvd_dvd_nat @ ( times_times_nat @ SV325 @ SY1434 ) @ SY1435 )
            | ( ( divide_divide_nat @ SY1435 @ ( times_times_nat @ SV325 @ SY1434 ) )
              = ( divide_divide_nat @ ( divide_divide_nat @ SY1435 @ SV325 ) @ SY1434 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11184]) ).

thf(11597,plain,
    ! [SV326: nat] :
      ( ( ! [SY1436: nat,SY1437: nat] :
            ( ~ ( dvd_dvd_nat @ SV326 @ SY1436 )
            | ( ( times_times_nat @ SY1437 @ ( divide_divide_nat @ SY1436 @ SV326 ) )
              = ( divide_divide_nat @ ( times_times_nat @ SY1437 @ SY1436 ) @ SV326 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11185]) ).

thf(11598,plain,
    ! [SV327: nat] :
      ( ( ! [SY1438: nat,SY1439: nat] :
            ( ~ ( ord_less_nat @ SV327 @ SY1438 )
            | ( ord_less_nat @ ( plus_plus_nat @ SV327 @ SY1439 ) @ ( plus_plus_nat @ SY1438 @ SY1439 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11186]) ).

thf(11599,plain,
    ! [SV328: nat] :
      ( ( ! [SY1440: nat,SY1441: nat,SY1442: nat] :
            ( ~ ~ ( ~ ( ord_less_eq_nat @ SV328 @ SY1440 )
                  | ( SY1441 != SY1442 ) )
            | ( ord_less_eq_nat @ ( plus_plus_nat @ SV328 @ SY1441 ) @ ( plus_plus_nat @ SY1440 @ SY1442 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11187]) ).

thf(11600,plain,
    ! [SV329: nat] :
      ( ( ! [SY1443: nat] :
            ( ( zero_zero_nat
              = ( plus_plus_nat @ SV329 @ SY1443 ) )
            = ( ~ ( ( SV329 != zero_zero_nat )
                  | ( SY1443 != zero_zero_nat ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11188]) ).

thf(11601,plain,
    ! [SV330: nat] :
      ( ( ! [SY1444: nat,SY1445: nat] :
            ( ~ ( dvd_dvd_nat @ SV330 @ SY1444 )
            | ( dvd_dvd_nat @ ( power_power_nat @ SV330 @ SY1445 ) @ ( power_power_nat @ SY1444 @ SY1445 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11189]) ).

thf(11602,plain,
    ! [SV331: nat] :
      ( ( ! [SY1446: nat] :
            ( ~ ( ( SV331 != zero_zero_nat ) )
            | ( ( power_power_nat @ SV331 @ SY1446 )
             != zero_zero_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11190]) ).

thf(11603,plain,
    ! [SV332: nat] :
      ( ( ! [SY1447: nat,SY1448: list_VEBT_VEBT,SY1449: vEBT_VEBT,SY1450: vEBT_VEBT] :
            ( ~ ( ( SV332 != SY1447 ) )
            | ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SY1448 @ SV332 @ SY1449 ) @ SY1447 @ SY1450 )
              = ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SY1448 @ SY1447 @ SY1450 ) @ SV332 @ SY1449 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11191]) ).

thf(11604,plain,
    ! [SV333: $o] :
      ( ( ! [SY1451: $o] :
            ( ( zero_n2687167440665602831ol_nat
              @ ~ ( ~ SV333
                  | ~ SY1451 ) )
            = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ SV333 ) @ ( zero_n2687167440665602831ol_nat @ SY1451 ) ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[11192]) ).

thf(11605,plain,
    ( ( ! [SX0: $o] :
          ( ( zero_n2687167440665602831ol_nat
            @ ~ ( ~ $true
                | ~ SX0 ) )
          = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ $true ) @ ( zero_n2687167440665602831ol_nat @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[11192]) ).

thf(11606,plain,
    ( ( ! [SX0: $o] :
          ( ( zero_n2687167440665602831ol_nat
            @ ~ ( ~ $false
                | ~ SX0 ) )
          = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ $false ) @ ( zero_n2687167440665602831ol_nat @ SX0 ) ) ) )
    = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[11192]) ).

thf(11607,plain,
    ! [SV334: nat] :
      ( ( ! [SY1452: nat,SY1453: nat] :
            ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV334 @ SY1452 ) @ ( plus_plus_nat @ SY1453 @ SY1452 ) )
            | ( ord_less_nat @ SV334 @ SY1453 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11193]) ).

thf(11608,plain,
    ! [SV335: nat] :
      ( ( ! [SY1454: nat,SY1455: nat,SY1456: nat] :
            ( ~ ~ ( ( SV335 != SY1454 )
                  | ~ ( ord_less_eq_nat @ SY1455 @ SY1456 ) )
            | ( ord_less_eq_nat @ ( plus_plus_nat @ SV335 @ SY1455 ) @ ( plus_plus_nat @ SY1454 @ SY1456 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11194]) ).

thf(11609,plain,
    ! [SV336: nat] :
      ( ( ! [SY1457: nat,SY1458: nat] :
            ( ~ ( dvd_dvd_nat @ SV336 @ SY1457 )
            | ( ( dvd_dvd_nat @ SV336 @ ( plus_plus_nat @ SY1458 @ SY1457 ) )
              = ( dvd_dvd_nat @ SV336 @ SY1458 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11195]) ).

thf(11610,plain,
    ! [SV337: nat] :
      ( ( ! [SY1459: nat,SY1460: nat] :
            ( ( SV337
             != ( plus_plus_nat @ SY1459 @ SY1460 ) )
            | ( ( suc @ SV337 )
              = ( plus_plus_nat @ SY1459 @ ( suc @ SY1460 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11196]) ).

thf(11611,plain,
    ! [SV338: nat] :
      ( ( ! [SY1461: nat,SY1462: nat] :
            ( ~ ( dvd_dvd_nat @ SV338 @ SY1461 )
            | ~ ( dvd_dvd_nat @ SV338 @ SY1462 )
            | ( dvd_dvd_nat @ SV338 @ ( plus_plus_nat @ SY1461 @ SY1462 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11197]) ).

thf(11612,plain,
    ! [SV339: nat] :
      ( ( ! [SY1463: nat,SY1464: nat] :
            ( ( ( plus_plus_nat @ SV339 @ SY1463 )
             != ( plus_plus_nat @ SV339 @ SY1464 ) )
            | ( SY1463 = SY1464 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11198]) ).

thf(11613,plain,
    ! [SV340: nat] :
      ( ( ~ ! [SY1465: nat] :
              ( SV340
             != ( plus_plus_nat @ SY1465 @ SY1465 ) )
        | ~ ! [SY1466: nat] :
              ( SV340
             != ( plus_plus_nat @ SY1466 @ ( suc @ SY1466 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11199]) ).

thf(11614,plain,
    ! [SV341: nat] :
      ( ( ! [SY1467: nat,SY1468: nat,SY1469: nat] :
            ( ~ ~ ( ~ ( ord_less_eq_nat @ SV341 @ SY1467 )
                  | ~ ( ord_less_eq_nat @ SY1468 @ SY1469 ) )
            | ( ord_less_eq_nat @ ( plus_plus_nat @ SV341 @ SY1468 ) @ ( plus_plus_nat @ SY1467 @ SY1469 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11200]) ).

thf(11615,plain,
    ! [SV342: nat] :
      ( ( ! [SY1470: nat,SY1471: nat] :
            ( ~ ( ( SV342 != zero_zero_nat ) )
            | ( ( divide_divide_nat @ ( times_times_nat @ SV342 @ SY1470 ) @ ( times_times_nat @ SV342 @ SY1471 ) )
              = ( divide_divide_nat @ SY1470 @ SY1471 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11201]) ).

thf(11616,plain,
    ! [SV343: nat] :
      ( ( ! [SY1472: nat,SY1473: nat] :
            ( ~ ( ord_less_nat @ SV343 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1472 ) )
            | ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ SY1473 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1472 ) ) @ SV343 ) @ SY1472 )
              = SY1473 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11202]) ).

thf(11617,plain,
    ! [SV344: nat] :
      ( ( ! [SY1474: nat,SY1475: nat] :
            ( ~ ( dvd_dvd_nat @ SV344 @ SY1474 )
            | ( ( divide_divide_nat @ ( plus_plus_nat @ SY1475 @ SY1474 ) @ SV344 )
              = ( plus_plus_nat @ ( divide_divide_nat @ SY1475 @ SV344 ) @ ( divide_divide_nat @ SY1474 @ SV344 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11203]) ).

thf(11618,plain,
    ! [SV345: nat] :
      ( ( ! [SY1476: nat,SY1477: nat] :
            ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV345 @ SY1476 ) @ SY1477 )
            | ( ord_less_eq_nat @ SY1476 @ SY1477 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11204]) ).

thf(11619,plain,
    ! [SV346: nat] :
      ( ( ! [SY1478: nat,SY1479: nat] :
            ( ~ ( dvd_dvd_nat @ ( times_times_nat @ SV346 @ SY1478 ) @ SY1479 )
            | ( dvd_dvd_nat @ SY1478 @ SY1479 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11205]) ).

thf(11620,plain,
    ! [SV347: nat] :
      ( ( ! [SY1480: nat,SY1481: nat] :
            ( ~ ( dvd_dvd_nat @ SV347 @ SY1480 )
            | ~ ( dvd_dvd_nat @ SV347 @ SY1481 )
            | ( ( dvd_dvd_nat @ ( divide_divide_nat @ SY1480 @ SV347 ) @ ( divide_divide_nat @ SY1481 @ SV347 ) )
              = ( dvd_dvd_nat @ SY1480 @ SY1481 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11206]) ).

thf(11621,plain,
    ! [SV348: nat] :
      ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV348 )
        | ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ SV348 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
          = SV348 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11207]) ).

thf(11622,plain,
    ! [SV349: nat] :
      ( ( ! [SY1482: nat] :
            ~ ! [SY1483: nat] :
                ~ ~ ! [SY1484: nat] :
                      ~ ~ ! [SY1485: nat] :
                            ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ SY1483 @ SV349 )
                                      | ~ ( dvd_dvd_nat @ SY1483 @ SY1482 ) )
                                | ~ ( ( ( times_times_nat @ SV349 @ SY1484 )
                                      = ( plus_plus_nat @ ( times_times_nat @ SY1482 @ SY1485 ) @ SY1483 ) )
                                    | ( ( times_times_nat @ SY1482 @ SY1484 )
                                      = ( plus_plus_nat @ ( times_times_nat @ SV349 @ SY1485 ) @ SY1483 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11208]) ).

thf(11623,plain,
    ! [SV350: nat] :
      ( ( ! [SY1486: nat] :
            ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV350 )
            | ( ord_less_eq_nat @ SY1486 @ ( power_power_nat @ SV350 @ SY1486 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11209]) ).

thf(11624,plain,
    ! [SV351: nat] :
      ( ( ! [SY1487: nat] :
            ( ( one_one_nat
              = ( times_times_nat @ SV351 @ SY1487 ) )
            = ( ~ ( ( SV351 != one_one_nat )
                  | ( SY1487 != one_one_nat ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11210]) ).

thf(11625,plain,
    ! [SV352: nat] :
      ( ( ! [SY1488: nat,SY1489: nat,SY1490: nat] :
            ( ~ ( ord_less_eq_nat @ SV352 @ SY1488 )
            | ~ ( ord_less_eq_nat @ SY1489 @ SY1490 )
            | ( ord_less_eq_nat @ ( plus_plus_nat @ SV352 @ SY1489 ) @ ( plus_plus_nat @ SY1488 @ SY1490 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11211]) ).

thf(11626,plain,
    ! [SV353: nat] :
      ( ( ! [SY1491: nat,SY1492: nat,SY1493: nat,SY1494: nat] :
            ( ~ ( ( SV353 != zero_zero_nat ) )
            | ~ ~ ( ( SY1491 != SY1492 )
                  | ~ ( ( SY1493 != SY1494 ) ) )
            | ( ( plus_plus_nat @ SY1491 @ ( times_times_nat @ SV353 @ SY1493 ) )
             != ( plus_plus_nat @ SY1492 @ ( times_times_nat @ SV353 @ SY1494 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11212]) ).

thf(11627,plain,
    ! [SV354: nat] :
      ( ( ! [SY1495: nat,SY1496: nat] :
            ( ~ ( dvd_dvd_nat @ SV354 @ SY1495 )
            | ( ( dvd_dvd_nat @ SV354 @ ( plus_plus_nat @ SY1495 @ SY1496 ) )
              = ( dvd_dvd_nat @ SV354 @ SY1496 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11213]) ).

thf(11628,plain,
    ! [SV355: nat > nat] :
      ( ( ! [SY1497: nat > nat] :
            ( ~ ( summable_nat @ SV355 )
            | ~ ( summable_nat @ SY1497 )
            | ( summable_nat
              @ ^ [SY1498: nat] : ( plus_plus_nat @ ( SV355 @ SY1498 ) @ ( SY1497 @ SY1498 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11214]) ).

thf(11629,plain,
    ! [SV356: nat] :
      ( ( ! [SY1499: nat,SY1500: nat] :
            ~ ( ~ ( ( SV356 != zero_zero_nat )
                  | ( ( divide_divide_nat @ ( times_times_nat @ SV356 @ SY1499 ) @ ( times_times_nat @ SV356 @ SY1500 ) )
                    = zero_zero_nat ) )
              | ~ ( ~ ( ( SV356 != zero_zero_nat ) )
                  | ( ( divide_divide_nat @ ( times_times_nat @ SV356 @ SY1499 ) @ ( times_times_nat @ SV356 @ SY1500 ) )
                    = ( divide_divide_nat @ SY1499 @ SY1500 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11215]) ).

thf(11630,plain,
    ! [SV357: nat] :
      ( ( ! [SY1501: nat,SY1502: nat] :
            ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV357 @ SY1501 ) @ ( plus_plus_nat @ SY1502 @ SY1501 ) )
            | ( ord_less_eq_nat @ SV357 @ SY1502 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11216]) ).

thf(11631,plain,
    ! [SV358: num] :
      ( ( one
       != ( bit0 @ SV358 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11217]) ).

thf(11632,plain,
    ! [SV359: nat] :
      ( ( ! [SY1503: nat] :
            ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV359 )
            | ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1503 )
            | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV359 @ SY1503 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11218]) ).

thf(11633,plain,
    ! [SV360: nat] :
      ( ( ! [SY1504: nat] :
            ( ~ ( dvd_dvd_nat @ SV360 @ SY1504 )
            | ( ( times_times_nat @ ( divide_divide_nat @ SY1504 @ SV360 ) @ SV360 )
              = SY1504 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11219]) ).

thf(11634,plain,
    ! [SV361: nat] :
      ( ( ! [SY1505: nat,SY1506: nat] :
            ( ( ( divide_divide_nat @ SV361 @ SY1505 )
             != ( divide_divide_nat @ SY1506 @ SY1505 ) )
            | ~ ( dvd_dvd_nat @ SY1505 @ SV361 )
            | ~ ( dvd_dvd_nat @ SY1505 @ SY1506 )
            | ( SV361 = SY1506 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11220]) ).

thf(11635,plain,
    ! [SV362: nat] :
      ( ( ! [SY1507: nat,SY1508: nat] :
            ( ~ ( dvd_dvd_nat @ SV362 @ SY1507 )
            | ~ ( dvd_dvd_nat @ SV362 @ SY1508 )
            | ( ( ( divide_divide_nat @ SY1507 @ SV362 )
                = ( divide_divide_nat @ SY1508 @ SV362 ) )
              = ( SY1507 = SY1508 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11221]) ).

thf(11636,plain,
    ! [SV363: nat] :
      ( ( ! [SY1509: nat] :
            ( ~ ( dvd_dvd_nat @ SV363 @ SY1509 )
            | ~ ! [SY1510: nat] :
                  ( SY1509
                 != ( times_times_nat @ SV363 @ SY1510 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11222]) ).

thf(11637,plain,
    ! [SV364: nat] :
      ( ( ! [SY1511: nat,SY1512: nat,SY1513: nat] :
            ( ~ ( ord_less_nat @ SV364 @ SY1511 )
            | ~ ( ord_less_nat @ SY1512 @ SY1513 )
            | ( ord_less_nat @ ( plus_plus_nat @ SV364 @ SY1512 ) @ ( plus_plus_nat @ SY1511 @ SY1513 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11223]) ).

thf(11638,plain,
    ! [SV365: nat] :
      ( ( ! [SY1514: nat,SY1515: nat,SY1516: nat] :
            ( ~ ( ord_less_eq_nat @ SV365 @ SY1514 )
            | ~ ( ord_less_eq_nat @ SY1515 @ SY1516 )
            | ( ord_less_eq_nat @ ( plus_plus_nat @ SV365 @ SY1515 ) @ ( plus_plus_nat @ SY1514 @ SY1516 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11224]) ).

thf(11639,plain,
    ! [SV366: nat] :
      ( ( ! [SY1517: nat,SY1518: nat] :
            ( ~ ( dvd_dvd_nat @ ( times_times_nat @ SV366 @ SY1517 ) @ SY1518 )
            | ( dvd_dvd_nat @ SV366 @ SY1518 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11225]) ).

thf(11640,plain,
    ! [SV367: nat] :
      ( ( ! [SY1519: nat,SY1520: nat] :
            ( ( SV367
             != ( times_times_nat @ SY1519 @ SY1520 ) )
            | ( dvd_dvd_nat @ SY1519 @ SV367 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11226]) ).

thf(11641,plain,
    ! [SV368: nat] :
      ( ( ! [SY1521: nat,SY1522: nat] :
            ( ~ ( ord_less_eq_nat @ SV368 @ SY1521 )
            | ( ord_less_eq_nat @ ( plus_plus_nat @ SY1522 @ SV368 ) @ ( plus_plus_nat @ SY1522 @ SY1521 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11227]) ).

thf(11642,plain,
    ! [SV369: nat] :
      ( ( ! [SY1523: nat,SY1524: nat] :
            ( ( ( plus_plus_nat @ SV369 @ SY1523 )
             != SY1524 )
            | ( SV369
              = ( minus_minus_nat @ SY1524 @ SY1523 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11228]) ).

thf(11643,plain,
    ! [SV370: nat] :
      ( ( ! [SY1525: nat,SY1526: nat] :
            ( ~ ( ord_less_nat @ SV370 @ SY1525 )
            | ( ord_less_nat @ ( plus_plus_nat @ SY1526 @ SV370 ) @ ( plus_plus_nat @ SY1526 @ SY1525 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11229]) ).

thf(11644,plain,
    ! [SV371: nat] :
      ( ( ! [SY1527: nat,SY1528: nat] :
            ( ~ ( dvd_dvd_nat @ SV371 @ SY1527 )
            | ( dvd_dvd_nat @ SV371 @ ( times_times_nat @ SY1528 @ SY1527 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11230]) ).

thf(11645,plain,
    ! [SV372: nat] :
      ( ( ! [SY1529: nat,SY1530: nat] :
            ( ~ ( dvd_dvd_nat @ SV372 @ SY1529 )
            | ( dvd_dvd_nat @ SV372 @ ( times_times_nat @ SY1529 @ SY1530 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11231]) ).

thf(11646,plain,
    ! [SV373: option_nat] :
      ( ( ! [SY1531: option_nat] :
            ( ( ( SV373 = none_nat )
             != ( SY1531 = none_nat ) )
            | ~ ( ~ ( ( SV373 != none_nat ) )
                | ~ ( ( SY1531 != none_nat ) )
                | ( ( the_nat @ SV373 )
                  = ( the_nat @ SY1531 ) ) )
            | ( SV373 = SY1531 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11232]) ).

thf(11647,plain,
    ! [SV374: nat > $o] :
      ( ( ! [SY1532: nat] :
            ( ~ ! [SY1533: nat] :
                  ( ( ( divide_divide_nat @ SY1533 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                   != SY1533 )
                  | ( SV374 @ SY1533 ) )
            | ~ ! [SY1534: nat,SY1535: $o] :
                  ( ~ ( SV374 @ SY1534 )
                  | ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ SY1535 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1534 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                   != SY1534 )
                  | ( SV374 @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ SY1535 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1534 ) ) ) )
            | ( SV374 @ SY1532 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11233]) ).

thf(11648,plain,
    ( ( ! [SV375: nat] :
          ( ( ord_less_eq_nat @ SV375 )
          = ( ^ [SY1536: nat] :
                ~ ! [SY1537: nat] :
                    ( SY1536
                   != ( plus_plus_nat @ SV375 @ SY1537 ) ) ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11234]) ).

thf(11649,plain,
    ( ( ord_less_eq_nat
      = ( ^ [SX0: nat,SX1: nat] :
            ~ ! [SX2: nat] :
                ( SX1
               != ( plus_plus_nat @ SX0 @ SX2 ) ) ) )
    = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11234]) ).

thf(11650,plain,
    ! [SV376: num] :
      ( ( ! [SY1538: num] :
            ( ( bit0 @ SV376 )
           != ( bit1 @ SY1538 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11235]) ).

thf(11651,plain,
    ! [SV377: nat] :
      ( ( ! [SY1539: nat,SY1540: nat] :
            ( ~ ( dvd_dvd_nat @ SV377 @ SY1539 )
            | ( ( power_power_nat @ ( divide_divide_nat @ SY1539 @ SV377 ) @ SY1540 )
              = ( divide_divide_nat @ ( power_power_nat @ SY1539 @ SY1540 ) @ ( power_power_nat @ SV377 @ SY1540 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11236]) ).

thf(11652,plain,
    ! [SV378: nat] :
      ( ( ! [SY1541: nat,SY1542: nat,SY1543: nat] :
            ( ~ ( ord_less_eq_nat @ SV378 @ SY1541 )
            | ~ ( ord_less_eq_nat @ SY1542 @ SY1543 )
            | ( ord_less_eq_nat @ ( times_times_nat @ SV378 @ SY1542 ) @ ( times_times_nat @ SY1541 @ SY1543 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11237]) ).

thf(11653,plain,
    ! [SV379: nat] :
      ( ( ! [SY1544: nat,SY1545: nat,SY1546: nat] :
            ( ~ ~ ( ~ ( ord_less_nat @ SV379 @ SY1544 )
                  | ( SY1545 != SY1546 ) )
            | ( ord_less_nat @ ( plus_plus_nat @ SV379 @ SY1545 ) @ ( plus_plus_nat @ SY1544 @ SY1546 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11238]) ).

thf(11654,plain,
    ! [SV380: nat] :
      ( ( ! [SY1547: nat,SY1548: nat] :
            ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV380 @ SY1547 ) @ ( plus_plus_nat @ SV380 @ SY1548 ) )
            | ( ord_less_eq_nat @ SY1547 @ SY1548 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11239]) ).

thf(11655,plain,
    ! [SV381: nat] :
      ( ( ! [SY1549: nat] :
            ( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV381 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ SY1549 )
            | ( ord_less_eq_nat @ SV381 @ SY1549 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11240]) ).

thf(11656,plain,
    ! [SV382: num] :
      ( ( ~ ( ( SV382 != one ) )
        | ~ ! [SY1550: num] :
              ( SV382
             != ( bit0 @ SY1550 ) )
        | ~ ! [SY1551: num] :
              ( SV382
             != ( bit1 @ SY1551 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11241]) ).

thf(11657,plain,
    ! [SV383: nat] :
      ( ( ! [SY1552: nat,SY1553: list_VEBT_VEBT,SY1554: vEBT_VEBT] :
            ( ~ ( ( SV383 != SY1552 ) )
            | ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ SY1553 @ SV383 @ SY1554 ) @ SY1552 )
              = ( nth_VEBT_VEBT @ SY1553 @ SY1552 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11242]) ).

thf(11658,plain,
    ! [SV384: nat] :
      ( ( ! [SY1555: nat,SY1556: nat,SY1557: nat,SY1558: nat] :
            ( ( ( modulo_modulo_nat @ SV384 @ SY1555 )
             != ( modulo_modulo_nat @ SY1556 @ SY1555 ) )
            | ( ( modulo_modulo_nat @ SY1557 @ SY1555 )
             != ( modulo_modulo_nat @ SY1558 @ SY1555 ) )
            | ( ( modulo_modulo_nat @ ( plus_plus_nat @ SV384 @ SY1557 ) @ SY1555 )
              = ( modulo_modulo_nat @ ( plus_plus_nat @ SY1556 @ SY1558 ) @ SY1555 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11243]) ).

thf(11659,plain,
    ! [SV385: num] :
      ( ( one
       != ( bit1 @ SV385 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11244]) ).

thf(11660,plain,
    ! [SV386: nat] :
      ( ( ! [SY1559: nat,SY1560: nat] :
            ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV386 @ SY1559 ) @ SY1560 )
            | ( ord_less_eq_nat @ SV386 @ SY1560 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11245]) ).

thf(11661,plain,
    ! [SV387: nat] :
      ( ( ! [SY1561: nat,SY1562: nat] :
            ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV387 @ SY1561 ) @ ( plus_plus_nat @ SV387 @ SY1562 ) )
            | ( ord_less_nat @ SY1561 @ SY1562 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11246]) ).

thf(11662,plain,
    ! [SV388: nat > nat] :
      ( ( ! [SY1563: nat,SY1564: nat > nat,SY1565: nat] :
            ( ~ ( sums_nat @ SV388 @ SY1563 )
            | ~ ( sums_nat @ SY1564 @ SY1565 )
            | ( sums_nat
              @ ^ [SY1566: nat] : ( plus_plus_nat @ ( SV388 @ SY1566 ) @ ( SY1564 @ SY1566 ) )
              @ ( plus_plus_nat @ SY1563 @ SY1565 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11247]) ).

thf(11663,plain,
    ! [SV389: nat] :
      ( ( ! [SY1567: nat,SY1568: nat] :
            ( ~ ( ord_less_nat @ SV389 @ SY1567 )
            | ( ord_less_nat @ SV389 @ ( plus_plus_nat @ SY1567 @ SY1568 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11248]) ).

thf(11664,plain,
    ! [SV390: nat] :
      ( ( ! [SY1569: nat,SY1570: nat] :
            ( ~ ( ord_less_eq_nat @ SV390 @ SY1569 )
            | ( ord_less_eq_nat @ SV390 @ ( plus_plus_nat @ SY1569 @ SY1570 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11249]) ).

thf(11665,plain,
    ! [SV391: nat,SV1: nat] :
      ( ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ SV1 @ SV391 ) @ ( vEBT_VEBT_low @ SV1 @ SV391 ) @ SV391 )
        = SV1 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11250]) ).

thf(11666,plain,
    ! [SV392: nat,SV2: nat] :
      ( ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV2 @ SV392 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV2 ) )
        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV392 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11251]) ).

thf(11667,plain,
    ! [SV393: nat] :
      ( ( ( vEBT_VEBT_high @ SV393 )
        = ( ^ [SY1571: nat] : ( divide_divide_nat @ SV393 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1571 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11252]) ).

thf(11668,plain,
    ! [SV394: nat] :
      ( ( ( vEBT_VEBT_bit_concat @ SV394 )
        = ( ^ [SY1572: nat,SY1573: nat] : ( plus_plus_nat @ ( times_times_nat @ SV394 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1573 ) ) @ SY1572 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11254]) ).

thf(11669,plain,
    ! [SV395: nat,SV6: num] :
      ( ( ! [SY1574: nat] :
            ( ( times_times_nat @ ( numeral_numeral_nat @ SV6 ) @ ( plus_plus_nat @ SV395 @ SY1574 ) )
            = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ SV6 ) @ SV395 ) @ ( times_times_nat @ ( numeral_numeral_nat @ SV6 ) @ SY1574 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11257]) ).

thf(11670,plain,
    ! [SV396: nat,SV7: nat] :
      ( ( ! [SY1575: num] :
            ( ( times_times_nat @ ( plus_plus_nat @ SV7 @ SV396 ) @ ( numeral_numeral_nat @ SY1575 ) )
            = ( plus_plus_nat @ ( times_times_nat @ SV7 @ ( numeral_numeral_nat @ SY1575 ) ) @ ( times_times_nat @ SV396 @ ( numeral_numeral_nat @ SY1575 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11258]) ).

thf(11671,plain,
    ! [SV397: nat,SV8: nat] :
      ( ( ( power_power_nat @ ( plus_plus_nat @ SV8 @ SV397 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
        = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ SV8 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ SV397 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV8 ) @ SV397 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11259]) ).

thf(11672,plain,
    ! [SV398: nat,SV9: nat] :
      ( ( ! [SY1576: nat] :
            ( ( divide_divide_nat @ ( divide_divide_nat @ SV9 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV398 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1576 ) )
            = ( divide_divide_nat @ SV9 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV398 @ SY1576 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11260]) ).

thf(11673,plain,
    ! [SV399: num,SV10: num] :
      ( ( ( ( numeral_numeral_nat @ SV10 )
          = ( numeral_numeral_nat @ SV399 ) )
        = ( SV10 = SV399 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11261]) ).

thf(11674,plain,
    ! [SV400: num,SV11: num] :
      ( ( ! [SY1577: nat] :
            ( ( times_times_nat @ ( numeral_numeral_nat @ SV11 ) @ ( times_times_nat @ ( numeral_numeral_nat @ SV400 ) @ SY1577 ) )
            = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ SV11 @ SV400 ) ) @ SY1577 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11262]) ).

thf(11675,plain,
    ! [SV401: num,SV12: num] :
      ( ( ( times_times_nat @ ( numeral_numeral_nat @ SV12 ) @ ( numeral_numeral_nat @ SV401 ) )
        = ( numeral_numeral_nat @ ( times_times_num @ SV12 @ SV401 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11263]) ).

thf(11676,plain,
    ! [SV402: num,SV13: num] :
      ( ( ! [SY1578: nat] :
            ( ( plus_plus_nat @ ( numeral_numeral_nat @ SV13 ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ SV402 ) @ SY1578 ) )
            = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ SV13 @ SV402 ) ) @ SY1578 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11264]) ).

thf(11677,plain,
    ! [SV403: num,SV14: num] :
      ( ( ( plus_plus_nat @ ( numeral_numeral_nat @ SV14 ) @ ( numeral_numeral_nat @ SV403 ) )
        = ( numeral_numeral_nat @ ( plus_plus_num @ SV14 @ SV403 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11265]) ).

thf(11678,plain,
    ! [SV404: num,SV16: nat] :
      ( ( ! [SY1579: num] :
            ( ( power_power_nat @ ( power_power_nat @ SV16 @ ( numeral_numeral_nat @ SV404 ) ) @ ( numeral_numeral_nat @ SY1579 ) )
            = ( power_power_nat @ SV16 @ ( numeral_numeral_nat @ ( times_times_num @ SV404 @ SY1579 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11267]) ).

thf(11679,plain,
    ! [SV405: num,SV17: nat] :
      ( ( ! [SY1580: num,SY1581: nat] :
            ( ( times_times_nat @ ( power_power_nat @ SV17 @ ( numeral_numeral_nat @ SV405 ) ) @ ( times_times_nat @ ( power_power_nat @ SV17 @ ( numeral_numeral_nat @ SY1580 ) ) @ SY1581 ) )
            = ( times_times_nat @ ( power_power_nat @ SV17 @ ( numeral_numeral_nat @ ( plus_plus_num @ SV405 @ SY1580 ) ) ) @ SY1581 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11268]) ).

thf(11680,plain,
    ! [SV406: num,SV18: nat] :
      ( ( ! [SY1582: num] :
            ( ( times_times_nat @ ( power_power_nat @ SV18 @ ( numeral_numeral_nat @ SV406 ) ) @ ( power_power_nat @ SV18 @ ( numeral_numeral_nat @ SY1582 ) ) )
            = ( power_power_nat @ SV18 @ ( numeral_numeral_nat @ ( plus_plus_num @ SV406 @ SY1582 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11269]) ).

thf(11681,plain,
    ! [SV407: num,SV20: nat] :
      ( ( ! [SY1583: num] :
            ( ( divide_divide_nat @ ( divide_divide_nat @ SV20 @ ( numeral_numeral_nat @ SV407 ) ) @ ( numeral_numeral_nat @ SY1583 ) )
            = ( divide_divide_nat @ SV20 @ ( numeral_numeral_nat @ ( times_times_num @ SV407 @ SY1583 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11271]) ).

thf(11682,plain,
    ! [SV408: nat,SV22: nat] :
      ( ( ! [SY1584: nat] :
            ( ( power_power_nat @ ( times_times_nat @ SV22 @ SV408 ) @ SY1584 )
            = ( times_times_nat @ ( power_power_nat @ SV22 @ SY1584 ) @ ( power_power_nat @ SV408 @ SY1584 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11273]) ).

thf(11683,plain,
    ! [SV409: nat,SV23: nat] :
      ( ( ( times_times_nat @ ( power_power_nat @ SV23 @ SV409 ) @ SV23 )
        = ( times_times_nat @ SV23 @ ( power_power_nat @ SV23 @ SV409 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11274]) ).

thf(11684,plain,
    ! [SV410: nat,SV24: nat] :
      ( ( ! [SY1585: nat] :
            ( ( power_power_nat @ SV24 @ ( times_times_nat @ SV410 @ SY1585 ) )
            = ( power_power_nat @ ( power_power_nat @ SV24 @ SV410 ) @ SY1585 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11275]) ).

thf(11685,plain,
    ! [SV411: nat,SV25: real] :
      ( ( ! [SY1586: nat] :
            ( ( power_power_real @ SV25 @ ( times_times_nat @ SV411 @ SY1586 ) )
            = ( power_power_real @ ( power_power_real @ SV25 @ SV411 ) @ SY1586 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11276]) ).

thf(11686,plain,
    ! [SV412: nat,SV26: int] :
      ( ( ! [SY1587: nat] :
            ( ( power_power_int @ SV26 @ ( times_times_nat @ SV412 @ SY1587 ) )
            = ( power_power_int @ ( power_power_int @ SV26 @ SV412 ) @ SY1587 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11277]) ).

thf(11687,plain,
    ! [SV413: nat,SV27: complex] :
      ( ( ! [SY1588: nat] :
            ( ( power_power_complex @ SV27 @ ( times_times_nat @ SV413 @ SY1588 ) )
            = ( power_power_complex @ ( power_power_complex @ SV27 @ SV413 ) @ SY1588 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11278]) ).

thf(11688,plain,
    ! [SV414: nat,SV28: nat] :
      ( ( ! [SY1589: nat] :
            ( ( divide_divide_nat @ SV28 @ ( times_times_nat @ SV414 @ SY1589 ) )
            = ( divide_divide_nat @ ( divide_divide_nat @ SV28 @ SV414 ) @ SY1589 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11279]) ).

thf(11689,plain,
    ! [SV415: nat,SV32: nat] :
      ( ( ! [SY1590: nat] :
            ( ( power_power_nat @ SV32 @ ( plus_plus_nat @ SV415 @ SY1590 ) )
            = ( times_times_nat @ ( power_power_nat @ SV32 @ SV415 ) @ ( power_power_nat @ SV32 @ SY1590 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11283]) ).

thf(11690,plain,
    ! [SV416: nat,SV34: nat] :
      ( ( ( plus_plus_nat @ SV34 @ ( plus_plus_nat @ SV34 @ SV416 ) )
        = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV34 ) @ SV416 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11285]) ).

thf(11691,plain,
    ! [SV417: nat,SV39: nat] :
      ( ( ( power_power_nat @ SV39 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV417 ) )
        = ( power_power_nat @ ( power_power_nat @ SV39 @ SV417 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11290]) ).

thf(11692,plain,
    ! [SV418: nat,SV40: real] :
      ( ( ( power_power_real @ SV40 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV418 ) )
        = ( power_power_real @ ( power_power_real @ SV40 @ SV418 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11291]) ).

thf(11693,plain,
    ! [SV419: nat,SV41: int] :
      ( ( ( power_power_int @ SV41 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV419 ) )
        = ( power_power_int @ ( power_power_int @ SV41 @ SV419 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11292]) ).

thf(11694,plain,
    ! [SV420: nat,SV42: complex] :
      ( ( ( power_power_complex @ SV42 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV420 ) )
        = ( power_power_complex @ ( power_power_complex @ SV42 @ SV420 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11293]) ).

thf(11695,plain,
    ! [SV421: nat,SV43: list_VEBT_VEBT] :
      ( ( ( list_u1324408373059187874T_VEBT @ SV43 @ SV421 @ ( nth_VEBT_VEBT @ SV43 @ SV421 ) )
        = SV43 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11294]) ).

thf(11696,plain,
    ! [SV422: nat,SV44: list_VEBT_VEBT] :
      ( ( ! [SY1591: vEBT_VEBT] :
            ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV44 @ SV422 @ SY1591 ) )
            = ( size_s6755466524823107622T_VEBT @ SV44 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11295]) ).

thf(11697,plain,
    ! [SV423: nat,SV45: list_VEBT_VEBT] :
      ( ( ! [SY1592: vEBT_VEBT,SY1593: vEBT_VEBT] :
            ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV45 @ SV423 @ SY1592 ) @ SV423 @ SY1593 )
            = ( list_u1324408373059187874T_VEBT @ SV45 @ SV423 @ SY1593 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11296]) ).

thf(11698,plain,
    ! [SV424: nat,SV46: nat] :
      ( ( ord_less_eq_nat @ ( divide_divide_nat @ SV46 @ SV424 ) @ SV46 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11297]) ).

thf(11699,plain,
    ! [SV425: nat,SV47: nat] :
      ( ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ SV47 @ SV425 ) @ SV425 ) @ SV47 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11298]) ).

thf(11700,plain,
    ! [SV426: nat,SV48: nat] :
      ( ( ord_less_eq_nat @ ( times_times_nat @ SV48 @ ( divide_divide_nat @ SV426 @ SV48 ) ) @ SV426 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11299]) ).

thf(11701,plain,
    ! [SV427: nat,SV49: nat] :
      ( ( ( ord_less_eq_nat @ ( power_power_nat @ SV49 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ SV427 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = ( ord_less_eq_nat @ SV49 @ SV427 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11300]) ).

thf(11702,plain,
    ! [SV52: num] :
      ( ( ord_less_num @ SV52 @ one )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[11303]) ).

thf(11703,plain,
    ! [SV428: num,SV53: num] :
      ( ( ( ord_less_num @ ( bit0 @ SV53 ) @ ( bit0 @ SV428 ) )
        = ( ord_less_num @ SV53 @ SV428 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11304]) ).

thf(11704,plain,
    ! [SV429: num,SV54: num] :
      ( ( ( ( bit0 @ SV54 )
          = ( bit0 @ SV429 ) )
        = ( SV54 = SV429 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11305]) ).

thf(11705,plain,
    ! [SV430: num,SV58: num] :
      ( ( ( plus_plus_num @ ( bit0 @ SV58 ) @ ( bit0 @ SV430 ) )
        = ( bit0 @ ( plus_plus_num @ SV58 @ SV430 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11309]) ).

thf(11706,plain,
    ! [SV431: num,SV59: num] :
      ( ( ( times_times_num @ ( bit0 @ SV59 ) @ ( bit0 @ SV431 ) )
        = ( bit0 @ ( bit0 @ ( times_times_num @ SV59 @ SV431 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11310]) ).

thf(11707,plain,
    ! [SV432: num,SV62: num] :
      ( ( ( ord_less_eq_num @ ( bit0 @ SV62 ) @ ( bit0 @ SV432 ) )
        = ( ord_less_eq_num @ SV62 @ SV432 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11313]) ).

thf(11708,plain,
    ! [SV64: num] :
      ( ( ~ ( ( one_one_nat
              = ( numeral_numeral_nat @ SV64 ) )
            | ( one = SV64 ) )
        | ~ ( ( one_one_nat
             != ( numeral_numeral_nat @ SV64 ) )
            | ( one != SV64 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11315]) ).

thf(11709,plain,
    ! [SV64: num] :
      ( ( ( one_one_nat
          = ( numeral_numeral_nat @ SV64 ) )
        = ( one = SV64 ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11315]) ).

thf(11710,plain,
    ! [SV65: num] :
      ( ( ~ ( ( ( numeral_numeral_nat @ SV65 )
              = one_one_nat )
            | ( SV65 = one ) )
        | ~ ( ( ( numeral_numeral_nat @ SV65 )
             != one_one_nat )
            | ( SV65 != one ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11316]) ).

thf(11711,plain,
    ! [SV65: num] :
      ( ( ( ( numeral_numeral_nat @ SV65 )
          = one_one_nat )
        = ( SV65 = one ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11316]) ).

thf(11712,plain,
    ! [SV66: num] :
      ( ( ord_less_eq_num @ ( bit0 @ SV66 ) @ one )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[11317]) ).

thf(11713,plain,
    ! [SV67: num] :
      ( ( ~ ( ( ord_less_eq_num @ SV67 @ one )
            | ( SV67 = one ) )
        | ~ ( ~ ( ord_less_eq_num @ SV67 @ one )
            | ( SV67 != one ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11318]) ).

thf(11714,plain,
    ! [SV67: num] :
      ( ( ( ord_less_eq_num @ SV67 @ one )
        = ( SV67 = one ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11318]) ).

thf(11715,plain,
    ! [SV433: nat,SV69: nat] :
      ( ( ! [SY1594: nat,SY1595: nat] :
            ( ( plus_plus_nat @ ( times_times_nat @ SV69 @ SV433 ) @ ( plus_plus_nat @ ( times_times_nat @ SY1594 @ SV433 ) @ SY1595 ) )
            = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV69 @ SY1594 ) @ SV433 ) @ SY1595 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11320]) ).

thf(11716,plain,
    ! [SV434: nat,SV70: nat] :
      ( ( ( plus_plus_nat @ SV70 @ ( suc @ SV434 ) )
        = ( suc @ ( plus_plus_nat @ SV70 @ SV434 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11321]) ).

thf(11717,plain,
    ! [SV435: nat,SV71: nat] :
      ( ( ! [SY1596: nat] :
            ( ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SV435 ) @ ( plus_plus_nat @ SV71 @ SY1596 ) )
            = ( ord_less_nat @ SV435 @ SY1596 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11322]) ).

thf(11718,plain,
    ! [SV436: nat,SV72: nat] :
      ( ( ! [SY1597: nat] :
            ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV72 @ SV436 ) @ ( plus_plus_nat @ SV72 @ SY1597 ) )
            = ( ord_less_eq_nat @ SV436 @ SY1597 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11323]) ).

thf(11719,plain,
    ! [SV437: nat,SV73: nat] :
      ( ( ! [SY1598: nat] :
            ( ( minus_minus_nat @ ( minus_minus_nat @ SV73 @ SV437 ) @ SY1598 )
            = ( minus_minus_nat @ SV73 @ ( plus_plus_nat @ SV437 @ SY1598 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11324]) ).

thf(11720,plain,
    ! [SV438: nat,SV74: nat] :
      ( ( ( times_times_nat @ SV74 @ ( suc @ SV438 ) )
        = ( plus_plus_nat @ SV74 @ ( times_times_nat @ SV74 @ SV438 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11325]) ).

thf(11721,plain,
    ! [SV439: nat,SV78: nat] :
      ( ( ( minus_minus_nat @ ( plus_plus_nat @ SV78 @ SV439 ) @ SV439 )
        = SV78 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11329]) ).

thf(11722,plain,
    ! [SV440: nat,SV79: nat] :
      ( ( ( minus_minus_nat @ ( plus_plus_nat @ SV79 @ SV440 ) @ SV79 )
        = SV440 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11330]) ).

thf(11723,plain,
    ! [SV441: nat,SV80: nat] :
      ( ( ! [SY1599: nat] :
            ( ( minus_minus_nat @ ( plus_plus_nat @ SV80 @ SV441 ) @ ( plus_plus_nat @ SY1599 @ SV441 ) )
            = ( minus_minus_nat @ SV80 @ SY1599 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11331]) ).

thf(11724,plain,
    ! [SV442: nat,SV81: nat] :
      ( ( ! [SY1600: nat] :
            ( ( minus_minus_nat @ ( plus_plus_nat @ SV81 @ SV442 ) @ ( plus_plus_nat @ SV81 @ SY1600 ) )
            = ( minus_minus_nat @ SV442 @ SY1600 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11332]) ).

thf(11725,plain,
    ! [SV443: nat,SV82: nat] :
      ( ( ( plus_plus_nat @ ( suc @ SV82 ) @ SV443 )
        = ( plus_plus_nat @ SV82 @ ( suc @ SV443 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11333]) ).

thf(11726,plain,
    ! [SV444: nat,SV83: nat] :
      ( ( ( plus_plus_nat @ ( suc @ SV83 ) @ SV444 )
        = ( suc @ ( plus_plus_nat @ SV83 @ SV444 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11334]) ).

thf(11727,plain,
    ! [SV445: nat,SV84: nat] :
      ( ( ! [SY1601: nat] :
            ( ( times_times_nat @ SV84 @ ( minus_minus_nat @ SV445 @ SY1601 ) )
            = ( minus_minus_nat @ ( times_times_nat @ SV84 @ SV445 ) @ ( times_times_nat @ SV84 @ SY1601 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11335]) ).

thf(11728,plain,
    ! [SV446: nat,SV85: nat] :
      ( ( ! [SY1602: nat] :
            ( ( times_times_nat @ ( minus_minus_nat @ SV85 @ SV446 ) @ SY1602 )
            = ( minus_minus_nat @ ( times_times_nat @ SV85 @ SY1602 ) @ ( times_times_nat @ SV446 @ SY1602 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11336]) ).

thf(11729,plain,
    ! [SV447: nat,SV86: nat] :
      ( ( ! [SY1603: nat] :
            ( ( ( times_times_nat @ ( suc @ SV86 ) @ SV447 )
              = ( times_times_nat @ ( suc @ SV86 ) @ SY1603 ) )
            = ( SV447 = SY1603 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11337]) ).

thf(11730,plain,
    ! [SV448: nat,SV88: nat] :
      ( ( ( times_times_nat @ ( suc @ SV88 ) @ SV448 )
        = ( plus_plus_nat @ SV448 @ ( times_times_nat @ SV88 @ SV448 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11339]) ).

thf(11731,plain,
    ! [SV449: num,SV89: nat] :
      ( ( ( power_power_nat @ SV89 @ ( numeral_numeral_nat @ ( bit0 @ SV449 ) ) )
        = ( times_times_nat @ ( power_power_nat @ SV89 @ ( numeral_numeral_nat @ SV449 ) ) @ ( power_power_nat @ SV89 @ ( numeral_numeral_nat @ SV449 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11340]) ).

thf(11732,plain,
    ! [SV450: nat,SV90: nat] :
      ( ( ( power_power_nat @ SV90 @ ( suc @ SV450 ) )
        = ( times_times_nat @ ( power_power_nat @ SV90 @ SV450 ) @ SV90 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11341]) ).

thf(11733,plain,
    ! [SV451: nat,SV91: nat] :
      ( ( ( power_power_nat @ SV91 @ ( suc @ SV451 ) )
        = ( times_times_nat @ SV91 @ ( power_power_nat @ SV91 @ SV451 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11342]) ).

thf(11734,plain,
    ! [SV452: nat,SV92: nat] :
      ( ( ( power_power_nat @ SV92 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV452 ) ) )
        = ( times_times_nat @ SV92 @ ( power_power_nat @ ( power_power_nat @ SV92 @ SV452 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11343]) ).

thf(11735,plain,
    ! [SV453: nat,SV93: nat] :
      ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV93 @ SV453 ) @ SV453 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11344]) ).

thf(11736,plain,
    ! [SV454: nat,SV94: nat] :
      ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV94 @ SV454 ) @ SV94 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11345]) ).

thf(11737,plain,
    ! [SV455: nat,SV95: nat] :
      ( ( ord_less_eq_nat @ SV95 @ ( plus_plus_nat @ SV455 @ SV95 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11346]) ).

thf(11738,plain,
    ! [SV456: nat,SV96: nat] :
      ( ( ord_less_eq_nat @ SV96 @ ( plus_plus_nat @ SV96 @ SV456 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11347]) ).

thf(11739,plain,
    ! [SV457: nat,SV99: nat] :
      ( ( ! [SY1604: nat] :
            ( ( times_times_nat @ SV99 @ ( plus_plus_nat @ SV457 @ SY1604 ) )
            = ( plus_plus_nat @ ( times_times_nat @ SV99 @ SV457 ) @ ( times_times_nat @ SV99 @ SY1604 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11350]) ).

thf(11740,plain,
    ! [SV458: nat,SV100: nat] :
      ( ( ! [SY1605: nat] :
            ( ( times_times_nat @ ( plus_plus_nat @ SV100 @ SV458 ) @ SY1605 )
            = ( plus_plus_nat @ ( times_times_nat @ SV100 @ SY1605 ) @ ( times_times_nat @ SV458 @ SY1605 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11351]) ).

thf(11741,plain,
    ! [SV459: nat,SV104: nat] :
      ( ( ! [SY1606: nat] :
            ( ( plus_plus_nat @ ( ord_max_nat @ SV104 @ SV459 ) @ SY1606 )
            = ( ord_max_nat @ ( plus_plus_nat @ SV104 @ SY1606 ) @ ( plus_plus_nat @ SV459 @ SY1606 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11355]) ).

thf(11742,plain,
    ! [SV460: nat,SV105: nat] :
      ( ( ! [SY1607: nat] :
            ( ( plus_plus_nat @ SV105 @ ( ord_max_nat @ SV460 @ SY1607 ) )
            = ( ord_max_nat @ ( plus_plus_nat @ SV105 @ SV460 ) @ ( plus_plus_nat @ SV105 @ SY1607 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11356]) ).

thf(11743,plain,
    ! [SV461: nat,SV106: nat] :
      ( ( ! [SY1608: nat] :
            ( ( times_times_nat @ ( ord_max_nat @ SV106 @ SV461 ) @ SY1608 )
            = ( ord_max_nat @ ( times_times_nat @ SV106 @ SY1608 ) @ ( times_times_nat @ SV461 @ SY1608 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11357]) ).

thf(11744,plain,
    ! [SV462: nat,SV107: nat] :
      ( ( ! [SY1609: nat] :
            ( ( times_times_nat @ SV107 @ ( ord_max_nat @ SV462 @ SY1609 ) )
            = ( ord_max_nat @ ( times_times_nat @ SV107 @ SV462 ) @ ( times_times_nat @ SV107 @ SY1609 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11358]) ).

thf(11745,plain,
    ! [SV463: nat,SV108: nat] :
      ( ( ! [SY1610: nat] :
            ( ( times_times_nat @ ( plus_plus_nat @ SV108 @ SV463 ) @ SY1610 )
            = ( plus_plus_nat @ ( times_times_nat @ SV108 @ SY1610 ) @ ( times_times_nat @ SV463 @ SY1610 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11359]) ).

thf(11746,plain,
    ! [SV464: nat,SV109: nat] :
      ( ( ! [SY1611: nat] :
            ( ( times_times_nat @ SV109 @ ( plus_plus_nat @ SV464 @ SY1611 ) )
            = ( plus_plus_nat @ ( times_times_nat @ SV109 @ SV464 ) @ ( times_times_nat @ SV109 @ SY1611 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11360]) ).

thf(11747,plain,
    ! [SV465: nat,SV110: nat] :
      ( ( ! [SY1612: nat] :
            ( ( times_times_nat @ ( plus_plus_nat @ SV110 @ SV465 ) @ SY1612 )
            = ( plus_plus_nat @ ( times_times_nat @ SV110 @ SY1612 ) @ ( times_times_nat @ SV465 @ SY1612 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11361]) ).

thf(11748,plain,
    ! [SV466: nat,SV111: nat] :
      ( ( ! [SY1613: nat,SY1614: nat] :
            ( ( plus_plus_nat @ ( times_times_nat @ SV111 @ SV466 ) @ ( plus_plus_nat @ ( times_times_nat @ SY1613 @ SV466 ) @ SY1614 ) )
            = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV111 @ SY1613 ) @ SV466 ) @ SY1614 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11362]) ).

thf(11749,plain,
    ! [SV467: nat,SV112: nat] :
      ( ( ! [SY1615: nat] :
            ( ( times_times_nat @ ( minus_minus_nat @ SV112 @ SV467 ) @ SY1615 )
            = ( minus_minus_nat @ ( times_times_nat @ SV112 @ SY1615 ) @ ( times_times_nat @ SV467 @ SY1615 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11363]) ).

thf(11750,plain,
    ! [SV468: nat,SV113: nat] :
      ( ( ! [SY1616: nat] :
            ( ( times_times_nat @ SV113 @ ( minus_minus_nat @ SV468 @ SY1616 ) )
            = ( minus_minus_nat @ ( times_times_nat @ SV113 @ SV468 ) @ ( times_times_nat @ SV113 @ SY1616 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11364]) ).

thf(11751,plain,
    ! [SV469: nat] :
      ( ( SV469
        = ( times_times_nat @ one_one_nat @ SV469 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11365]) ).

thf(11752,plain,
    ! [SV115: nat] :
      ( ( ! [SV470: nat] :
            ( ( times_times_nat @ SV470 @ SV115 )
            = ( times_times_nat @ SV115 @ SV470 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11367]) ).

thf(11753,plain,
    ! [SV115: nat] :
      ( ( ( ^ [SY1105: nat] : ( times_times_nat @ SY1105 @ SV115 ) )
        = ( times_times_nat @ SV115 ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11367]) ).

thf(11754,plain,
    ! [SV471: nat,SV116: nat] :
      ( ( ( minus_minus_nat @ ( plus_plus_nat @ SV116 @ SV471 ) @ SV471 )
        = SV116 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11368]) ).

thf(11755,plain,
    ! [SV472: nat,SV117: nat] :
      ( ( ! [SY1617: nat] :
            ( ( minus_minus_nat @ ( plus_plus_nat @ SV117 @ SV472 ) @ ( plus_plus_nat @ SY1617 @ SV472 ) )
            = ( minus_minus_nat @ SV117 @ SY1617 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11369]) ).

thf(11756,plain,
    ! [SV473: nat,SV118: nat] :
      ( ( ( minus_minus_nat @ ( plus_plus_nat @ SV118 @ SV473 ) @ SV118 )
        = SV473 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11370]) ).

thf(11757,plain,
    ! [SV474: nat,SV119: nat] :
      ( ( ! [SY1618: nat] :
            ( ( minus_minus_nat @ ( plus_plus_nat @ SV119 @ SV474 ) @ ( plus_plus_nat @ SV119 @ SY1618 ) )
            = ( minus_minus_nat @ SV474 @ SY1618 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11371]) ).

thf(11758,plain,
    ! [SV475: nat,SV120: nat] :
      ( ( ! [SY1619: nat] :
            ( ( ( plus_plus_nat @ SV120 @ SV475 )
              = ( plus_plus_nat @ SV120 @ SY1619 ) )
            = ( SV475 = SY1619 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11372]) ).

thf(11759,plain,
    ! [SV476: nat,SV121: nat] :
      ( ( ! [SY1620: nat] :
            ( ( ( plus_plus_nat @ SV121 @ SV476 )
              = ( plus_plus_nat @ SY1620 @ SV476 ) )
            = ( SV121 = SY1620 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11373]) ).

thf(11760,plain,
    ! [SV477: nat,SV122: nat] :
      ( ( ! [SY1621: nat] :
            ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ SV477 ) @ ( plus_plus_nat @ SV122 @ SY1621 ) )
            = ( ord_less_eq_nat @ SV477 @ SY1621 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11374]) ).

thf(11761,plain,
    ! [SV478: nat,SV123: nat] :
      ( ( ! [SY1622: nat] :
            ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV123 @ SV478 ) @ ( plus_plus_nat @ SY1622 @ SV478 ) )
            = ( ord_less_eq_nat @ SV123 @ SY1622 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11375]) ).

thf(11762,plain,
    ! [SV479: nat,SV124: nat] :
      ( ( ! [SY1623: nat] :
            ( ( ord_less_nat @ ( plus_plus_nat @ SV124 @ SV479 ) @ ( plus_plus_nat @ SV124 @ SY1623 ) )
            = ( ord_less_nat @ SV479 @ SY1623 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11376]) ).

thf(11763,plain,
    ! [SV480: nat,SV125: nat] :
      ( ( ! [SY1624: nat] :
            ( ( ord_less_nat @ ( plus_plus_nat @ SV125 @ SV480 ) @ ( plus_plus_nat @ SY1624 @ SV480 ) )
            = ( ord_less_nat @ SV125 @ SY1624 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11377]) ).

thf(11764,plain,
    ! [SV481: nat,SV128: nat] :
      ( ( ! [SY1625: nat] :
            ( ( times_times_nat @ ( times_times_nat @ SV128 @ SV481 ) @ SY1625 )
            = ( times_times_nat @ SV128 @ ( times_times_nat @ SV481 @ SY1625 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11380]) ).

thf(11765,plain,
    ! [SV482: nat,SV129: nat] :
      ( ( ! [SY1626: nat] :
            ( ( times_times_nat @ ( times_times_nat @ SV129 @ SV482 ) @ SY1626 )
            = ( times_times_nat @ SV129 @ ( times_times_nat @ SV482 @ SY1626 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11381]) ).

thf(11766,plain,
    ! [SV483: nat] :
      ( ( ( times_times_nat @ SV483 )
        = ( ^ [SY1627: nat] : ( times_times_nat @ SY1627 @ SV483 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11382]) ).

thf(11767,plain,
    ! [SV484: nat,SV131: nat] :
      ( ( ! [SY1628: nat] :
            ( ( times_times_nat @ SV131 @ ( times_times_nat @ SV484 @ SY1628 ) )
            = ( times_times_nat @ SV484 @ ( times_times_nat @ SV131 @ SY1628 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11384]) ).

thf(11768,plain,
    ! [SV485: nat,SV132: nat] :
      ( ( ! [SY1629: nat] :
            ( ( plus_plus_nat @ ( plus_plus_nat @ SV132 @ SV485 ) @ SY1629 )
            = ( plus_plus_nat @ SV132 @ ( plus_plus_nat @ SV485 @ SY1629 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11385]) ).

thf(11769,plain,
    ! [SV486: nat,SV133: nat] :
      ( ( ! [SY1630: nat] :
            ( ( plus_plus_nat @ ( plus_plus_nat @ SV133 @ SV486 ) @ SY1630 )
            = ( plus_plus_nat @ SV133 @ ( plus_plus_nat @ SV486 @ SY1630 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11386]) ).

thf(11770,plain,
    ! [SV487: nat] :
      ( ( ( plus_plus_nat @ SV487 )
        = ( ^ [SY1631: nat] : ( plus_plus_nat @ SY1631 @ SV487 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11387]) ).

thf(11771,plain,
    ! [SV488: nat,SV135: nat] :
      ( ( ! [SY1632: nat] :
            ( ( plus_plus_nat @ SV135 @ ( plus_plus_nat @ SV488 @ SY1632 ) )
            = ( plus_plus_nat @ SV488 @ ( plus_plus_nat @ SV135 @ SY1632 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11389]) ).

thf(11772,plain,
    ! [SV489: nat,SV138: nat] :
      ( ( ! [SY1633: nat] :
            ( ( minus_minus_nat @ ( minus_minus_nat @ SV138 @ SV489 ) @ SY1633 )
            = ( minus_minus_nat @ SV138 @ ( plus_plus_nat @ SV489 @ SY1633 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11392]) ).

thf(11773,plain,
    ! [SV490: nat,SV139: nat] :
      ( ( ! [SY1634: nat] :
            ( ( plus_plus_nat @ ( ord_max_nat @ SV139 @ SV490 ) @ SY1634 )
            = ( ord_max_nat @ ( plus_plus_nat @ SV139 @ SY1634 ) @ ( plus_plus_nat @ SV490 @ SY1634 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11393]) ).

thf(11774,plain,
    ! [SV491: nat,SV140: nat] :
      ( ( ! [SY1635: nat] :
            ( ( plus_plus_nat @ SV140 @ ( ord_max_nat @ SV491 @ SY1635 ) )
            = ( ord_max_nat @ ( plus_plus_nat @ SV140 @ SV491 ) @ ( plus_plus_nat @ SV140 @ SY1635 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11394]) ).

thf(11775,plain,
    ! [SV492: nat] :
      ( ( ( vEBT_VEBT_low @ SV492 )
        = ( ^ [SY1636: nat] : ( modulo_modulo_nat @ SV492 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1636 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11395]) ).

thf(11776,plain,
    ! [SV493: nat,SV142: nat] :
      ( ( ! [SY1637: nat] :
            ( ( ( times_times_nat @ SV142 @ SV493 )
              = ( times_times_nat @ SY1637 @ SV493 ) )
            = ( ( SV493 = zero_zero_nat )
              | ( SV142 = SY1637 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11397]) ).

thf(11777,plain,
    ! [SV494: nat,SV143: nat] :
      ( ( ! [SY1638: nat] :
            ( ( ( times_times_nat @ SV143 @ SV494 )
              = ( times_times_nat @ SV143 @ SY1638 ) )
            = ( ( SV143 = zero_zero_nat )
              | ( SV494 = SY1638 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11398]) ).

thf(11778,plain,
    ! [SV495: nat,SV144: nat] :
      ( ( ( ( times_times_nat @ SV144 @ SV495 )
          = zero_zero_nat )
        = ( ( SV144 = zero_zero_nat )
          | ( SV495 = zero_zero_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11399]) ).

thf(11779,plain,
    ! [SV496: nat,SV148: nat] :
      ( ( ( SV148
          = ( plus_plus_nat @ SV148 @ SV496 ) )
        = ( SV496 = zero_zero_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11403]) ).

thf(11780,plain,
    ! [SV497: nat,SV149: nat] :
      ( ( ( SV149
          = ( plus_plus_nat @ SV497 @ SV149 ) )
        = ( SV497 = zero_zero_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11404]) ).

thf(11781,plain,
    ! [SV498: nat,SV150: nat] :
      ( ( ( ( plus_plus_nat @ SV150 @ SV498 )
          = SV150 )
        = ( SV498 = zero_zero_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11405]) ).

thf(11782,plain,
    ! [SV499: nat,SV151: nat] :
      ( ( ( ( plus_plus_nat @ SV151 @ SV499 )
          = SV499 )
        = ( SV151 = zero_zero_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11406]) ).

thf(11783,plain,
    ! [SV500: nat,SV157: nat] :
      ( ( ( modulo_modulo_nat @ ( plus_plus_nat @ SV157 @ SV500 ) @ SV500 )
        = ( modulo_modulo_nat @ SV157 @ SV500 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11412]) ).

thf(11784,plain,
    ! [SV501: nat,SV158: nat] :
      ( ( ( modulo_modulo_nat @ ( plus_plus_nat @ SV158 @ SV501 ) @ SV158 )
        = ( modulo_modulo_nat @ SV501 @ SV158 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11413]) ).

thf(11785,plain,
    ! [SV502: nat,SV160: nat] :
      ( ( ! [SY1639: nat] :
            ( ( ( times_times_nat @ SV160 @ SV502 )
              = ( times_times_nat @ SY1639 @ SV502 ) )
            = ( ( SV160 = SY1639 )
              | ( SV502 = zero_zero_nat ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11415]) ).

thf(11786,plain,
    ! [SV503: nat,SV161: nat] :
      ( ( ! [SY1640: nat] :
            ( ( ( times_times_nat @ SV161 @ SV503 )
              = ( times_times_nat @ SV161 @ SY1640 ) )
            = ( ( SV503 = SY1640 )
              | ( SV161 = zero_zero_nat ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11416]) ).

thf(11787,plain,
    ! [SV504: nat,SV163: nat] :
      ( ( ( ( times_times_nat @ SV163 @ SV504 )
          = zero_zero_nat )
        = ( ( SV163 = zero_zero_nat )
          | ( SV504 = zero_zero_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11418]) ).

thf(11788,plain,
    ! [SV505: nat,SV165: nat] :
      ( ( ! [SY1641: nat] :
            ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ SV165 @ SV505 ) @ SY1641 ) @ SV165 )
            = ( modulo_modulo_nat @ SY1641 @ SV165 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11420]) ).

thf(11789,plain,
    ! [SV506: nat,SV166: nat] :
      ( ( ! [SY1642: nat] :
            ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ SV166 @ SV506 ) @ SY1642 ) @ SV506 )
            = ( modulo_modulo_nat @ SY1642 @ SV506 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11421]) ).

thf(11790,plain,
    ! [SV507: nat,SV167: nat] :
      ( ( ! [SY1643: nat] :
            ( ( modulo_modulo_nat @ ( plus_plus_nat @ SV167 @ ( times_times_nat @ SV507 @ SY1643 ) ) @ SV507 )
            = ( modulo_modulo_nat @ SV167 @ SV507 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11422]) ).

thf(11791,plain,
    ! [SV508: nat,SV168: nat] :
      ( ( ! [SY1644: nat] :
            ( ( modulo_modulo_nat @ ( plus_plus_nat @ SV168 @ ( times_times_nat @ SV508 @ SY1644 ) ) @ SY1644 )
            = ( modulo_modulo_nat @ SV168 @ SY1644 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11423]) ).

thf(11792,plain,
    ! [SV169: nat] :
      ( ( ~ ( ( ( power_power_nat @ SV169 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
              = zero_zero_nat )
            | ( SV169 = zero_zero_nat ) )
        | ~ ( ( ( power_power_nat @ SV169 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
             != zero_zero_nat )
            | ( SV169 != zero_zero_nat ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11424]) ).

thf(11793,plain,
    ! [SV169: nat] :
      ( ( ( ( power_power_nat @ SV169 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = zero_zero_nat )
        = ( SV169 = zero_zero_nat ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11424]) ).

thf(11794,plain,
    ! [SV509: nat,SV170: nat] :
      ( ( ! [SY1645: nat] :
            ( ( modulo_modulo_nat @ ( times_times_nat @ SV170 @ ( modulo_modulo_nat @ SV509 @ SY1645 ) ) @ SY1645 )
            = ( modulo_modulo_nat @ ( times_times_nat @ SV170 @ SV509 ) @ SY1645 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11425]) ).

thf(11795,plain,
    ! [SV510: nat,SV171: nat] :
      ( ( ! [SY1646: nat] :
            ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ SV171 @ SV510 ) @ SY1646 ) @ SV510 )
            = ( modulo_modulo_nat @ ( times_times_nat @ SV171 @ SY1646 ) @ SV510 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11426]) ).

thf(11796,plain,
    ! [SV511: nat,SV172: nat] :
      ( ( ! [SY1647: nat] :
            ( ( times_times_nat @ SV172 @ ( modulo_modulo_nat @ SV511 @ SY1647 ) )
            = ( modulo_modulo_nat @ ( times_times_nat @ SV172 @ SV511 ) @ ( times_times_nat @ SV172 @ SY1647 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11427]) ).

thf(11797,plain,
    ! [SV512: nat,SV173: nat] :
      ( ( ! [SY1648: nat] :
            ( ( modulo_modulo_nat @ ( times_times_nat @ SV173 @ SV512 ) @ ( times_times_nat @ SY1648 @ SV512 ) )
            = ( times_times_nat @ ( modulo_modulo_nat @ SV173 @ SY1648 ) @ SV512 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11428]) ).

thf(11798,plain,
    ! [SV513: nat,SV174: nat] :
      ( ( ! [SY1649: nat] :
            ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ SV174 @ SV513 ) @ ( modulo_modulo_nat @ SY1649 @ SV513 ) ) @ SV513 )
            = ( modulo_modulo_nat @ ( times_times_nat @ SV174 @ SY1649 ) @ SV513 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11429]) ).

thf(11799,plain,
    ! [SV514: nat,SV175: nat] :
      ( ( ! [SY1650: nat] :
            ( ( modulo_modulo_nat @ ( plus_plus_nat @ SV175 @ ( modulo_modulo_nat @ SV514 @ SY1650 ) ) @ SY1650 )
            = ( modulo_modulo_nat @ ( plus_plus_nat @ SV175 @ SV514 ) @ SY1650 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11430]) ).

thf(11800,plain,
    ! [SV515: nat,SV176: nat] :
      ( ( ! [SY1651: nat] :
            ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ SV176 @ SV515 ) @ SY1651 ) @ SV515 )
            = ( modulo_modulo_nat @ ( plus_plus_nat @ SV176 @ SY1651 ) @ SV515 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11431]) ).

thf(11801,plain,
    ! [SV516: nat,SV177: nat] :
      ( ( ! [SY1652: nat] :
            ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ SV177 @ SV516 ) @ ( modulo_modulo_nat @ SY1652 @ SV516 ) ) @ SV516 )
            = ( modulo_modulo_nat @ ( plus_plus_nat @ SV177 @ SY1652 ) @ SV516 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11432]) ).

thf(11802,plain,
    ! [SV517: nat,SV178: nat] :
      ( ( ! [SY1653: nat] :
            ( ( modulo_modulo_nat @ ( power_power_nat @ ( modulo_modulo_nat @ SV178 @ SV517 ) @ SY1653 ) @ SV517 )
            = ( modulo_modulo_nat @ ( power_power_nat @ SV178 @ SY1653 ) @ SV517 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11433]) ).

thf(11803,plain,
    ! [SV518: num,SV179: num] :
      ( ( ! [SY1654: num] :
            ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV179 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) )
              = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SY1654 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) ) )
            = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV179 ) @ ( numeral_numeral_nat @ SV518 ) )
              = ( modulo_modulo_nat @ ( numeral_numeral_nat @ SY1654 ) @ ( numeral_numeral_nat @ SV518 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11434]) ).

thf(11804,plain,
    ! [SV519: num,SV180: num] :
      ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV180 ) @ ( numeral_numeral_nat @ one ) )
        = ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV519 ) @ ( numeral_numeral_nat @ one ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11435]) ).

thf(11805,plain,
    ! [SV520: nat,SV185: nat] :
      ( ( ! [SY1655: nat] :
            ( ( ( times_times_nat @ SV185 @ SV520 )
              = ( times_times_nat @ SV185 @ SY1655 ) )
            = ( ( SV185 = zero_zero_nat )
              | ( SV520 = SY1655 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11440]) ).

thf(11806,plain,
    ! [SV521: nat] :
      ( ( zero_zero_nat
        = ( times_times_nat @ zero_zero_nat @ SV521 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11441]) ).

thf(11807,plain,
    ! [SV522: nat,SV187: nat] :
      ( ( ! [SY1656: nat] :
            ( ( divide_divide_nat @ ( plus_plus_nat @ SV187 @ SV522 ) @ SY1656 )
            = ( plus_plus_nat @ ( plus_plus_nat @ ( divide_divide_nat @ SV187 @ SY1656 ) @ ( divide_divide_nat @ SV522 @ SY1656 ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ SV187 @ SY1656 ) @ ( modulo_modulo_nat @ SV522 @ SY1656 ) ) @ SY1656 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11443]) ).

thf(11808,plain,
    ! [SV523: nat,SV188: nat] :
      ( ( ! [SY1657: nat] :
            ( ( divide_divide_nat @ ( times_times_nat @ SV188 @ SV523 ) @ SY1657 )
            = ( plus_plus_nat @ ( times_times_nat @ SV188 @ ( divide_divide_nat @ SV523 @ SY1657 ) ) @ ( divide_divide_nat @ ( times_times_nat @ SV188 @ ( modulo_modulo_nat @ SV523 @ SY1657 ) ) @ SY1657 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11444]) ).

thf(11809,plain,
    ! [SV524: nat,SV189: nat] :
      ( ( ( plus_plus_nat @ ( times_times_nat @ SV189 @ ( divide_divide_nat @ SV524 @ SV189 ) ) @ ( modulo_modulo_nat @ SV524 @ SV189 ) )
        = SV524 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11445]) ).

thf(11810,plain,
    ! [SV525: nat,SV190: nat] :
      ( ( ( plus_plus_nat @ ( modulo_modulo_nat @ SV190 @ SV525 ) @ ( times_times_nat @ SV525 @ ( divide_divide_nat @ SV190 @ SV525 ) ) )
        = SV190 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11446]) ).

thf(11811,plain,
    ! [SV526: nat,SV191: nat] :
      ( ( ( plus_plus_nat @ ( modulo_modulo_nat @ SV191 @ SV526 ) @ ( times_times_nat @ ( divide_divide_nat @ SV191 @ SV526 ) @ SV526 ) )
        = SV191 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11447]) ).

thf(11812,plain,
    ! [SV527: nat,SV192: nat] :
      ( ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ SV192 @ SV527 ) @ SV527 ) @ ( modulo_modulo_nat @ SV192 @ SV527 ) )
        = SV192 )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11448]) ).

thf(11813,plain,
    ! [SV528: nat,SV193: nat] :
      ( ( SV193
        = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ SV193 @ SV528 ) @ SV528 ) @ ( modulo_modulo_nat @ SV193 @ SV528 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11449]) ).

thf(11814,plain,
    ! [SV529: nat,SV194: nat] :
      ( ( ! [SY1658: nat] :
            ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ SV194 @ SV529 ) @ SV529 ) @ ( modulo_modulo_nat @ SV194 @ SV529 ) ) @ SY1658 )
            = ( plus_plus_nat @ SV194 @ SY1658 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11450]) ).

thf(11815,plain,
    ! [SV530: nat,SV195: nat] :
      ( ( ! [SY1659: nat] :
            ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ SV195 @ ( divide_divide_nat @ SV530 @ SV195 ) ) @ ( modulo_modulo_nat @ SV530 @ SV195 ) ) @ SY1659 )
            = ( plus_plus_nat @ SV530 @ SY1659 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11451]) ).

thf(11816,plain,
    ! [SV531: nat,SV196: nat] :
      ( ( ! [SY1660: nat] :
            ( ( modulo_modulo_nat @ SV196 @ ( times_times_nat @ SV531 @ SY1660 ) )
            = ( plus_plus_nat @ ( times_times_nat @ SV531 @ ( modulo_modulo_nat @ ( divide_divide_nat @ SV196 @ SV531 ) @ SY1660 ) ) @ ( modulo_modulo_nat @ SV196 @ SV531 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11452]) ).

thf(11817,plain,
    ! [SV532: nat,SV197: nat] :
      ( ( ! [SY1661: nat] :
            ( ( modulo_modulo_nat @ ( divide_divide_nat @ SV197 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV532 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1661 ) )
            = ( divide_divide_nat @ ( modulo_modulo_nat @ SV197 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV532 @ SY1661 ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV532 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11453]) ).

thf(11818,plain,
    ! [SV533: nat,SV198: nat] :
      ( ( SV198
        = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ SV198 @ SV533 ) @ SV533 ) @ ( modulo_modulo_nat @ SV198 @ SV533 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11454]) ).

thf(11819,plain,
    ! [SV534: num,SV199: num] :
      ( ( ( ( bit0 @ SV199 )
          = ( bit0 @ SV534 ) )
        = ( SV199 = SV534 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11455]) ).

thf(11820,plain,
    ! [SV535: nat,SV201: nat] :
      ( ( ( dvd_dvd_nat @ SV201 @ ( plus_plus_nat @ SV535 @ SV201 ) )
        = ( dvd_dvd_nat @ SV201 @ SV535 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11457]) ).

thf(11821,plain,
    ! [SV536: nat,SV202: nat] :
      ( ( ( dvd_dvd_nat @ SV202 @ ( plus_plus_nat @ SV202 @ SV536 ) )
        = ( dvd_dvd_nat @ SV202 @ SV536 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11458]) ).

thf(11822,plain,
    ! [SV537: nat,SV203: nat] :
      ( ( ! [SY1662: nat] :
            ( ( dvd_dvd_nat @ SV203 @ ( plus_plus_nat @ SV537 @ ( times_times_nat @ SY1662 @ SV203 ) ) )
            = ( dvd_dvd_nat @ SV203 @ SV537 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11459]) ).

thf(11823,plain,
    ! [SV538: nat,SV204: nat] :
      ( ( ! [SY1663: nat] :
            ( ( dvd_dvd_nat @ SV204 @ ( plus_plus_nat @ ( times_times_nat @ SV538 @ SV204 ) @ SY1663 ) )
            = ( dvd_dvd_nat @ SV204 @ SY1663 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11460]) ).

thf(11824,plain,
    ! [SV539: nat,SV205: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ SV205 @ SV539 ) )
        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11461]) ).

thf(11825,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11462]) ).

thf(11826,plain,
    ! [SV541: nat,SV207: nat] :
      ( ( dvd_dvd_nat @ SV207 @ ( times_times_nat @ SV541 @ SV207 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11463]) ).

thf(11827,plain,
    ! [SV542: nat,SV208: nat] :
      ( ( dvd_dvd_nat @ SV208 @ ( times_times_nat @ SV208 @ SV542 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11464]) ).

thf(11828,plain,
    ! [SV543: int,SV209: nat] :
      ( ( ! [SY1664: nat,SY1665: int,SY1666: int] :
            ( ( bit_concat_bit @ SV209 @ SV543 @ ( bit_concat_bit @ SY1664 @ SY1665 @ SY1666 ) )
            = ( bit_concat_bit @ ( plus_plus_nat @ SY1664 @ SV209 ) @ ( bit_concat_bit @ SV209 @ SV543 @ SY1665 ) @ SY1666 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11465]) ).

thf(11829,plain,
    ! [SV544: set_nat,SV211: nat > nat] :
      ( ( ! [SY1667: nat > nat,SY1668: set_nat] :
            ( ( times_times_nat @ ( groups3542108847815614940at_nat @ SV211 @ SV544 ) @ ( groups3542108847815614940at_nat @ SY1667 @ SY1668 ) )
            = ( groups3542108847815614940at_nat
              @ ^ [SY1228: nat] :
                  ( groups3542108847815614940at_nat
                  @ ^ [SY1229: nat] : ( times_times_nat @ ( SV211 @ SY1228 ) @ ( SY1667 @ SY1229 ) )
                  @ SY1668 )
              @ SV544 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11467]) ).

thf(11830,plain,
    ! [SV545: set_nat,SV212: nat > nat] :
      ( ( ! [SY1671: nat] :
            ( ( times_times_nat @ ( groups3542108847815614940at_nat @ SV212 @ SV545 ) @ SY1671 )
            = ( groups3542108847815614940at_nat
              @ ^ [SY1232: nat] : ( times_times_nat @ ( SV212 @ SY1232 ) @ SY1671 )
              @ SV545 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11468]) ).

thf(11831,plain,
    ! [SV546: nat > nat,SV213: nat] :
      ( ( ! [SY1673: set_nat] :
            ( ( times_times_nat @ SV213 @ ( groups3542108847815614940at_nat @ SV546 @ SY1673 ) )
            = ( groups3542108847815614940at_nat
              @ ^ [SY1674: nat] : ( times_times_nat @ SV213 @ ( SV546 @ SY1674 ) )
              @ SY1673 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11469]) ).

thf(11832,plain,
    ! [SV547: nat > nat,SV214: nat > nat] :
      ( ( ! [SY1675: set_nat] :
            ( ( groups3542108847815614940at_nat
              @ ^ [SY1676: nat] : ( plus_plus_nat @ ( SV214 @ SY1676 ) @ ( SV547 @ SY1676 ) )
              @ SY1675 )
            = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ SV214 @ SY1675 ) @ ( groups3542108847815614940at_nat @ SV547 @ SY1675 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11470]) ).

thf(11833,plain,
    ! [SV548: nat,SV215: nat] :
      ( ( ( SV215
          = ( plus_plus_nat @ SV215 @ SV548 ) )
        = ( SV548 = zero_zero_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11471]) ).

thf(11834,plain,
    ! [SV549: nat,SV216: nat] :
      ( ( ! [SY1677: nat,SY1678: nat] :
            ( ( ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV549 ) @ ( times_times_nat @ SY1677 @ SY1678 ) )
              = ( plus_plus_nat @ ( times_times_nat @ SV216 @ SY1678 ) @ ( times_times_nat @ SY1677 @ SV549 ) ) )
            = ( ( SV216 = SY1677 )
              | ( SV549 = SY1678 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11472]) ).

thf(11835,plain,
    ! [SV550: num,SV217: nat] :
      ( ( ( power_power_nat @ SV217 @ ( numeral_numeral_nat @ ( bit1 @ SV550 ) ) )
        = ( times_times_nat @ ( times_times_nat @ SV217 @ ( power_power_nat @ SV217 @ ( numeral_numeral_nat @ SV550 ) ) ) @ ( power_power_nat @ SV217 @ ( numeral_numeral_nat @ SV550 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11473]) ).

thf(11836,plain,
    ! [SV551: nat,SV221: nat] :
      ( ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ SV221 @ SV551 ) )
        = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ SV221 ) @ ( semiri1316708129612266289at_nat @ SV551 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11477]) ).

thf(11837,plain,
    ! [SV552: nat,SV222: nat] :
      ( ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ SV222 @ SV552 ) )
        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ SV222 ) @ ( semiri1316708129612266289at_nat @ SV552 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11478]) ).

thf(11838,plain,
    ! [SV553: nat,SV223: nat] :
      ( ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ SV223 @ SV553 ) )
        = ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV223 ) @ SV553 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11479]) ).

thf(11839,plain,
    ! [SV554: nat,SV224: nat] :
      ( ( ! [SY1679: nat] :
            ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV224 ) @ SV554 )
              = ( semiri1316708129612266289at_nat @ SY1679 ) )
            = ( ( power_power_nat @ SV224 @ SV554 )
              = SY1679 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11480]) ).

thf(11840,plain,
    ! [SV555: nat,SV225: nat] :
      ( ( ! [SY1680: nat] :
            ( ( ( semiri1316708129612266289at_nat @ SV225 )
              = ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV555 ) @ SY1680 ) )
            = ( SV225
              = ( power_power_nat @ SV555 @ SY1680 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11481]) ).

thf(11841,plain,
    ! [SV556: nat,SV226: num] :
      ( ( ! [SY1681: nat] :
            ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
              = ( semiri1316708129612266289at_nat @ SY1681 ) )
            = ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
              = SY1681 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11482]) ).

thf(11842,plain,
    ! [SV557: num,SV227: nat] :
      ( ( ! [SY1682: nat] :
            ( ( ( semiri1316708129612266289at_nat @ SV227 )
              = ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SY1682 ) )
            = ( SV227
              = ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SY1682 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11483]) ).

thf(11843,plain,
    ! [SV558: nat,SV228: nat] :
      ( ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ SV228 ) @ SV558 )
        = ( times_times_nat @ SV558 @ ( semiri1316708129612266289at_nat @ SV228 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11484]) ).

thf(11844,plain,
    ! [SV559: nat,SV229: nat] :
      ( ( ! [SY1683: nat] :
            ( ( divide_divide_nat @ SV229 @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ SV559 ) @ ( semiri1316708129612266289at_nat @ SY1683 ) ) )
            = ( divide_divide_nat @ ( divide_divide_nat @ SV229 @ ( semiri1316708129612266289at_nat @ SV559 ) ) @ ( semiri1316708129612266289at_nat @ SY1683 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11485]) ).

thf(11845,plain,
    ! [SV560: nat,SV230: nat] :
      ( ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ SV230 @ SV560 ) )
        = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ SV230 ) @ ( semiri1316708129612266289at_nat @ SV560 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11486]) ).

thf(11846,plain,
    ! [SV561: nat,SV231: nat > real] :
      ( ( ( summable_real
          @ ^ [SY1684: nat] : ( SV231 @ ( plus_plus_nat @ SY1684 @ SV561 ) ) )
        = ( summable_real @ SV231 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11487]) ).

thf(11847,plain,
    ! [SV562: nat,SV232: nat > complex] :
      ( ( ( summable_complex
          @ ^ [SY1685: nat] : ( SV232 @ ( plus_plus_nat @ SY1685 @ SV562 ) ) )
        = ( summable_complex @ SV232 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11488]) ).

thf(11848,plain,
    ! [SV563: nat > nat,SV233: nat > nat] :
      ( ( ! [SY1686: set_nat] :
            ( ( groups708209901874060359at_nat
              @ ^ [SY1687: nat] : ( times_times_nat @ ( SV233 @ SY1687 ) @ ( SV563 @ SY1687 ) )
              @ SY1686 )
            = ( times_times_nat @ ( groups708209901874060359at_nat @ SV233 @ SY1686 ) @ ( groups708209901874060359at_nat @ SV563 @ SY1686 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11489]) ).

thf(11849,plain,
    ! [SV564: set_nat,SV234: nat > nat] :
      ( ( ! [SY1688: nat] :
            ( ( power_power_nat @ ( groups708209901874060359at_nat @ SV234 @ SV564 ) @ SY1688 )
            = ( groups708209901874060359at_nat
              @ ^ [SY1268: nat] : ( power_power_nat @ ( SV234 @ SY1268 ) @ SY1688 )
              @ SV564 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11490]) ).

thf(11850,plain,
    ! [SV565: nat,SV235: nat] :
      ( ( ! [SY1690: nat] :
            ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ SV235 @ SV565 ) @ SY1690 ) @ ( plus_plus_nat @ SV235 @ SY1690 ) ) @ ( binomial @ ( plus_plus_nat @ SV235 @ SY1690 ) @ SY1690 ) )
            = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ SV235 @ SV565 ) @ SY1690 ) @ SY1690 ) @ ( binomial @ ( plus_plus_nat @ SV235 @ SV565 ) @ SV235 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11491]) ).

thf(11851,plain,
    ! [SV566: nat,SV236: nat] :
      ( ( ! [SY1691: real] :
            ( ( root @ ( times_times_nat @ SV236 @ SV566 ) @ SY1691 )
            = ( root @ SV236 @ ( root @ SV566 @ SY1691 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11492]) ).

thf(11852,plain,
    ! [SV567: nat] :
      ( ( ( bit_se547839408752420682it_nat @ SV567 )
        = ( ^ [SY1692: nat] : ( times_times_nat @ SY1692 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV567 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11495]) ).

thf(11853,plain,
    ! [SV568: nat] :
      ( ( ( bit_se8570568707652914677it_nat @ SV568 )
        = ( ^ [SY1693: nat] : ( divide_divide_nat @ SY1693 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV568 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11497]) ).

thf(11854,plain,
    ! [SV569: nat,SV242: nat] :
      ( ( ! [SY1694: nat] :
            ( ( times_times_nat @ SV242 @ ( gcd_gcd_nat @ SV569 @ SY1694 ) )
            = ( gcd_gcd_nat @ ( times_times_nat @ SV242 @ SV569 ) @ ( times_times_nat @ SV242 @ SY1694 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11500]) ).

thf(11855,plain,
    ! [SV243: $o] :
      ( ( ( SV243 = $true )
        = $true )
      | ( ( SV243 = $false )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11501]) ).

thf(11856,plain,
    ( ( ( $true = $true )
      = $true )
    | ( ( $true = $false )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11502]) ).

thf(11857,plain,
    ( ( ( $false = $true )
      = $true )
    | ( ( $false = $false )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11503]) ).

thf(11858,plain,
    ! [SV570: nat,SV244: nat] :
      ( ( ! [SY1695: nat] :
            ( ~ ( ( SV244 != zero_zero_nat ) )
            | ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ SV244 @ SV570 ) @ SY1695 ) @ SV244 )
              = ( plus_plus_nat @ SV570 @ ( divide_divide_nat @ SY1695 @ SV244 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11505]) ).

thf(11859,plain,
    ! [SV571: nat,SV245: nat] :
      ( ( ! [SY1696: nat] :
            ( ~ ( ord_less_nat @ SV245 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV571 ) )
            | ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ SY1696 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV571 ) ) @ SV245 ) @ SV571 )
              = SV245 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11506]) ).

thf(11860,plain,
    ! [SV572: nat,SV246: nat] :
      ( ( ! [SY1697: nat] :
            ( ~ ( dvd_dvd_nat @ SV246 @ SV572 )
            | ( ( divide_divide_nat @ ( plus_plus_nat @ SV572 @ SY1697 ) @ SV246 )
              = ( plus_plus_nat @ ( divide_divide_nat @ SV572 @ SV246 ) @ ( divide_divide_nat @ SY1697 @ SV246 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11507]) ).

thf(11861,plain,
    ( ( ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ maxs ) @ sK1_SX0 ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[11508]) ).

thf(11862,plain,
    ! [SV573: nat,SV247: nat] :
      ( ( ! [SY1698: nat] :
            ( ~ ( ord_less_nat @ SV247 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV573 @ SY1698 ) ) )
            | ( ord_less_nat @ ( vEBT_VEBT_high @ SV247 @ SV573 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1698 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11509]) ).

thf(11863,plain,
    ! [SV574: nat,SV248: nat] :
      ( ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV248 ) )
       != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV574 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11510]) ).

thf(11864,plain,
    ! [SV575: nat,SV249: nat] :
      ( ( ! [SY1699: nat] :
            ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV249 @ SV575 ) @ SY1699 )
            | ( ord_less_nat @ SV249 @ SY1699 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11511]) ).

thf(11865,plain,
    ! [SV576: nat,SV250: nat] :
      ( ( ! [SY1700: nat] :
            ( ( ( times_times_nat @ SV250 @ SV576 )
             != ( times_times_nat @ SV576 @ SV250 ) )
            | ( ( times_times_nat @ ( power_power_nat @ SV250 @ SY1700 ) @ SV576 )
              = ( times_times_nat @ SV576 @ ( power_power_nat @ SV250 @ SY1700 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11512]) ).

thf(11866,plain,
    ! [SV577: nat,SV251: nat] :
      ( ( ( ( times_times_nat @ SV251 @ SV577 )
         != zero_zero_nat )
        | ( SV251 = zero_zero_nat )
        | ( SV577 = zero_zero_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11513]) ).

thf(11867,plain,
    ! [SV578: nat,SV252: nat] :
      ( ( ! [SY1701: nat] :
            ( ~ ( ( SV252 != zero_zero_nat ) )
            | ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ SV578 @ SV252 ) @ SY1701 ) @ SV252 )
              = ( plus_plus_nat @ SV578 @ ( divide_divide_nat @ SY1701 @ SV252 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11514]) ).

thf(11868,plain,
    ! [SV579: nat,SV253: nat] :
      ( ( ! [SY1702: nat,SY1703: nat] :
            ( ~ ( ord_less_nat @ SV253 @ SV579 )
            | ( ( plus_plus_nat @ SY1702 @ SV579 )
             != ( plus_plus_nat @ SV253 @ SY1703 ) )
            | ( ord_less_nat @ SY1702 @ SY1703 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11515]) ).

thf(11869,plain,
    ! [SV580: nat,SV254: nat] :
      ( ( ! [SY1704: nat] :
            ( ~ ( dvd_dvd_nat @ ( times_times_nat @ SV254 @ SV580 ) @ SY1704 )
            | ( dvd_dvd_nat @ SV254 @ ( divide_divide_nat @ SY1704 @ SV580 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11516]) ).

thf(11870,plain,
    ! [SV581: nat,SV255: nat] :
      ( ( ! [SY1705: nat] :
            ~ ( ~ ( ( SV255 != zero_zero_nat )
                  | ( ( divide_divide_nat @ ( times_times_nat @ SV255 @ SV581 ) @ ( times_times_nat @ SV255 @ SY1705 ) )
                    = zero_zero_nat ) )
              | ~ ( ~ ( ( SV255 != zero_zero_nat ) )
                  | ( ( divide_divide_nat @ ( times_times_nat @ SV255 @ SV581 ) @ ( times_times_nat @ SV255 @ SY1705 ) )
                    = ( divide_divide_nat @ SV581 @ SY1705 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11517]) ).

thf(11871,plain,
    ! [SV582: nat,SV256: nat] :
      ( ( ~ ( ( SV256 != zero_zero_nat ) )
        | ( ( divide_divide_nat @ ( times_times_nat @ SV256 @ SV582 ) @ SV256 )
          = SV582 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11518]) ).

thf(11872,plain,
    ! [SV583: nat,SV257: nat] :
      ( ( ! [SY1706: nat] :
            ( ~ ( ( SV257 != zero_zero_nat ) )
            | ( ( ( times_times_nat @ SV583 @ SV257 )
                = ( times_times_nat @ SY1706 @ SV257 ) )
              = ( SV583 = SY1706 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11519]) ).

thf(11873,plain,
    ! [SV584: nat,SV258: nat] :
      ( ( ! [SY1707: nat] :
            ( ~ ( dvd_dvd_nat @ SV258 @ ( times_times_nat @ SV584 @ SY1707 ) )
            | ~ ! [SY1708: nat,SY1709: nat] :
                  ( ( SV258
                   != ( times_times_nat @ SY1708 @ SY1709 ) )
                  | ~ ( dvd_dvd_nat @ SY1708 @ SV584 )
                  | ~ ( dvd_dvd_nat @ SY1709 @ SY1707 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11520]) ).

thf(11874,plain,
    ! [SV585: nat,SV259: nat] :
      ( ( ~ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV259 @ SV585 ) )
             != zero_zero_nat ) )
        | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV585 )
         != zero_zero_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11521]) ).

thf(11875,plain,
    ( ( ~ ( vEBT_V8194947554948674370ptions @ summary @ maxs ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[11522]) ).

thf(11876,plain,
    ( ( ~ ( ( maxs
           != ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) )
    = $false ),
    inference(extcnf_or_neg,[status(thm)],[11522]) ).

thf(11877,plain,
    ! [SV586: nat,SV260: nat] :
      ( ( ! [SY1710: nat,SY1711: nat] :
            ( ~ ~ ( ( SV260 != SV586 )
                  | ( SY1710 != SY1711 ) )
            | ( ( plus_plus_nat @ SV260 @ SY1710 )
              = ( plus_plus_nat @ SV586 @ SY1711 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11523]) ).

thf(11878,plain,
    ! [SV587: nat,SV261: nat] :
      ( ( ! [SY1712: nat] :
            ( ~ ( dvd_dvd_nat @ SV261 @ SV587 )
            | ~ ( dvd_dvd_nat @ SV261 @ SY1712 )
            | ( ( divide_divide_nat @ ( plus_plus_nat @ SV587 @ SY1712 ) @ SV261 )
              = ( plus_plus_nat @ ( divide_divide_nat @ SV587 @ SV261 ) @ ( divide_divide_nat @ SY1712 @ SV261 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11524]) ).

thf(11879,plain,
    ! [SV588: nat,SV262: nat] :
      ( ( ! [SY1713: nat] :
            ( ~ ( dvd_dvd_nat @ SV262 @ SV588 )
            | ~ ( dvd_dvd_nat @ SV588 @ SY1713 )
            | ( ( divide_divide_nat @ ( divide_divide_nat @ SY1713 @ SV262 ) @ ( divide_divide_nat @ SV588 @ SV262 ) )
              = ( divide_divide_nat @ SY1713 @ SV588 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11525]) ).

thf(11880,plain,
    ! [SV589: nat,SV263: nat] :
      ( ( ! [SY1714: nat,SY1715: nat] :
            ( ( SV263
             != ( plus_plus_nat @ SV589 @ SY1714 ) )
            | ( ( plus_plus_nat @ SV263 @ SY1715 )
              = ( plus_plus_nat @ SV589 @ ( plus_plus_nat @ SY1714 @ SY1715 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11526]) ).

thf(11881,plain,
    ! [SV590: nat,SV264: nat > complex] :
      ( ( ~ ( summable_complex @ SV264 )
        | ( summable_complex
          @ ^ [SY1716: nat] : ( SV264 @ ( plus_plus_nat @ SY1716 @ SV590 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11527]) ).

thf(11882,plain,
    ! [SV591: nat,SV265: nat] :
      ( ( ! [SY1717: nat] :
            ( ~ ( ord_less_eq_nat @ SV265 @ SV591 )
            | ( ord_less_eq_nat @ ( times_times_nat @ SV265 @ SY1717 ) @ ( times_times_nat @ SV591 @ SY1717 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11528]) ).

thf(11883,plain,
    ! [SV592: nat,SV266: nat] :
      ( ( ! [SY1718: nat] :
            ( ~ ( ( SV266 != zero_zero_nat ) )
            | ( ( divide_divide_nat @ ( times_times_nat @ SV592 @ SV266 ) @ ( times_times_nat @ SY1718 @ SV266 ) )
              = ( divide_divide_nat @ SV592 @ SY1718 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11529]) ).

thf(11884,plain,
    ! [SV267: num] :
      ( ( one
        = ( bit1 @ SV267 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[11530]) ).

thf(11885,plain,
    ! [SV593: nat,SV268: nat] :
      ( ( ! [SY1719: nat] :
            ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV268 @ SV593 ) @ SY1719 )
            | ~ ( ~ ( ord_less_eq_nat @ SV268 @ SY1719 )
                | ~ ( ord_less_eq_nat @ SV593 @ SY1719 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11531]) ).

thf(11886,plain,
    ! [SV594: nat,SV269: nat] :
      ( ( ! [SY1720: nat] :
            ( ~ ( ( SV269 != zero_zero_nat ) )
            | ( ( divide_divide_nat @ ( plus_plus_nat @ SV594 @ ( times_times_nat @ SV269 @ SY1720 ) ) @ SV269 )
              = ( plus_plus_nat @ SY1720 @ ( divide_divide_nat @ SV594 @ SV269 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11532]) ).

thf(11887,plain,
    ! [SV270: num] :
      ( ( one
        = ( bit0 @ SV270 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[11533]) ).

thf(11888,plain,
    ! [SV595: nat] :
      ( ( ( ^ [SY1721: nat] : ( SV595 = SY1721 ) )
        = ( ^ [SY1722: nat] :
              ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                 != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1722 ) )
                | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                 != ( divide_divide_nat @ SY1722 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11534]) ).

thf(11889,plain,
    ! [SV596: nat,SV272: nat] :
      ( ( ! [SY1723: nat,SY1724: nat] :
            ( ~ ( dvd_dvd_nat @ SV272 @ SV596 )
            | ~ ( dvd_dvd_nat @ SY1723 @ SY1724 )
            | ( dvd_dvd_nat @ ( times_times_nat @ SV272 @ SY1723 ) @ ( times_times_nat @ SV596 @ SY1724 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11536]) ).

thf(11890,plain,
    ! [SV597: nat,SV273: nat] :
      ( ( ! [SY1725: nat] :
            ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
              = ( modulo_modulo_nat @ SY1725 @ SV597 ) )
            = ( ~ ! [SY1726: nat] :
                    ~ ~ ! [SY1727: nat] :
                          ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SY1726 ) )
                         != ( plus_plus_nat @ SY1725 @ ( times_times_nat @ SV597 @ SY1727 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11537]) ).

thf(11891,plain,
    ! [SV598: nat,SV274: nat] :
      ( ( ! [SY1728: nat] :
            ( ( ( plus_plus_nat @ SV274 @ SV598 )
             != ( plus_plus_nat @ SY1728 @ SV598 ) )
            | ( SV274 = SY1728 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11538]) ).

thf(11892,plain,
    ! [SV599: nat,SV275: nat] :
      ( ( ! [SY1729: nat] :
            ( ~ ( ( SV275 != zero_zero_nat ) )
            | ( ( divide_divide_nat @ ( plus_plus_nat @ SV599 @ ( times_times_nat @ SY1729 @ SV275 ) ) @ SV275 )
              = ( plus_plus_nat @ SY1729 @ ( divide_divide_nat @ SV599 @ SV275 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11539]) ).

thf(11893,plain,
    ! [SV600: nat,SV276: nat] :
      ( ( ! [SY1730: nat] :
            ( ~ ( ord_less_eq_nat @ SV276 @ SV600 )
            | ( ord_less_eq_nat @ ( times_times_nat @ SY1730 @ SV276 ) @ ( times_times_nat @ SY1730 @ SV600 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11541]) ).

thf(11894,plain,
    ! [SV277: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV277 ) )
        = $true )
      | ( ( ~ ! [SY1343: nat] :
                ( SV277
               != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1343 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11542]) ).

thf(11895,plain,
    ! [SV278: num] :
      ( ( ( bit0 @ SV278 )
        = one )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[11543]) ).

thf(11896,plain,
    ! [SV279: num] :
      ( ( ( bit1 @ SV279 )
        = one )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[11544]) ).

thf(11897,plain,
    ! [SV601: nat,SV280: nat] :
      ( ( ~ ( ( ( times_times_nat @ SV280 @ SV601 )
             != zero_zero_nat ) )
        | ~ ( ~ ( ( SV280 != zero_zero_nat ) )
            | ~ ( ( SV601 != zero_zero_nat ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11545]) ).

thf(11898,plain,
    ! [SV602: nat,SV281: nat] :
      ( ( ! [SY1731: nat] :
            ( ~ ( ord_less_nat @ SV281 @ ( times_times_nat @ SV602 @ SY1731 ) )
            | ( ord_less_nat @ ( divide_divide_nat @ SV281 @ SY1731 ) @ SV602 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11546]) ).

thf(11899,plain,
    ( ( ( some_nat @ sK2_SX0 )
     != ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[11547]) ).

thf(11900,plain,
    ! [SV603: nat,SV282: nat] :
      ( ( ! [SY1732: nat,SY1733: nat] :
            ( ( SV282
             != ( plus_plus_nat @ SV603 @ SY1732 ) )
            | ( ( plus_plus_nat @ SY1733 @ SV282 )
              = ( plus_plus_nat @ SV603 @ ( plus_plus_nat @ SY1733 @ SY1732 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11548]) ).

thf(11901,plain,
    ! [SV604: nat,SV283: nat] :
      ( ( ! [SY1734: nat] :
            ( ( ( times_times_nat @ SV283 @ SV604 )
             != one_one_nat )
            | ( ( times_times_nat @ ( power_power_nat @ SV283 @ SY1734 ) @ ( power_power_nat @ SV604 @ SY1734 ) )
              = one_one_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11549]) ).

thf(11902,plain,
    ! [SV605: nat,SV284: nat] :
      ( ( ! [SY1735: nat,SY1736: nat] :
            ( ( ~ ( ~ ( ( SV284 != SV605 ) )
                  | ~ ( ( SY1735 != SY1736 ) ) ) )
            = ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SY1735 ) @ ( times_times_nat @ SV605 @ SY1736 ) )
             != ( plus_plus_nat @ ( times_times_nat @ SV284 @ SY1736 ) @ ( times_times_nat @ SV605 @ SY1735 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11550]) ).

thf(11903,plain,
    ! [SV606: nat,SV285: nat] :
      ( ( ! [SY1737: nat] :
            ( ~ ( ( SV285 != zero_zero_nat ) )
            | ( ( ( times_times_nat @ SV285 @ SV606 )
                = ( times_times_nat @ SV285 @ SY1737 ) )
              = ( SV606 = SY1737 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11551]) ).

thf(11904,plain,
    ! [SV607: nat,SV286: nat] :
      ( ( ! [SY1738: nat] :
            ( ~ ( dvd_dvd_nat @ SV286 @ SV607 )
            | ( ( times_times_nat @ ( divide_divide_nat @ SV607 @ SV286 ) @ SY1738 )
              = ( divide_divide_nat @ ( times_times_nat @ SV607 @ SY1738 ) @ SV286 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11552]) ).

thf(11905,plain,
    ! [SV608: nat,SV287: nat] :
      ( ( ~ ( ( SV287 != zero_zero_nat ) )
        | ~ ( ( SV608 != zero_zero_nat ) )
        | ( ( times_times_nat @ SV287 @ SV608 )
         != zero_zero_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11553]) ).

thf(11906,plain,
    ( ( ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ summin ) @ sK3_SX0 ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[11554]) ).

thf(11907,plain,
    ! [SV609: nat,SV288: nat] :
      ( ( ( ( divide_divide_nat @ SV288 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
         != ( divide_divide_nat @ SV609 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV288 )
         != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV609 ) )
        | ( SV288 = SV609 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11555]) ).

thf(11908,plain,
    ! [SV610: nat,SV289: nat] :
      ( ( ! [SY1739: nat] :
            ( ~ ( ord_less_eq_nat @ SV289 @ SV610 )
            | ( ord_less_eq_nat @ ( plus_plus_nat @ SV289 @ SY1739 ) @ ( plus_plus_nat @ SV610 @ SY1739 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11557]) ).

thf(11909,plain,
    ! [SV611: nat,SV290: nat] :
      ( ( ! [SY1740: nat,SY1741: nat] :
            ( ~ ~ ( ~ ( ord_less_nat @ SV290 @ SV611 )
                  | ~ ( ord_less_nat @ SY1740 @ SY1741 ) )
            | ( ord_less_nat @ ( plus_plus_nat @ SV290 @ SY1740 ) @ ( plus_plus_nat @ SV611 @ SY1741 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11558]) ).

thf(11910,plain,
    ! [SV612: nat,SV291: nat] :
      ( ( ~ ( dvd_dvd_nat @ SV291 @ SV612 )
        | ( ( times_times_nat @ SV291 @ ( divide_divide_nat @ SV612 @ SV291 ) )
          = SV612 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11559]) ).

thf(11911,plain,
    ! [SV613: num,SV292: num] :
      ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV292 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV613 ) ) )
       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ SV613 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11560]) ).

thf(11912,plain,
    ! [SV614: nat,SV293: nat] :
      ( ( ~ ( ( SV293 != zero_zero_nat ) )
        | ( ( divide_divide_nat @ ( times_times_nat @ SV614 @ SV293 ) @ SV293 )
          = SV614 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11561]) ).

thf(11913,plain,
    ! [SV615: nat,SV294: nat] :
      ( ( ! [SY1742: nat,SY1743: nat] :
            ( ~ ~ ( ( SV294 != SV615 )
                  | ~ ( ord_less_nat @ SY1742 @ SY1743 ) )
            | ( ord_less_nat @ ( plus_plus_nat @ SV294 @ SY1742 ) @ ( plus_plus_nat @ SV615 @ SY1743 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11562]) ).

thf(11914,plain,
    ! [SV616: num,SV295: num] :
      ( ( ( bit1 @ SV295 )
       != ( bit0 @ SV616 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11563]) ).

thf(11915,plain,
    ! [SV617: nat,SV296: nat] :
      ( ( ! [SY1744: nat,SY1745: nat] :
            ( ~ ( ord_less_nat @ SV296 @ SV617 )
            | ~ ( ord_less_nat @ SY1744 @ SY1745 )
            | ( ord_less_nat @ ( plus_plus_nat @ SV296 @ SY1744 ) @ ( plus_plus_nat @ SV617 @ SY1745 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11564]) ).

thf(11916,plain,
    ! [SV618: nat,SV297: nat] :
      ( ( ! [SY1746: nat,SY1747: nat] :
            ( ~ ( dvd_dvd_nat @ SV297 @ SV618 )
            | ~ ( dvd_dvd_nat @ SY1746 @ SY1747 )
            | ( ( times_times_nat @ ( divide_divide_nat @ SV618 @ SV297 ) @ ( divide_divide_nat @ SY1747 @ SY1746 ) )
              = ( divide_divide_nat @ ( times_times_nat @ SV618 @ SY1747 ) @ ( times_times_nat @ SV297 @ SY1746 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11565]) ).

thf(11917,plain,
    ! [SV619: nat,SV298: nat] :
      ( ( ~ ( ord_less_eq_nat @ SV298 @ SV619 )
        | ~ ! [SY1748: nat] :
              ( SV619
             != ( plus_plus_nat @ SV298 @ SY1748 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11566]) ).

thf(11918,plain,
    ! [SV620: nat,SV299: nat] :
      ( ( ! [SY1749: nat] :
            ( ~ ( ord_less_eq_nat @ SV299 @ SV620 )
            | ( ord_less_eq_nat @ SV299 @ ( plus_plus_nat @ SY1749 @ SV620 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11567]) ).

thf(11919,plain,
    ! [SV621: nat,SV300: nat] :
      ( ( ( ( times_times_nat @ SV300 @ SV621 )
          = one_one_nat )
        = ( ~ ( ( SV300 != one_one_nat )
              | ( SV621 != one_one_nat ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11568]) ).

thf(11920,plain,
    ( ( ( some_nat @ sK4_SX0 )
     != ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ maxs ) ) )
    = $false ),
    inference(extcnf_forall_neg,[status(esa)],[11569]) ).

thf(11921,plain,
    ! [SV622: nat] :
      ( ( ( dvd_dvd_nat @ SV622 )
        = ( ^ [SY1750: nat] :
              ~ ! [SY1751: nat] :
                  ( SY1750
                 != ( times_times_nat @ SV622 @ SY1751 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11570]) ).

thf(11922,plain,
    ! [SV623: nat,SV302: nat > real] :
      ( ( ~ ( summable_real @ SV302 )
        | ( summable_real
          @ ^ [SY1752: nat] : ( SV302 @ ( plus_plus_nat @ SY1752 @ SV623 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11572]) ).

thf(11923,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) ) )
        = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
         != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11573]) ).

thf(11924,plain,
    ! [SV625: nat,SV304: nat] :
      ( ( ! [SY1753: nat] :
            ( ~ ( ord_less_nat @ SV304 @ SV625 )
            | ( ord_less_nat @ ( plus_plus_nat @ SV304 @ SY1753 ) @ ( plus_plus_nat @ SV625 @ SY1753 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11574]) ).

thf(11925,plain,
    ! [SV626: nat,SV305: nat] :
      ( ( ( ( plus_plus_nat @ SV305 @ SV626 )
          = zero_zero_nat )
        = ( ~ ( ( SV305 != zero_zero_nat )
              | ( SV626 != zero_zero_nat ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11575]) ).

thf(11926,plain,
    ! [SV306: num] :
      ( ( zero_zero_nat
        = ( numeral_numeral_nat @ SV306 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[11576]) ).

thf(11927,plain,
    ! [SV627: nat,SV307: nat] :
      ( ( ( ( plus_plus_nat @ SV307 @ SV627 )
         != SV307 )
        | ( SV627 = zero_zero_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11577]) ).

thf(11928,plain,
    ! [SV628: nat,SV308: nat] :
      ( ( ! [SY1754: nat] :
            ( ~ ( ord_less_eq_nat @ SV308 @ SV628 )
            | ( ord_less_eq_nat @ ( divide_divide_nat @ SV308 @ SY1754 ) @ ( divide_divide_nat @ SV628 @ SY1754 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11578]) ).

thf(11929,plain,
    ! [SV629: nat,SV309: nat] :
      ( ( ~ ( ord_less_eq_nat @ SV309 @ SV629 )
        | ~ ! [SY1755: nat] :
              ( SV629
             != ( plus_plus_nat @ SV309 @ SY1755 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11579]) ).

thf(11930,plain,
    ! [SV630: nat,SV310: nat] :
      ( ( ( ( plus_plus_nat @ SV310 @ SV630 )
          = zero_zero_nat )
        = ( ~ ( ( SV310 != zero_zero_nat )
              | ( SV630 != zero_zero_nat ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11580]) ).

thf(11931,plain,
    ! [SV631: nat,SV311: nat] :
      ( ( ! [SY1756: nat] :
            ( ~ ( dvd_dvd_nat @ SV311 @ ( times_times_nat @ SV631 @ SY1756 ) )
            | ~ ! [SY1757: nat] :
                  ~ ~ ! [SY1758: nat] :
                        ~ ~ ( ~ ~ ( ( SV311
                                   != ( times_times_nat @ SY1757 @ SY1758 ) )
                                  | ~ ( dvd_dvd_nat @ SY1757 @ SV631 ) )
                            | ~ ( dvd_dvd_nat @ SY1758 @ SY1756 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11581]) ).

thf(11932,plain,
    ! [SV632: nat,SV312: nat] :
      ( ( ! [SY1759: nat,SY1760: nat,SY1761: nat] :
            ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
            | ~ ( dvd_dvd_nat @ SV312 @ SY1759 )
            | ~ ( ( ( times_times_nat @ SV632 @ SY1760 )
                  = ( plus_plus_nat @ ( times_times_nat @ SY1759 @ SY1761 ) @ SV312 ) )
                | ( ( times_times_nat @ SY1759 @ SY1760 )
                  = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SY1761 ) @ SV312 ) ) )
            | ~ ! [SY1762: nat] :
                  ~ ~ ! [SY1763: nat] :
                        ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
                                  | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SY1759 ) ) )
                            | ~ ( ( ( times_times_nat @ SV632 @ SY1762 )
                                  = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SY1759 ) @ SY1763 ) @ SV312 ) )
                                | ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SY1759 ) @ SY1762 )
                                  = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SY1763 ) @ SV312 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11582]) ).

thf(11933,plain,
    ! [SV633: nat,SV313: nat] :
      ( ( ! [SY1764: nat] :
            ( ~ ( ord_less_eq_nat @ SV313 @ SV633 )
            | ( ord_less_eq_nat @ ( plus_plus_nat @ SV313 @ SY1764 ) @ ( plus_plus_nat @ SV633 @ SY1764 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11583]) ).

thf(11934,plain,
    ! [SV634: nat,SV314: nat] :
      ( ( ! [SY1765: nat] :
            ( ~ ( dvd_dvd_nat @ SV314 @ SV634 )
            | ~ ( dvd_dvd_nat @ SV634 @ SY1765 )
            | ( ( divide_divide_nat @ SY1765 @ ( divide_divide_nat @ SV634 @ SV314 ) )
              = ( times_times_nat @ ( divide_divide_nat @ SY1765 @ SV634 ) @ SV314 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11584]) ).

thf(11935,plain,
    ! [SV635: nat,SV315: nat] :
      ( ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV315 )
       != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV635 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11585]) ).

thf(11936,plain,
    ! [SV636: num,SV316: num > $o] :
      ( ( ~ ( SV316 @ one )
        | ~ ! [SY1414: num] :
              ( ~ ( SV316 @ SY1414 )
              | ( SV316 @ ( inc @ SY1414 ) ) )
        | ( SV316 @ SV636 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11586]) ).

thf(11937,plain,
    ! [SV637: nat,SV317: nat] :
      ( ( ~ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV317 @ SV637 ) )
             != zero_zero_nat ) )
        | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV317 )
         != zero_zero_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11587]) ).

thf(11938,plain,
    ! [SV638: num,SV318: num] :
      ( ( ( bit0 @ SV318 )
       != ( bit1 @ SV638 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11588]) ).

thf(11939,plain,
    ! [SV639: nat,SV319: nat > nat > $o] :
      ( ( ! [SY1767: nat] :
            ( ~ ! [SY1419: nat,SY1420: nat] :
                  ( ( SV319 @ SY1419 @ SY1420 )
                  = ( SV319 @ SY1420 @ SY1419 ) )
            | ~ ! [SY1421: nat] : ( SV319 @ SY1421 @ zero_zero_nat )
            | ~ ! [SY1422: nat,SY1423: nat] :
                  ( ~ ( SV319 @ SY1422 @ SY1423 )
                  | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) )
            | ( SV319 @ SV639 @ SY1767 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11589]) ).

thf(11940,plain,
    ! [SV640: num,SV320: num] :
      ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ SV320 ) ) )
       != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV640 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV320 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11590]) ).

thf(11941,plain,
    ! [SV641: nat,SV321: nat] :
      ( ( ! [SY1773: nat] :
            ( ~ ( ord_less_nat @ SV321 @ SV641 )
            | ( ord_less_nat @ SV321 @ ( plus_plus_nat @ SY1773 @ SV641 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11591]) ).

thf(11942,plain,
    ! [SV642: nat,SV322: nat] :
      ( ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 )
        = ( ~ ( ~ ( ( SV322 != SV642 ) )
              | ~ ( vEBT_V8194947554948674370ptions @ summary @ SV642 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11592]) ).

thf(11943,plain,
    ! [SV643: nat,SV323: nat] :
      ( ( ! [SY1774: nat,SY1775: nat,SY1776: nat] :
            ( ( ( modulo_modulo_nat @ SV323 @ SV643 )
             != ( modulo_modulo_nat @ SY1774 @ SV643 ) )
            | ( ( modulo_modulo_nat @ SY1775 @ SV643 )
             != ( modulo_modulo_nat @ SY1776 @ SV643 ) )
            | ( ( modulo_modulo_nat @ ( times_times_nat @ SV323 @ SY1775 ) @ SV643 )
              = ( modulo_modulo_nat @ ( times_times_nat @ SY1774 @ SY1776 ) @ SV643 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11593]) ).

thf(11944,plain,
    ! [SV644: nat] :
      ( ( ( ord_less_eq_nat @ SV644 )
        = ( ^ [SY1777: nat] :
              ~ ! [SY1778: nat] :
                  ( SY1777
                 != ( plus_plus_nat @ SV644 @ SY1778 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11594]) ).

thf(11945,plain,
    ! [SV645: nat,SV325: nat] :
      ( ( ! [SY1779: nat] :
            ( ~ ( dvd_dvd_nat @ ( times_times_nat @ SV325 @ SV645 ) @ SY1779 )
            | ( ( divide_divide_nat @ SY1779 @ ( times_times_nat @ SV325 @ SV645 ) )
              = ( divide_divide_nat @ ( divide_divide_nat @ SY1779 @ SV325 ) @ SV645 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11596]) ).

thf(11946,plain,
    ! [SV646: nat,SV326: nat] :
      ( ( ! [SY1780: nat] :
            ( ~ ( dvd_dvd_nat @ SV326 @ SV646 )
            | ( ( times_times_nat @ SY1780 @ ( divide_divide_nat @ SV646 @ SV326 ) )
              = ( divide_divide_nat @ ( times_times_nat @ SY1780 @ SV646 ) @ SV326 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11597]) ).

thf(11947,plain,
    ! [SV647: nat,SV327: nat] :
      ( ( ! [SY1781: nat] :
            ( ~ ( ord_less_nat @ SV327 @ SV647 )
            | ( ord_less_nat @ ( plus_plus_nat @ SV327 @ SY1781 ) @ ( plus_plus_nat @ SV647 @ SY1781 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11598]) ).

thf(11948,plain,
    ! [SV648: nat,SV328: nat] :
      ( ( ! [SY1782: nat,SY1783: nat] :
            ( ~ ~ ( ~ ( ord_less_eq_nat @ SV328 @ SV648 )
                  | ( SY1782 != SY1783 ) )
            | ( ord_less_eq_nat @ ( plus_plus_nat @ SV328 @ SY1782 ) @ ( plus_plus_nat @ SV648 @ SY1783 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11599]) ).

thf(11949,plain,
    ! [SV649: nat,SV329: nat] :
      ( ( ( zero_zero_nat
          = ( plus_plus_nat @ SV329 @ SV649 ) )
        = ( ~ ( ( SV329 != zero_zero_nat )
              | ( SV649 != zero_zero_nat ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11600]) ).

thf(11950,plain,
    ! [SV650: nat,SV330: nat] :
      ( ( ! [SY1784: nat] :
            ( ~ ( dvd_dvd_nat @ SV330 @ SV650 )
            | ( dvd_dvd_nat @ ( power_power_nat @ SV330 @ SY1784 ) @ ( power_power_nat @ SV650 @ SY1784 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11601]) ).

thf(11951,plain,
    ! [SV651: nat,SV331: nat] :
      ( ( ~ ( ( SV331 != zero_zero_nat ) )
        | ( ( power_power_nat @ SV331 @ SV651 )
         != zero_zero_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11602]) ).

thf(11952,plain,
    ! [SV652: nat,SV332: nat] :
      ( ( ! [SY1785: list_VEBT_VEBT,SY1786: vEBT_VEBT,SY1787: vEBT_VEBT] :
            ( ~ ( ( SV332 != SV652 ) )
            | ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SY1785 @ SV332 @ SY1786 ) @ SV652 @ SY1787 )
              = ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SY1785 @ SV652 @ SY1787 ) @ SV332 @ SY1786 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11603]) ).

thf(11953,plain,
    ! [SV653: $o,SV333: $o] :
      ( ( ( zero_n2687167440665602831ol_nat
          @ ~ ( ~ SV333
              | ~ SV653 ) )
        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ SV333 ) @ ( zero_n2687167440665602831ol_nat @ SV653 ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[11604]) ).

thf(11954,plain,
    ! [SV333: $o] :
      ( ( ( zero_n2687167440665602831ol_nat
          @ ~ ( ~ SV333
              | ~ $true ) )
        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ SV333 ) @ ( zero_n2687167440665602831ol_nat @ $true ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[11604]) ).

thf(11955,plain,
    ! [SV333: $o] :
      ( ( ( zero_n2687167440665602831ol_nat
          @ ~ ( ~ SV333
              | ~ $false ) )
        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ SV333 ) @ ( zero_n2687167440665602831ol_nat @ $false ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[11604]) ).

thf(11956,plain,
    ! [SV654: $o] :
      ( ( ( zero_n2687167440665602831ol_nat
          @ ~ ( ~ $true
              | ~ SV654 ) )
        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ $true ) @ ( zero_n2687167440665602831ol_nat @ SV654 ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[11605]) ).

thf(11957,plain,
    ( ( ( zero_n2687167440665602831ol_nat
        @ ~ ( ~ $true
            | ~ $true ) )
      = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ $true ) @ ( zero_n2687167440665602831ol_nat @ $true ) ) )
    = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[11605]) ).

thf(11958,plain,
    ( ( ( zero_n2687167440665602831ol_nat
        @ ~ ( ~ $true
            | ~ $false ) )
      = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ $true ) @ ( zero_n2687167440665602831ol_nat @ $false ) ) )
    = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[11605]) ).

thf(11959,plain,
    ! [SV655: $o] :
      ( ( ( zero_n2687167440665602831ol_nat
          @ ~ ( ~ $false
              | ~ SV655 ) )
        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ $false ) @ ( zero_n2687167440665602831ol_nat @ SV655 ) ) )
      = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[11606]) ).

thf(11960,plain,
    ( ( ( zero_n2687167440665602831ol_nat
        @ ~ ( ~ $false
            | ~ $true ) )
      = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ $false ) @ ( zero_n2687167440665602831ol_nat @ $true ) ) )
    = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[11606]) ).

thf(11961,plain,
    ( ( ( zero_n2687167440665602831ol_nat
        @ ~ ( ~ $false
            | ~ $false ) )
      = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ $false ) @ ( zero_n2687167440665602831ol_nat @ $false ) ) )
    = $true ),
    inference(extcnf_forall_special_pos,[status(thm)],[11606]) ).

thf(11962,plain,
    ! [SV656: nat,SV334: nat] :
      ( ( ! [SY1788: nat] :
            ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV334 @ SV656 ) @ ( plus_plus_nat @ SY1788 @ SV656 ) )
            | ( ord_less_nat @ SV334 @ SY1788 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11607]) ).

thf(11963,plain,
    ! [SV657: nat,SV335: nat] :
      ( ( ! [SY1789: nat,SY1790: nat] :
            ( ~ ~ ( ( SV335 != SV657 )
                  | ~ ( ord_less_eq_nat @ SY1789 @ SY1790 ) )
            | ( ord_less_eq_nat @ ( plus_plus_nat @ SV335 @ SY1789 ) @ ( plus_plus_nat @ SV657 @ SY1790 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11608]) ).

thf(11964,plain,
    ! [SV658: nat,SV336: nat] :
      ( ( ! [SY1791: nat] :
            ( ~ ( dvd_dvd_nat @ SV336 @ SV658 )
            | ( ( dvd_dvd_nat @ SV336 @ ( plus_plus_nat @ SY1791 @ SV658 ) )
              = ( dvd_dvd_nat @ SV336 @ SY1791 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11609]) ).

thf(11965,plain,
    ! [SV659: nat,SV337: nat] :
      ( ( ! [SY1792: nat] :
            ( ( SV337
             != ( plus_plus_nat @ SV659 @ SY1792 ) )
            | ( ( suc @ SV337 )
              = ( plus_plus_nat @ SV659 @ ( suc @ SY1792 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11610]) ).

thf(11966,plain,
    ! [SV660: nat,SV338: nat] :
      ( ( ! [SY1793: nat] :
            ( ~ ( dvd_dvd_nat @ SV338 @ SV660 )
            | ~ ( dvd_dvd_nat @ SV338 @ SY1793 )
            | ( dvd_dvd_nat @ SV338 @ ( plus_plus_nat @ SV660 @ SY1793 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11611]) ).

thf(11967,plain,
    ! [SV661: nat,SV339: nat] :
      ( ( ! [SY1794: nat] :
            ( ( ( plus_plus_nat @ SV339 @ SV661 )
             != ( plus_plus_nat @ SV339 @ SY1794 ) )
            | ( SV661 = SY1794 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11612]) ).

thf(11968,plain,
    ! [SV340: nat] :
      ( ( ( ~ ! [SY1465: nat] :
                ( SV340
               != ( plus_plus_nat @ SY1465 @ SY1465 ) ) )
        = $true )
      | ( ( ~ ! [SY1466: nat] :
                ( SV340
               != ( plus_plus_nat @ SY1466 @ ( suc @ SY1466 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11613]) ).

thf(11969,plain,
    ! [SV662: nat,SV341: nat] :
      ( ( ! [SY1795: nat,SY1796: nat] :
            ( ~ ~ ( ~ ( ord_less_eq_nat @ SV341 @ SV662 )
                  | ~ ( ord_less_eq_nat @ SY1795 @ SY1796 ) )
            | ( ord_less_eq_nat @ ( plus_plus_nat @ SV341 @ SY1795 ) @ ( plus_plus_nat @ SV662 @ SY1796 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11614]) ).

thf(11970,plain,
    ! [SV663: nat,SV342: nat] :
      ( ( ! [SY1797: nat] :
            ( ~ ( ( SV342 != zero_zero_nat ) )
            | ( ( divide_divide_nat @ ( times_times_nat @ SV342 @ SV663 ) @ ( times_times_nat @ SV342 @ SY1797 ) )
              = ( divide_divide_nat @ SV663 @ SY1797 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11615]) ).

thf(11971,plain,
    ! [SV664: nat,SV343: nat] :
      ( ( ! [SY1798: nat] :
            ( ~ ( ord_less_nat @ SV343 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV664 ) )
            | ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ SY1798 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV664 ) ) @ SV343 ) @ SV664 )
              = SY1798 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11616]) ).

thf(11972,plain,
    ! [SV665: nat,SV344: nat] :
      ( ( ! [SY1799: nat] :
            ( ~ ( dvd_dvd_nat @ SV344 @ SV665 )
            | ( ( divide_divide_nat @ ( plus_plus_nat @ SY1799 @ SV665 ) @ SV344 )
              = ( plus_plus_nat @ ( divide_divide_nat @ SY1799 @ SV344 ) @ ( divide_divide_nat @ SV665 @ SV344 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11617]) ).

thf(11973,plain,
    ! [SV666: nat,SV345: nat] :
      ( ( ! [SY1800: nat] :
            ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV345 @ SV666 ) @ SY1800 )
            | ( ord_less_eq_nat @ SV666 @ SY1800 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11618]) ).

thf(11974,plain,
    ! [SV667: nat,SV346: nat] :
      ( ( ! [SY1801: nat] :
            ( ~ ( dvd_dvd_nat @ ( times_times_nat @ SV346 @ SV667 ) @ SY1801 )
            | ( dvd_dvd_nat @ SV667 @ SY1801 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11619]) ).

thf(11975,plain,
    ! [SV668: nat,SV347: nat] :
      ( ( ! [SY1802: nat] :
            ( ~ ( dvd_dvd_nat @ SV347 @ SV668 )
            | ~ ( dvd_dvd_nat @ SV347 @ SY1802 )
            | ( ( dvd_dvd_nat @ ( divide_divide_nat @ SV668 @ SV347 ) @ ( divide_divide_nat @ SY1802 @ SV347 ) )
              = ( dvd_dvd_nat @ SV668 @ SY1802 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11620]) ).

thf(11976,plain,
    ! [SV348: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV348 ) )
        = $true )
      | ( ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ SV348 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
          = SV348 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11621]) ).

thf(11977,plain,
    ! [SV669: nat,SV349: nat] :
      ( ( ~ ! [SY1803: nat] :
              ~ ~ ! [SY1804: nat] :
                    ~ ~ ! [SY1805: nat] :
                          ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ SY1803 @ SV349 )
                                    | ~ ( dvd_dvd_nat @ SY1803 @ SV669 ) )
                              | ~ ( ( ( times_times_nat @ SV349 @ SY1804 )
                                    = ( plus_plus_nat @ ( times_times_nat @ SV669 @ SY1805 ) @ SY1803 ) )
                                  | ( ( times_times_nat @ SV669 @ SY1804 )
                                    = ( plus_plus_nat @ ( times_times_nat @ SV349 @ SY1805 ) @ SY1803 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11622]) ).

thf(11978,plain,
    ! [SV670: nat,SV350: nat] :
      ( ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV350 )
        | ( ord_less_eq_nat @ SV670 @ ( power_power_nat @ SV350 @ SV670 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11623]) ).

thf(11979,plain,
    ! [SV671: nat,SV351: nat] :
      ( ( ( one_one_nat
          = ( times_times_nat @ SV351 @ SV671 ) )
        = ( ~ ( ( SV351 != one_one_nat )
              | ( SV671 != one_one_nat ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11624]) ).

thf(11980,plain,
    ! [SV672: nat,SV352: nat] :
      ( ( ! [SY1806: nat,SY1807: nat] :
            ( ~ ( ord_less_eq_nat @ SV352 @ SV672 )
            | ~ ( ord_less_eq_nat @ SY1806 @ SY1807 )
            | ( ord_less_eq_nat @ ( plus_plus_nat @ SV352 @ SY1806 ) @ ( plus_plus_nat @ SV672 @ SY1807 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11625]) ).

thf(11981,plain,
    ! [SV673: nat,SV353: nat] :
      ( ( ! [SY1808: nat,SY1809: nat,SY1810: nat] :
            ( ~ ( ( SV353 != zero_zero_nat ) )
            | ~ ~ ( ( SV673 != SY1808 )
                  | ~ ( ( SY1809 != SY1810 ) ) )
            | ( ( plus_plus_nat @ SV673 @ ( times_times_nat @ SV353 @ SY1809 ) )
             != ( plus_plus_nat @ SY1808 @ ( times_times_nat @ SV353 @ SY1810 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11626]) ).

thf(11982,plain,
    ! [SV674: nat,SV354: nat] :
      ( ( ! [SY1811: nat] :
            ( ~ ( dvd_dvd_nat @ SV354 @ SV674 )
            | ( ( dvd_dvd_nat @ SV354 @ ( plus_plus_nat @ SV674 @ SY1811 ) )
              = ( dvd_dvd_nat @ SV354 @ SY1811 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11627]) ).

thf(11983,plain,
    ! [SV675: nat > nat,SV355: nat > nat] :
      ( ( ~ ( summable_nat @ SV355 )
        | ~ ( summable_nat @ SV675 )
        | ( summable_nat
          @ ^ [SY1812: nat] : ( plus_plus_nat @ ( SV355 @ SY1812 ) @ ( SV675 @ SY1812 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11628]) ).

thf(11984,plain,
    ! [SV676: nat,SV356: nat] :
      ( ( ! [SY1813: nat] :
            ~ ( ~ ( ( SV356 != zero_zero_nat )
                  | ( ( divide_divide_nat @ ( times_times_nat @ SV356 @ SV676 ) @ ( times_times_nat @ SV356 @ SY1813 ) )
                    = zero_zero_nat ) )
              | ~ ( ~ ( ( SV356 != zero_zero_nat ) )
                  | ( ( divide_divide_nat @ ( times_times_nat @ SV356 @ SV676 ) @ ( times_times_nat @ SV356 @ SY1813 ) )
                    = ( divide_divide_nat @ SV676 @ SY1813 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11629]) ).

thf(11985,plain,
    ! [SV677: nat,SV357: nat] :
      ( ( ! [SY1814: nat] :
            ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV357 @ SV677 ) @ ( plus_plus_nat @ SY1814 @ SV677 ) )
            | ( ord_less_eq_nat @ SV357 @ SY1814 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11630]) ).

thf(11986,plain,
    ! [SV358: num] :
      ( ( one
        = ( bit0 @ SV358 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[11631]) ).

thf(11987,plain,
    ! [SV678: nat,SV359: nat] :
      ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV359 )
        | ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV678 )
        | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV359 @ SV678 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11632]) ).

thf(11988,plain,
    ! [SV679: nat,SV360: nat] :
      ( ( ~ ( dvd_dvd_nat @ SV360 @ SV679 )
        | ( ( times_times_nat @ ( divide_divide_nat @ SV679 @ SV360 ) @ SV360 )
          = SV679 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11633]) ).

thf(11989,plain,
    ! [SV680: nat,SV361: nat] :
      ( ( ! [SY1815: nat] :
            ( ( ( divide_divide_nat @ SV361 @ SV680 )
             != ( divide_divide_nat @ SY1815 @ SV680 ) )
            | ~ ( dvd_dvd_nat @ SV680 @ SV361 )
            | ~ ( dvd_dvd_nat @ SV680 @ SY1815 )
            | ( SV361 = SY1815 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11634]) ).

thf(11990,plain,
    ! [SV681: nat,SV362: nat] :
      ( ( ! [SY1816: nat] :
            ( ~ ( dvd_dvd_nat @ SV362 @ SV681 )
            | ~ ( dvd_dvd_nat @ SV362 @ SY1816 )
            | ( ( ( divide_divide_nat @ SV681 @ SV362 )
                = ( divide_divide_nat @ SY1816 @ SV362 ) )
              = ( SV681 = SY1816 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11635]) ).

thf(11991,plain,
    ! [SV682: nat,SV363: nat] :
      ( ( ~ ( dvd_dvd_nat @ SV363 @ SV682 )
        | ~ ! [SY1817: nat] :
              ( SV682
             != ( times_times_nat @ SV363 @ SY1817 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11636]) ).

thf(11992,plain,
    ! [SV683: nat,SV364: nat] :
      ( ( ! [SY1818: nat,SY1819: nat] :
            ( ~ ( ord_less_nat @ SV364 @ SV683 )
            | ~ ( ord_less_nat @ SY1818 @ SY1819 )
            | ( ord_less_nat @ ( plus_plus_nat @ SV364 @ SY1818 ) @ ( plus_plus_nat @ SV683 @ SY1819 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11637]) ).

thf(11993,plain,
    ! [SV684: nat,SV365: nat] :
      ( ( ! [SY1820: nat,SY1821: nat] :
            ( ~ ( ord_less_eq_nat @ SV365 @ SV684 )
            | ~ ( ord_less_eq_nat @ SY1820 @ SY1821 )
            | ( ord_less_eq_nat @ ( plus_plus_nat @ SV365 @ SY1820 ) @ ( plus_plus_nat @ SV684 @ SY1821 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11638]) ).

thf(11994,plain,
    ! [SV685: nat,SV366: nat] :
      ( ( ! [SY1822: nat] :
            ( ~ ( dvd_dvd_nat @ ( times_times_nat @ SV366 @ SV685 ) @ SY1822 )
            | ( dvd_dvd_nat @ SV366 @ SY1822 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11639]) ).

thf(11995,plain,
    ! [SV686: nat,SV367: nat] :
      ( ( ! [SY1823: nat] :
            ( ( SV367
             != ( times_times_nat @ SV686 @ SY1823 ) )
            | ( dvd_dvd_nat @ SV686 @ SV367 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11640]) ).

thf(11996,plain,
    ! [SV687: nat,SV368: nat] :
      ( ( ! [SY1824: nat] :
            ( ~ ( ord_less_eq_nat @ SV368 @ SV687 )
            | ( ord_less_eq_nat @ ( plus_plus_nat @ SY1824 @ SV368 ) @ ( plus_plus_nat @ SY1824 @ SV687 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11641]) ).

thf(11997,plain,
    ! [SV688: nat,SV369: nat] :
      ( ( ! [SY1825: nat] :
            ( ( ( plus_plus_nat @ SV369 @ SV688 )
             != SY1825 )
            | ( SV369
              = ( minus_minus_nat @ SY1825 @ SV688 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11642]) ).

thf(11998,plain,
    ! [SV689: nat,SV370: nat] :
      ( ( ! [SY1826: nat] :
            ( ~ ( ord_less_nat @ SV370 @ SV689 )
            | ( ord_less_nat @ ( plus_plus_nat @ SY1826 @ SV370 ) @ ( plus_plus_nat @ SY1826 @ SV689 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11643]) ).

thf(11999,plain,
    ! [SV690: nat,SV371: nat] :
      ( ( ! [SY1827: nat] :
            ( ~ ( dvd_dvd_nat @ SV371 @ SV690 )
            | ( dvd_dvd_nat @ SV371 @ ( times_times_nat @ SY1827 @ SV690 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11644]) ).

thf(12000,plain,
    ! [SV691: nat,SV372: nat] :
      ( ( ! [SY1828: nat] :
            ( ~ ( dvd_dvd_nat @ SV372 @ SV691 )
            | ( dvd_dvd_nat @ SV372 @ ( times_times_nat @ SV691 @ SY1828 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11645]) ).

thf(12001,plain,
    ! [SV692: option_nat,SV373: option_nat] :
      ( ( ( ( SV373 = none_nat )
         != ( SV692 = none_nat ) )
        | ~ ( ~ ( ( SV373 != none_nat ) )
            | ~ ( ( SV692 != none_nat ) )
            | ( ( the_nat @ SV373 )
              = ( the_nat @ SV692 ) ) )
        | ( SV373 = SV692 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11646]) ).

thf(12002,plain,
    ! [SV693: nat,SV374: nat > $o] :
      ( ( ~ ! [SY1533: nat] :
              ( ( ( divide_divide_nat @ SY1533 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
               != SY1533 )
              | ( SV374 @ SY1533 ) )
        | ~ ! [SY1534: nat,SY1535: $o] :
              ( ~ ( SV374 @ SY1534 )
              | ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ SY1535 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1534 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
               != SY1534 )
              | ( SV374 @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ SY1535 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1534 ) ) ) )
        | ( SV374 @ SV693 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11647]) ).

thf(12003,plain,
    ! [SV694: nat] :
      ( ( ( ord_less_eq_nat @ SV694 )
        = ( ^ [SY1832: nat] :
              ~ ! [SY1833: nat] :
                  ( SY1832
                 != ( plus_plus_nat @ SV694 @ SY1833 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11648]) ).

thf(12004,plain,
    ! [SV695: num,SV376: num] :
      ( ( ( bit0 @ SV376 )
       != ( bit1 @ SV695 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11650]) ).

thf(12005,plain,
    ! [SV696: nat,SV377: nat] :
      ( ( ! [SY1834: nat] :
            ( ~ ( dvd_dvd_nat @ SV377 @ SV696 )
            | ( ( power_power_nat @ ( divide_divide_nat @ SV696 @ SV377 ) @ SY1834 )
              = ( divide_divide_nat @ ( power_power_nat @ SV696 @ SY1834 ) @ ( power_power_nat @ SV377 @ SY1834 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11651]) ).

thf(12006,plain,
    ! [SV697: nat,SV378: nat] :
      ( ( ! [SY1835: nat,SY1836: nat] :
            ( ~ ( ord_less_eq_nat @ SV378 @ SV697 )
            | ~ ( ord_less_eq_nat @ SY1835 @ SY1836 )
            | ( ord_less_eq_nat @ ( times_times_nat @ SV378 @ SY1835 ) @ ( times_times_nat @ SV697 @ SY1836 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11652]) ).

thf(12007,plain,
    ! [SV698: nat,SV379: nat] :
      ( ( ! [SY1837: nat,SY1838: nat] :
            ( ~ ~ ( ~ ( ord_less_nat @ SV379 @ SV698 )
                  | ( SY1837 != SY1838 ) )
            | ( ord_less_nat @ ( plus_plus_nat @ SV379 @ SY1837 ) @ ( plus_plus_nat @ SV698 @ SY1838 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11653]) ).

thf(12008,plain,
    ! [SV699: nat,SV380: nat] :
      ( ( ! [SY1839: nat] :
            ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV380 @ SV699 ) @ ( plus_plus_nat @ SV380 @ SY1839 ) )
            | ( ord_less_eq_nat @ SV699 @ SY1839 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11654]) ).

thf(12009,plain,
    ! [SV700: nat,SV381: nat] :
      ( ( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV381 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ SV700 )
        | ( ord_less_eq_nat @ SV381 @ SV700 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11655]) ).

thf(12010,plain,
    ! [SV382: num] :
      ( ( ( ~ ( ( SV382 != one ) ) )
        = $true )
      | ( ( ~ ! [SY1550: num] :
                ( SV382
               != ( bit0 @ SY1550 ) )
          | ~ ! [SY1551: num] :
                ( SV382
               != ( bit1 @ SY1551 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11656]) ).

thf(12011,plain,
    ! [SV701: nat,SV383: nat] :
      ( ( ! [SY1840: list_VEBT_VEBT,SY1841: vEBT_VEBT] :
            ( ~ ( ( SV383 != SV701 ) )
            | ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ SY1840 @ SV383 @ SY1841 ) @ SV701 )
              = ( nth_VEBT_VEBT @ SY1840 @ SV701 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11657]) ).

thf(12012,plain,
    ! [SV702: nat,SV384: nat] :
      ( ( ! [SY1842: nat,SY1843: nat,SY1844: nat] :
            ( ( ( modulo_modulo_nat @ SV384 @ SV702 )
             != ( modulo_modulo_nat @ SY1842 @ SV702 ) )
            | ( ( modulo_modulo_nat @ SY1843 @ SV702 )
             != ( modulo_modulo_nat @ SY1844 @ SV702 ) )
            | ( ( modulo_modulo_nat @ ( plus_plus_nat @ SV384 @ SY1843 ) @ SV702 )
              = ( modulo_modulo_nat @ ( plus_plus_nat @ SY1842 @ SY1844 ) @ SV702 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11658]) ).

thf(12013,plain,
    ! [SV385: num] :
      ( ( one
        = ( bit1 @ SV385 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[11659]) ).

thf(12014,plain,
    ! [SV703: nat,SV386: nat] :
      ( ( ! [SY1845: nat] :
            ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV386 @ SV703 ) @ SY1845 )
            | ( ord_less_eq_nat @ SV386 @ SY1845 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11660]) ).

thf(12015,plain,
    ! [SV704: nat,SV387: nat] :
      ( ( ! [SY1846: nat] :
            ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV387 @ SV704 ) @ ( plus_plus_nat @ SV387 @ SY1846 ) )
            | ( ord_less_nat @ SV704 @ SY1846 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11661]) ).

thf(12016,plain,
    ! [SV705: nat,SV388: nat > nat] :
      ( ( ! [SY1847: nat > nat,SY1848: nat] :
            ( ~ ( sums_nat @ SV388 @ SV705 )
            | ~ ( sums_nat @ SY1847 @ SY1848 )
            | ( sums_nat
              @ ^ [SY1566: nat] : ( plus_plus_nat @ ( SV388 @ SY1566 ) @ ( SY1847 @ SY1566 ) )
              @ ( plus_plus_nat @ SV705 @ SY1848 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11662]) ).

thf(12017,plain,
    ! [SV706: nat,SV389: nat] :
      ( ( ! [SY1850: nat] :
            ( ~ ( ord_less_nat @ SV389 @ SV706 )
            | ( ord_less_nat @ SV389 @ ( plus_plus_nat @ SV706 @ SY1850 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11663]) ).

thf(12018,plain,
    ! [SV707: nat,SV390: nat] :
      ( ( ! [SY1851: nat] :
            ( ~ ( ord_less_eq_nat @ SV390 @ SV707 )
            | ( ord_less_eq_nat @ SV390 @ ( plus_plus_nat @ SV707 @ SY1851 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11664]) ).

thf(12019,plain,
    ! [SV393: nat] :
      ( ( ! [SV708: nat] :
            ( ( vEBT_VEBT_high @ SV393 @ SV708 )
            = ( divide_divide_nat @ SV393 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV708 ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11667]) ).

thf(12020,plain,
    ! [SV393: nat] :
      ( ( ( vEBT_VEBT_high @ SV393 )
        = ( ^ [SY1571: nat] : ( divide_divide_nat @ SV393 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1571 ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11667]) ).

thf(12021,plain,
    ! [SV394: nat] :
      ( ( ! [SV709: nat] :
            ( ( vEBT_VEBT_bit_concat @ SV394 @ SV709 )
            = ( ^ [SY1852: nat] : ( plus_plus_nat @ ( times_times_nat @ SV394 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1852 ) ) @ SV709 ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11668]) ).

thf(12022,plain,
    ! [SV394: nat] :
      ( ( ( vEBT_VEBT_bit_concat @ SV394 )
        = ( ^ [SY1572: nat,SY1573: nat] : ( plus_plus_nat @ ( times_times_nat @ SV394 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1573 ) ) @ SY1572 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11668]) ).

thf(12023,plain,
    ! [SV710: nat,SV395: nat,SV6: num] :
      ( ( ( times_times_nat @ ( numeral_numeral_nat @ SV6 ) @ ( plus_plus_nat @ SV395 @ SV710 ) )
        = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ SV6 ) @ SV395 ) @ ( times_times_nat @ ( numeral_numeral_nat @ SV6 ) @ SV710 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11669]) ).

thf(12024,plain,
    ! [SV711: num,SV396: nat,SV7: nat] :
      ( ( ( times_times_nat @ ( plus_plus_nat @ SV7 @ SV396 ) @ ( numeral_numeral_nat @ SV711 ) )
        = ( plus_plus_nat @ ( times_times_nat @ SV7 @ ( numeral_numeral_nat @ SV711 ) ) @ ( times_times_nat @ SV396 @ ( numeral_numeral_nat @ SV711 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11670]) ).

thf(12025,plain,
    ! [SV712: nat,SV398: nat,SV9: nat] :
      ( ( ( divide_divide_nat @ ( divide_divide_nat @ SV9 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV398 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV712 ) )
        = ( divide_divide_nat @ SV9 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV398 @ SV712 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11672]) ).

thf(12026,plain,
    ! [SV399: num,SV10: num] :
      ( ( ~ ( ( ( numeral_numeral_nat @ SV10 )
              = ( numeral_numeral_nat @ SV399 ) )
            | ( SV10 = SV399 ) )
        | ~ ( ( ( numeral_numeral_nat @ SV10 )
             != ( numeral_numeral_nat @ SV399 ) )
            | ( SV10 != SV399 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11673]) ).

thf(12027,plain,
    ! [SV399: num,SV10: num] :
      ( ( ( ( numeral_numeral_nat @ SV10 )
          = ( numeral_numeral_nat @ SV399 ) )
        = ( SV10 = SV399 ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11673]) ).

thf(12028,plain,
    ! [SV713: nat,SV400: num,SV11: num] :
      ( ( ( times_times_nat @ ( numeral_numeral_nat @ SV11 ) @ ( times_times_nat @ ( numeral_numeral_nat @ SV400 ) @ SV713 ) )
        = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ SV11 @ SV400 ) ) @ SV713 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11674]) ).

thf(12029,plain,
    ! [SV714: nat,SV402: num,SV13: num] :
      ( ( ( plus_plus_nat @ ( numeral_numeral_nat @ SV13 ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ SV402 ) @ SV714 ) )
        = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ SV13 @ SV402 ) ) @ SV714 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11676]) ).

thf(12030,plain,
    ! [SV715: num,SV404: num,SV16: nat] :
      ( ( ( power_power_nat @ ( power_power_nat @ SV16 @ ( numeral_numeral_nat @ SV404 ) ) @ ( numeral_numeral_nat @ SV715 ) )
        = ( power_power_nat @ SV16 @ ( numeral_numeral_nat @ ( times_times_num @ SV404 @ SV715 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11678]) ).

thf(12031,plain,
    ! [SV716: num,SV405: num,SV17: nat] :
      ( ( ! [SY1853: nat] :
            ( ( times_times_nat @ ( power_power_nat @ SV17 @ ( numeral_numeral_nat @ SV405 ) ) @ ( times_times_nat @ ( power_power_nat @ SV17 @ ( numeral_numeral_nat @ SV716 ) ) @ SY1853 ) )
            = ( times_times_nat @ ( power_power_nat @ SV17 @ ( numeral_numeral_nat @ ( plus_plus_num @ SV405 @ SV716 ) ) ) @ SY1853 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11679]) ).

thf(12032,plain,
    ! [SV717: num,SV406: num,SV18: nat] :
      ( ( ( times_times_nat @ ( power_power_nat @ SV18 @ ( numeral_numeral_nat @ SV406 ) ) @ ( power_power_nat @ SV18 @ ( numeral_numeral_nat @ SV717 ) ) )
        = ( power_power_nat @ SV18 @ ( numeral_numeral_nat @ ( plus_plus_num @ SV406 @ SV717 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11680]) ).

thf(12033,plain,
    ! [SV718: num,SV407: num,SV20: nat] :
      ( ( ( divide_divide_nat @ ( divide_divide_nat @ SV20 @ ( numeral_numeral_nat @ SV407 ) ) @ ( numeral_numeral_nat @ SV718 ) )
        = ( divide_divide_nat @ SV20 @ ( numeral_numeral_nat @ ( times_times_num @ SV407 @ SV718 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11681]) ).

thf(12034,plain,
    ! [SV719: nat,SV408: nat,SV22: nat] :
      ( ( ( power_power_nat @ ( times_times_nat @ SV22 @ SV408 ) @ SV719 )
        = ( times_times_nat @ ( power_power_nat @ SV22 @ SV719 ) @ ( power_power_nat @ SV408 @ SV719 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11682]) ).

thf(12035,plain,
    ! [SV720: nat,SV410: nat,SV24: nat] :
      ( ( ( power_power_nat @ SV24 @ ( times_times_nat @ SV410 @ SV720 ) )
        = ( power_power_nat @ ( power_power_nat @ SV24 @ SV410 ) @ SV720 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11684]) ).

thf(12036,plain,
    ! [SV721: nat,SV411: nat,SV25: real] :
      ( ( ( power_power_real @ SV25 @ ( times_times_nat @ SV411 @ SV721 ) )
        = ( power_power_real @ ( power_power_real @ SV25 @ SV411 ) @ SV721 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11685]) ).

thf(12037,plain,
    ! [SV722: nat,SV412: nat,SV26: int] :
      ( ( ( power_power_int @ SV26 @ ( times_times_nat @ SV412 @ SV722 ) )
        = ( power_power_int @ ( power_power_int @ SV26 @ SV412 ) @ SV722 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11686]) ).

thf(12038,plain,
    ! [SV723: nat,SV413: nat,SV27: complex] :
      ( ( ( power_power_complex @ SV27 @ ( times_times_nat @ SV413 @ SV723 ) )
        = ( power_power_complex @ ( power_power_complex @ SV27 @ SV413 ) @ SV723 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11687]) ).

thf(12039,plain,
    ! [SV724: nat,SV414: nat,SV28: nat] :
      ( ( ( divide_divide_nat @ SV28 @ ( times_times_nat @ SV414 @ SV724 ) )
        = ( divide_divide_nat @ ( divide_divide_nat @ SV28 @ SV414 ) @ SV724 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11688]) ).

thf(12040,plain,
    ! [SV725: nat,SV415: nat,SV32: nat] :
      ( ( ( power_power_nat @ SV32 @ ( plus_plus_nat @ SV415 @ SV725 ) )
        = ( times_times_nat @ ( power_power_nat @ SV32 @ SV415 ) @ ( power_power_nat @ SV32 @ SV725 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11689]) ).

thf(12041,plain,
    ! [SV726: vEBT_VEBT,SV422: nat,SV44: list_VEBT_VEBT] :
      ( ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV44 @ SV422 @ SV726 ) )
        = ( size_s6755466524823107622T_VEBT @ SV44 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11696]) ).

thf(12042,plain,
    ! [SV727: vEBT_VEBT,SV423: nat,SV45: list_VEBT_VEBT] :
      ( ( ! [SY1854: vEBT_VEBT] :
            ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV45 @ SV423 @ SV727 ) @ SV423 @ SY1854 )
            = ( list_u1324408373059187874T_VEBT @ SV45 @ SV423 @ SY1854 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11697]) ).

thf(12043,plain,
    ! [SV427: nat,SV49: nat] :
      ( ( ~ ( ( ord_less_eq_nat @ ( power_power_nat @ SV49 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ SV427 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
            | ( ord_less_eq_nat @ SV49 @ SV427 ) )
        | ~ ( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV49 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ SV427 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
            | ~ ( ord_less_eq_nat @ SV49 @ SV427 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11701]) ).

thf(12044,plain,
    ! [SV427: nat,SV49: nat] :
      ( ( ( ord_less_eq_nat @ ( power_power_nat @ SV49 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ SV427 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = ( ord_less_eq_nat @ SV49 @ SV427 ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11701]) ).

thf(12045,plain,
    ! [SV428: num,SV53: num] :
      ( ( ~ ( ( ord_less_num @ ( bit0 @ SV53 ) @ ( bit0 @ SV428 ) )
            | ( ord_less_num @ SV53 @ SV428 ) )
        | ~ ( ~ ( ord_less_num @ ( bit0 @ SV53 ) @ ( bit0 @ SV428 ) )
            | ~ ( ord_less_num @ SV53 @ SV428 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11703]) ).

thf(12046,plain,
    ! [SV428: num,SV53: num] :
      ( ( ( ord_less_num @ ( bit0 @ SV53 ) @ ( bit0 @ SV428 ) )
        = ( ord_less_num @ SV53 @ SV428 ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11703]) ).

thf(12047,plain,
    ! [SV429: num,SV54: num] :
      ( ( ~ ( ( ( bit0 @ SV54 )
              = ( bit0 @ SV429 ) )
            | ( SV54 = SV429 ) )
        | ~ ( ( ( bit0 @ SV54 )
             != ( bit0 @ SV429 ) )
            | ( SV54 != SV429 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11704]) ).

thf(12048,plain,
    ! [SV429: num,SV54: num] :
      ( ( ( ( bit0 @ SV54 )
          = ( bit0 @ SV429 ) )
        = ( SV54 = SV429 ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11704]) ).

thf(12049,plain,
    ! [SV432: num,SV62: num] :
      ( ( ~ ( ( ord_less_eq_num @ ( bit0 @ SV62 ) @ ( bit0 @ SV432 ) )
            | ( ord_less_eq_num @ SV62 @ SV432 ) )
        | ~ ( ~ ( ord_less_eq_num @ ( bit0 @ SV62 ) @ ( bit0 @ SV432 ) )
            | ~ ( ord_less_eq_num @ SV62 @ SV432 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11707]) ).

thf(12050,plain,
    ! [SV432: num,SV62: num] :
      ( ( ( ord_less_eq_num @ ( bit0 @ SV62 ) @ ( bit0 @ SV432 ) )
        = ( ord_less_eq_num @ SV62 @ SV432 ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11707]) ).

thf(12051,plain,
    ! [SV64: num] :
      ( ( ( ~ ( ( one_one_nat
                = ( numeral_numeral_nat @ SV64 ) )
              | ( one = SV64 ) ) )
        = $true )
      | ( ( ~ ( ( one_one_nat
               != ( numeral_numeral_nat @ SV64 ) )
              | ( one != SV64 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11708]) ).

thf(12052,plain,
    ! [SV65: num] :
      ( ( ( ~ ( ( ( numeral_numeral_nat @ SV65 )
                = one_one_nat )
              | ( SV65 = one ) ) )
        = $true )
      | ( ( ~ ( ( ( numeral_numeral_nat @ SV65 )
               != one_one_nat )
              | ( SV65 != one ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11710]) ).

thf(12053,plain,
    ! [SV67: num] :
      ( ( ( ~ ( ( ord_less_eq_num @ SV67 @ one )
              | ( SV67 = one ) ) )
        = $true )
      | ( ( ~ ( ~ ( ord_less_eq_num @ SV67 @ one )
              | ( SV67 != one ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11713]) ).

thf(12054,plain,
    ! [SV728: nat,SV433: nat,SV69: nat] :
      ( ( ! [SY1855: nat] :
            ( ( plus_plus_nat @ ( times_times_nat @ SV69 @ SV433 ) @ ( plus_plus_nat @ ( times_times_nat @ SV728 @ SV433 ) @ SY1855 ) )
            = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV69 @ SV728 ) @ SV433 ) @ SY1855 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11715]) ).

thf(12055,plain,
    ! [SV729: nat,SV435: nat,SV71: nat] :
      ( ( ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SV435 ) @ ( plus_plus_nat @ SV71 @ SV729 ) )
        = ( ord_less_nat @ SV435 @ SV729 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11717]) ).

thf(12056,plain,
    ! [SV730: nat,SV436: nat,SV72: nat] :
      ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV72 @ SV436 ) @ ( plus_plus_nat @ SV72 @ SV730 ) )
        = ( ord_less_eq_nat @ SV436 @ SV730 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11718]) ).

thf(12057,plain,
    ! [SV731: nat,SV437: nat,SV73: nat] :
      ( ( ( minus_minus_nat @ ( minus_minus_nat @ SV73 @ SV437 ) @ SV731 )
        = ( minus_minus_nat @ SV73 @ ( plus_plus_nat @ SV437 @ SV731 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11719]) ).

thf(12058,plain,
    ! [SV732: nat,SV441: nat,SV80: nat] :
      ( ( ( minus_minus_nat @ ( plus_plus_nat @ SV80 @ SV441 ) @ ( plus_plus_nat @ SV732 @ SV441 ) )
        = ( minus_minus_nat @ SV80 @ SV732 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11723]) ).

thf(12059,plain,
    ! [SV733: nat,SV442: nat,SV81: nat] :
      ( ( ( minus_minus_nat @ ( plus_plus_nat @ SV81 @ SV442 ) @ ( plus_plus_nat @ SV81 @ SV733 ) )
        = ( minus_minus_nat @ SV442 @ SV733 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11724]) ).

thf(12060,plain,
    ! [SV734: nat,SV445: nat,SV84: nat] :
      ( ( ( times_times_nat @ SV84 @ ( minus_minus_nat @ SV445 @ SV734 ) )
        = ( minus_minus_nat @ ( times_times_nat @ SV84 @ SV445 ) @ ( times_times_nat @ SV84 @ SV734 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11727]) ).

thf(12061,plain,
    ! [SV735: nat,SV446: nat,SV85: nat] :
      ( ( ( times_times_nat @ ( minus_minus_nat @ SV85 @ SV446 ) @ SV735 )
        = ( minus_minus_nat @ ( times_times_nat @ SV85 @ SV735 ) @ ( times_times_nat @ SV446 @ SV735 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11728]) ).

thf(12062,plain,
    ! [SV736: nat,SV447: nat,SV86: nat] :
      ( ( ( ( times_times_nat @ ( suc @ SV86 ) @ SV447 )
          = ( times_times_nat @ ( suc @ SV86 ) @ SV736 ) )
        = ( SV447 = SV736 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11729]) ).

thf(12063,plain,
    ! [SV453: nat,SV93: nat] :
      ( ( ord_less_nat @ ( plus_plus_nat @ SV93 @ SV453 ) @ SV453 )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[11735]) ).

thf(12064,plain,
    ! [SV454: nat,SV94: nat] :
      ( ( ord_less_nat @ ( plus_plus_nat @ SV94 @ SV454 ) @ SV94 )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[11736]) ).

thf(12065,plain,
    ! [SV737: nat,SV457: nat,SV99: nat] :
      ( ( ( times_times_nat @ SV99 @ ( plus_plus_nat @ SV457 @ SV737 ) )
        = ( plus_plus_nat @ ( times_times_nat @ SV99 @ SV457 ) @ ( times_times_nat @ SV99 @ SV737 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11739]) ).

thf(12066,plain,
    ! [SV738: nat,SV458: nat,SV100: nat] :
      ( ( ( times_times_nat @ ( plus_plus_nat @ SV100 @ SV458 ) @ SV738 )
        = ( plus_plus_nat @ ( times_times_nat @ SV100 @ SV738 ) @ ( times_times_nat @ SV458 @ SV738 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11740]) ).

thf(12067,plain,
    ! [SV739: nat,SV459: nat,SV104: nat] :
      ( ( ( plus_plus_nat @ ( ord_max_nat @ SV104 @ SV459 ) @ SV739 )
        = ( ord_max_nat @ ( plus_plus_nat @ SV104 @ SV739 ) @ ( plus_plus_nat @ SV459 @ SV739 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11741]) ).

thf(12068,plain,
    ! [SV740: nat,SV460: nat,SV105: nat] :
      ( ( ( plus_plus_nat @ SV105 @ ( ord_max_nat @ SV460 @ SV740 ) )
        = ( ord_max_nat @ ( plus_plus_nat @ SV105 @ SV460 ) @ ( plus_plus_nat @ SV105 @ SV740 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11742]) ).

thf(12069,plain,
    ! [SV741: nat,SV461: nat,SV106: nat] :
      ( ( ( times_times_nat @ ( ord_max_nat @ SV106 @ SV461 ) @ SV741 )
        = ( ord_max_nat @ ( times_times_nat @ SV106 @ SV741 ) @ ( times_times_nat @ SV461 @ SV741 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11743]) ).

thf(12070,plain,
    ! [SV742: nat,SV462: nat,SV107: nat] :
      ( ( ( times_times_nat @ SV107 @ ( ord_max_nat @ SV462 @ SV742 ) )
        = ( ord_max_nat @ ( times_times_nat @ SV107 @ SV462 ) @ ( times_times_nat @ SV107 @ SV742 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11744]) ).

thf(12071,plain,
    ! [SV743: nat,SV463: nat,SV108: nat] :
      ( ( ( times_times_nat @ ( plus_plus_nat @ SV108 @ SV463 ) @ SV743 )
        = ( plus_plus_nat @ ( times_times_nat @ SV108 @ SV743 ) @ ( times_times_nat @ SV463 @ SV743 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11745]) ).

thf(12072,plain,
    ! [SV744: nat,SV464: nat,SV109: nat] :
      ( ( ( times_times_nat @ SV109 @ ( plus_plus_nat @ SV464 @ SV744 ) )
        = ( plus_plus_nat @ ( times_times_nat @ SV109 @ SV464 ) @ ( times_times_nat @ SV109 @ SV744 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11746]) ).

thf(12073,plain,
    ! [SV745: nat,SV465: nat,SV110: nat] :
      ( ( ( times_times_nat @ ( plus_plus_nat @ SV110 @ SV465 ) @ SV745 )
        = ( plus_plus_nat @ ( times_times_nat @ SV110 @ SV745 ) @ ( times_times_nat @ SV465 @ SV745 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11747]) ).

thf(12074,plain,
    ! [SV746: nat,SV466: nat,SV111: nat] :
      ( ( ! [SY1856: nat] :
            ( ( plus_plus_nat @ ( times_times_nat @ SV111 @ SV466 ) @ ( plus_plus_nat @ ( times_times_nat @ SV746 @ SV466 ) @ SY1856 ) )
            = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV111 @ SV746 ) @ SV466 ) @ SY1856 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11748]) ).

thf(12075,plain,
    ! [SV747: nat,SV467: nat,SV112: nat] :
      ( ( ( times_times_nat @ ( minus_minus_nat @ SV112 @ SV467 ) @ SV747 )
        = ( minus_minus_nat @ ( times_times_nat @ SV112 @ SV747 ) @ ( times_times_nat @ SV467 @ SV747 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11749]) ).

thf(12076,plain,
    ! [SV748: nat,SV468: nat,SV113: nat] :
      ( ( ( times_times_nat @ SV113 @ ( minus_minus_nat @ SV468 @ SV748 ) )
        = ( minus_minus_nat @ ( times_times_nat @ SV113 @ SV468 ) @ ( times_times_nat @ SV113 @ SV748 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11750]) ).

thf(12077,plain,
    ! [SV115: nat,SV749: nat] :
      ( ( ( times_times_nat @ SV749 @ SV115 )
        = ( times_times_nat @ SV115 @ SV749 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11752]) ).

thf(12078,plain,
    ! [SV750: nat,SV472: nat,SV117: nat] :
      ( ( ( minus_minus_nat @ ( plus_plus_nat @ SV117 @ SV472 ) @ ( plus_plus_nat @ SV750 @ SV472 ) )
        = ( minus_minus_nat @ SV117 @ SV750 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11755]) ).

thf(12079,plain,
    ! [SV751: nat,SV474: nat,SV119: nat] :
      ( ( ( minus_minus_nat @ ( plus_plus_nat @ SV119 @ SV474 ) @ ( plus_plus_nat @ SV119 @ SV751 ) )
        = ( minus_minus_nat @ SV474 @ SV751 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11757]) ).

thf(12080,plain,
    ! [SV752: nat,SV475: nat,SV120: nat] :
      ( ( ( ( plus_plus_nat @ SV120 @ SV475 )
          = ( plus_plus_nat @ SV120 @ SV752 ) )
        = ( SV475 = SV752 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11758]) ).

thf(12081,plain,
    ! [SV753: nat,SV476: nat,SV121: nat] :
      ( ( ( ( plus_plus_nat @ SV121 @ SV476 )
          = ( plus_plus_nat @ SV753 @ SV476 ) )
        = ( SV121 = SV753 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11759]) ).

thf(12082,plain,
    ! [SV754: nat,SV477: nat,SV122: nat] :
      ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ SV477 ) @ ( plus_plus_nat @ SV122 @ SV754 ) )
        = ( ord_less_eq_nat @ SV477 @ SV754 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11760]) ).

thf(12083,plain,
    ! [SV755: nat,SV478: nat,SV123: nat] :
      ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV123 @ SV478 ) @ ( plus_plus_nat @ SV755 @ SV478 ) )
        = ( ord_less_eq_nat @ SV123 @ SV755 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11761]) ).

thf(12084,plain,
    ! [SV756: nat,SV479: nat,SV124: nat] :
      ( ( ( ord_less_nat @ ( plus_plus_nat @ SV124 @ SV479 ) @ ( plus_plus_nat @ SV124 @ SV756 ) )
        = ( ord_less_nat @ SV479 @ SV756 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11762]) ).

thf(12085,plain,
    ! [SV757: nat,SV480: nat,SV125: nat] :
      ( ( ( ord_less_nat @ ( plus_plus_nat @ SV125 @ SV480 ) @ ( plus_plus_nat @ SV757 @ SV480 ) )
        = ( ord_less_nat @ SV125 @ SV757 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11763]) ).

thf(12086,plain,
    ! [SV758: nat,SV481: nat,SV128: nat] :
      ( ( ( times_times_nat @ ( times_times_nat @ SV128 @ SV481 ) @ SV758 )
        = ( times_times_nat @ SV128 @ ( times_times_nat @ SV481 @ SV758 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11764]) ).

thf(12087,plain,
    ! [SV759: nat,SV482: nat,SV129: nat] :
      ( ( ( times_times_nat @ ( times_times_nat @ SV129 @ SV482 ) @ SV759 )
        = ( times_times_nat @ SV129 @ ( times_times_nat @ SV482 @ SV759 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11765]) ).

thf(12088,plain,
    ! [SV483: nat] :
      ( ( ! [SV760: nat] :
            ( ( times_times_nat @ SV483 @ SV760 )
            = ( times_times_nat @ SV760 @ SV483 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11766]) ).

thf(12089,plain,
    ! [SV483: nat] :
      ( ( ( times_times_nat @ SV483 )
        = ( ^ [SY1627: nat] : ( times_times_nat @ SY1627 @ SV483 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11766]) ).

thf(12090,plain,
    ! [SV761: nat,SV484: nat,SV131: nat] :
      ( ( ( times_times_nat @ SV131 @ ( times_times_nat @ SV484 @ SV761 ) )
        = ( times_times_nat @ SV484 @ ( times_times_nat @ SV131 @ SV761 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11767]) ).

thf(12091,plain,
    ! [SV762: nat,SV485: nat,SV132: nat] :
      ( ( ( plus_plus_nat @ ( plus_plus_nat @ SV132 @ SV485 ) @ SV762 )
        = ( plus_plus_nat @ SV132 @ ( plus_plus_nat @ SV485 @ SV762 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11768]) ).

thf(12092,plain,
    ! [SV763: nat,SV486: nat,SV133: nat] :
      ( ( ( plus_plus_nat @ ( plus_plus_nat @ SV133 @ SV486 ) @ SV763 )
        = ( plus_plus_nat @ SV133 @ ( plus_plus_nat @ SV486 @ SV763 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11769]) ).

thf(12093,plain,
    ! [SV487: nat] :
      ( ( ! [SV764: nat] :
            ( ( plus_plus_nat @ SV487 @ SV764 )
            = ( plus_plus_nat @ SV764 @ SV487 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11770]) ).

thf(12094,plain,
    ! [SV487: nat] :
      ( ( ( plus_plus_nat @ SV487 )
        = ( ^ [SY1631: nat] : ( plus_plus_nat @ SY1631 @ SV487 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11770]) ).

thf(12095,plain,
    ! [SV765: nat,SV488: nat,SV135: nat] :
      ( ( ( plus_plus_nat @ SV135 @ ( plus_plus_nat @ SV488 @ SV765 ) )
        = ( plus_plus_nat @ SV488 @ ( plus_plus_nat @ SV135 @ SV765 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11771]) ).

thf(12096,plain,
    ! [SV766: nat,SV489: nat,SV138: nat] :
      ( ( ( minus_minus_nat @ ( minus_minus_nat @ SV138 @ SV489 ) @ SV766 )
        = ( minus_minus_nat @ SV138 @ ( plus_plus_nat @ SV489 @ SV766 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11772]) ).

thf(12097,plain,
    ! [SV767: nat,SV490: nat,SV139: nat] :
      ( ( ( plus_plus_nat @ ( ord_max_nat @ SV139 @ SV490 ) @ SV767 )
        = ( ord_max_nat @ ( plus_plus_nat @ SV139 @ SV767 ) @ ( plus_plus_nat @ SV490 @ SV767 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11773]) ).

thf(12098,plain,
    ! [SV768: nat,SV491: nat,SV140: nat] :
      ( ( ( plus_plus_nat @ SV140 @ ( ord_max_nat @ SV491 @ SV768 ) )
        = ( ord_max_nat @ ( plus_plus_nat @ SV140 @ SV491 ) @ ( plus_plus_nat @ SV140 @ SV768 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11774]) ).

thf(12099,plain,
    ! [SV492: nat] :
      ( ( ! [SV769: nat] :
            ( ( vEBT_VEBT_low @ SV492 @ SV769 )
            = ( modulo_modulo_nat @ SV492 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV769 ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11775]) ).

thf(12100,plain,
    ! [SV492: nat] :
      ( ( ( vEBT_VEBT_low @ SV492 )
        = ( ^ [SY1636: nat] : ( modulo_modulo_nat @ SV492 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1636 ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11775]) ).

thf(12101,plain,
    ! [SV770: nat,SV493: nat,SV142: nat] :
      ( ( ( ( times_times_nat @ SV142 @ SV493 )
          = ( times_times_nat @ SV770 @ SV493 ) )
        = ( ( SV493 = zero_zero_nat )
          | ( SV142 = SV770 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11776]) ).

thf(12102,plain,
    ! [SV771: nat,SV494: nat,SV143: nat] :
      ( ( ( ( times_times_nat @ SV143 @ SV494 )
          = ( times_times_nat @ SV143 @ SV771 ) )
        = ( ( SV143 = zero_zero_nat )
          | ( SV494 = SV771 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11777]) ).

thf(12103,plain,
    ! [SV495: nat,SV144: nat] :
      ( ( ~ ( ( ( times_times_nat @ SV144 @ SV495 )
              = zero_zero_nat )
            | ( SV144 = zero_zero_nat )
            | ( SV495 = zero_zero_nat ) )
        | ~ ( ( ( times_times_nat @ SV144 @ SV495 )
             != zero_zero_nat )
            | ~ ( ( SV144 = zero_zero_nat )
                | ( SV495 = zero_zero_nat ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11778]) ).

thf(12104,plain,
    ! [SV495: nat,SV144: nat] :
      ( ( ( ( times_times_nat @ SV144 @ SV495 )
          = zero_zero_nat )
        = ( ( SV144 = zero_zero_nat )
          | ( SV495 = zero_zero_nat ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11778]) ).

thf(12105,plain,
    ! [SV496: nat,SV148: nat] :
      ( ( ~ ( ( SV148
              = ( plus_plus_nat @ SV148 @ SV496 ) )
            | ( SV496 = zero_zero_nat ) )
        | ~ ( ( SV148
             != ( plus_plus_nat @ SV148 @ SV496 ) )
            | ( SV496 != zero_zero_nat ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11779]) ).

thf(12106,plain,
    ! [SV496: nat,SV148: nat] :
      ( ( ( SV148
          = ( plus_plus_nat @ SV148 @ SV496 ) )
        = ( SV496 = zero_zero_nat ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11779]) ).

thf(12107,plain,
    ! [SV497: nat,SV149: nat] :
      ( ( ~ ( ( SV149
              = ( plus_plus_nat @ SV497 @ SV149 ) )
            | ( SV497 = zero_zero_nat ) )
        | ~ ( ( SV149
             != ( plus_plus_nat @ SV497 @ SV149 ) )
            | ( SV497 != zero_zero_nat ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11780]) ).

thf(12108,plain,
    ! [SV497: nat,SV149: nat] :
      ( ( ( SV149
          = ( plus_plus_nat @ SV497 @ SV149 ) )
        = ( SV497 = zero_zero_nat ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11780]) ).

thf(12109,plain,
    ! [SV498: nat,SV150: nat] :
      ( ( ~ ( ( ( plus_plus_nat @ SV150 @ SV498 )
              = SV150 )
            | ( SV498 = zero_zero_nat ) )
        | ~ ( ( ( plus_plus_nat @ SV150 @ SV498 )
             != SV150 )
            | ( SV498 != zero_zero_nat ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11781]) ).

thf(12110,plain,
    ! [SV498: nat,SV150: nat] :
      ( ( ( ( plus_plus_nat @ SV150 @ SV498 )
          = SV150 )
        = ( SV498 = zero_zero_nat ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11781]) ).

thf(12111,plain,
    ! [SV499: nat,SV151: nat] :
      ( ( ~ ( ( ( plus_plus_nat @ SV151 @ SV499 )
              = SV499 )
            | ( SV151 = zero_zero_nat ) )
        | ~ ( ( ( plus_plus_nat @ SV151 @ SV499 )
             != SV499 )
            | ( SV151 != zero_zero_nat ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11782]) ).

thf(12112,plain,
    ! [SV499: nat,SV151: nat] :
      ( ( ( ( plus_plus_nat @ SV151 @ SV499 )
          = SV499 )
        = ( SV151 = zero_zero_nat ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11782]) ).

thf(12113,plain,
    ! [SV772: nat,SV502: nat,SV160: nat] :
      ( ( ( ( times_times_nat @ SV160 @ SV502 )
          = ( times_times_nat @ SV772 @ SV502 ) )
        = ( ( SV160 = SV772 )
          | ( SV502 = zero_zero_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11785]) ).

thf(12114,plain,
    ! [SV773: nat,SV503: nat,SV161: nat] :
      ( ( ( ( times_times_nat @ SV161 @ SV503 )
          = ( times_times_nat @ SV161 @ SV773 ) )
        = ( ( SV503 = SV773 )
          | ( SV161 = zero_zero_nat ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11786]) ).

thf(12115,plain,
    ! [SV504: nat,SV163: nat] :
      ( ( ~ ( ( ( times_times_nat @ SV163 @ SV504 )
              = zero_zero_nat )
            | ( SV163 = zero_zero_nat )
            | ( SV504 = zero_zero_nat ) )
        | ~ ( ( ( times_times_nat @ SV163 @ SV504 )
             != zero_zero_nat )
            | ~ ( ( SV163 = zero_zero_nat )
                | ( SV504 = zero_zero_nat ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11787]) ).

thf(12116,plain,
    ! [SV504: nat,SV163: nat] :
      ( ( ( ( times_times_nat @ SV163 @ SV504 )
          = zero_zero_nat )
        = ( ( SV163 = zero_zero_nat )
          | ( SV504 = zero_zero_nat ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11787]) ).

thf(12117,plain,
    ! [SV774: nat,SV505: nat,SV165: nat] :
      ( ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ SV165 @ SV505 ) @ SV774 ) @ SV165 )
        = ( modulo_modulo_nat @ SV774 @ SV165 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11788]) ).

thf(12118,plain,
    ! [SV775: nat,SV506: nat,SV166: nat] :
      ( ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ SV166 @ SV506 ) @ SV775 ) @ SV506 )
        = ( modulo_modulo_nat @ SV775 @ SV506 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11789]) ).

thf(12119,plain,
    ! [SV776: nat,SV507: nat,SV167: nat] :
      ( ( ( modulo_modulo_nat @ ( plus_plus_nat @ SV167 @ ( times_times_nat @ SV507 @ SV776 ) ) @ SV507 )
        = ( modulo_modulo_nat @ SV167 @ SV507 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11790]) ).

thf(12120,plain,
    ! [SV777: nat,SV508: nat,SV168: nat] :
      ( ( ( modulo_modulo_nat @ ( plus_plus_nat @ SV168 @ ( times_times_nat @ SV508 @ SV777 ) ) @ SV777 )
        = ( modulo_modulo_nat @ SV168 @ SV777 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11791]) ).

thf(12121,plain,
    ! [SV169: nat] :
      ( ( ( ~ ( ( ( power_power_nat @ SV169 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                = zero_zero_nat )
              | ( SV169 = zero_zero_nat ) ) )
        = $true )
      | ( ( ~ ( ( ( power_power_nat @ SV169 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
               != zero_zero_nat )
              | ( SV169 != zero_zero_nat ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11792]) ).

thf(12122,plain,
    ! [SV778: nat,SV509: nat,SV170: nat] :
      ( ( ( modulo_modulo_nat @ ( times_times_nat @ SV170 @ ( modulo_modulo_nat @ SV509 @ SV778 ) ) @ SV778 )
        = ( modulo_modulo_nat @ ( times_times_nat @ SV170 @ SV509 ) @ SV778 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11794]) ).

thf(12123,plain,
    ! [SV779: nat,SV510: nat,SV171: nat] :
      ( ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ SV171 @ SV510 ) @ SV779 ) @ SV510 )
        = ( modulo_modulo_nat @ ( times_times_nat @ SV171 @ SV779 ) @ SV510 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11795]) ).

thf(12124,plain,
    ! [SV780: nat,SV511: nat,SV172: nat] :
      ( ( ( times_times_nat @ SV172 @ ( modulo_modulo_nat @ SV511 @ SV780 ) )
        = ( modulo_modulo_nat @ ( times_times_nat @ SV172 @ SV511 ) @ ( times_times_nat @ SV172 @ SV780 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11796]) ).

thf(12125,plain,
    ! [SV781: nat,SV512: nat,SV173: nat] :
      ( ( ( modulo_modulo_nat @ ( times_times_nat @ SV173 @ SV512 ) @ ( times_times_nat @ SV781 @ SV512 ) )
        = ( times_times_nat @ ( modulo_modulo_nat @ SV173 @ SV781 ) @ SV512 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11797]) ).

thf(12126,plain,
    ! [SV782: nat,SV513: nat,SV174: nat] :
      ( ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ SV174 @ SV513 ) @ ( modulo_modulo_nat @ SV782 @ SV513 ) ) @ SV513 )
        = ( modulo_modulo_nat @ ( times_times_nat @ SV174 @ SV782 ) @ SV513 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11798]) ).

thf(12127,plain,
    ! [SV783: nat,SV514: nat,SV175: nat] :
      ( ( ( modulo_modulo_nat @ ( plus_plus_nat @ SV175 @ ( modulo_modulo_nat @ SV514 @ SV783 ) ) @ SV783 )
        = ( modulo_modulo_nat @ ( plus_plus_nat @ SV175 @ SV514 ) @ SV783 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11799]) ).

thf(12128,plain,
    ! [SV784: nat,SV515: nat,SV176: nat] :
      ( ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ SV176 @ SV515 ) @ SV784 ) @ SV515 )
        = ( modulo_modulo_nat @ ( plus_plus_nat @ SV176 @ SV784 ) @ SV515 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11800]) ).

thf(12129,plain,
    ! [SV785: nat,SV516: nat,SV177: nat] :
      ( ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ SV177 @ SV516 ) @ ( modulo_modulo_nat @ SV785 @ SV516 ) ) @ SV516 )
        = ( modulo_modulo_nat @ ( plus_plus_nat @ SV177 @ SV785 ) @ SV516 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11801]) ).

thf(12130,plain,
    ! [SV786: nat,SV517: nat,SV178: nat] :
      ( ( ( modulo_modulo_nat @ ( power_power_nat @ ( modulo_modulo_nat @ SV178 @ SV517 ) @ SV786 ) @ SV517 )
        = ( modulo_modulo_nat @ ( power_power_nat @ SV178 @ SV786 ) @ SV517 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11802]) ).

thf(12131,plain,
    ! [SV787: num,SV518: num,SV179: num] :
      ( ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV179 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) )
          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV787 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) ) )
        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV179 ) @ ( numeral_numeral_nat @ SV518 ) )
          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV787 ) @ ( numeral_numeral_nat @ SV518 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11803]) ).

thf(12132,plain,
    ! [SV788: nat,SV520: nat,SV185: nat] :
      ( ( ( ( times_times_nat @ SV185 @ SV520 )
          = ( times_times_nat @ SV185 @ SV788 ) )
        = ( ( SV185 = zero_zero_nat )
          | ( SV520 = SV788 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11805]) ).

thf(12133,plain,
    ! [SV789: nat,SV522: nat,SV187: nat] :
      ( ( ( divide_divide_nat @ ( plus_plus_nat @ SV187 @ SV522 ) @ SV789 )
        = ( plus_plus_nat @ ( plus_plus_nat @ ( divide_divide_nat @ SV187 @ SV789 ) @ ( divide_divide_nat @ SV522 @ SV789 ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ SV187 @ SV789 ) @ ( modulo_modulo_nat @ SV522 @ SV789 ) ) @ SV789 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11807]) ).

thf(12134,plain,
    ! [SV790: nat,SV523: nat,SV188: nat] :
      ( ( ( divide_divide_nat @ ( times_times_nat @ SV188 @ SV523 ) @ SV790 )
        = ( plus_plus_nat @ ( times_times_nat @ SV188 @ ( divide_divide_nat @ SV523 @ SV790 ) ) @ ( divide_divide_nat @ ( times_times_nat @ SV188 @ ( modulo_modulo_nat @ SV523 @ SV790 ) ) @ SV790 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11808]) ).

thf(12135,plain,
    ! [SV791: nat,SV529: nat,SV194: nat] :
      ( ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ SV194 @ SV529 ) @ SV529 ) @ ( modulo_modulo_nat @ SV194 @ SV529 ) ) @ SV791 )
        = ( plus_plus_nat @ SV194 @ SV791 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11814]) ).

thf(12136,plain,
    ! [SV792: nat,SV530: nat,SV195: nat] :
      ( ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ SV195 @ ( divide_divide_nat @ SV530 @ SV195 ) ) @ ( modulo_modulo_nat @ SV530 @ SV195 ) ) @ SV792 )
        = ( plus_plus_nat @ SV530 @ SV792 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11815]) ).

thf(12137,plain,
    ! [SV793: nat,SV531: nat,SV196: nat] :
      ( ( ( modulo_modulo_nat @ SV196 @ ( times_times_nat @ SV531 @ SV793 ) )
        = ( plus_plus_nat @ ( times_times_nat @ SV531 @ ( modulo_modulo_nat @ ( divide_divide_nat @ SV196 @ SV531 ) @ SV793 ) ) @ ( modulo_modulo_nat @ SV196 @ SV531 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11816]) ).

thf(12138,plain,
    ! [SV794: nat,SV532: nat,SV197: nat] :
      ( ( ( modulo_modulo_nat @ ( divide_divide_nat @ SV197 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV532 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV794 ) )
        = ( divide_divide_nat @ ( modulo_modulo_nat @ SV197 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV532 @ SV794 ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV532 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11817]) ).

thf(12139,plain,
    ! [SV534: num,SV199: num] :
      ( ( ~ ( ( ( bit0 @ SV199 )
              = ( bit0 @ SV534 ) )
            | ( SV199 = SV534 ) )
        | ~ ( ( ( bit0 @ SV199 )
             != ( bit0 @ SV534 ) )
            | ( SV199 != SV534 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11819]) ).

thf(12140,plain,
    ! [SV534: num,SV199: num] :
      ( ( ( ( bit0 @ SV199 )
          = ( bit0 @ SV534 ) )
        = ( SV199 = SV534 ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11819]) ).

thf(12141,plain,
    ! [SV535: nat,SV201: nat] :
      ( ( ~ ( ( dvd_dvd_nat @ SV201 @ ( plus_plus_nat @ SV535 @ SV201 ) )
            | ( dvd_dvd_nat @ SV201 @ SV535 ) )
        | ~ ( ~ ( dvd_dvd_nat @ SV201 @ ( plus_plus_nat @ SV535 @ SV201 ) )
            | ~ ( dvd_dvd_nat @ SV201 @ SV535 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11820]) ).

thf(12142,plain,
    ! [SV535: nat,SV201: nat] :
      ( ( ( dvd_dvd_nat @ SV201 @ ( plus_plus_nat @ SV535 @ SV201 ) )
        = ( dvd_dvd_nat @ SV201 @ SV535 ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11820]) ).

thf(12143,plain,
    ! [SV536: nat,SV202: nat] :
      ( ( ~ ( ( dvd_dvd_nat @ SV202 @ ( plus_plus_nat @ SV202 @ SV536 ) )
            | ( dvd_dvd_nat @ SV202 @ SV536 ) )
        | ~ ( ~ ( dvd_dvd_nat @ SV202 @ ( plus_plus_nat @ SV202 @ SV536 ) )
            | ~ ( dvd_dvd_nat @ SV202 @ SV536 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11821]) ).

thf(12144,plain,
    ! [SV536: nat,SV202: nat] :
      ( ( ( dvd_dvd_nat @ SV202 @ ( plus_plus_nat @ SV202 @ SV536 ) )
        = ( dvd_dvd_nat @ SV202 @ SV536 ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11821]) ).

thf(12145,plain,
    ! [SV795: nat,SV537: nat,SV203: nat] :
      ( ( ( dvd_dvd_nat @ SV203 @ ( plus_plus_nat @ SV537 @ ( times_times_nat @ SV795 @ SV203 ) ) )
        = ( dvd_dvd_nat @ SV203 @ SV537 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11822]) ).

thf(12146,plain,
    ! [SV796: nat,SV538: nat,SV204: nat] :
      ( ( ( dvd_dvd_nat @ SV204 @ ( plus_plus_nat @ ( times_times_nat @ SV538 @ SV204 ) @ SV796 ) )
        = ( dvd_dvd_nat @ SV204 @ SV796 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11823]) ).

thf(12147,plain,
    ! [SV539: nat,SV205: nat] :
      ( ( ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ SV205 @ SV539 ) )
            | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
            | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 ) )
        | ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ SV205 @ SV539 ) )
            | ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
                | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11824]) ).

thf(12148,plain,
    ! [SV539: nat,SV205: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ SV205 @ SV539 ) )
        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11824]) ).

thf(12149,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        | ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
            | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
             != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11825]) ).

thf(12150,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11825]) ).

thf(12151,plain,
    ! [SV797: nat,SV543: int,SV209: nat] :
      ( ( ! [SY1857: int,SY1858: int] :
            ( ( bit_concat_bit @ SV209 @ SV543 @ ( bit_concat_bit @ SV797 @ SY1857 @ SY1858 ) )
            = ( bit_concat_bit @ ( plus_plus_nat @ SV797 @ SV209 ) @ ( bit_concat_bit @ SV209 @ SV543 @ SY1857 ) @ SY1858 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11828]) ).

thf(12152,plain,
    ! [SV798: nat > nat,SV544: set_nat,SV211: nat > nat] :
      ( ( ! [SY1859: set_nat] :
            ( ( times_times_nat @ ( groups3542108847815614940at_nat @ SV211 @ SV544 ) @ ( groups3542108847815614940at_nat @ SV798 @ SY1859 ) )
            = ( groups3542108847815614940at_nat
              @ ^ [SY1860: nat] :
                  ( groups3542108847815614940at_nat
                  @ ^ [SY1861: nat] : ( times_times_nat @ ( SV211 @ SY1860 ) @ ( SV798 @ SY1861 ) )
                  @ SY1859 )
              @ SV544 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11829]) ).

thf(12153,plain,
    ! [SV799: nat,SV545: set_nat,SV212: nat > nat] :
      ( ( ( times_times_nat @ ( groups3542108847815614940at_nat @ SV212 @ SV545 ) @ SV799 )
        = ( groups3542108847815614940at_nat
          @ ^ [SY1862: nat] : ( times_times_nat @ ( SV212 @ SY1862 ) @ SV799 )
          @ SV545 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11830]) ).

thf(12154,plain,
    ! [SV800: set_nat,SV546: nat > nat,SV213: nat] :
      ( ( ( times_times_nat @ SV213 @ ( groups3542108847815614940at_nat @ SV546 @ SV800 ) )
        = ( groups3542108847815614940at_nat
          @ ^ [SY1674: nat] : ( times_times_nat @ SV213 @ ( SV546 @ SY1674 ) )
          @ SV800 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11831]) ).

thf(12155,plain,
    ! [SV801: set_nat,SV547: nat > nat,SV214: nat > nat] :
      ( ( ( groups3542108847815614940at_nat
          @ ^ [SY1676: nat] : ( plus_plus_nat @ ( SV214 @ SY1676 ) @ ( SV547 @ SY1676 ) )
          @ SV801 )
        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ SV214 @ SV801 ) @ ( groups3542108847815614940at_nat @ SV547 @ SV801 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11832]) ).

thf(12156,plain,
    ! [SV548: nat,SV215: nat] :
      ( ( ~ ( ( SV215
              = ( plus_plus_nat @ SV215 @ SV548 ) )
            | ( SV548 = zero_zero_nat ) )
        | ~ ( ( SV215
             != ( plus_plus_nat @ SV215 @ SV548 ) )
            | ( SV548 != zero_zero_nat ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11833]) ).

thf(12157,plain,
    ! [SV548: nat,SV215: nat] :
      ( ( ( SV215
          = ( plus_plus_nat @ SV215 @ SV548 ) )
        = ( SV548 = zero_zero_nat ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11833]) ).

thf(12158,plain,
    ! [SV802: nat,SV549: nat,SV216: nat] :
      ( ( ! [SY1865: nat] :
            ( ( ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV549 ) @ ( times_times_nat @ SV802 @ SY1865 ) )
              = ( plus_plus_nat @ ( times_times_nat @ SV216 @ SY1865 ) @ ( times_times_nat @ SV802 @ SV549 ) ) )
            = ( ( SV216 = SV802 )
              | ( SV549 = SY1865 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11834]) ).

thf(12159,plain,
    ! [SV803: nat,SV554: nat,SV224: nat] :
      ( ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV224 ) @ SV554 )
          = ( semiri1316708129612266289at_nat @ SV803 ) )
        = ( ( power_power_nat @ SV224 @ SV554 )
          = SV803 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11839]) ).

thf(12160,plain,
    ! [SV804: nat,SV555: nat,SV225: nat] :
      ( ( ( ( semiri1316708129612266289at_nat @ SV225 )
          = ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV555 ) @ SV804 ) )
        = ( SV225
          = ( power_power_nat @ SV555 @ SV804 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11840]) ).

thf(12161,plain,
    ! [SV805: nat,SV556: nat,SV226: num] :
      ( ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
          = ( semiri1316708129612266289at_nat @ SV805 ) )
        = ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
          = SV805 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11841]) ).

thf(12162,plain,
    ! [SV806: nat,SV557: num,SV227: nat] :
      ( ( ( ( semiri1316708129612266289at_nat @ SV227 )
          = ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
        = ( SV227
          = ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11842]) ).

thf(12163,plain,
    ! [SV807: nat,SV559: nat,SV229: nat] :
      ( ( ( divide_divide_nat @ SV229 @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ SV559 ) @ ( semiri1316708129612266289at_nat @ SV807 ) ) )
        = ( divide_divide_nat @ ( divide_divide_nat @ SV229 @ ( semiri1316708129612266289at_nat @ SV559 ) ) @ ( semiri1316708129612266289at_nat @ SV807 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11844]) ).

thf(12164,plain,
    ! [SV561: nat,SV231: nat > real] :
      ( ( ~ ( ( summable_real
              @ ^ [SY1684: nat] : ( SV231 @ ( plus_plus_nat @ SY1684 @ SV561 ) ) )
            | ( summable_real @ SV231 ) )
        | ~ ( ~ ( summable_real
                @ ^ [SY1684: nat] : ( SV231 @ ( plus_plus_nat @ SY1684 @ SV561 ) ) )
            | ~ ( summable_real @ SV231 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11846]) ).

thf(12165,plain,
    ! [SV561: nat,SV231: nat > real] :
      ( ( ( summable_real
          @ ^ [SY1684: nat] : ( SV231 @ ( plus_plus_nat @ SY1684 @ SV561 ) ) )
        = ( summable_real @ SV231 ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11846]) ).

thf(12166,plain,
    ! [SV562: nat,SV232: nat > complex] :
      ( ( ~ ( ( summable_complex
              @ ^ [SY1685: nat] : ( SV232 @ ( plus_plus_nat @ SY1685 @ SV562 ) ) )
            | ( summable_complex @ SV232 ) )
        | ~ ( ~ ( summable_complex
                @ ^ [SY1685: nat] : ( SV232 @ ( plus_plus_nat @ SY1685 @ SV562 ) ) )
            | ~ ( summable_complex @ SV232 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11847]) ).

thf(12167,plain,
    ! [SV562: nat,SV232: nat > complex] :
      ( ( ( summable_complex
          @ ^ [SY1685: nat] : ( SV232 @ ( plus_plus_nat @ SY1685 @ SV562 ) ) )
        = ( summable_complex @ SV232 ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11847]) ).

thf(12168,plain,
    ! [SV808: set_nat,SV563: nat > nat,SV233: nat > nat] :
      ( ( ( groups708209901874060359at_nat
          @ ^ [SY1687: nat] : ( times_times_nat @ ( SV233 @ SY1687 ) @ ( SV563 @ SY1687 ) )
          @ SV808 )
        = ( times_times_nat @ ( groups708209901874060359at_nat @ SV233 @ SV808 ) @ ( groups708209901874060359at_nat @ SV563 @ SV808 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11848]) ).

thf(12169,plain,
    ! [SV809: nat,SV564: set_nat,SV234: nat > nat] :
      ( ( ( power_power_nat @ ( groups708209901874060359at_nat @ SV234 @ SV564 ) @ SV809 )
        = ( groups708209901874060359at_nat
          @ ^ [SY1867: nat] : ( power_power_nat @ ( SV234 @ SY1867 ) @ SV809 )
          @ SV564 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11849]) ).

thf(12170,plain,
    ! [SV810: nat,SV565: nat,SV235: nat] :
      ( ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ SV235 @ SV565 ) @ SV810 ) @ ( plus_plus_nat @ SV235 @ SV810 ) ) @ ( binomial @ ( plus_plus_nat @ SV235 @ SV810 ) @ SV810 ) )
        = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ SV235 @ SV565 ) @ SV810 ) @ SV810 ) @ ( binomial @ ( plus_plus_nat @ SV235 @ SV565 ) @ SV235 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11850]) ).

thf(12171,plain,
    ! [SV811: real,SV566: nat,SV236: nat] :
      ( ( ( root @ ( times_times_nat @ SV236 @ SV566 ) @ SV811 )
        = ( root @ SV236 @ ( root @ SV566 @ SV811 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11851]) ).

thf(12172,plain,
    ! [SV567: nat] :
      ( ( ! [SV812: nat] :
            ( ( bit_se547839408752420682it_nat @ SV567 @ SV812 )
            = ( times_times_nat @ SV812 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV567 ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11852]) ).

thf(12173,plain,
    ! [SV567: nat] :
      ( ( ( bit_se547839408752420682it_nat @ SV567 )
        = ( ^ [SY1692: nat] : ( times_times_nat @ SY1692 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV567 ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11852]) ).

thf(12174,plain,
    ! [SV568: nat] :
      ( ( ! [SV813: nat] :
            ( ( bit_se8570568707652914677it_nat @ SV568 @ SV813 )
            = ( divide_divide_nat @ SV813 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV568 ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11853]) ).

thf(12175,plain,
    ! [SV568: nat] :
      ( ( ( bit_se8570568707652914677it_nat @ SV568 )
        = ( ^ [SY1693: nat] : ( divide_divide_nat @ SY1693 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV568 ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11853]) ).

thf(12176,plain,
    ! [SV814: nat,SV569: nat,SV242: nat] :
      ( ( ( times_times_nat @ SV242 @ ( gcd_gcd_nat @ SV569 @ SV814 ) )
        = ( gcd_gcd_nat @ ( times_times_nat @ SV242 @ SV569 ) @ ( times_times_nat @ SV242 @ SV814 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11854]) ).

thf(12177,plain,
    ! [SV243: $o] :
      ( ( ( ~ ( SV243
              | $true )
          | ~ ( ~ SV243
              | ~ $true ) )
        = $true )
      | ( ( SV243 = $false )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[11855]) ).

thf(12178,plain,
    ! [SV243: $o] :
      ( ( ( SV243 = $true )
        = $true )
      | ( ( SV243 = $false )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[11855]) ).

thf(12179,plain,
    ( ( ( ~ ( $true
            | $true )
        | ~ ( ~ $true
            | ~ $true ) )
      = $true )
    | ( ( $true = $false )
      = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[11856]) ).

thf(12180,plain,
    ( ( ( $true = $true )
      = $true )
    | ( ( $true = $false )
      = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[11856]) ).

thf(12181,plain,
    ( ( ( ~ ( $false
            | $true )
        | ~ ( ~ $false
            | ~ $true ) )
      = $true )
    | ( ( $false = $false )
      = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[11857]) ).

thf(12182,plain,
    ( ( ( $false = $true )
      = $true )
    | ( ( $false = $false )
      = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[11857]) ).

thf(12183,plain,
    ! [SV815: nat,SV570: nat,SV244: nat] :
      ( ( ~ ( ( SV244 != zero_zero_nat ) )
        | ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ SV244 @ SV570 ) @ SV815 ) @ SV244 )
          = ( plus_plus_nat @ SV570 @ ( divide_divide_nat @ SV815 @ SV244 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11858]) ).

thf(12184,plain,
    ! [SV816: nat,SV571: nat,SV245: nat] :
      ( ( ~ ( ord_less_nat @ SV245 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV571 ) )
        | ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ SV816 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV571 ) ) @ SV245 ) @ SV571 )
          = SV245 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11859]) ).

thf(12185,plain,
    ! [SV817: nat,SV572: nat,SV246: nat] :
      ( ( ~ ( dvd_dvd_nat @ SV246 @ SV572 )
        | ( ( divide_divide_nat @ ( plus_plus_nat @ SV572 @ SV817 ) @ SV246 )
          = ( plus_plus_nat @ ( divide_divide_nat @ SV572 @ SV246 ) @ ( divide_divide_nat @ SV817 @ SV246 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11860]) ).

thf(12186,plain,
    ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ maxs ) @ sK1_SX0 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[11861]) ).

thf(12187,plain,
    ! [SV818: nat,SV573: nat,SV247: nat] :
      ( ( ~ ( ord_less_nat @ SV247 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV573 @ SV818 ) ) )
        | ( ord_less_nat @ ( vEBT_VEBT_high @ SV247 @ SV573 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV818 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11862]) ).

thf(12188,plain,
    ! [SV574: nat,SV248: nat] :
      ( ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV248 ) )
        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV574 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[11863]) ).

thf(12189,plain,
    ! [SV819: nat,SV575: nat,SV249: nat] :
      ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV249 @ SV575 ) @ SV819 )
        | ( ord_less_nat @ SV249 @ SV819 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11864]) ).

thf(12190,plain,
    ! [SV820: nat,SV576: nat,SV250: nat] :
      ( ( ( ( times_times_nat @ SV250 @ SV576 )
         != ( times_times_nat @ SV576 @ SV250 ) )
        | ( ( times_times_nat @ ( power_power_nat @ SV250 @ SV820 ) @ SV576 )
          = ( times_times_nat @ SV576 @ ( power_power_nat @ SV250 @ SV820 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11865]) ).

thf(12191,plain,
    ! [SV577: nat,SV251: nat] :
      ( ( ( ( times_times_nat @ SV251 @ SV577 )
         != zero_zero_nat )
        = $true )
      | ( ( ( SV251 = zero_zero_nat )
          | ( SV577 = zero_zero_nat ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11866]) ).

thf(12192,plain,
    ! [SV821: nat,SV578: nat,SV252: nat] :
      ( ( ~ ( ( SV252 != zero_zero_nat ) )
        | ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ SV578 @ SV252 ) @ SV821 ) @ SV252 )
          = ( plus_plus_nat @ SV578 @ ( divide_divide_nat @ SV821 @ SV252 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11867]) ).

thf(12193,plain,
    ! [SV822: nat,SV579: nat,SV253: nat] :
      ( ( ! [SY1868: nat] :
            ( ~ ( ord_less_nat @ SV253 @ SV579 )
            | ( ( plus_plus_nat @ SV822 @ SV579 )
             != ( plus_plus_nat @ SV253 @ SY1868 ) )
            | ( ord_less_nat @ SV822 @ SY1868 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11868]) ).

thf(12194,plain,
    ! [SV823: nat,SV580: nat,SV254: nat] :
      ( ( ~ ( dvd_dvd_nat @ ( times_times_nat @ SV254 @ SV580 ) @ SV823 )
        | ( dvd_dvd_nat @ SV254 @ ( divide_divide_nat @ SV823 @ SV580 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11869]) ).

thf(12195,plain,
    ! [SV824: nat,SV581: nat,SV255: nat] :
      ( ( ~ ( ~ ( ( SV255 != zero_zero_nat )
                | ( ( divide_divide_nat @ ( times_times_nat @ SV255 @ SV581 ) @ ( times_times_nat @ SV255 @ SV824 ) )
                  = zero_zero_nat ) )
            | ~ ( ~ ( ( SV255 != zero_zero_nat ) )
                | ( ( divide_divide_nat @ ( times_times_nat @ SV255 @ SV581 ) @ ( times_times_nat @ SV255 @ SV824 ) )
                  = ( divide_divide_nat @ SV581 @ SV824 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11870]) ).

thf(12196,plain,
    ! [SV582: nat,SV256: nat] :
      ( ( ( ~ ( ( SV256 != zero_zero_nat ) ) )
        = $true )
      | ( ( ( divide_divide_nat @ ( times_times_nat @ SV256 @ SV582 ) @ SV256 )
          = SV582 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11871]) ).

thf(12197,plain,
    ! [SV825: nat,SV583: nat,SV257: nat] :
      ( ( ~ ( ( SV257 != zero_zero_nat ) )
        | ( ( ( times_times_nat @ SV583 @ SV257 )
            = ( times_times_nat @ SV825 @ SV257 ) )
          = ( SV583 = SV825 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11872]) ).

thf(12198,plain,
    ! [SV826: nat,SV584: nat,SV258: nat] :
      ( ( ~ ( dvd_dvd_nat @ SV258 @ ( times_times_nat @ SV584 @ SV826 ) )
        | ~ ! [SY1869: nat,SY1870: nat] :
              ( ( SV258
               != ( times_times_nat @ SY1869 @ SY1870 ) )
              | ~ ( dvd_dvd_nat @ SY1869 @ SV584 )
              | ~ ( dvd_dvd_nat @ SY1870 @ SV826 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11873]) ).

thf(12199,plain,
    ! [SV585: nat,SV259: nat] :
      ( ( ( ~ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV259 @ SV585 ) )
               != zero_zero_nat ) ) )
        = $true )
      | ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV585 )
         != zero_zero_nat )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11874]) ).

thf(12200,plain,
    ( ( vEBT_V8194947554948674370ptions @ summary @ maxs )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[11875]) ).

thf(12201,plain,
    ( ( maxs
     != ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[11876]) ).

thf(12202,plain,
    ! [SV827: nat,SV586: nat,SV260: nat] :
      ( ( ! [SY1871: nat] :
            ( ~ ~ ( ( SV260 != SV586 )
                  | ( SV827 != SY1871 ) )
            | ( ( plus_plus_nat @ SV260 @ SV827 )
              = ( plus_plus_nat @ SV586 @ SY1871 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11877]) ).

thf(12203,plain,
    ! [SV828: nat,SV587: nat,SV261: nat] :
      ( ( ~ ( dvd_dvd_nat @ SV261 @ SV587 )
        | ~ ( dvd_dvd_nat @ SV261 @ SV828 )
        | ( ( divide_divide_nat @ ( plus_plus_nat @ SV587 @ SV828 ) @ SV261 )
          = ( plus_plus_nat @ ( divide_divide_nat @ SV587 @ SV261 ) @ ( divide_divide_nat @ SV828 @ SV261 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11878]) ).

thf(12204,plain,
    ! [SV829: nat,SV588: nat,SV262: nat] :
      ( ( ~ ( dvd_dvd_nat @ SV262 @ SV588 )
        | ~ ( dvd_dvd_nat @ SV588 @ SV829 )
        | ( ( divide_divide_nat @ ( divide_divide_nat @ SV829 @ SV262 ) @ ( divide_divide_nat @ SV588 @ SV262 ) )
          = ( divide_divide_nat @ SV829 @ SV588 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11879]) ).

thf(12205,plain,
    ! [SV830: nat,SV589: nat,SV263: nat] :
      ( ( ! [SY1872: nat] :
            ( ( SV263
             != ( plus_plus_nat @ SV589 @ SV830 ) )
            | ( ( plus_plus_nat @ SV263 @ SY1872 )
              = ( plus_plus_nat @ SV589 @ ( plus_plus_nat @ SV830 @ SY1872 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11880]) ).

thf(12206,plain,
    ! [SV590: nat,SV264: nat > complex] :
      ( ( ( ~ ( summable_complex @ SV264 ) )
        = $true )
      | ( ( summable_complex
          @ ^ [SY1716: nat] : ( SV264 @ ( plus_plus_nat @ SY1716 @ SV590 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11881]) ).

thf(12207,plain,
    ! [SV831: nat,SV591: nat,SV265: nat] :
      ( ( ~ ( ord_less_eq_nat @ SV265 @ SV591 )
        | ( ord_less_eq_nat @ ( times_times_nat @ SV265 @ SV831 ) @ ( times_times_nat @ SV591 @ SV831 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11882]) ).

thf(12208,plain,
    ! [SV832: nat,SV592: nat,SV266: nat] :
      ( ( ~ ( ( SV266 != zero_zero_nat ) )
        | ( ( divide_divide_nat @ ( times_times_nat @ SV592 @ SV266 ) @ ( times_times_nat @ SV832 @ SV266 ) )
          = ( divide_divide_nat @ SV592 @ SV832 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11883]) ).

thf(12209,plain,
    ! [SV833: nat,SV593: nat,SV268: nat] :
      ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV268 @ SV593 ) @ SV833 )
        | ~ ( ~ ( ord_less_eq_nat @ SV268 @ SV833 )
            | ~ ( ord_less_eq_nat @ SV593 @ SV833 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11885]) ).

thf(12210,plain,
    ! [SV834: nat,SV594: nat,SV269: nat] :
      ( ( ~ ( ( SV269 != zero_zero_nat ) )
        | ( ( divide_divide_nat @ ( plus_plus_nat @ SV594 @ ( times_times_nat @ SV269 @ SV834 ) ) @ SV269 )
          = ( plus_plus_nat @ SV834 @ ( divide_divide_nat @ SV594 @ SV269 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11886]) ).

thf(12211,plain,
    ! [SV595: nat] :
      ( ( ! [SV835: nat] :
            ( ( SV595 = SV835 )
            = ( ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                   != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV835 ) )
                  | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                   != ( divide_divide_nat @ SV835 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11888]) ).

thf(12212,plain,
    ! [SV595: nat] :
      ( ( ( ^ [SY1721: nat] : ( SV595 = SY1721 ) )
        = ( ^ [SY1722: nat] :
              ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                 != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1722 ) )
                | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                 != ( divide_divide_nat @ SY1722 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11888]) ).

thf(12213,plain,
    ! [SV836: nat,SV596: nat,SV272: nat] :
      ( ( ! [SY1873: nat] :
            ( ~ ( dvd_dvd_nat @ SV272 @ SV596 )
            | ~ ( dvd_dvd_nat @ SV836 @ SY1873 )
            | ( dvd_dvd_nat @ ( times_times_nat @ SV272 @ SV836 ) @ ( times_times_nat @ SV596 @ SY1873 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11889]) ).

thf(12214,plain,
    ! [SV837: nat,SV597: nat,SV273: nat] :
      ( ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
          = ( modulo_modulo_nat @ SV837 @ SV597 ) )
        = ( ~ ! [SY1874: nat] :
                ~ ~ ! [SY1875: nat] :
                      ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SY1874 ) )
                     != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1875 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11890]) ).

thf(12215,plain,
    ! [SV838: nat,SV598: nat,SV274: nat] :
      ( ( ( ( plus_plus_nat @ SV274 @ SV598 )
         != ( plus_plus_nat @ SV838 @ SV598 ) )
        | ( SV274 = SV838 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11891]) ).

thf(12216,plain,
    ! [SV839: nat,SV599: nat,SV275: nat] :
      ( ( ~ ( ( SV275 != zero_zero_nat ) )
        | ( ( divide_divide_nat @ ( plus_plus_nat @ SV599 @ ( times_times_nat @ SV839 @ SV275 ) ) @ SV275 )
          = ( plus_plus_nat @ SV839 @ ( divide_divide_nat @ SV599 @ SV275 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11892]) ).

thf(12217,plain,
    ! [SV840: nat,SV600: nat,SV276: nat] :
      ( ( ~ ( ord_less_eq_nat @ SV276 @ SV600 )
        | ( ord_less_eq_nat @ ( times_times_nat @ SV840 @ SV276 ) @ ( times_times_nat @ SV840 @ SV600 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11893]) ).

thf(12218,plain,
    ! [SV277: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV277 )
        = $false )
      | ( ( ~ ! [SY1343: nat] :
                ( SV277
               != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1343 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[11894]) ).

thf(12219,plain,
    ! [SV601: nat,SV280: nat] :
      ( ( ( ~ ( ( ( times_times_nat @ SV280 @ SV601 )
               != zero_zero_nat ) ) )
        = $true )
      | ( ( ~ ( ~ ( ( SV280 != zero_zero_nat ) )
              | ~ ( ( SV601 != zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11897]) ).

thf(12220,plain,
    ! [SV841: nat,SV602: nat,SV281: nat] :
      ( ( ~ ( ord_less_nat @ SV281 @ ( times_times_nat @ SV602 @ SV841 ) )
        | ( ord_less_nat @ ( divide_divide_nat @ SV281 @ SV841 ) @ SV602 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11898]) ).

thf(12221,plain,
    ( ( ( some_nat @ sK2_SX0 )
      = ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[11899]) ).

thf(12222,plain,
    ! [SV842: nat,SV603: nat,SV282: nat] :
      ( ( ! [SY1876: nat] :
            ( ( SV282
             != ( plus_plus_nat @ SV603 @ SV842 ) )
            | ( ( plus_plus_nat @ SY1876 @ SV282 )
              = ( plus_plus_nat @ SV603 @ ( plus_plus_nat @ SY1876 @ SV842 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11900]) ).

thf(12223,plain,
    ! [SV843: nat,SV604: nat,SV283: nat] :
      ( ( ( ( times_times_nat @ SV283 @ SV604 )
         != one_one_nat )
        | ( ( times_times_nat @ ( power_power_nat @ SV283 @ SV843 ) @ ( power_power_nat @ SV604 @ SV843 ) )
          = one_one_nat ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11901]) ).

thf(12224,plain,
    ! [SV844: nat,SV605: nat,SV284: nat] :
      ( ( ! [SY1877: nat] :
            ( ( ~ ( ~ ( ( SV284 != SV605 ) )
                  | ~ ( ( SV844 != SY1877 ) ) ) )
            = ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SY1877 ) )
             != ( plus_plus_nat @ ( times_times_nat @ SV284 @ SY1877 ) @ ( times_times_nat @ SV605 @ SV844 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11902]) ).

thf(12225,plain,
    ! [SV845: nat,SV606: nat,SV285: nat] :
      ( ( ~ ( ( SV285 != zero_zero_nat ) )
        | ( ( ( times_times_nat @ SV285 @ SV606 )
            = ( times_times_nat @ SV285 @ SV845 ) )
          = ( SV606 = SV845 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11903]) ).

thf(12226,plain,
    ! [SV846: nat,SV607: nat,SV286: nat] :
      ( ( ~ ( dvd_dvd_nat @ SV286 @ SV607 )
        | ( ( times_times_nat @ ( divide_divide_nat @ SV607 @ SV286 ) @ SV846 )
          = ( divide_divide_nat @ ( times_times_nat @ SV607 @ SV846 ) @ SV286 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11904]) ).

thf(12227,plain,
    ! [SV608: nat,SV287: nat] :
      ( ( ( ~ ( ( SV287 != zero_zero_nat ) ) )
        = $true )
      | ( ( ~ ( ( SV608 != zero_zero_nat ) )
          | ( ( times_times_nat @ SV287 @ SV608 )
           != zero_zero_nat ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11905]) ).

thf(12228,plain,
    ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ summin ) @ sK3_SX0 )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[11906]) ).

thf(12229,plain,
    ! [SV609: nat,SV288: nat] :
      ( ( ( ( divide_divide_nat @ SV288 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
         != ( divide_divide_nat @ SV609 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $true )
      | ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV288 )
           != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV609 ) )
          | ( SV288 = SV609 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11907]) ).

thf(12230,plain,
    ! [SV847: nat,SV610: nat,SV289: nat] :
      ( ( ~ ( ord_less_eq_nat @ SV289 @ SV610 )
        | ( ord_less_eq_nat @ ( plus_plus_nat @ SV289 @ SV847 ) @ ( plus_plus_nat @ SV610 @ SV847 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11908]) ).

thf(12231,plain,
    ! [SV848: nat,SV611: nat,SV290: nat] :
      ( ( ! [SY1878: nat] :
            ( ~ ~ ( ~ ( ord_less_nat @ SV290 @ SV611 )
                  | ~ ( ord_less_nat @ SV848 @ SY1878 ) )
            | ( ord_less_nat @ ( plus_plus_nat @ SV290 @ SV848 ) @ ( plus_plus_nat @ SV611 @ SY1878 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11909]) ).

thf(12232,plain,
    ! [SV612: nat,SV291: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV291 @ SV612 ) )
        = $true )
      | ( ( ( times_times_nat @ SV291 @ ( divide_divide_nat @ SV612 @ SV291 ) )
          = SV612 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11910]) ).

thf(12233,plain,
    ! [SV613: num,SV292: num] :
      ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV292 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV613 ) ) )
        = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ SV613 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[11911]) ).

thf(12234,plain,
    ! [SV614: nat,SV293: nat] :
      ( ( ( ~ ( ( SV293 != zero_zero_nat ) ) )
        = $true )
      | ( ( ( divide_divide_nat @ ( times_times_nat @ SV614 @ SV293 ) @ SV293 )
          = SV614 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11912]) ).

thf(12235,plain,
    ! [SV849: nat,SV615: nat,SV294: nat] :
      ( ( ! [SY1879: nat] :
            ( ~ ~ ( ( SV294 != SV615 )
                  | ~ ( ord_less_nat @ SV849 @ SY1879 ) )
            | ( ord_less_nat @ ( plus_plus_nat @ SV294 @ SV849 ) @ ( plus_plus_nat @ SV615 @ SY1879 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11913]) ).

thf(12236,plain,
    ! [SV616: num,SV295: num] :
      ( ( ( bit1 @ SV295 )
        = ( bit0 @ SV616 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[11914]) ).

thf(12237,plain,
    ! [SV850: nat,SV617: nat,SV296: nat] :
      ( ( ! [SY1880: nat] :
            ( ~ ( ord_less_nat @ SV296 @ SV617 )
            | ~ ( ord_less_nat @ SV850 @ SY1880 )
            | ( ord_less_nat @ ( plus_plus_nat @ SV296 @ SV850 ) @ ( plus_plus_nat @ SV617 @ SY1880 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11915]) ).

thf(12238,plain,
    ! [SV851: nat,SV618: nat,SV297: nat] :
      ( ( ! [SY1881: nat] :
            ( ~ ( dvd_dvd_nat @ SV297 @ SV618 )
            | ~ ( dvd_dvd_nat @ SV851 @ SY1881 )
            | ( ( times_times_nat @ ( divide_divide_nat @ SV618 @ SV297 ) @ ( divide_divide_nat @ SY1881 @ SV851 ) )
              = ( divide_divide_nat @ ( times_times_nat @ SV618 @ SY1881 ) @ ( times_times_nat @ SV297 @ SV851 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11916]) ).

thf(12239,plain,
    ! [SV619: nat,SV298: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV298 @ SV619 ) )
        = $true )
      | ( ( ~ ! [SY1748: nat] :
                ( SV619
               != ( plus_plus_nat @ SV298 @ SY1748 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11917]) ).

thf(12240,plain,
    ! [SV852: nat,SV620: nat,SV299: nat] :
      ( ( ~ ( ord_less_eq_nat @ SV299 @ SV620 )
        | ( ord_less_eq_nat @ SV299 @ ( plus_plus_nat @ SV852 @ SV620 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11918]) ).

thf(12241,plain,
    ! [SV621: nat,SV300: nat] :
      ( ( ~ ( ( ( times_times_nat @ SV300 @ SV621 )
              = one_one_nat )
            | ~ ( ( SV300 != one_one_nat )
                | ( SV621 != one_one_nat ) ) )
        | ~ ( ( ( times_times_nat @ SV300 @ SV621 )
             != one_one_nat )
            | ~ ~ ( ( SV300 != one_one_nat )
                  | ( SV621 != one_one_nat ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11919]) ).

thf(12242,plain,
    ! [SV621: nat,SV300: nat] :
      ( ( ( ( times_times_nat @ SV300 @ SV621 )
          = one_one_nat )
        = ( ~ ( ( SV300 != one_one_nat )
              | ( SV621 != one_one_nat ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11919]) ).

thf(12243,plain,
    ( ( ( some_nat @ sK4_SX0 )
      = ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ treeList @ maxs ) ) )
    = $true ),
    inference(extcnf_not_neg,[status(thm)],[11920]) ).

thf(12244,plain,
    ! [SV622: nat] :
      ( ( ! [SV853: nat] :
            ( ( dvd_dvd_nat @ SV622 @ SV853 )
            = ( ~ ! [SY1882: nat] :
                    ( SV853
                   != ( times_times_nat @ SV622 @ SY1882 ) ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11921]) ).

thf(12245,plain,
    ! [SV622: nat] :
      ( ( ( dvd_dvd_nat @ SV622 )
        = ( ^ [SY1750: nat] :
              ~ ! [SY1751: nat] :
                  ( SY1750
                 != ( times_times_nat @ SV622 @ SY1751 ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11921]) ).

thf(12246,plain,
    ! [SV623: nat,SV302: nat > real] :
      ( ( ( ~ ( summable_real @ SV302 ) )
        = $true )
      | ( ( summable_real
          @ ^ [SY1752: nat] : ( SV302 @ ( plus_plus_nat @ SY1752 @ SV623 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11922]) ).

thf(12247,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
            | ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
             != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) )
        | ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
            | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
                 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11923]) ).

thf(12248,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) ) )
        = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
         != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11923]) ).

thf(12249,plain,
    ! [SV854: nat,SV625: nat,SV304: nat] :
      ( ( ~ ( ord_less_nat @ SV304 @ SV625 )
        | ( ord_less_nat @ ( plus_plus_nat @ SV304 @ SV854 ) @ ( plus_plus_nat @ SV625 @ SV854 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11924]) ).

thf(12250,plain,
    ! [SV626: nat,SV305: nat] :
      ( ( ~ ( ( ( plus_plus_nat @ SV305 @ SV626 )
              = zero_zero_nat )
            | ~ ( ( SV305 != zero_zero_nat )
                | ( SV626 != zero_zero_nat ) ) )
        | ~ ( ( ( plus_plus_nat @ SV305 @ SV626 )
             != zero_zero_nat )
            | ~ ~ ( ( SV305 != zero_zero_nat )
                  | ( SV626 != zero_zero_nat ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11925]) ).

thf(12251,plain,
    ! [SV626: nat,SV305: nat] :
      ( ( ( ( plus_plus_nat @ SV305 @ SV626 )
          = zero_zero_nat )
        = ( ~ ( ( SV305 != zero_zero_nat )
              | ( SV626 != zero_zero_nat ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11925]) ).

thf(12252,plain,
    ! [SV627: nat,SV307: nat] :
      ( ( ( ( plus_plus_nat @ SV307 @ SV627 )
         != SV307 )
        = $true )
      | ( ( SV627 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11927]) ).

thf(12253,plain,
    ! [SV855: nat,SV628: nat,SV308: nat] :
      ( ( ~ ( ord_less_eq_nat @ SV308 @ SV628 )
        | ( ord_less_eq_nat @ ( divide_divide_nat @ SV308 @ SV855 ) @ ( divide_divide_nat @ SV628 @ SV855 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11928]) ).

thf(12254,plain,
    ! [SV629: nat,SV309: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV309 @ SV629 ) )
        = $true )
      | ( ( ~ ! [SY1755: nat] :
                ( SV629
               != ( plus_plus_nat @ SV309 @ SY1755 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11929]) ).

thf(12255,plain,
    ! [SV630: nat,SV310: nat] :
      ( ( ~ ( ( ( plus_plus_nat @ SV310 @ SV630 )
              = zero_zero_nat )
            | ~ ( ( SV310 != zero_zero_nat )
                | ( SV630 != zero_zero_nat ) ) )
        | ~ ( ( ( plus_plus_nat @ SV310 @ SV630 )
             != zero_zero_nat )
            | ~ ~ ( ( SV310 != zero_zero_nat )
                  | ( SV630 != zero_zero_nat ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11930]) ).

thf(12256,plain,
    ! [SV630: nat,SV310: nat] :
      ( ( ( ( plus_plus_nat @ SV310 @ SV630 )
          = zero_zero_nat )
        = ( ~ ( ( SV310 != zero_zero_nat )
              | ( SV630 != zero_zero_nat ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11930]) ).

thf(12257,plain,
    ! [SV856: nat,SV631: nat,SV311: nat] :
      ( ( ~ ( dvd_dvd_nat @ SV311 @ ( times_times_nat @ SV631 @ SV856 ) )
        | ~ ! [SY1883: nat] :
              ~ ~ ! [SY1884: nat] :
                    ~ ~ ( ~ ~ ( ( SV311
                               != ( times_times_nat @ SY1883 @ SY1884 ) )
                              | ~ ( dvd_dvd_nat @ SY1883 @ SV631 ) )
                        | ~ ( dvd_dvd_nat @ SY1884 @ SV856 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11931]) ).

thf(12258,plain,
    ! [SV857: nat,SV632: nat,SV312: nat] :
      ( ( ! [SY1885: nat,SY1886: nat] :
            ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
            | ~ ( dvd_dvd_nat @ SV312 @ SV857 )
            | ~ ( ( ( times_times_nat @ SV632 @ SY1885 )
                  = ( plus_plus_nat @ ( times_times_nat @ SV857 @ SY1886 ) @ SV312 ) )
                | ( ( times_times_nat @ SV857 @ SY1885 )
                  = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SY1886 ) @ SV312 ) ) )
            | ~ ! [SY1887: nat] :
                  ~ ~ ! [SY1888: nat] :
                        ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
                                  | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) )
                            | ~ ( ( ( times_times_nat @ SV632 @ SY1887 )
                                  = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1888 ) @ SV312 ) )
                                | ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1887 )
                                  = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SY1888 ) @ SV312 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11932]) ).

thf(12259,plain,
    ! [SV858: nat,SV633: nat,SV313: nat] :
      ( ( ~ ( ord_less_eq_nat @ SV313 @ SV633 )
        | ( ord_less_eq_nat @ ( plus_plus_nat @ SV313 @ SV858 ) @ ( plus_plus_nat @ SV633 @ SV858 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11933]) ).

thf(12260,plain,
    ! [SV859: nat,SV634: nat,SV314: nat] :
      ( ( ~ ( dvd_dvd_nat @ SV314 @ SV634 )
        | ~ ( dvd_dvd_nat @ SV634 @ SV859 )
        | ( ( divide_divide_nat @ SV859 @ ( divide_divide_nat @ SV634 @ SV314 ) )
          = ( times_times_nat @ ( divide_divide_nat @ SV859 @ SV634 ) @ SV314 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11934]) ).

thf(12261,plain,
    ! [SV635: nat,SV315: nat] :
      ( ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV315 )
        = ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV635 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[11935]) ).

thf(12262,plain,
    ! [SV636: num,SV316: num > $o] :
      ( ( ( ~ ( SV316 @ one ) )
        = $true )
      | ( ( ~ ! [SY1414: num] :
                ( ~ ( SV316 @ SY1414 )
                | ( SV316 @ ( inc @ SY1414 ) ) )
          | ( SV316 @ SV636 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11936]) ).

thf(12263,plain,
    ! [SV637: nat,SV317: nat] :
      ( ( ( ~ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV317 @ SV637 ) )
               != zero_zero_nat ) ) )
        = $true )
      | ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV317 )
         != zero_zero_nat )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11937]) ).

thf(12264,plain,
    ! [SV638: num,SV318: num] :
      ( ( ( bit0 @ SV318 )
        = ( bit1 @ SV638 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[11938]) ).

thf(12265,plain,
    ! [SV860: nat,SV639: nat,SV319: nat > nat > $o] :
      ( ( ~ ! [SY1419: nat,SY1420: nat] :
              ( ( SV319 @ SY1419 @ SY1420 )
              = ( SV319 @ SY1420 @ SY1419 ) )
        | ~ ! [SY1421: nat] : ( SV319 @ SY1421 @ zero_zero_nat )
        | ~ ! [SY1422: nat,SY1423: nat] :
              ( ~ ( SV319 @ SY1422 @ SY1423 )
              | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) )
        | ( SV319 @ SV639 @ SV860 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11939]) ).

thf(12266,plain,
    ! [SV640: num,SV320: num] :
      ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ SV320 ) ) )
        = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV640 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV320 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[11940]) ).

thf(12267,plain,
    ! [SV861: nat,SV641: nat,SV321: nat] :
      ( ( ~ ( ord_less_nat @ SV321 @ SV641 )
        | ( ord_less_nat @ SV321 @ ( plus_plus_nat @ SV861 @ SV641 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11941]) ).

thf(12268,plain,
    ! [SV642: nat,SV322: nat] :
      ( ( ~ ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 )
            | ~ ( ~ ( ( SV322 != SV642 ) )
                | ~ ( vEBT_V8194947554948674370ptions @ summary @ SV642 ) ) )
        | ~ ( ~ ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 )
            | ~ ~ ( ~ ( ( SV322 != SV642 ) )
                  | ~ ( vEBT_V8194947554948674370ptions @ summary @ SV642 ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11942]) ).

thf(12269,plain,
    ! [SV642: nat,SV322: nat] :
      ( ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 )
        = ( ~ ( ~ ( ( SV322 != SV642 ) )
              | ~ ( vEBT_V8194947554948674370ptions @ summary @ SV642 ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11942]) ).

thf(12270,plain,
    ! [SV862: nat,SV643: nat,SV323: nat] :
      ( ( ! [SY1894: nat,SY1895: nat] :
            ( ( ( modulo_modulo_nat @ SV323 @ SV643 )
             != ( modulo_modulo_nat @ SV862 @ SV643 ) )
            | ( ( modulo_modulo_nat @ SY1894 @ SV643 )
             != ( modulo_modulo_nat @ SY1895 @ SV643 ) )
            | ( ( modulo_modulo_nat @ ( times_times_nat @ SV323 @ SY1894 ) @ SV643 )
              = ( modulo_modulo_nat @ ( times_times_nat @ SV862 @ SY1895 ) @ SV643 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11943]) ).

thf(12271,plain,
    ! [SV644: nat] :
      ( ( ! [SV863: nat] :
            ( ( ord_less_eq_nat @ SV644 @ SV863 )
            = ( ~ ! [SY1896: nat] :
                    ( SV863
                   != ( plus_plus_nat @ SV644 @ SY1896 ) ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11944]) ).

thf(12272,plain,
    ! [SV644: nat] :
      ( ( ( ord_less_eq_nat @ SV644 )
        = ( ^ [SY1777: nat] :
              ~ ! [SY1778: nat] :
                  ( SY1777
                 != ( plus_plus_nat @ SV644 @ SY1778 ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11944]) ).

thf(12273,plain,
    ! [SV864: nat,SV645: nat,SV325: nat] :
      ( ( ~ ( dvd_dvd_nat @ ( times_times_nat @ SV325 @ SV645 ) @ SV864 )
        | ( ( divide_divide_nat @ SV864 @ ( times_times_nat @ SV325 @ SV645 ) )
          = ( divide_divide_nat @ ( divide_divide_nat @ SV864 @ SV325 ) @ SV645 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11945]) ).

thf(12274,plain,
    ! [SV865: nat,SV646: nat,SV326: nat] :
      ( ( ~ ( dvd_dvd_nat @ SV326 @ SV646 )
        | ( ( times_times_nat @ SV865 @ ( divide_divide_nat @ SV646 @ SV326 ) )
          = ( divide_divide_nat @ ( times_times_nat @ SV865 @ SV646 ) @ SV326 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11946]) ).

thf(12275,plain,
    ! [SV866: nat,SV647: nat,SV327: nat] :
      ( ( ~ ( ord_less_nat @ SV327 @ SV647 )
        | ( ord_less_nat @ ( plus_plus_nat @ SV327 @ SV866 ) @ ( plus_plus_nat @ SV647 @ SV866 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11947]) ).

thf(12276,plain,
    ! [SV867: nat,SV648: nat,SV328: nat] :
      ( ( ! [SY1897: nat] :
            ( ~ ~ ( ~ ( ord_less_eq_nat @ SV328 @ SV648 )
                  | ( SV867 != SY1897 ) )
            | ( ord_less_eq_nat @ ( plus_plus_nat @ SV328 @ SV867 ) @ ( plus_plus_nat @ SV648 @ SY1897 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11948]) ).

thf(12277,plain,
    ! [SV649: nat,SV329: nat] :
      ( ( ~ ( ( zero_zero_nat
              = ( plus_plus_nat @ SV329 @ SV649 ) )
            | ~ ( ( SV329 != zero_zero_nat )
                | ( SV649 != zero_zero_nat ) ) )
        | ~ ( ( zero_zero_nat
             != ( plus_plus_nat @ SV329 @ SV649 ) )
            | ~ ~ ( ( SV329 != zero_zero_nat )
                  | ( SV649 != zero_zero_nat ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11949]) ).

thf(12278,plain,
    ! [SV649: nat,SV329: nat] :
      ( ( ( zero_zero_nat
          = ( plus_plus_nat @ SV329 @ SV649 ) )
        = ( ~ ( ( SV329 != zero_zero_nat )
              | ( SV649 != zero_zero_nat ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11949]) ).

thf(12279,plain,
    ! [SV868: nat,SV650: nat,SV330: nat] :
      ( ( ~ ( dvd_dvd_nat @ SV330 @ SV650 )
        | ( dvd_dvd_nat @ ( power_power_nat @ SV330 @ SV868 ) @ ( power_power_nat @ SV650 @ SV868 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11950]) ).

thf(12280,plain,
    ! [SV651: nat,SV331: nat] :
      ( ( ( ~ ( ( SV331 != zero_zero_nat ) ) )
        = $true )
      | ( ( ( power_power_nat @ SV331 @ SV651 )
         != zero_zero_nat )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11951]) ).

thf(12281,plain,
    ! [SV869: list_VEBT_VEBT,SV652: nat,SV332: nat] :
      ( ( ! [SY1898: vEBT_VEBT,SY1899: vEBT_VEBT] :
            ( ~ ( ( SV332 != SV652 ) )
            | ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV869 @ SV332 @ SY1898 ) @ SV652 @ SY1899 )
              = ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV869 @ SV652 @ SY1899 ) @ SV332 @ SY1898 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11952]) ).

thf(12282,plain,
    ! [SV870: nat,SV656: nat,SV334: nat] :
      ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV334 @ SV656 ) @ ( plus_plus_nat @ SV870 @ SV656 ) )
        | ( ord_less_nat @ SV334 @ SV870 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11962]) ).

thf(12283,plain,
    ! [SV871: nat,SV657: nat,SV335: nat] :
      ( ( ! [SY1900: nat] :
            ( ~ ~ ( ( SV335 != SV657 )
                  | ~ ( ord_less_eq_nat @ SV871 @ SY1900 ) )
            | ( ord_less_eq_nat @ ( plus_plus_nat @ SV335 @ SV871 ) @ ( plus_plus_nat @ SV657 @ SY1900 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11963]) ).

thf(12284,plain,
    ! [SV872: nat,SV658: nat,SV336: nat] :
      ( ( ~ ( dvd_dvd_nat @ SV336 @ SV658 )
        | ( ( dvd_dvd_nat @ SV336 @ ( plus_plus_nat @ SV872 @ SV658 ) )
          = ( dvd_dvd_nat @ SV336 @ SV872 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11964]) ).

thf(12285,plain,
    ! [SV873: nat,SV659: nat,SV337: nat] :
      ( ( ( SV337
         != ( plus_plus_nat @ SV659 @ SV873 ) )
        | ( ( suc @ SV337 )
          = ( plus_plus_nat @ SV659 @ ( suc @ SV873 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11965]) ).

thf(12286,plain,
    ! [SV874: nat,SV660: nat,SV338: nat] :
      ( ( ~ ( dvd_dvd_nat @ SV338 @ SV660 )
        | ~ ( dvd_dvd_nat @ SV338 @ SV874 )
        | ( dvd_dvd_nat @ SV338 @ ( plus_plus_nat @ SV660 @ SV874 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11966]) ).

thf(12287,plain,
    ! [SV875: nat,SV661: nat,SV339: nat] :
      ( ( ( ( plus_plus_nat @ SV339 @ SV661 )
         != ( plus_plus_nat @ SV339 @ SV875 ) )
        | ( SV661 = SV875 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11967]) ).

thf(12288,plain,
    ! [SV340: nat] :
      ( ( ( ! [SY1465: nat] :
              ( SV340
             != ( plus_plus_nat @ SY1465 @ SY1465 ) ) )
        = $false )
      | ( ( ~ ! [SY1466: nat] :
                ( SV340
               != ( plus_plus_nat @ SY1466 @ ( suc @ SY1466 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[11968]) ).

thf(12289,plain,
    ! [SV876: nat,SV662: nat,SV341: nat] :
      ( ( ! [SY1901: nat] :
            ( ~ ~ ( ~ ( ord_less_eq_nat @ SV341 @ SV662 )
                  | ~ ( ord_less_eq_nat @ SV876 @ SY1901 ) )
            | ( ord_less_eq_nat @ ( plus_plus_nat @ SV341 @ SV876 ) @ ( plus_plus_nat @ SV662 @ SY1901 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11969]) ).

thf(12290,plain,
    ! [SV877: nat,SV663: nat,SV342: nat] :
      ( ( ~ ( ( SV342 != zero_zero_nat ) )
        | ( ( divide_divide_nat @ ( times_times_nat @ SV342 @ SV663 ) @ ( times_times_nat @ SV342 @ SV877 ) )
          = ( divide_divide_nat @ SV663 @ SV877 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11970]) ).

thf(12291,plain,
    ! [SV878: nat,SV664: nat,SV343: nat] :
      ( ( ~ ( ord_less_nat @ SV343 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV664 ) )
        | ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ SV878 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV664 ) ) @ SV343 ) @ SV664 )
          = SV878 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11971]) ).

thf(12292,plain,
    ! [SV879: nat,SV665: nat,SV344: nat] :
      ( ( ~ ( dvd_dvd_nat @ SV344 @ SV665 )
        | ( ( divide_divide_nat @ ( plus_plus_nat @ SV879 @ SV665 ) @ SV344 )
          = ( plus_plus_nat @ ( divide_divide_nat @ SV879 @ SV344 ) @ ( divide_divide_nat @ SV665 @ SV344 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11972]) ).

thf(12293,plain,
    ! [SV880: nat,SV666: nat,SV345: nat] :
      ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV345 @ SV666 ) @ SV880 )
        | ( ord_less_eq_nat @ SV666 @ SV880 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11973]) ).

thf(12294,plain,
    ! [SV881: nat,SV667: nat,SV346: nat] :
      ( ( ~ ( dvd_dvd_nat @ ( times_times_nat @ SV346 @ SV667 ) @ SV881 )
        | ( dvd_dvd_nat @ SV667 @ SV881 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11974]) ).

thf(12295,plain,
    ! [SV882: nat,SV668: nat,SV347: nat] :
      ( ( ~ ( dvd_dvd_nat @ SV347 @ SV668 )
        | ~ ( dvd_dvd_nat @ SV347 @ SV882 )
        | ( ( dvd_dvd_nat @ ( divide_divide_nat @ SV668 @ SV347 ) @ ( divide_divide_nat @ SV882 @ SV347 ) )
          = ( dvd_dvd_nat @ SV668 @ SV882 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11975]) ).

thf(12296,plain,
    ! [SV348: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV348 )
        = $false )
      | ( ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ SV348 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
          = SV348 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[11976]) ).

thf(12297,plain,
    ! [SV669: nat,SV349: nat] :
      ( ( ! [SY1803: nat] :
            ~ ~ ! [SY1804: nat] :
                  ~ ~ ! [SY1805: nat] :
                        ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ SY1803 @ SV349 )
                                  | ~ ( dvd_dvd_nat @ SY1803 @ SV669 ) )
                            | ~ ( ( ( times_times_nat @ SV349 @ SY1804 )
                                  = ( plus_plus_nat @ ( times_times_nat @ SV669 @ SY1805 ) @ SY1803 ) )
                                | ( ( times_times_nat @ SV669 @ SY1804 )
                                  = ( plus_plus_nat @ ( times_times_nat @ SV349 @ SY1805 ) @ SY1803 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[11977]) ).

thf(12298,plain,
    ! [SV670: nat,SV350: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV350 ) )
        = $true )
      | ( ( ord_less_eq_nat @ SV670 @ ( power_power_nat @ SV350 @ SV670 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11978]) ).

thf(12299,plain,
    ! [SV671: nat,SV351: nat] :
      ( ( ~ ( ( one_one_nat
              = ( times_times_nat @ SV351 @ SV671 ) )
            | ~ ( ( SV351 != one_one_nat )
                | ( SV671 != one_one_nat ) ) )
        | ~ ( ( one_one_nat
             != ( times_times_nat @ SV351 @ SV671 ) )
            | ~ ~ ( ( SV351 != one_one_nat )
                  | ( SV671 != one_one_nat ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11979]) ).

thf(12300,plain,
    ! [SV671: nat,SV351: nat] :
      ( ( ( one_one_nat
          = ( times_times_nat @ SV351 @ SV671 ) )
        = ( ~ ( ( SV351 != one_one_nat )
              | ( SV671 != one_one_nat ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[11979]) ).

thf(12301,plain,
    ! [SV883: nat,SV672: nat,SV352: nat] :
      ( ( ! [SY1902: nat] :
            ( ~ ( ord_less_eq_nat @ SV352 @ SV672 )
            | ~ ( ord_less_eq_nat @ SV883 @ SY1902 )
            | ( ord_less_eq_nat @ ( plus_plus_nat @ SV352 @ SV883 ) @ ( plus_plus_nat @ SV672 @ SY1902 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11980]) ).

thf(12302,plain,
    ! [SV884: nat,SV673: nat,SV353: nat] :
      ( ( ! [SY1903: nat,SY1904: nat] :
            ( ~ ( ( SV353 != zero_zero_nat ) )
            | ~ ~ ( ( SV673 != SV884 )
                  | ~ ( ( SY1903 != SY1904 ) ) )
            | ( ( plus_plus_nat @ SV673 @ ( times_times_nat @ SV353 @ SY1903 ) )
             != ( plus_plus_nat @ SV884 @ ( times_times_nat @ SV353 @ SY1904 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11981]) ).

thf(12303,plain,
    ! [SV885: nat,SV674: nat,SV354: nat] :
      ( ( ~ ( dvd_dvd_nat @ SV354 @ SV674 )
        | ( ( dvd_dvd_nat @ SV354 @ ( plus_plus_nat @ SV674 @ SV885 ) )
          = ( dvd_dvd_nat @ SV354 @ SV885 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11982]) ).

thf(12304,plain,
    ! [SV675: nat > nat,SV355: nat > nat] :
      ( ( ( ~ ( summable_nat @ SV355 ) )
        = $true )
      | ( ( ~ ( summable_nat @ SV675 )
          | ( summable_nat
            @ ^ [SY1812: nat] : ( plus_plus_nat @ ( SV355 @ SY1812 ) @ ( SV675 @ SY1812 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11983]) ).

thf(12305,plain,
    ! [SV886: nat,SV676: nat,SV356: nat] :
      ( ( ~ ( ~ ( ( SV356 != zero_zero_nat )
                | ( ( divide_divide_nat @ ( times_times_nat @ SV356 @ SV676 ) @ ( times_times_nat @ SV356 @ SV886 ) )
                  = zero_zero_nat ) )
            | ~ ( ~ ( ( SV356 != zero_zero_nat ) )
                | ( ( divide_divide_nat @ ( times_times_nat @ SV356 @ SV676 ) @ ( times_times_nat @ SV356 @ SV886 ) )
                  = ( divide_divide_nat @ SV676 @ SV886 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11984]) ).

thf(12306,plain,
    ! [SV887: nat,SV677: nat,SV357: nat] :
      ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV357 @ SV677 ) @ ( plus_plus_nat @ SV887 @ SV677 ) )
        | ( ord_less_eq_nat @ SV357 @ SV887 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11985]) ).

thf(12307,plain,
    ! [SV678: nat,SV359: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV359 ) )
        = $true )
      | ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV678 )
          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV359 @ SV678 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11987]) ).

thf(12308,plain,
    ! [SV679: nat,SV360: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV360 @ SV679 ) )
        = $true )
      | ( ( ( times_times_nat @ ( divide_divide_nat @ SV679 @ SV360 ) @ SV360 )
          = SV679 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11988]) ).

thf(12309,plain,
    ! [SV888: nat,SV680: nat,SV361: nat] :
      ( ( ( ( divide_divide_nat @ SV361 @ SV680 )
         != ( divide_divide_nat @ SV888 @ SV680 ) )
        | ~ ( dvd_dvd_nat @ SV680 @ SV361 )
        | ~ ( dvd_dvd_nat @ SV680 @ SV888 )
        | ( SV361 = SV888 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11989]) ).

thf(12310,plain,
    ! [SV889: nat,SV681: nat,SV362: nat] :
      ( ( ~ ( dvd_dvd_nat @ SV362 @ SV681 )
        | ~ ( dvd_dvd_nat @ SV362 @ SV889 )
        | ( ( ( divide_divide_nat @ SV681 @ SV362 )
            = ( divide_divide_nat @ SV889 @ SV362 ) )
          = ( SV681 = SV889 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11990]) ).

thf(12311,plain,
    ! [SV682: nat,SV363: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV363 @ SV682 ) )
        = $true )
      | ( ( ~ ! [SY1817: nat] :
                ( SV682
               != ( times_times_nat @ SV363 @ SY1817 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[11991]) ).

thf(12312,plain,
    ! [SV890: nat,SV683: nat,SV364: nat] :
      ( ( ! [SY1905: nat] :
            ( ~ ( ord_less_nat @ SV364 @ SV683 )
            | ~ ( ord_less_nat @ SV890 @ SY1905 )
            | ( ord_less_nat @ ( plus_plus_nat @ SV364 @ SV890 ) @ ( plus_plus_nat @ SV683 @ SY1905 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11992]) ).

thf(12313,plain,
    ! [SV891: nat,SV684: nat,SV365: nat] :
      ( ( ! [SY1906: nat] :
            ( ~ ( ord_less_eq_nat @ SV365 @ SV684 )
            | ~ ( ord_less_eq_nat @ SV891 @ SY1906 )
            | ( ord_less_eq_nat @ ( plus_plus_nat @ SV365 @ SV891 ) @ ( plus_plus_nat @ SV684 @ SY1906 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11993]) ).

thf(12314,plain,
    ! [SV892: nat,SV685: nat,SV366: nat] :
      ( ( ~ ( dvd_dvd_nat @ ( times_times_nat @ SV366 @ SV685 ) @ SV892 )
        | ( dvd_dvd_nat @ SV366 @ SV892 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11994]) ).

thf(12315,plain,
    ! [SV893: nat,SV686: nat,SV367: nat] :
      ( ( ( SV367
         != ( times_times_nat @ SV686 @ SV893 ) )
        | ( dvd_dvd_nat @ SV686 @ SV367 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11995]) ).

thf(12316,plain,
    ! [SV894: nat,SV687: nat,SV368: nat] :
      ( ( ~ ( ord_less_eq_nat @ SV368 @ SV687 )
        | ( ord_less_eq_nat @ ( plus_plus_nat @ SV894 @ SV368 ) @ ( plus_plus_nat @ SV894 @ SV687 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11996]) ).

thf(12317,plain,
    ! [SV895: nat,SV688: nat,SV369: nat] :
      ( ( ( ( plus_plus_nat @ SV369 @ SV688 )
         != SV895 )
        | ( SV369
          = ( minus_minus_nat @ SV895 @ SV688 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11997]) ).

thf(12318,plain,
    ! [SV896: nat,SV689: nat,SV370: nat] :
      ( ( ~ ( ord_less_nat @ SV370 @ SV689 )
        | ( ord_less_nat @ ( plus_plus_nat @ SV896 @ SV370 ) @ ( plus_plus_nat @ SV896 @ SV689 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11998]) ).

thf(12319,plain,
    ! [SV897: nat,SV690: nat,SV371: nat] :
      ( ( ~ ( dvd_dvd_nat @ SV371 @ SV690 )
        | ( dvd_dvd_nat @ SV371 @ ( times_times_nat @ SV897 @ SV690 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[11999]) ).

thf(12320,plain,
    ! [SV898: nat,SV691: nat,SV372: nat] :
      ( ( ~ ( dvd_dvd_nat @ SV372 @ SV691 )
        | ( dvd_dvd_nat @ SV372 @ ( times_times_nat @ SV691 @ SV898 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12000]) ).

thf(12321,plain,
    ! [SV692: option_nat,SV373: option_nat] :
      ( ( ( ( SV373 = none_nat )
         != ( SV692 = none_nat ) )
        = $true )
      | ( ( ~ ( ~ ( ( SV373 != none_nat ) )
              | ~ ( ( SV692 != none_nat ) )
              | ( ( the_nat @ SV373 )
                = ( the_nat @ SV692 ) ) )
          | ( SV373 = SV692 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12001]) ).

thf(12322,plain,
    ! [SV693: nat,SV374: nat > $o] :
      ( ( ( ~ ! [SY1533: nat] :
                ( ( ( divide_divide_nat @ SY1533 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                 != SY1533 )
                | ( SV374 @ SY1533 ) ) )
        = $true )
      | ( ( ~ ! [SY1534: nat,SY1535: $o] :
                ( ~ ( SV374 @ SY1534 )
                | ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ SY1535 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1534 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                 != SY1534 )
                | ( SV374 @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ SY1535 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1534 ) ) ) )
          | ( SV374 @ SV693 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12002]) ).

thf(12323,plain,
    ! [SV694: nat] :
      ( ( ! [SV899: nat] :
            ( ( ord_less_eq_nat @ SV694 @ SV899 )
            = ( ~ ! [SY1907: nat] :
                    ( SV899
                   != ( plus_plus_nat @ SV694 @ SY1907 ) ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12003]) ).

thf(12324,plain,
    ! [SV694: nat] :
      ( ( ( ord_less_eq_nat @ SV694 )
        = ( ^ [SY1832: nat] :
              ~ ! [SY1833: nat] :
                  ( SY1832
                 != ( plus_plus_nat @ SV694 @ SY1833 ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12003]) ).

thf(12325,plain,
    ! [SV695: num,SV376: num] :
      ( ( ( bit0 @ SV376 )
        = ( bit1 @ SV695 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[12004]) ).

thf(12326,plain,
    ! [SV900: nat,SV696: nat,SV377: nat] :
      ( ( ~ ( dvd_dvd_nat @ SV377 @ SV696 )
        | ( ( power_power_nat @ ( divide_divide_nat @ SV696 @ SV377 ) @ SV900 )
          = ( divide_divide_nat @ ( power_power_nat @ SV696 @ SV900 ) @ ( power_power_nat @ SV377 @ SV900 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12005]) ).

thf(12327,plain,
    ! [SV901: nat,SV697: nat,SV378: nat] :
      ( ( ! [SY1908: nat] :
            ( ~ ( ord_less_eq_nat @ SV378 @ SV697 )
            | ~ ( ord_less_eq_nat @ SV901 @ SY1908 )
            | ( ord_less_eq_nat @ ( times_times_nat @ SV378 @ SV901 ) @ ( times_times_nat @ SV697 @ SY1908 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12006]) ).

thf(12328,plain,
    ! [SV902: nat,SV698: nat,SV379: nat] :
      ( ( ! [SY1909: nat] :
            ( ~ ~ ( ~ ( ord_less_nat @ SV379 @ SV698 )
                  | ( SV902 != SY1909 ) )
            | ( ord_less_nat @ ( plus_plus_nat @ SV379 @ SV902 ) @ ( plus_plus_nat @ SV698 @ SY1909 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12007]) ).

thf(12329,plain,
    ! [SV903: nat,SV699: nat,SV380: nat] :
      ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV380 @ SV699 ) @ ( plus_plus_nat @ SV380 @ SV903 ) )
        | ( ord_less_eq_nat @ SV699 @ SV903 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12008]) ).

thf(12330,plain,
    ! [SV700: nat,SV381: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV381 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ SV700 ) )
        = $true )
      | ( ( ord_less_eq_nat @ SV381 @ SV700 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12009]) ).

thf(12331,plain,
    ! [SV382: num] :
      ( ( ( SV382 != one )
        = $false )
      | ( ( ~ ! [SY1550: num] :
                ( SV382
               != ( bit0 @ SY1550 ) )
          | ~ ! [SY1551: num] :
                ( SV382
               != ( bit1 @ SY1551 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12010]) ).

thf(12332,plain,
    ! [SV904: list_VEBT_VEBT,SV701: nat,SV383: nat] :
      ( ( ! [SY1910: vEBT_VEBT] :
            ( ~ ( ( SV383 != SV701 ) )
            | ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ SV904 @ SV383 @ SY1910 ) @ SV701 )
              = ( nth_VEBT_VEBT @ SV904 @ SV701 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12011]) ).

thf(12333,plain,
    ! [SV905: nat,SV702: nat,SV384: nat] :
      ( ( ! [SY1911: nat,SY1912: nat] :
            ( ( ( modulo_modulo_nat @ SV384 @ SV702 )
             != ( modulo_modulo_nat @ SV905 @ SV702 ) )
            | ( ( modulo_modulo_nat @ SY1911 @ SV702 )
             != ( modulo_modulo_nat @ SY1912 @ SV702 ) )
            | ( ( modulo_modulo_nat @ ( plus_plus_nat @ SV384 @ SY1911 ) @ SV702 )
              = ( modulo_modulo_nat @ ( plus_plus_nat @ SV905 @ SY1912 ) @ SV702 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12012]) ).

thf(12334,plain,
    ! [SV906: nat,SV703: nat,SV386: nat] :
      ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV386 @ SV703 ) @ SV906 )
        | ( ord_less_eq_nat @ SV386 @ SV906 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12014]) ).

thf(12335,plain,
    ! [SV907: nat,SV704: nat,SV387: nat] :
      ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV387 @ SV704 ) @ ( plus_plus_nat @ SV387 @ SV907 ) )
        | ( ord_less_nat @ SV704 @ SV907 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12015]) ).

thf(12336,plain,
    ! [SV908: nat > nat,SV705: nat,SV388: nat > nat] :
      ( ( ! [SY1913: nat] :
            ( ~ ( sums_nat @ SV388 @ SV705 )
            | ~ ( sums_nat @ SV908 @ SY1913 )
            | ( sums_nat
              @ ^ [SY1914: nat] : ( plus_plus_nat @ ( SV388 @ SY1914 ) @ ( SV908 @ SY1914 ) )
              @ ( plus_plus_nat @ SV705 @ SY1913 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12016]) ).

thf(12337,plain,
    ! [SV909: nat,SV706: nat,SV389: nat] :
      ( ( ~ ( ord_less_nat @ SV389 @ SV706 )
        | ( ord_less_nat @ SV389 @ ( plus_plus_nat @ SV706 @ SV909 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12017]) ).

thf(12338,plain,
    ! [SV910: nat,SV707: nat,SV390: nat] :
      ( ( ~ ( ord_less_eq_nat @ SV390 @ SV707 )
        | ( ord_less_eq_nat @ SV390 @ ( plus_plus_nat @ SV707 @ SV910 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12018]) ).

thf(12339,plain,
    ! [SV911: nat,SV393: nat] :
      ( ( ( vEBT_VEBT_high @ SV393 @ SV911 )
        = ( divide_divide_nat @ SV393 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV911 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12019]) ).

thf(12340,plain,
    ! [SV912: nat,SV394: nat] :
      ( ( ( vEBT_VEBT_bit_concat @ SV394 @ SV912 )
        = ( ^ [SY1915: nat] : ( plus_plus_nat @ ( times_times_nat @ SV394 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1915 ) ) @ SV912 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12021]) ).

thf(12341,plain,
    ! [SV399: num,SV10: num] :
      ( ( ( ~ ( ( ( numeral_numeral_nat @ SV10 )
                = ( numeral_numeral_nat @ SV399 ) )
              | ( SV10 = SV399 ) ) )
        = $true )
      | ( ( ~ ( ( ( numeral_numeral_nat @ SV10 )
               != ( numeral_numeral_nat @ SV399 ) )
              | ( SV10 != SV399 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12026]) ).

thf(12342,plain,
    ! [SV913: nat,SV716: num,SV405: num,SV17: nat] :
      ( ( ( times_times_nat @ ( power_power_nat @ SV17 @ ( numeral_numeral_nat @ SV405 ) ) @ ( times_times_nat @ ( power_power_nat @ SV17 @ ( numeral_numeral_nat @ SV716 ) ) @ SV913 ) )
        = ( times_times_nat @ ( power_power_nat @ SV17 @ ( numeral_numeral_nat @ ( plus_plus_num @ SV405 @ SV716 ) ) ) @ SV913 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12031]) ).

thf(12343,plain,
    ! [SV914: vEBT_VEBT,SV727: vEBT_VEBT,SV423: nat,SV45: list_VEBT_VEBT] :
      ( ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV45 @ SV423 @ SV727 ) @ SV423 @ SV914 )
        = ( list_u1324408373059187874T_VEBT @ SV45 @ SV423 @ SV914 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12042]) ).

thf(12344,plain,
    ! [SV427: nat,SV49: nat] :
      ( ( ( ~ ( ( ord_less_eq_nat @ ( power_power_nat @ SV49 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ SV427 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
              | ( ord_less_eq_nat @ SV49 @ SV427 ) ) )
        = $true )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV49 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ SV427 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
              | ~ ( ord_less_eq_nat @ SV49 @ SV427 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12043]) ).

thf(12345,plain,
    ! [SV428: num,SV53: num] :
      ( ( ( ~ ( ( ord_less_num @ ( bit0 @ SV53 ) @ ( bit0 @ SV428 ) )
              | ( ord_less_num @ SV53 @ SV428 ) ) )
        = $true )
      | ( ( ~ ( ~ ( ord_less_num @ ( bit0 @ SV53 ) @ ( bit0 @ SV428 ) )
              | ~ ( ord_less_num @ SV53 @ SV428 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12045]) ).

thf(12346,plain,
    ! [SV429: num,SV54: num] :
      ( ( ( ~ ( ( ( bit0 @ SV54 )
                = ( bit0 @ SV429 ) )
              | ( SV54 = SV429 ) ) )
        = $true )
      | ( ( ~ ( ( ( bit0 @ SV54 )
               != ( bit0 @ SV429 ) )
              | ( SV54 != SV429 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12047]) ).

thf(12347,plain,
    ! [SV432: num,SV62: num] :
      ( ( ( ~ ( ( ord_less_eq_num @ ( bit0 @ SV62 ) @ ( bit0 @ SV432 ) )
              | ( ord_less_eq_num @ SV62 @ SV432 ) ) )
        = $true )
      | ( ( ~ ( ~ ( ord_less_eq_num @ ( bit0 @ SV62 ) @ ( bit0 @ SV432 ) )
              | ~ ( ord_less_eq_num @ SV62 @ SV432 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12049]) ).

thf(12348,plain,
    ! [SV64: num] :
      ( ( ( ( one_one_nat
            = ( numeral_numeral_nat @ SV64 ) )
          | ( one = SV64 ) )
        = $false )
      | ( ( ~ ( ( one_one_nat
               != ( numeral_numeral_nat @ SV64 ) )
              | ( one != SV64 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12051]) ).

thf(12349,plain,
    ! [SV65: num] :
      ( ( ( ( ( numeral_numeral_nat @ SV65 )
            = one_one_nat )
          | ( SV65 = one ) )
        = $false )
      | ( ( ~ ( ( ( numeral_numeral_nat @ SV65 )
               != one_one_nat )
              | ( SV65 != one ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12052]) ).

thf(12350,plain,
    ! [SV67: num] :
      ( ( ( ( ord_less_eq_num @ SV67 @ one )
          | ( SV67 = one ) )
        = $false )
      | ( ( ~ ( ~ ( ord_less_eq_num @ SV67 @ one )
              | ( SV67 != one ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12053]) ).

thf(12351,plain,
    ! [SV915: nat,SV728: nat,SV433: nat,SV69: nat] :
      ( ( ( plus_plus_nat @ ( times_times_nat @ SV69 @ SV433 ) @ ( plus_plus_nat @ ( times_times_nat @ SV728 @ SV433 ) @ SV915 ) )
        = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV69 @ SV728 ) @ SV433 ) @ SV915 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12054]) ).

thf(12352,plain,
    ! [SV729: nat,SV435: nat,SV71: nat] :
      ( ( ~ ( ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SV435 ) @ ( plus_plus_nat @ SV71 @ SV729 ) )
            | ( ord_less_nat @ SV435 @ SV729 ) )
        | ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SV435 ) @ ( plus_plus_nat @ SV71 @ SV729 ) )
            | ~ ( ord_less_nat @ SV435 @ SV729 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12055]) ).

thf(12353,plain,
    ! [SV729: nat,SV435: nat,SV71: nat] :
      ( ( ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SV435 ) @ ( plus_plus_nat @ SV71 @ SV729 ) )
        = ( ord_less_nat @ SV435 @ SV729 ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12055]) ).

thf(12354,plain,
    ! [SV730: nat,SV436: nat,SV72: nat] :
      ( ( ~ ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV72 @ SV436 ) @ ( plus_plus_nat @ SV72 @ SV730 ) )
            | ( ord_less_eq_nat @ SV436 @ SV730 ) )
        | ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV72 @ SV436 ) @ ( plus_plus_nat @ SV72 @ SV730 ) )
            | ~ ( ord_less_eq_nat @ SV436 @ SV730 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12056]) ).

thf(12355,plain,
    ! [SV730: nat,SV436: nat,SV72: nat] :
      ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV72 @ SV436 ) @ ( plus_plus_nat @ SV72 @ SV730 ) )
        = ( ord_less_eq_nat @ SV436 @ SV730 ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12056]) ).

thf(12356,plain,
    ! [SV736: nat,SV447: nat,SV86: nat] :
      ( ( ~ ( ( ( times_times_nat @ ( suc @ SV86 ) @ SV447 )
              = ( times_times_nat @ ( suc @ SV86 ) @ SV736 ) )
            | ( SV447 = SV736 ) )
        | ~ ( ( ( times_times_nat @ ( suc @ SV86 ) @ SV447 )
             != ( times_times_nat @ ( suc @ SV86 ) @ SV736 ) )
            | ( SV447 != SV736 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12062]) ).

thf(12357,plain,
    ! [SV736: nat,SV447: nat,SV86: nat] :
      ( ( ( ( times_times_nat @ ( suc @ SV86 ) @ SV447 )
          = ( times_times_nat @ ( suc @ SV86 ) @ SV736 ) )
        = ( SV447 = SV736 ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12062]) ).

thf(12358,plain,
    ! [SV916: nat,SV746: nat,SV466: nat,SV111: nat] :
      ( ( ( plus_plus_nat @ ( times_times_nat @ SV111 @ SV466 ) @ ( plus_plus_nat @ ( times_times_nat @ SV746 @ SV466 ) @ SV916 ) )
        = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV111 @ SV746 ) @ SV466 ) @ SV916 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12074]) ).

thf(12359,plain,
    ! [SV752: nat,SV475: nat,SV120: nat] :
      ( ( ~ ( ( ( plus_plus_nat @ SV120 @ SV475 )
              = ( plus_plus_nat @ SV120 @ SV752 ) )
            | ( SV475 = SV752 ) )
        | ~ ( ( ( plus_plus_nat @ SV120 @ SV475 )
             != ( plus_plus_nat @ SV120 @ SV752 ) )
            | ( SV475 != SV752 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12080]) ).

thf(12360,plain,
    ! [SV752: nat,SV475: nat,SV120: nat] :
      ( ( ( ( plus_plus_nat @ SV120 @ SV475 )
          = ( plus_plus_nat @ SV120 @ SV752 ) )
        = ( SV475 = SV752 ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12080]) ).

thf(12361,plain,
    ! [SV753: nat,SV476: nat,SV121: nat] :
      ( ( ~ ( ( ( plus_plus_nat @ SV121 @ SV476 )
              = ( plus_plus_nat @ SV753 @ SV476 ) )
            | ( SV121 = SV753 ) )
        | ~ ( ( ( plus_plus_nat @ SV121 @ SV476 )
             != ( plus_plus_nat @ SV753 @ SV476 ) )
            | ( SV121 != SV753 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12081]) ).

thf(12362,plain,
    ! [SV753: nat,SV476: nat,SV121: nat] :
      ( ( ( ( plus_plus_nat @ SV121 @ SV476 )
          = ( plus_plus_nat @ SV753 @ SV476 ) )
        = ( SV121 = SV753 ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12081]) ).

thf(12363,plain,
    ! [SV754: nat,SV477: nat,SV122: nat] :
      ( ( ~ ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ SV477 ) @ ( plus_plus_nat @ SV122 @ SV754 ) )
            | ( ord_less_eq_nat @ SV477 @ SV754 ) )
        | ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ SV477 ) @ ( plus_plus_nat @ SV122 @ SV754 ) )
            | ~ ( ord_less_eq_nat @ SV477 @ SV754 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12082]) ).

thf(12364,plain,
    ! [SV754: nat,SV477: nat,SV122: nat] :
      ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ SV477 ) @ ( plus_plus_nat @ SV122 @ SV754 ) )
        = ( ord_less_eq_nat @ SV477 @ SV754 ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12082]) ).

thf(12365,plain,
    ! [SV755: nat,SV478: nat,SV123: nat] :
      ( ( ~ ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV123 @ SV478 ) @ ( plus_plus_nat @ SV755 @ SV478 ) )
            | ( ord_less_eq_nat @ SV123 @ SV755 ) )
        | ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV123 @ SV478 ) @ ( plus_plus_nat @ SV755 @ SV478 ) )
            | ~ ( ord_less_eq_nat @ SV123 @ SV755 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12083]) ).

thf(12366,plain,
    ! [SV755: nat,SV478: nat,SV123: nat] :
      ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV123 @ SV478 ) @ ( plus_plus_nat @ SV755 @ SV478 ) )
        = ( ord_less_eq_nat @ SV123 @ SV755 ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12083]) ).

thf(12367,plain,
    ! [SV756: nat,SV479: nat,SV124: nat] :
      ( ( ~ ( ( ord_less_nat @ ( plus_plus_nat @ SV124 @ SV479 ) @ ( plus_plus_nat @ SV124 @ SV756 ) )
            | ( ord_less_nat @ SV479 @ SV756 ) )
        | ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV124 @ SV479 ) @ ( plus_plus_nat @ SV124 @ SV756 ) )
            | ~ ( ord_less_nat @ SV479 @ SV756 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12084]) ).

thf(12368,plain,
    ! [SV756: nat,SV479: nat,SV124: nat] :
      ( ( ( ord_less_nat @ ( plus_plus_nat @ SV124 @ SV479 ) @ ( plus_plus_nat @ SV124 @ SV756 ) )
        = ( ord_less_nat @ SV479 @ SV756 ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12084]) ).

thf(12369,plain,
    ! [SV757: nat,SV480: nat,SV125: nat] :
      ( ( ~ ( ( ord_less_nat @ ( plus_plus_nat @ SV125 @ SV480 ) @ ( plus_plus_nat @ SV757 @ SV480 ) )
            | ( ord_less_nat @ SV125 @ SV757 ) )
        | ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV125 @ SV480 ) @ ( plus_plus_nat @ SV757 @ SV480 ) )
            | ~ ( ord_less_nat @ SV125 @ SV757 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12085]) ).

thf(12370,plain,
    ! [SV757: nat,SV480: nat,SV125: nat] :
      ( ( ( ord_less_nat @ ( plus_plus_nat @ SV125 @ SV480 ) @ ( plus_plus_nat @ SV757 @ SV480 ) )
        = ( ord_less_nat @ SV125 @ SV757 ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12085]) ).

thf(12371,plain,
    ! [SV917: nat,SV483: nat] :
      ( ( ( times_times_nat @ SV483 @ SV917 )
        = ( times_times_nat @ SV917 @ SV483 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12088]) ).

thf(12372,plain,
    ! [SV918: nat,SV487: nat] :
      ( ( ( plus_plus_nat @ SV487 @ SV918 )
        = ( plus_plus_nat @ SV918 @ SV487 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12093]) ).

thf(12373,plain,
    ! [SV919: nat,SV492: nat] :
      ( ( ( vEBT_VEBT_low @ SV492 @ SV919 )
        = ( modulo_modulo_nat @ SV492 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV919 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12099]) ).

thf(12374,plain,
    ! [SV770: nat,SV493: nat,SV142: nat] :
      ( ( ~ ( ( ( times_times_nat @ SV142 @ SV493 )
              = ( times_times_nat @ SV770 @ SV493 ) )
            | ( SV493 = zero_zero_nat )
            | ( SV142 = SV770 ) )
        | ~ ( ( ( times_times_nat @ SV142 @ SV493 )
             != ( times_times_nat @ SV770 @ SV493 ) )
            | ~ ( ( SV493 = zero_zero_nat )
                | ( SV142 = SV770 ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12101]) ).

thf(12375,plain,
    ! [SV770: nat,SV493: nat,SV142: nat] :
      ( ( ( ( times_times_nat @ SV142 @ SV493 )
          = ( times_times_nat @ SV770 @ SV493 ) )
        = ( ( SV493 = zero_zero_nat )
          | ( SV142 = SV770 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12101]) ).

thf(12376,plain,
    ! [SV771: nat,SV494: nat,SV143: nat] :
      ( ( ~ ( ( ( times_times_nat @ SV143 @ SV494 )
              = ( times_times_nat @ SV143 @ SV771 ) )
            | ( SV143 = zero_zero_nat )
            | ( SV494 = SV771 ) )
        | ~ ( ( ( times_times_nat @ SV143 @ SV494 )
             != ( times_times_nat @ SV143 @ SV771 ) )
            | ~ ( ( SV143 = zero_zero_nat )
                | ( SV494 = SV771 ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12102]) ).

thf(12377,plain,
    ! [SV771: nat,SV494: nat,SV143: nat] :
      ( ( ( ( times_times_nat @ SV143 @ SV494 )
          = ( times_times_nat @ SV143 @ SV771 ) )
        = ( ( SV143 = zero_zero_nat )
          | ( SV494 = SV771 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12102]) ).

thf(12378,plain,
    ! [SV495: nat,SV144: nat] :
      ( ( ( ~ ( ( ( times_times_nat @ SV144 @ SV495 )
                = zero_zero_nat )
              | ( SV144 = zero_zero_nat )
              | ( SV495 = zero_zero_nat ) ) )
        = $true )
      | ( ( ~ ( ( ( times_times_nat @ SV144 @ SV495 )
               != zero_zero_nat )
              | ~ ( ( SV144 = zero_zero_nat )
                  | ( SV495 = zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12103]) ).

thf(12379,plain,
    ! [SV496: nat,SV148: nat] :
      ( ( ( ~ ( ( SV148
                = ( plus_plus_nat @ SV148 @ SV496 ) )
              | ( SV496 = zero_zero_nat ) ) )
        = $true )
      | ( ( ~ ( ( SV148
               != ( plus_plus_nat @ SV148 @ SV496 ) )
              | ( SV496 != zero_zero_nat ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12105]) ).

thf(12380,plain,
    ! [SV497: nat,SV149: nat] :
      ( ( ( ~ ( ( SV149
                = ( plus_plus_nat @ SV497 @ SV149 ) )
              | ( SV497 = zero_zero_nat ) ) )
        = $true )
      | ( ( ~ ( ( SV149
               != ( plus_plus_nat @ SV497 @ SV149 ) )
              | ( SV497 != zero_zero_nat ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12107]) ).

thf(12381,plain,
    ! [SV498: nat,SV150: nat] :
      ( ( ( ~ ( ( ( plus_plus_nat @ SV150 @ SV498 )
                = SV150 )
              | ( SV498 = zero_zero_nat ) ) )
        = $true )
      | ( ( ~ ( ( ( plus_plus_nat @ SV150 @ SV498 )
               != SV150 )
              | ( SV498 != zero_zero_nat ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12109]) ).

thf(12382,plain,
    ! [SV499: nat,SV151: nat] :
      ( ( ( ~ ( ( ( plus_plus_nat @ SV151 @ SV499 )
                = SV499 )
              | ( SV151 = zero_zero_nat ) ) )
        = $true )
      | ( ( ~ ( ( ( plus_plus_nat @ SV151 @ SV499 )
               != SV499 )
              | ( SV151 != zero_zero_nat ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12111]) ).

thf(12383,plain,
    ! [SV772: nat,SV502: nat,SV160: nat] :
      ( ( ~ ( ( ( times_times_nat @ SV160 @ SV502 )
              = ( times_times_nat @ SV772 @ SV502 ) )
            | ( SV160 = SV772 )
            | ( SV502 = zero_zero_nat ) )
        | ~ ( ( ( times_times_nat @ SV160 @ SV502 )
             != ( times_times_nat @ SV772 @ SV502 ) )
            | ~ ( ( SV160 = SV772 )
                | ( SV502 = zero_zero_nat ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12113]) ).

thf(12384,plain,
    ! [SV772: nat,SV502: nat,SV160: nat] :
      ( ( ( ( times_times_nat @ SV160 @ SV502 )
          = ( times_times_nat @ SV772 @ SV502 ) )
        = ( ( SV160 = SV772 )
          | ( SV502 = zero_zero_nat ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12113]) ).

thf(12385,plain,
    ! [SV773: nat,SV503: nat,SV161: nat] :
      ( ( ~ ( ( ( times_times_nat @ SV161 @ SV503 )
              = ( times_times_nat @ SV161 @ SV773 ) )
            | ( SV503 = SV773 )
            | ( SV161 = zero_zero_nat ) )
        | ~ ( ( ( times_times_nat @ SV161 @ SV503 )
             != ( times_times_nat @ SV161 @ SV773 ) )
            | ~ ( ( SV503 = SV773 )
                | ( SV161 = zero_zero_nat ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12114]) ).

thf(12386,plain,
    ! [SV773: nat,SV503: nat,SV161: nat] :
      ( ( ( ( times_times_nat @ SV161 @ SV503 )
          = ( times_times_nat @ SV161 @ SV773 ) )
        = ( ( SV503 = SV773 )
          | ( SV161 = zero_zero_nat ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12114]) ).

thf(12387,plain,
    ! [SV504: nat,SV163: nat] :
      ( ( ( ~ ( ( ( times_times_nat @ SV163 @ SV504 )
                = zero_zero_nat )
              | ( SV163 = zero_zero_nat )
              | ( SV504 = zero_zero_nat ) ) )
        = $true )
      | ( ( ~ ( ( ( times_times_nat @ SV163 @ SV504 )
               != zero_zero_nat )
              | ~ ( ( SV163 = zero_zero_nat )
                  | ( SV504 = zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12115]) ).

thf(12388,plain,
    ! [SV169: nat] :
      ( ( ( ( ( power_power_nat @ SV169 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
            = zero_zero_nat )
          | ( SV169 = zero_zero_nat ) )
        = $false )
      | ( ( ~ ( ( ( power_power_nat @ SV169 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
               != zero_zero_nat )
              | ( SV169 != zero_zero_nat ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12121]) ).

thf(12389,plain,
    ! [SV787: num,SV518: num,SV179: num] :
      ( ( ~ ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV179 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) )
              = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV787 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) ) )
            | ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV179 ) @ ( numeral_numeral_nat @ SV518 ) )
              = ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV787 ) @ ( numeral_numeral_nat @ SV518 ) ) ) )
        | ~ ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV179 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) )
             != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV787 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) ) )
            | ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV179 ) @ ( numeral_numeral_nat @ SV518 ) )
             != ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV787 ) @ ( numeral_numeral_nat @ SV518 ) ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12131]) ).

thf(12390,plain,
    ! [SV787: num,SV518: num,SV179: num] :
      ( ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV179 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) )
          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV787 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) ) )
        = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV179 ) @ ( numeral_numeral_nat @ SV518 ) )
          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV787 ) @ ( numeral_numeral_nat @ SV518 ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12131]) ).

thf(12391,plain,
    ! [SV788: nat,SV520: nat,SV185: nat] :
      ( ( ~ ( ( ( times_times_nat @ SV185 @ SV520 )
              = ( times_times_nat @ SV185 @ SV788 ) )
            | ( SV185 = zero_zero_nat )
            | ( SV520 = SV788 ) )
        | ~ ( ( ( times_times_nat @ SV185 @ SV520 )
             != ( times_times_nat @ SV185 @ SV788 ) )
            | ~ ( ( SV185 = zero_zero_nat )
                | ( SV520 = SV788 ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12132]) ).

thf(12392,plain,
    ! [SV788: nat,SV520: nat,SV185: nat] :
      ( ( ( ( times_times_nat @ SV185 @ SV520 )
          = ( times_times_nat @ SV185 @ SV788 ) )
        = ( ( SV185 = zero_zero_nat )
          | ( SV520 = SV788 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12132]) ).

thf(12393,plain,
    ! [SV534: num,SV199: num] :
      ( ( ( ~ ( ( ( bit0 @ SV199 )
                = ( bit0 @ SV534 ) )
              | ( SV199 = SV534 ) ) )
        = $true )
      | ( ( ~ ( ( ( bit0 @ SV199 )
               != ( bit0 @ SV534 ) )
              | ( SV199 != SV534 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12139]) ).

thf(12394,plain,
    ! [SV535: nat,SV201: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ SV201 @ ( plus_plus_nat @ SV535 @ SV201 ) )
              | ( dvd_dvd_nat @ SV201 @ SV535 ) ) )
        = $true )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ SV201 @ ( plus_plus_nat @ SV535 @ SV201 ) )
              | ~ ( dvd_dvd_nat @ SV201 @ SV535 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12141]) ).

thf(12395,plain,
    ! [SV536: nat,SV202: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ SV202 @ ( plus_plus_nat @ SV202 @ SV536 ) )
              | ( dvd_dvd_nat @ SV202 @ SV536 ) ) )
        = $true )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ SV202 @ ( plus_plus_nat @ SV202 @ SV536 ) )
              | ~ ( dvd_dvd_nat @ SV202 @ SV536 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12143]) ).

thf(12396,plain,
    ! [SV795: nat,SV537: nat,SV203: nat] :
      ( ( ~ ( ( dvd_dvd_nat @ SV203 @ ( plus_plus_nat @ SV537 @ ( times_times_nat @ SV795 @ SV203 ) ) )
            | ( dvd_dvd_nat @ SV203 @ SV537 ) )
        | ~ ( ~ ( dvd_dvd_nat @ SV203 @ ( plus_plus_nat @ SV537 @ ( times_times_nat @ SV795 @ SV203 ) ) )
            | ~ ( dvd_dvd_nat @ SV203 @ SV537 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12145]) ).

thf(12397,plain,
    ! [SV795: nat,SV537: nat,SV203: nat] :
      ( ( ( dvd_dvd_nat @ SV203 @ ( plus_plus_nat @ SV537 @ ( times_times_nat @ SV795 @ SV203 ) ) )
        = ( dvd_dvd_nat @ SV203 @ SV537 ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12145]) ).

thf(12398,plain,
    ! [SV796: nat,SV538: nat,SV204: nat] :
      ( ( ~ ( ( dvd_dvd_nat @ SV204 @ ( plus_plus_nat @ ( times_times_nat @ SV538 @ SV204 ) @ SV796 ) )
            | ( dvd_dvd_nat @ SV204 @ SV796 ) )
        | ~ ( ~ ( dvd_dvd_nat @ SV204 @ ( plus_plus_nat @ ( times_times_nat @ SV538 @ SV204 ) @ SV796 ) )
            | ~ ( dvd_dvd_nat @ SV204 @ SV796 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12146]) ).

thf(12399,plain,
    ! [SV796: nat,SV538: nat,SV204: nat] :
      ( ( ( dvd_dvd_nat @ SV204 @ ( plus_plus_nat @ ( times_times_nat @ SV538 @ SV204 ) @ SV796 ) )
        = ( dvd_dvd_nat @ SV204 @ SV796 ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12146]) ).

thf(12400,plain,
    ! [SV539: nat,SV205: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ SV205 @ SV539 ) )
              | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
              | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 ) ) )
        = $true )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ SV205 @ SV539 ) )
              | ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
                  | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12147]) ).

thf(12401,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
              | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
                = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
              | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
               != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12149]) ).

thf(12402,plain,
    ! [SV920: int,SV797: nat,SV543: int,SV209: nat] :
      ( ( ! [SY1916: int] :
            ( ( bit_concat_bit @ SV209 @ SV543 @ ( bit_concat_bit @ SV797 @ SV920 @ SY1916 ) )
            = ( bit_concat_bit @ ( plus_plus_nat @ SV797 @ SV209 ) @ ( bit_concat_bit @ SV209 @ SV543 @ SV920 ) @ SY1916 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12151]) ).

thf(12403,plain,
    ! [SV921: set_nat,SV798: nat > nat,SV544: set_nat,SV211: nat > nat] :
      ( ( ( times_times_nat @ ( groups3542108847815614940at_nat @ SV211 @ SV544 ) @ ( groups3542108847815614940at_nat @ SV798 @ SV921 ) )
        = ( groups3542108847815614940at_nat
          @ ^ [SY1917: nat] :
              ( groups3542108847815614940at_nat
              @ ^ [SY1861: nat] : ( times_times_nat @ ( SV211 @ SY1917 ) @ ( SV798 @ SY1861 ) )
              @ SV921 )
          @ SV544 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12152]) ).

thf(12404,plain,
    ! [SV548: nat,SV215: nat] :
      ( ( ( ~ ( ( SV215
                = ( plus_plus_nat @ SV215 @ SV548 ) )
              | ( SV548 = zero_zero_nat ) ) )
        = $true )
      | ( ( ~ ( ( SV215
               != ( plus_plus_nat @ SV215 @ SV548 ) )
              | ( SV548 != zero_zero_nat ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12156]) ).

thf(12405,plain,
    ! [SV922: nat,SV802: nat,SV549: nat,SV216: nat] :
      ( ( ( ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV549 ) @ ( times_times_nat @ SV802 @ SV922 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV922 ) @ ( times_times_nat @ SV802 @ SV549 ) ) )
        = ( ( SV216 = SV802 )
          | ( SV549 = SV922 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12158]) ).

thf(12406,plain,
    ! [SV803: nat,SV554: nat,SV224: nat] :
      ( ( ~ ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV224 ) @ SV554 )
              = ( semiri1316708129612266289at_nat @ SV803 ) )
            | ( ( power_power_nat @ SV224 @ SV554 )
              = SV803 ) )
        | ~ ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV224 ) @ SV554 )
             != ( semiri1316708129612266289at_nat @ SV803 ) )
            | ( ( power_power_nat @ SV224 @ SV554 )
             != SV803 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12159]) ).

thf(12407,plain,
    ! [SV803: nat,SV554: nat,SV224: nat] :
      ( ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV224 ) @ SV554 )
          = ( semiri1316708129612266289at_nat @ SV803 ) )
        = ( ( power_power_nat @ SV224 @ SV554 )
          = SV803 ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12159]) ).

thf(12408,plain,
    ! [SV804: nat,SV555: nat,SV225: nat] :
      ( ( ~ ( ( ( semiri1316708129612266289at_nat @ SV225 )
              = ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV555 ) @ SV804 ) )
            | ( SV225
              = ( power_power_nat @ SV555 @ SV804 ) ) )
        | ~ ( ( ( semiri1316708129612266289at_nat @ SV225 )
             != ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV555 ) @ SV804 ) )
            | ( SV225
             != ( power_power_nat @ SV555 @ SV804 ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12160]) ).

thf(12409,plain,
    ! [SV804: nat,SV555: nat,SV225: nat] :
      ( ( ( ( semiri1316708129612266289at_nat @ SV225 )
          = ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV555 ) @ SV804 ) )
        = ( SV225
          = ( power_power_nat @ SV555 @ SV804 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12160]) ).

thf(12410,plain,
    ! [SV805: nat,SV556: nat,SV226: num] :
      ( ( ~ ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
              = ( semiri1316708129612266289at_nat @ SV805 ) )
            | ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
              = SV805 ) )
        | ~ ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
             != ( semiri1316708129612266289at_nat @ SV805 ) )
            | ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
             != SV805 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12161]) ).

thf(12411,plain,
    ! [SV805: nat,SV556: nat,SV226: num] :
      ( ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
          = ( semiri1316708129612266289at_nat @ SV805 ) )
        = ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
          = SV805 ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12161]) ).

thf(12412,plain,
    ! [SV806: nat,SV557: num,SV227: nat] :
      ( ( ~ ( ( ( semiri1316708129612266289at_nat @ SV227 )
              = ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
            | ( SV227
              = ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) ) )
        | ~ ( ( ( semiri1316708129612266289at_nat @ SV227 )
             != ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
            | ( SV227
             != ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12162]) ).

thf(12413,plain,
    ! [SV806: nat,SV557: num,SV227: nat] :
      ( ( ( ( semiri1316708129612266289at_nat @ SV227 )
          = ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
        = ( SV227
          = ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12162]) ).

thf(12414,plain,
    ! [SV561: nat,SV231: nat > real] :
      ( ( ( ~ ( ( summable_real
                @ ^ [SY1684: nat] : ( SV231 @ ( plus_plus_nat @ SY1684 @ SV561 ) ) )
              | ( summable_real @ SV231 ) ) )
        = $true )
      | ( ( ~ ( ~ ( summable_real
                  @ ^ [SY1684: nat] : ( SV231 @ ( plus_plus_nat @ SY1684 @ SV561 ) ) )
              | ~ ( summable_real @ SV231 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12164]) ).

thf(12415,plain,
    ! [SV562: nat,SV232: nat > complex] :
      ( ( ( ~ ( ( summable_complex
                @ ^ [SY1685: nat] : ( SV232 @ ( plus_plus_nat @ SY1685 @ SV562 ) ) )
              | ( summable_complex @ SV232 ) ) )
        = $true )
      | ( ( ~ ( ~ ( summable_complex
                  @ ^ [SY1685: nat] : ( SV232 @ ( plus_plus_nat @ SY1685 @ SV562 ) ) )
              | ~ ( summable_complex @ SV232 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12166]) ).

thf(12416,plain,
    ! [SV923: nat,SV567: nat] :
      ( ( ( bit_se547839408752420682it_nat @ SV567 @ SV923 )
        = ( times_times_nat @ SV923 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV567 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12172]) ).

thf(12417,plain,
    ! [SV924: nat,SV568: nat] :
      ( ( ( bit_se8570568707652914677it_nat @ SV568 @ SV924 )
        = ( divide_divide_nat @ SV924 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV568 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12174]) ).

thf(12418,plain,
    ! [SV243: $o] :
      ( ( ( ~ ( SV243
              | $true ) )
        = $true )
      | ( ( ~ ( ~ SV243
              | ~ $true ) )
        = $true )
      | ( ( SV243 = $false )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12177]) ).

thf(12419,plain,
    ! [SV243: $o] :
      ( ( ( ~ ( SV243
              | $false )
          | ~ ( ~ SV243
              | ~ $false ) )
        = $true )
      | ( ( SV243 = $true )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[12178]) ).

thf(12420,plain,
    ! [SV243: $o] :
      ( ( ( SV243 = $false )
        = $true )
      | ( ( SV243 = $true )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[12178]) ).

thf(12421,plain,
    ( ( ( ~ ( $true
            | $true ) )
      = $true )
    | ( ( ~ ( ~ $true
            | ~ $true ) )
      = $true )
    | ( ( $true = $false )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12179]) ).

thf(12422,plain,
    ( ( ( ~ ( $true
            | $false )
        | ~ ( ~ $true
            | ~ $false ) )
      = $true )
    | ( ( $true = $true )
      = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[12180]) ).

thf(12423,plain,
    ( ( ( $true = $false )
      = $true )
    | ( ( $true = $true )
      = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[12180]) ).

thf(12424,plain,
    ( ( ( ~ ( $false
            | $true ) )
      = $true )
    | ( ( ~ ( ~ $false
            | ~ $true ) )
      = $true )
    | ( ( $false = $false )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12181]) ).

thf(12425,plain,
    ( ( ( ~ ( $false
            | $false )
        | ~ ( ~ $false
            | ~ $false ) )
      = $true )
    | ( ( $false = $true )
      = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[12182]) ).

thf(12426,plain,
    ( ( ( $false = $false )
      = $true )
    | ( ( $false = $true )
      = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[12182]) ).

thf(12427,plain,
    ! [SV815: nat,SV570: nat,SV244: nat] :
      ( ( ( ~ ( ( SV244 != zero_zero_nat ) ) )
        = $true )
      | ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ SV244 @ SV570 ) @ SV815 ) @ SV244 )
          = ( plus_plus_nat @ SV570 @ ( divide_divide_nat @ SV815 @ SV244 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12183]) ).

thf(12428,plain,
    ! [SV816: nat,SV571: nat,SV245: nat] :
      ( ( ( ~ ( ord_less_nat @ SV245 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV571 ) ) )
        = $true )
      | ( ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ SV816 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV571 ) ) @ SV245 ) @ SV571 )
          = SV245 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12184]) ).

thf(12429,plain,
    ! [SV817: nat,SV572: nat,SV246: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV246 @ SV572 ) )
        = $true )
      | ( ( ( divide_divide_nat @ ( plus_plus_nat @ SV572 @ SV817 ) @ SV246 )
          = ( plus_plus_nat @ ( divide_divide_nat @ SV572 @ SV246 ) @ ( divide_divide_nat @ SV817 @ SV246 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12185]) ).

thf(12430,plain,
    ! [SV818: nat,SV573: nat,SV247: nat] :
      ( ( ( ~ ( ord_less_nat @ SV247 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV573 @ SV818 ) ) ) )
        = $true )
      | ( ( ord_less_nat @ ( vEBT_VEBT_high @ SV247 @ SV573 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV818 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12187]) ).

thf(12431,plain,
    ! [SV819: nat,SV575: nat,SV249: nat] :
      ( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV249 @ SV575 ) @ SV819 ) )
        = $true )
      | ( ( ord_less_nat @ SV249 @ SV819 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12189]) ).

thf(12432,plain,
    ! [SV820: nat,SV576: nat,SV250: nat] :
      ( ( ( ( times_times_nat @ SV250 @ SV576 )
         != ( times_times_nat @ SV576 @ SV250 ) )
        = $true )
      | ( ( ( times_times_nat @ ( power_power_nat @ SV250 @ SV820 ) @ SV576 )
          = ( times_times_nat @ SV576 @ ( power_power_nat @ SV250 @ SV820 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12190]) ).

thf(12433,plain,
    ! [SV577: nat,SV251: nat] :
      ( ( ( ( times_times_nat @ SV251 @ SV577 )
          = zero_zero_nat )
        = $false )
      | ( ( ( SV251 = zero_zero_nat )
          | ( SV577 = zero_zero_nat ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12191]) ).

thf(12434,plain,
    ! [SV821: nat,SV578: nat,SV252: nat] :
      ( ( ( ~ ( ( SV252 != zero_zero_nat ) ) )
        = $true )
      | ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ SV578 @ SV252 ) @ SV821 ) @ SV252 )
          = ( plus_plus_nat @ SV578 @ ( divide_divide_nat @ SV821 @ SV252 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12192]) ).

thf(12435,plain,
    ! [SV925: nat,SV822: nat,SV579: nat,SV253: nat] :
      ( ( ~ ( ord_less_nat @ SV253 @ SV579 )
        | ( ( plus_plus_nat @ SV822 @ SV579 )
         != ( plus_plus_nat @ SV253 @ SV925 ) )
        | ( ord_less_nat @ SV822 @ SV925 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12193]) ).

thf(12436,plain,
    ! [SV823: nat,SV580: nat,SV254: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( times_times_nat @ SV254 @ SV580 ) @ SV823 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV254 @ ( divide_divide_nat @ SV823 @ SV580 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12194]) ).

thf(12437,plain,
    ! [SV824: nat,SV581: nat,SV255: nat] :
      ( ( ~ ( ( SV255 != zero_zero_nat )
            | ( ( divide_divide_nat @ ( times_times_nat @ SV255 @ SV581 ) @ ( times_times_nat @ SV255 @ SV824 ) )
              = zero_zero_nat ) )
        | ~ ( ~ ( ( SV255 != zero_zero_nat ) )
            | ( ( divide_divide_nat @ ( times_times_nat @ SV255 @ SV581 ) @ ( times_times_nat @ SV255 @ SV824 ) )
              = ( divide_divide_nat @ SV581 @ SV824 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[12195]) ).

thf(12438,plain,
    ! [SV582: nat,SV256: nat] :
      ( ( ( SV256 != zero_zero_nat )
        = $false )
      | ( ( ( divide_divide_nat @ ( times_times_nat @ SV256 @ SV582 ) @ SV256 )
          = SV582 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12196]) ).

thf(12439,plain,
    ! [SV825: nat,SV583: nat,SV257: nat] :
      ( ( ( ~ ( ( SV257 != zero_zero_nat ) ) )
        = $true )
      | ( ( ( ( times_times_nat @ SV583 @ SV257 )
            = ( times_times_nat @ SV825 @ SV257 ) )
          = ( SV583 = SV825 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12197]) ).

thf(12440,plain,
    ! [SV826: nat,SV584: nat,SV258: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV258 @ ( times_times_nat @ SV584 @ SV826 ) ) )
        = $true )
      | ( ( ~ ! [SY1869: nat,SY1870: nat] :
                ( ( SV258
                 != ( times_times_nat @ SY1869 @ SY1870 ) )
                | ~ ( dvd_dvd_nat @ SY1869 @ SV584 )
                | ~ ( dvd_dvd_nat @ SY1870 @ SV826 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12198]) ).

thf(12441,plain,
    ! [SV585: nat,SV259: nat] :
      ( ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV259 @ SV585 ) )
         != zero_zero_nat )
        = $false )
      | ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV585 )
         != zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12199]) ).

thf(12442,plain,
    ( ( maxs
      = ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ summin @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) @ lx ) @ na ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[12201]) ).

thf(12443,plain,
    ! [SV926: nat,SV827: nat,SV586: nat,SV260: nat] :
      ( ( ~ ~ ( ( SV260 != SV586 )
              | ( SV827 != SV926 ) )
        | ( ( plus_plus_nat @ SV260 @ SV827 )
          = ( plus_plus_nat @ SV586 @ SV926 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12202]) ).

thf(12444,plain,
    ! [SV828: nat,SV587: nat,SV261: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV261 @ SV587 ) )
        = $true )
      | ( ( ~ ( dvd_dvd_nat @ SV261 @ SV828 )
          | ( ( divide_divide_nat @ ( plus_plus_nat @ SV587 @ SV828 ) @ SV261 )
            = ( plus_plus_nat @ ( divide_divide_nat @ SV587 @ SV261 ) @ ( divide_divide_nat @ SV828 @ SV261 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12203]) ).

thf(12445,plain,
    ! [SV829: nat,SV588: nat,SV262: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV262 @ SV588 ) )
        = $true )
      | ( ( ~ ( dvd_dvd_nat @ SV588 @ SV829 )
          | ( ( divide_divide_nat @ ( divide_divide_nat @ SV829 @ SV262 ) @ ( divide_divide_nat @ SV588 @ SV262 ) )
            = ( divide_divide_nat @ SV829 @ SV588 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12204]) ).

thf(12446,plain,
    ! [SV927: nat,SV830: nat,SV589: nat,SV263: nat] :
      ( ( ( SV263
         != ( plus_plus_nat @ SV589 @ SV830 ) )
        | ( ( plus_plus_nat @ SV263 @ SV927 )
          = ( plus_plus_nat @ SV589 @ ( plus_plus_nat @ SV830 @ SV927 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12205]) ).

thf(12447,plain,
    ! [SV590: nat,SV264: nat > complex] :
      ( ( ( summable_complex @ SV264 )
        = $false )
      | ( ( summable_complex
          @ ^ [SY1716: nat] : ( SV264 @ ( plus_plus_nat @ SY1716 @ SV590 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12206]) ).

thf(12448,plain,
    ! [SV831: nat,SV591: nat,SV265: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV265 @ SV591 ) )
        = $true )
      | ( ( ord_less_eq_nat @ ( times_times_nat @ SV265 @ SV831 ) @ ( times_times_nat @ SV591 @ SV831 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12207]) ).

thf(12449,plain,
    ! [SV832: nat,SV592: nat,SV266: nat] :
      ( ( ( ~ ( ( SV266 != zero_zero_nat ) ) )
        = $true )
      | ( ( ( divide_divide_nat @ ( times_times_nat @ SV592 @ SV266 ) @ ( times_times_nat @ SV832 @ SV266 ) )
          = ( divide_divide_nat @ SV592 @ SV832 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12208]) ).

thf(12450,plain,
    ! [SV833: nat,SV593: nat,SV268: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV268 @ SV593 ) @ SV833 ) )
        = $true )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ SV268 @ SV833 )
              | ~ ( ord_less_eq_nat @ SV593 @ SV833 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12209]) ).

thf(12451,plain,
    ! [SV834: nat,SV594: nat,SV269: nat] :
      ( ( ( ~ ( ( SV269 != zero_zero_nat ) ) )
        = $true )
      | ( ( ( divide_divide_nat @ ( plus_plus_nat @ SV594 @ ( times_times_nat @ SV269 @ SV834 ) ) @ SV269 )
          = ( plus_plus_nat @ SV834 @ ( divide_divide_nat @ SV594 @ SV269 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12210]) ).

thf(12452,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( SV595 = SV928 )
        = ( ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
               != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
              | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
               != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12211]) ).

thf(12453,plain,
    ! [SV929: nat,SV836: nat,SV596: nat,SV272: nat] :
      ( ( ~ ( dvd_dvd_nat @ SV272 @ SV596 )
        | ~ ( dvd_dvd_nat @ SV836 @ SV929 )
        | ( dvd_dvd_nat @ ( times_times_nat @ SV272 @ SV836 ) @ ( times_times_nat @ SV596 @ SV929 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12213]) ).

thf(12454,plain,
    ! [SV837: nat,SV597: nat,SV273: nat] :
      ( ( ~ ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
              = ( modulo_modulo_nat @ SV837 @ SV597 ) )
            | ~ ! [SY1874: nat] :
                  ~ ~ ! [SY1875: nat] :
                        ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SY1874 ) )
                       != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1875 ) ) ) )
        | ~ ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
             != ( modulo_modulo_nat @ SV837 @ SV597 ) )
            | ~ ~ ! [SY1874: nat] :
                    ~ ~ ! [SY1875: nat] :
                          ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SY1874 ) )
                         != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1875 ) ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12214]) ).

thf(12455,plain,
    ! [SV837: nat,SV597: nat,SV273: nat] :
      ( ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
          = ( modulo_modulo_nat @ SV837 @ SV597 ) )
        = ( ~ ! [SY1874: nat] :
                ~ ~ ! [SY1875: nat] :
                      ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SY1874 ) )
                     != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1875 ) ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12214]) ).

thf(12456,plain,
    ! [SV838: nat,SV598: nat,SV274: nat] :
      ( ( ( ( plus_plus_nat @ SV274 @ SV598 )
         != ( plus_plus_nat @ SV838 @ SV598 ) )
        = $true )
      | ( ( SV274 = SV838 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12215]) ).

thf(12457,plain,
    ! [SV839: nat,SV599: nat,SV275: nat] :
      ( ( ( ~ ( ( SV275 != zero_zero_nat ) ) )
        = $true )
      | ( ( ( divide_divide_nat @ ( plus_plus_nat @ SV599 @ ( times_times_nat @ SV839 @ SV275 ) ) @ SV275 )
          = ( plus_plus_nat @ SV839 @ ( divide_divide_nat @ SV599 @ SV275 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12216]) ).

thf(12458,plain,
    ! [SV840: nat,SV600: nat,SV276: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV276 @ SV600 ) )
        = $true )
      | ( ( ord_less_eq_nat @ ( times_times_nat @ SV840 @ SV276 ) @ ( times_times_nat @ SV840 @ SV600 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12217]) ).

thf(12459,plain,
    ! [SV277: nat] :
      ( ( ( ! [SY1343: nat] :
              ( SV277
             != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1343 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV277 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12218]) ).

thf(12460,plain,
    ! [SV601: nat,SV280: nat] :
      ( ( ( ( times_times_nat @ SV280 @ SV601 )
         != zero_zero_nat )
        = $false )
      | ( ( ~ ( ~ ( ( SV280 != zero_zero_nat ) )
              | ~ ( ( SV601 != zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12219]) ).

thf(12461,plain,
    ! [SV841: nat,SV602: nat,SV281: nat] :
      ( ( ( ~ ( ord_less_nat @ SV281 @ ( times_times_nat @ SV602 @ SV841 ) ) )
        = $true )
      | ( ( ord_less_nat @ ( divide_divide_nat @ SV281 @ SV841 ) @ SV602 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12220]) ).

thf(12462,plain,
    ! [SV930: nat,SV842: nat,SV603: nat,SV282: nat] :
      ( ( ( SV282
         != ( plus_plus_nat @ SV603 @ SV842 ) )
        | ( ( plus_plus_nat @ SV930 @ SV282 )
          = ( plus_plus_nat @ SV603 @ ( plus_plus_nat @ SV930 @ SV842 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12222]) ).

thf(12463,plain,
    ! [SV843: nat,SV604: nat,SV283: nat] :
      ( ( ( ( times_times_nat @ SV283 @ SV604 )
         != one_one_nat )
        = $true )
      | ( ( ( times_times_nat @ ( power_power_nat @ SV283 @ SV843 ) @ ( power_power_nat @ SV604 @ SV843 ) )
          = one_one_nat )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12223]) ).

thf(12464,plain,
    ! [SV931: nat,SV844: nat,SV605: nat,SV284: nat] :
      ( ( ( ~ ( ~ ( ( SV284 != SV605 ) )
              | ~ ( ( SV844 != SV931 ) ) ) )
        = ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
         != ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12224]) ).

thf(12465,plain,
    ! [SV845: nat,SV606: nat,SV285: nat] :
      ( ( ( ~ ( ( SV285 != zero_zero_nat ) ) )
        = $true )
      | ( ( ( ( times_times_nat @ SV285 @ SV606 )
            = ( times_times_nat @ SV285 @ SV845 ) )
          = ( SV606 = SV845 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12225]) ).

thf(12466,plain,
    ! [SV846: nat,SV607: nat,SV286: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV286 @ SV607 ) )
        = $true )
      | ( ( ( times_times_nat @ ( divide_divide_nat @ SV607 @ SV286 ) @ SV846 )
          = ( divide_divide_nat @ ( times_times_nat @ SV607 @ SV846 ) @ SV286 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12226]) ).

thf(12467,plain,
    ! [SV608: nat,SV287: nat] :
      ( ( ( SV287 != zero_zero_nat )
        = $false )
      | ( ( ~ ( ( SV608 != zero_zero_nat ) )
          | ( ( times_times_nat @ SV287 @ SV608 )
           != zero_zero_nat ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12227]) ).

thf(12468,plain,
    ! [SV609: nat,SV288: nat] :
      ( ( ( ( divide_divide_nat @ SV288 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV609 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false )
      | ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV288 )
           != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV609 ) )
          | ( SV288 = SV609 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12229]) ).

thf(12469,plain,
    ! [SV847: nat,SV610: nat,SV289: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV289 @ SV610 ) )
        = $true )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV289 @ SV847 ) @ ( plus_plus_nat @ SV610 @ SV847 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12230]) ).

thf(12470,plain,
    ! [SV932: nat,SV848: nat,SV611: nat,SV290: nat] :
      ( ( ~ ~ ( ~ ( ord_less_nat @ SV290 @ SV611 )
              | ~ ( ord_less_nat @ SV848 @ SV932 ) )
        | ( ord_less_nat @ ( plus_plus_nat @ SV290 @ SV848 ) @ ( plus_plus_nat @ SV611 @ SV932 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12231]) ).

thf(12471,plain,
    ! [SV612: nat,SV291: nat] :
      ( ( ( dvd_dvd_nat @ SV291 @ SV612 )
        = $false )
      | ( ( ( times_times_nat @ SV291 @ ( divide_divide_nat @ SV612 @ SV291 ) )
          = SV612 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12232]) ).

thf(12472,plain,
    ! [SV614: nat,SV293: nat] :
      ( ( ( SV293 != zero_zero_nat )
        = $false )
      | ( ( ( divide_divide_nat @ ( times_times_nat @ SV614 @ SV293 ) @ SV293 )
          = SV614 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12234]) ).

thf(12473,plain,
    ! [SV933: nat,SV849: nat,SV615: nat,SV294: nat] :
      ( ( ~ ~ ( ( SV294 != SV615 )
              | ~ ( ord_less_nat @ SV849 @ SV933 ) )
        | ( ord_less_nat @ ( plus_plus_nat @ SV294 @ SV849 ) @ ( plus_plus_nat @ SV615 @ SV933 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12235]) ).

thf(12474,plain,
    ! [SV934: nat,SV850: nat,SV617: nat,SV296: nat] :
      ( ( ~ ( ord_less_nat @ SV296 @ SV617 )
        | ~ ( ord_less_nat @ SV850 @ SV934 )
        | ( ord_less_nat @ ( plus_plus_nat @ SV296 @ SV850 ) @ ( plus_plus_nat @ SV617 @ SV934 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12237]) ).

thf(12475,plain,
    ! [SV935: nat,SV851: nat,SV618: nat,SV297: nat] :
      ( ( ~ ( dvd_dvd_nat @ SV297 @ SV618 )
        | ~ ( dvd_dvd_nat @ SV851 @ SV935 )
        | ( ( times_times_nat @ ( divide_divide_nat @ SV618 @ SV297 ) @ ( divide_divide_nat @ SV935 @ SV851 ) )
          = ( divide_divide_nat @ ( times_times_nat @ SV618 @ SV935 ) @ ( times_times_nat @ SV297 @ SV851 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12238]) ).

thf(12476,plain,
    ! [SV619: nat,SV298: nat] :
      ( ( ( ord_less_eq_nat @ SV298 @ SV619 )
        = $false )
      | ( ( ~ ! [SY1748: nat] :
                ( SV619
               != ( plus_plus_nat @ SV298 @ SY1748 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12239]) ).

thf(12477,plain,
    ! [SV852: nat,SV620: nat,SV299: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV299 @ SV620 ) )
        = $true )
      | ( ( ord_less_eq_nat @ SV299 @ ( plus_plus_nat @ SV852 @ SV620 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12240]) ).

thf(12478,plain,
    ! [SV621: nat,SV300: nat] :
      ( ( ( ~ ( ( ( times_times_nat @ SV300 @ SV621 )
                = one_one_nat )
              | ~ ( ( SV300 != one_one_nat )
                  | ( SV621 != one_one_nat ) ) ) )
        = $true )
      | ( ( ~ ( ( ( times_times_nat @ SV300 @ SV621 )
               != one_one_nat )
              | ~ ~ ( ( SV300 != one_one_nat )
                    | ( SV621 != one_one_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12241]) ).

thf(12479,plain,
    ! [SV936: nat,SV622: nat] :
      ( ( ( dvd_dvd_nat @ SV622 @ SV936 )
        = ( ~ ! [SY1919: nat] :
                ( SV936
               != ( times_times_nat @ SV622 @ SY1919 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12244]) ).

thf(12480,plain,
    ! [SV623: nat,SV302: nat > real] :
      ( ( ( summable_real @ SV302 )
        = $false )
      | ( ( summable_real
          @ ^ [SY1752: nat] : ( SV302 @ ( plus_plus_nat @ SY1752 @ SV623 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12246]) ).

thf(12481,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
              | ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
               != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) )
        = $true )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
              | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
                   != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12247]) ).

thf(12482,plain,
    ! [SV854: nat,SV625: nat,SV304: nat] :
      ( ( ( ~ ( ord_less_nat @ SV304 @ SV625 ) )
        = $true )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV304 @ SV854 ) @ ( plus_plus_nat @ SV625 @ SV854 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12249]) ).

thf(12483,plain,
    ! [SV626: nat,SV305: nat] :
      ( ( ( ~ ( ( ( plus_plus_nat @ SV305 @ SV626 )
                = zero_zero_nat )
              | ~ ( ( SV305 != zero_zero_nat )
                  | ( SV626 != zero_zero_nat ) ) ) )
        = $true )
      | ( ( ~ ( ( ( plus_plus_nat @ SV305 @ SV626 )
               != zero_zero_nat )
              | ~ ~ ( ( SV305 != zero_zero_nat )
                    | ( SV626 != zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12250]) ).

thf(12484,plain,
    ! [SV627: nat,SV307: nat] :
      ( ( ( ( plus_plus_nat @ SV307 @ SV627 )
          = SV307 )
        = $false )
      | ( ( SV627 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12252]) ).

thf(12485,plain,
    ! [SV855: nat,SV628: nat,SV308: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV308 @ SV628 ) )
        = $true )
      | ( ( ord_less_eq_nat @ ( divide_divide_nat @ SV308 @ SV855 ) @ ( divide_divide_nat @ SV628 @ SV855 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12253]) ).

thf(12486,plain,
    ! [SV629: nat,SV309: nat] :
      ( ( ( ord_less_eq_nat @ SV309 @ SV629 )
        = $false )
      | ( ( ~ ! [SY1755: nat] :
                ( SV629
               != ( plus_plus_nat @ SV309 @ SY1755 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12254]) ).

thf(12487,plain,
    ! [SV630: nat,SV310: nat] :
      ( ( ( ~ ( ( ( plus_plus_nat @ SV310 @ SV630 )
                = zero_zero_nat )
              | ~ ( ( SV310 != zero_zero_nat )
                  | ( SV630 != zero_zero_nat ) ) ) )
        = $true )
      | ( ( ~ ( ( ( plus_plus_nat @ SV310 @ SV630 )
               != zero_zero_nat )
              | ~ ~ ( ( SV310 != zero_zero_nat )
                    | ( SV630 != zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12255]) ).

thf(12488,plain,
    ! [SV856: nat,SV631: nat,SV311: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV311 @ ( times_times_nat @ SV631 @ SV856 ) ) )
        = $true )
      | ( ( ~ ! [SY1883: nat] :
                ~ ~ ! [SY1884: nat] :
                      ~ ~ ( ~ ~ ( ( SV311
                                 != ( times_times_nat @ SY1883 @ SY1884 ) )
                                | ~ ( dvd_dvd_nat @ SY1883 @ SV631 ) )
                          | ~ ( dvd_dvd_nat @ SY1884 @ SV856 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12257]) ).

thf(12489,plain,
    ! [SV937: nat,SV857: nat,SV632: nat,SV312: nat] :
      ( ( ! [SY1920: nat] :
            ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
            | ~ ( dvd_dvd_nat @ SV312 @ SV857 )
            | ~ ( ( ( times_times_nat @ SV632 @ SV937 )
                  = ( plus_plus_nat @ ( times_times_nat @ SV857 @ SY1920 ) @ SV312 ) )
                | ( ( times_times_nat @ SV857 @ SV937 )
                  = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SY1920 ) @ SV312 ) ) )
            | ~ ! [SY1887: nat] :
                  ~ ~ ! [SY1888: nat] :
                        ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
                                  | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) )
                            | ~ ( ( ( times_times_nat @ SV632 @ SY1887 )
                                  = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1888 ) @ SV312 ) )
                                | ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1887 )
                                  = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SY1888 ) @ SV312 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12258]) ).

thf(12490,plain,
    ! [SV858: nat,SV633: nat,SV313: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV313 @ SV633 ) )
        = $true )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV313 @ SV858 ) @ ( plus_plus_nat @ SV633 @ SV858 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12259]) ).

thf(12491,plain,
    ! [SV859: nat,SV634: nat,SV314: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV314 @ SV634 ) )
        = $true )
      | ( ( ~ ( dvd_dvd_nat @ SV634 @ SV859 )
          | ( ( divide_divide_nat @ SV859 @ ( divide_divide_nat @ SV634 @ SV314 ) )
            = ( times_times_nat @ ( divide_divide_nat @ SV859 @ SV634 ) @ SV314 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12260]) ).

thf(12492,plain,
    ! [SV636: num,SV316: num > $o] :
      ( ( ( SV316 @ one )
        = $false )
      | ( ( ~ ! [SY1414: num] :
                ( ~ ( SV316 @ SY1414 )
                | ( SV316 @ ( inc @ SY1414 ) ) )
          | ( SV316 @ SV636 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12262]) ).

thf(12493,plain,
    ! [SV637: nat,SV317: nat] :
      ( ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV317 @ SV637 ) )
         != zero_zero_nat )
        = $false )
      | ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV317 )
         != zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12263]) ).

thf(12494,plain,
    ! [SV860: nat,SV639: nat,SV319: nat > nat > $o] :
      ( ( ( ~ ! [SY1419: nat,SY1420: nat] :
                ( ( SV319 @ SY1419 @ SY1420 )
                = ( SV319 @ SY1420 @ SY1419 ) ) )
        = $true )
      | ( ( ~ ! [SY1421: nat] : ( SV319 @ SY1421 @ zero_zero_nat )
          | ~ ! [SY1422: nat,SY1423: nat] :
                ( ~ ( SV319 @ SY1422 @ SY1423 )
                | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) )
          | ( SV319 @ SV639 @ SV860 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12265]) ).

thf(12495,plain,
    ! [SV861: nat,SV641: nat,SV321: nat] :
      ( ( ( ~ ( ord_less_nat @ SV321 @ SV641 ) )
        = $true )
      | ( ( ord_less_nat @ SV321 @ ( plus_plus_nat @ SV861 @ SV641 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12267]) ).

thf(12496,plain,
    ! [SV642: nat,SV322: nat] :
      ( ( ( ~ ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 )
              | ~ ( ~ ( ( SV322 != SV642 ) )
                  | ~ ( vEBT_V8194947554948674370ptions @ summary @ SV642 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 )
              | ~ ~ ( ~ ( ( SV322 != SV642 ) )
                    | ~ ( vEBT_V8194947554948674370ptions @ summary @ SV642 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12268]) ).

thf(12497,plain,
    ! [SV938: nat,SV862: nat,SV643: nat,SV323: nat] :
      ( ( ! [SY1923: nat] :
            ( ( ( modulo_modulo_nat @ SV323 @ SV643 )
             != ( modulo_modulo_nat @ SV862 @ SV643 ) )
            | ( ( modulo_modulo_nat @ SV938 @ SV643 )
             != ( modulo_modulo_nat @ SY1923 @ SV643 ) )
            | ( ( modulo_modulo_nat @ ( times_times_nat @ SV323 @ SV938 ) @ SV643 )
              = ( modulo_modulo_nat @ ( times_times_nat @ SV862 @ SY1923 ) @ SV643 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12270]) ).

thf(12498,plain,
    ! [SV939: nat,SV644: nat] :
      ( ( ( ord_less_eq_nat @ SV644 @ SV939 )
        = ( ~ ! [SY1924: nat] :
                ( SV939
               != ( plus_plus_nat @ SV644 @ SY1924 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12271]) ).

thf(12499,plain,
    ! [SV864: nat,SV645: nat,SV325: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( times_times_nat @ SV325 @ SV645 ) @ SV864 ) )
        = $true )
      | ( ( ( divide_divide_nat @ SV864 @ ( times_times_nat @ SV325 @ SV645 ) )
          = ( divide_divide_nat @ ( divide_divide_nat @ SV864 @ SV325 ) @ SV645 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12273]) ).

thf(12500,plain,
    ! [SV865: nat,SV646: nat,SV326: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV326 @ SV646 ) )
        = $true )
      | ( ( ( times_times_nat @ SV865 @ ( divide_divide_nat @ SV646 @ SV326 ) )
          = ( divide_divide_nat @ ( times_times_nat @ SV865 @ SV646 ) @ SV326 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12274]) ).

thf(12501,plain,
    ! [SV866: nat,SV647: nat,SV327: nat] :
      ( ( ( ~ ( ord_less_nat @ SV327 @ SV647 ) )
        = $true )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV327 @ SV866 ) @ ( plus_plus_nat @ SV647 @ SV866 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12275]) ).

thf(12502,plain,
    ! [SV940: nat,SV867: nat,SV648: nat,SV328: nat] :
      ( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV328 @ SV648 )
              | ( SV867 != SV940 ) )
        | ( ord_less_eq_nat @ ( plus_plus_nat @ SV328 @ SV867 ) @ ( plus_plus_nat @ SV648 @ SV940 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12276]) ).

thf(12503,plain,
    ! [SV649: nat,SV329: nat] :
      ( ( ( ~ ( ( zero_zero_nat
                = ( plus_plus_nat @ SV329 @ SV649 ) )
              | ~ ( ( SV329 != zero_zero_nat )
                  | ( SV649 != zero_zero_nat ) ) ) )
        = $true )
      | ( ( ~ ( ( zero_zero_nat
               != ( plus_plus_nat @ SV329 @ SV649 ) )
              | ~ ~ ( ( SV329 != zero_zero_nat )
                    | ( SV649 != zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12277]) ).

thf(12504,plain,
    ! [SV868: nat,SV650: nat,SV330: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV330 @ SV650 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( power_power_nat @ SV330 @ SV868 ) @ ( power_power_nat @ SV650 @ SV868 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12279]) ).

thf(12505,plain,
    ! [SV651: nat,SV331: nat] :
      ( ( ( SV331 != zero_zero_nat )
        = $false )
      | ( ( ( power_power_nat @ SV331 @ SV651 )
         != zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12280]) ).

thf(12506,plain,
    ! [SV941: vEBT_VEBT,SV869: list_VEBT_VEBT,SV652: nat,SV332: nat] :
      ( ( ! [SY1925: vEBT_VEBT] :
            ( ~ ( ( SV332 != SV652 ) )
            | ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV869 @ SV332 @ SV941 ) @ SV652 @ SY1925 )
              = ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV869 @ SV652 @ SY1925 ) @ SV332 @ SV941 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12281]) ).

thf(12507,plain,
    ! [SV870: nat,SV656: nat,SV334: nat] :
      ( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV334 @ SV656 ) @ ( plus_plus_nat @ SV870 @ SV656 ) ) )
        = $true )
      | ( ( ord_less_nat @ SV334 @ SV870 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12282]) ).

thf(12508,plain,
    ! [SV942: nat,SV871: nat,SV657: nat,SV335: nat] :
      ( ( ~ ~ ( ( SV335 != SV657 )
              | ~ ( ord_less_eq_nat @ SV871 @ SV942 ) )
        | ( ord_less_eq_nat @ ( plus_plus_nat @ SV335 @ SV871 ) @ ( plus_plus_nat @ SV657 @ SV942 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12283]) ).

thf(12509,plain,
    ! [SV872: nat,SV658: nat,SV336: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV336 @ SV658 ) )
        = $true )
      | ( ( ( dvd_dvd_nat @ SV336 @ ( plus_plus_nat @ SV872 @ SV658 ) )
          = ( dvd_dvd_nat @ SV336 @ SV872 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12284]) ).

thf(12510,plain,
    ! [SV873: nat,SV659: nat,SV337: nat] :
      ( ( ( SV337
         != ( plus_plus_nat @ SV659 @ SV873 ) )
        = $true )
      | ( ( ( suc @ SV337 )
          = ( plus_plus_nat @ SV659 @ ( suc @ SV873 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12285]) ).

thf(12511,plain,
    ! [SV874: nat,SV660: nat,SV338: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV338 @ SV660 ) )
        = $true )
      | ( ( ~ ( dvd_dvd_nat @ SV338 @ SV874 )
          | ( dvd_dvd_nat @ SV338 @ ( plus_plus_nat @ SV660 @ SV874 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12286]) ).

thf(12512,plain,
    ! [SV875: nat,SV661: nat,SV339: nat] :
      ( ( ( ( plus_plus_nat @ SV339 @ SV661 )
         != ( plus_plus_nat @ SV339 @ SV875 ) )
        = $true )
      | ( ( SV661 = SV875 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12287]) ).

thf(12513,plain,
    ! [SV340: nat] :
      ( ( ( SV340
         != ( plus_plus_nat @ ( sK5_SY1465 @ SV340 ) @ ( sK5_SY1465 @ SV340 ) ) )
        = $false )
      | ( ( ~ ! [SY1466: nat] :
                ( SV340
               != ( plus_plus_nat @ SY1466 @ ( suc @ SY1466 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[12288]) ).

thf(12514,plain,
    ! [SV943: nat,SV876: nat,SV662: nat,SV341: nat] :
      ( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV341 @ SV662 )
              | ~ ( ord_less_eq_nat @ SV876 @ SV943 ) )
        | ( ord_less_eq_nat @ ( plus_plus_nat @ SV341 @ SV876 ) @ ( plus_plus_nat @ SV662 @ SV943 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12289]) ).

thf(12515,plain,
    ! [SV877: nat,SV663: nat,SV342: nat] :
      ( ( ( ~ ( ( SV342 != zero_zero_nat ) ) )
        = $true )
      | ( ( ( divide_divide_nat @ ( times_times_nat @ SV342 @ SV663 ) @ ( times_times_nat @ SV342 @ SV877 ) )
          = ( divide_divide_nat @ SV663 @ SV877 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12290]) ).

thf(12516,plain,
    ! [SV878: nat,SV664: nat,SV343: nat] :
      ( ( ( ~ ( ord_less_nat @ SV343 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV664 ) ) )
        = $true )
      | ( ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ SV878 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV664 ) ) @ SV343 ) @ SV664 )
          = SV878 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12291]) ).

thf(12517,plain,
    ! [SV879: nat,SV665: nat,SV344: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV344 @ SV665 ) )
        = $true )
      | ( ( ( divide_divide_nat @ ( plus_plus_nat @ SV879 @ SV665 ) @ SV344 )
          = ( plus_plus_nat @ ( divide_divide_nat @ SV879 @ SV344 ) @ ( divide_divide_nat @ SV665 @ SV344 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12292]) ).

thf(12518,plain,
    ! [SV880: nat,SV666: nat,SV345: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV345 @ SV666 ) @ SV880 ) )
        = $true )
      | ( ( ord_less_eq_nat @ SV666 @ SV880 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12293]) ).

thf(12519,plain,
    ! [SV881: nat,SV667: nat,SV346: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( times_times_nat @ SV346 @ SV667 ) @ SV881 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV667 @ SV881 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12294]) ).

thf(12520,plain,
    ! [SV882: nat,SV668: nat,SV347: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV347 @ SV668 ) )
        = $true )
      | ( ( ~ ( dvd_dvd_nat @ SV347 @ SV882 )
          | ( ( dvd_dvd_nat @ ( divide_divide_nat @ SV668 @ SV347 ) @ ( divide_divide_nat @ SV882 @ SV347 ) )
            = ( dvd_dvd_nat @ SV668 @ SV882 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12295]) ).

thf(12521,plain,
    ! [SV349: nat,SV669: nat] :
      ( ( ~ ~ ! [SY1926: nat] :
                ~ ~ ! [SY1927: nat] :
                      ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ ( sK6_SY1803 @ SV669 @ SV349 ) @ SV349 )
                                | ~ ( dvd_dvd_nat @ ( sK6_SY1803 @ SV669 @ SV349 ) @ SV669 ) )
                          | ~ ( ( ( times_times_nat @ SV349 @ SY1926 )
                                = ( plus_plus_nat @ ( times_times_nat @ SV669 @ SY1927 ) @ ( sK6_SY1803 @ SV669 @ SV349 ) ) )
                              | ( ( times_times_nat @ SV669 @ SY1926 )
                                = ( plus_plus_nat @ ( times_times_nat @ SV349 @ SY1927 ) @ ( sK6_SY1803 @ SV669 @ SV349 ) ) ) ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[12297]) ).

thf(12522,plain,
    ! [SV670: nat,SV350: nat] :
      ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV350 )
        = $false )
      | ( ( ord_less_eq_nat @ SV670 @ ( power_power_nat @ SV350 @ SV670 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12298]) ).

thf(12523,plain,
    ! [SV671: nat,SV351: nat] :
      ( ( ( ~ ( ( one_one_nat
                = ( times_times_nat @ SV351 @ SV671 ) )
              | ~ ( ( SV351 != one_one_nat )
                  | ( SV671 != one_one_nat ) ) ) )
        = $true )
      | ( ( ~ ( ( one_one_nat
               != ( times_times_nat @ SV351 @ SV671 ) )
              | ~ ~ ( ( SV351 != one_one_nat )
                    | ( SV671 != one_one_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12299]) ).

thf(12524,plain,
    ! [SV944: nat,SV883: nat,SV672: nat,SV352: nat] :
      ( ( ~ ( ord_less_eq_nat @ SV352 @ SV672 )
        | ~ ( ord_less_eq_nat @ SV883 @ SV944 )
        | ( ord_less_eq_nat @ ( plus_plus_nat @ SV352 @ SV883 ) @ ( plus_plus_nat @ SV672 @ SV944 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12301]) ).

thf(12525,plain,
    ! [SV945: nat,SV884: nat,SV673: nat,SV353: nat] :
      ( ( ! [SY1928: nat] :
            ( ~ ( ( SV353 != zero_zero_nat ) )
            | ~ ~ ( ( SV673 != SV884 )
                  | ~ ( ( SV945 != SY1928 ) ) )
            | ( ( plus_plus_nat @ SV673 @ ( times_times_nat @ SV353 @ SV945 ) )
             != ( plus_plus_nat @ SV884 @ ( times_times_nat @ SV353 @ SY1928 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12302]) ).

thf(12526,plain,
    ! [SV885: nat,SV674: nat,SV354: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV354 @ SV674 ) )
        = $true )
      | ( ( ( dvd_dvd_nat @ SV354 @ ( plus_plus_nat @ SV674 @ SV885 ) )
          = ( dvd_dvd_nat @ SV354 @ SV885 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12303]) ).

thf(12527,plain,
    ! [SV675: nat > nat,SV355: nat > nat] :
      ( ( ( summable_nat @ SV355 )
        = $false )
      | ( ( ~ ( summable_nat @ SV675 )
          | ( summable_nat
            @ ^ [SY1812: nat] : ( plus_plus_nat @ ( SV355 @ SY1812 ) @ ( SV675 @ SY1812 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12304]) ).

thf(12528,plain,
    ! [SV886: nat,SV676: nat,SV356: nat] :
      ( ( ~ ( ( SV356 != zero_zero_nat )
            | ( ( divide_divide_nat @ ( times_times_nat @ SV356 @ SV676 ) @ ( times_times_nat @ SV356 @ SV886 ) )
              = zero_zero_nat ) )
        | ~ ( ~ ( ( SV356 != zero_zero_nat ) )
            | ( ( divide_divide_nat @ ( times_times_nat @ SV356 @ SV676 ) @ ( times_times_nat @ SV356 @ SV886 ) )
              = ( divide_divide_nat @ SV676 @ SV886 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[12305]) ).

thf(12529,plain,
    ! [SV887: nat,SV677: nat,SV357: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV357 @ SV677 ) @ ( plus_plus_nat @ SV887 @ SV677 ) ) )
        = $true )
      | ( ( ord_less_eq_nat @ SV357 @ SV887 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12306]) ).

thf(12530,plain,
    ! [SV678: nat,SV359: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV359 ) )
        = $false )
      | ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV678 )
          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV359 @ SV678 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12307]) ).

thf(12531,plain,
    ! [SV679: nat,SV360: nat] :
      ( ( ( dvd_dvd_nat @ SV360 @ SV679 )
        = $false )
      | ( ( ( times_times_nat @ ( divide_divide_nat @ SV679 @ SV360 ) @ SV360 )
          = SV679 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12308]) ).

thf(12532,plain,
    ! [SV888: nat,SV680: nat,SV361: nat] :
      ( ( ( ( divide_divide_nat @ SV361 @ SV680 )
         != ( divide_divide_nat @ SV888 @ SV680 ) )
        = $true )
      | ( ( ~ ( dvd_dvd_nat @ SV680 @ SV361 )
          | ~ ( dvd_dvd_nat @ SV680 @ SV888 )
          | ( SV361 = SV888 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12309]) ).

thf(12533,plain,
    ! [SV889: nat,SV681: nat,SV362: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV362 @ SV681 ) )
        = $true )
      | ( ( ~ ( dvd_dvd_nat @ SV362 @ SV889 )
          | ( ( ( divide_divide_nat @ SV681 @ SV362 )
              = ( divide_divide_nat @ SV889 @ SV362 ) )
            = ( SV681 = SV889 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12310]) ).

thf(12534,plain,
    ! [SV682: nat,SV363: nat] :
      ( ( ( dvd_dvd_nat @ SV363 @ SV682 )
        = $false )
      | ( ( ~ ! [SY1817: nat] :
                ( SV682
               != ( times_times_nat @ SV363 @ SY1817 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12311]) ).

thf(12535,plain,
    ! [SV946: nat,SV890: nat,SV683: nat,SV364: nat] :
      ( ( ~ ( ord_less_nat @ SV364 @ SV683 )
        | ~ ( ord_less_nat @ SV890 @ SV946 )
        | ( ord_less_nat @ ( plus_plus_nat @ SV364 @ SV890 ) @ ( plus_plus_nat @ SV683 @ SV946 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12312]) ).

thf(12536,plain,
    ! [SV947: nat,SV891: nat,SV684: nat,SV365: nat] :
      ( ( ~ ( ord_less_eq_nat @ SV365 @ SV684 )
        | ~ ( ord_less_eq_nat @ SV891 @ SV947 )
        | ( ord_less_eq_nat @ ( plus_plus_nat @ SV365 @ SV891 ) @ ( plus_plus_nat @ SV684 @ SV947 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12313]) ).

thf(12537,plain,
    ! [SV892: nat,SV685: nat,SV366: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( times_times_nat @ SV366 @ SV685 ) @ SV892 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV366 @ SV892 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12314]) ).

thf(12538,plain,
    ! [SV893: nat,SV686: nat,SV367: nat] :
      ( ( ( SV367
         != ( times_times_nat @ SV686 @ SV893 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV686 @ SV367 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12315]) ).

thf(12539,plain,
    ! [SV894: nat,SV687: nat,SV368: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV368 @ SV687 ) )
        = $true )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV894 @ SV368 ) @ ( plus_plus_nat @ SV894 @ SV687 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12316]) ).

thf(12540,plain,
    ! [SV895: nat,SV688: nat,SV369: nat] :
      ( ( ( ( plus_plus_nat @ SV369 @ SV688 )
         != SV895 )
        = $true )
      | ( ( SV369
          = ( minus_minus_nat @ SV895 @ SV688 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12317]) ).

thf(12541,plain,
    ! [SV896: nat,SV689: nat,SV370: nat] :
      ( ( ( ~ ( ord_less_nat @ SV370 @ SV689 ) )
        = $true )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV896 @ SV370 ) @ ( plus_plus_nat @ SV896 @ SV689 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12318]) ).

thf(12542,plain,
    ! [SV897: nat,SV690: nat,SV371: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV371 @ SV690 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV371 @ ( times_times_nat @ SV897 @ SV690 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12319]) ).

thf(12543,plain,
    ! [SV898: nat,SV691: nat,SV372: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV372 @ SV691 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV372 @ ( times_times_nat @ SV691 @ SV898 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12320]) ).

thf(12544,plain,
    ! [SV692: option_nat,SV373: option_nat] :
      ( ( ( ( SV373 = none_nat )
          = ( SV692 = none_nat ) )
        = $false )
      | ( ( ~ ( ~ ( ( SV373 != none_nat ) )
              | ~ ( ( SV692 != none_nat ) )
              | ( ( the_nat @ SV373 )
                = ( the_nat @ SV692 ) ) )
          | ( SV373 = SV692 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12321]) ).

thf(12545,plain,
    ! [SV693: nat,SV374: nat > $o] :
      ( ( ( ! [SY1533: nat] :
              ( ( ( divide_divide_nat @ SY1533 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
               != SY1533 )
              | ( SV374 @ SY1533 ) ) )
        = $false )
      | ( ( ~ ! [SY1534: nat,SY1535: $o] :
                ( ~ ( SV374 @ SY1534 )
                | ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ SY1535 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1534 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                 != SY1534 )
                | ( SV374 @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ SY1535 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1534 ) ) ) )
          | ( SV374 @ SV693 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12322]) ).

thf(12546,plain,
    ! [SV948: nat,SV694: nat] :
      ( ( ( ord_less_eq_nat @ SV694 @ SV948 )
        = ( ~ ! [SY1929: nat] :
                ( SV948
               != ( plus_plus_nat @ SV694 @ SY1929 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12323]) ).

thf(12547,plain,
    ! [SV900: nat,SV696: nat,SV377: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV377 @ SV696 ) )
        = $true )
      | ( ( ( power_power_nat @ ( divide_divide_nat @ SV696 @ SV377 ) @ SV900 )
          = ( divide_divide_nat @ ( power_power_nat @ SV696 @ SV900 ) @ ( power_power_nat @ SV377 @ SV900 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12326]) ).

thf(12548,plain,
    ! [SV949: nat,SV901: nat,SV697: nat,SV378: nat] :
      ( ( ~ ( ord_less_eq_nat @ SV378 @ SV697 )
        | ~ ( ord_less_eq_nat @ SV901 @ SV949 )
        | ( ord_less_eq_nat @ ( times_times_nat @ SV378 @ SV901 ) @ ( times_times_nat @ SV697 @ SV949 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12327]) ).

thf(12549,plain,
    ! [SV950: nat,SV902: nat,SV698: nat,SV379: nat] :
      ( ( ~ ~ ( ~ ( ord_less_nat @ SV379 @ SV698 )
              | ( SV902 != SV950 ) )
        | ( ord_less_nat @ ( plus_plus_nat @ SV379 @ SV902 ) @ ( plus_plus_nat @ SV698 @ SV950 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12328]) ).

thf(12550,plain,
    ! [SV903: nat,SV699: nat,SV380: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV380 @ SV699 ) @ ( plus_plus_nat @ SV380 @ SV903 ) ) )
        = $true )
      | ( ( ord_less_eq_nat @ SV699 @ SV903 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12329]) ).

thf(12551,plain,
    ! [SV700: nat,SV381: nat] :
      ( ( ( ord_less_eq_nat @ ( power_power_nat @ SV381 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ SV700 )
        = $false )
      | ( ( ord_less_eq_nat @ SV381 @ SV700 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12330]) ).

thf(12552,plain,
    ! [SV382: num] :
      ( ( ( SV382 = one )
        = $true )
      | ( ( ~ ! [SY1550: num] :
                ( SV382
               != ( bit0 @ SY1550 ) )
          | ~ ! [SY1551: num] :
                ( SV382
               != ( bit1 @ SY1551 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12331]) ).

thf(12553,plain,
    ! [SV951: vEBT_VEBT,SV904: list_VEBT_VEBT,SV701: nat,SV383: nat] :
      ( ( ~ ( ( SV383 != SV701 ) )
        | ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ SV904 @ SV383 @ SV951 ) @ SV701 )
          = ( nth_VEBT_VEBT @ SV904 @ SV701 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12332]) ).

thf(12554,plain,
    ! [SV952: nat,SV905: nat,SV702: nat,SV384: nat] :
      ( ( ! [SY1930: nat] :
            ( ( ( modulo_modulo_nat @ SV384 @ SV702 )
             != ( modulo_modulo_nat @ SV905 @ SV702 ) )
            | ( ( modulo_modulo_nat @ SV952 @ SV702 )
             != ( modulo_modulo_nat @ SY1930 @ SV702 ) )
            | ( ( modulo_modulo_nat @ ( plus_plus_nat @ SV384 @ SV952 ) @ SV702 )
              = ( modulo_modulo_nat @ ( plus_plus_nat @ SV905 @ SY1930 ) @ SV702 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12333]) ).

thf(12555,plain,
    ! [SV906: nat,SV703: nat,SV386: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV386 @ SV703 ) @ SV906 ) )
        = $true )
      | ( ( ord_less_eq_nat @ SV386 @ SV906 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12334]) ).

thf(12556,plain,
    ! [SV907: nat,SV704: nat,SV387: nat] :
      ( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV387 @ SV704 ) @ ( plus_plus_nat @ SV387 @ SV907 ) ) )
        = $true )
      | ( ( ord_less_nat @ SV704 @ SV907 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12335]) ).

thf(12557,plain,
    ! [SV953: nat,SV908: nat > nat,SV705: nat,SV388: nat > nat] :
      ( ( ~ ( sums_nat @ SV388 @ SV705 )
        | ~ ( sums_nat @ SV908 @ SV953 )
        | ( sums_nat
          @ ^ [SY1914: nat] : ( plus_plus_nat @ ( SV388 @ SY1914 ) @ ( SV908 @ SY1914 ) )
          @ ( plus_plus_nat @ SV705 @ SV953 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12336]) ).

thf(12558,plain,
    ! [SV909: nat,SV706: nat,SV389: nat] :
      ( ( ( ~ ( ord_less_nat @ SV389 @ SV706 ) )
        = $true )
      | ( ( ord_less_nat @ SV389 @ ( plus_plus_nat @ SV706 @ SV909 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12337]) ).

thf(12559,plain,
    ! [SV910: nat,SV707: nat,SV390: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV390 @ SV707 ) )
        = $true )
      | ( ( ord_less_eq_nat @ SV390 @ ( plus_plus_nat @ SV707 @ SV910 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12338]) ).

thf(12560,plain,
    ! [SV912: nat,SV394: nat] :
      ( ( ! [SV954: nat] :
            ( ( vEBT_VEBT_bit_concat @ SV394 @ SV912 @ SV954 )
            = ( plus_plus_nat @ ( times_times_nat @ SV394 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV954 ) ) @ SV912 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12340]) ).

thf(12561,plain,
    ! [SV912: nat,SV394: nat] :
      ( ( ( vEBT_VEBT_bit_concat @ SV394 @ SV912 )
        = ( ^ [SY1915: nat] : ( plus_plus_nat @ ( times_times_nat @ SV394 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1915 ) ) @ SV912 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12340]) ).

thf(12562,plain,
    ! [SV399: num,SV10: num] :
      ( ( ( ( ( numeral_numeral_nat @ SV10 )
            = ( numeral_numeral_nat @ SV399 ) )
          | ( SV10 = SV399 ) )
        = $false )
      | ( ( ~ ( ( ( numeral_numeral_nat @ SV10 )
               != ( numeral_numeral_nat @ SV399 ) )
              | ( SV10 != SV399 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12341]) ).

thf(12563,plain,
    ! [SV427: nat,SV49: nat] :
      ( ( ( ( ord_less_eq_nat @ ( power_power_nat @ SV49 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ SV427 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
          | ( ord_less_eq_nat @ SV49 @ SV427 ) )
        = $false )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV49 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ SV427 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
              | ~ ( ord_less_eq_nat @ SV49 @ SV427 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12344]) ).

thf(12564,plain,
    ! [SV428: num,SV53: num] :
      ( ( ( ( ord_less_num @ ( bit0 @ SV53 ) @ ( bit0 @ SV428 ) )
          | ( ord_less_num @ SV53 @ SV428 ) )
        = $false )
      | ( ( ~ ( ~ ( ord_less_num @ ( bit0 @ SV53 ) @ ( bit0 @ SV428 ) )
              | ~ ( ord_less_num @ SV53 @ SV428 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12345]) ).

thf(12565,plain,
    ! [SV429: num,SV54: num] :
      ( ( ( ( ( bit0 @ SV54 )
            = ( bit0 @ SV429 ) )
          | ( SV54 = SV429 ) )
        = $false )
      | ( ( ~ ( ( ( bit0 @ SV54 )
               != ( bit0 @ SV429 ) )
              | ( SV54 != SV429 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12346]) ).

thf(12566,plain,
    ! [SV432: num,SV62: num] :
      ( ( ( ( ord_less_eq_num @ ( bit0 @ SV62 ) @ ( bit0 @ SV432 ) )
          | ( ord_less_eq_num @ SV62 @ SV432 ) )
        = $false )
      | ( ( ~ ( ~ ( ord_less_eq_num @ ( bit0 @ SV62 ) @ ( bit0 @ SV432 ) )
              | ~ ( ord_less_eq_num @ SV62 @ SV432 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12347]) ).

thf(12567,plain,
    ! [SV64: num] :
      ( ( ( one_one_nat
          = ( numeral_numeral_nat @ SV64 ) )
        = $false )
      | ( ( ~ ( ( one_one_nat
               != ( numeral_numeral_nat @ SV64 ) )
              | ( one != SV64 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12348]) ).

thf(12568,plain,
    ! [SV64: num] :
      ( ( ( one = SV64 )
        = $false )
      | ( ( ~ ( ( one_one_nat
               != ( numeral_numeral_nat @ SV64 ) )
              | ( one != SV64 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12348]) ).

thf(12569,plain,
    ! [SV65: num] :
      ( ( ( ( numeral_numeral_nat @ SV65 )
          = one_one_nat )
        = $false )
      | ( ( ~ ( ( ( numeral_numeral_nat @ SV65 )
               != one_one_nat )
              | ( SV65 != one ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12349]) ).

thf(12570,plain,
    ! [SV65: num] :
      ( ( ( SV65 = one )
        = $false )
      | ( ( ~ ( ( ( numeral_numeral_nat @ SV65 )
               != one_one_nat )
              | ( SV65 != one ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12349]) ).

thf(12571,plain,
    ! [SV67: num] :
      ( ( ( ord_less_eq_num @ SV67 @ one )
        = $false )
      | ( ( ~ ( ~ ( ord_less_eq_num @ SV67 @ one )
              | ( SV67 != one ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12350]) ).

thf(12572,plain,
    ! [SV67: num] :
      ( ( ( SV67 = one )
        = $false )
      | ( ( ~ ( ~ ( ord_less_eq_num @ SV67 @ one )
              | ( SV67 != one ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12350]) ).

thf(12573,plain,
    ! [SV729: nat,SV435: nat,SV71: nat] :
      ( ( ( ~ ( ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SV435 ) @ ( plus_plus_nat @ SV71 @ SV729 ) )
              | ( ord_less_nat @ SV435 @ SV729 ) ) )
        = $true )
      | ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SV435 ) @ ( plus_plus_nat @ SV71 @ SV729 ) )
              | ~ ( ord_less_nat @ SV435 @ SV729 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12352]) ).

thf(12574,plain,
    ! [SV730: nat,SV436: nat,SV72: nat] :
      ( ( ( ~ ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV72 @ SV436 ) @ ( plus_plus_nat @ SV72 @ SV730 ) )
              | ( ord_less_eq_nat @ SV436 @ SV730 ) ) )
        = $true )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV72 @ SV436 ) @ ( plus_plus_nat @ SV72 @ SV730 ) )
              | ~ ( ord_less_eq_nat @ SV436 @ SV730 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12354]) ).

thf(12575,plain,
    ! [SV736: nat,SV447: nat,SV86: nat] :
      ( ( ( ~ ( ( ( times_times_nat @ ( suc @ SV86 ) @ SV447 )
                = ( times_times_nat @ ( suc @ SV86 ) @ SV736 ) )
              | ( SV447 = SV736 ) ) )
        = $true )
      | ( ( ~ ( ( ( times_times_nat @ ( suc @ SV86 ) @ SV447 )
               != ( times_times_nat @ ( suc @ SV86 ) @ SV736 ) )
              | ( SV447 != SV736 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12356]) ).

thf(12576,plain,
    ! [SV752: nat,SV475: nat,SV120: nat] :
      ( ( ( ~ ( ( ( plus_plus_nat @ SV120 @ SV475 )
                = ( plus_plus_nat @ SV120 @ SV752 ) )
              | ( SV475 = SV752 ) ) )
        = $true )
      | ( ( ~ ( ( ( plus_plus_nat @ SV120 @ SV475 )
               != ( plus_plus_nat @ SV120 @ SV752 ) )
              | ( SV475 != SV752 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12359]) ).

thf(12577,plain,
    ! [SV753: nat,SV476: nat,SV121: nat] :
      ( ( ( ~ ( ( ( plus_plus_nat @ SV121 @ SV476 )
                = ( plus_plus_nat @ SV753 @ SV476 ) )
              | ( SV121 = SV753 ) ) )
        = $true )
      | ( ( ~ ( ( ( plus_plus_nat @ SV121 @ SV476 )
               != ( plus_plus_nat @ SV753 @ SV476 ) )
              | ( SV121 != SV753 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12361]) ).

thf(12578,plain,
    ! [SV754: nat,SV477: nat,SV122: nat] :
      ( ( ( ~ ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ SV477 ) @ ( plus_plus_nat @ SV122 @ SV754 ) )
              | ( ord_less_eq_nat @ SV477 @ SV754 ) ) )
        = $true )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ SV477 ) @ ( plus_plus_nat @ SV122 @ SV754 ) )
              | ~ ( ord_less_eq_nat @ SV477 @ SV754 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12363]) ).

thf(12579,plain,
    ! [SV755: nat,SV478: nat,SV123: nat] :
      ( ( ( ~ ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV123 @ SV478 ) @ ( plus_plus_nat @ SV755 @ SV478 ) )
              | ( ord_less_eq_nat @ SV123 @ SV755 ) ) )
        = $true )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV123 @ SV478 ) @ ( plus_plus_nat @ SV755 @ SV478 ) )
              | ~ ( ord_less_eq_nat @ SV123 @ SV755 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12365]) ).

thf(12580,plain,
    ! [SV756: nat,SV479: nat,SV124: nat] :
      ( ( ( ~ ( ( ord_less_nat @ ( plus_plus_nat @ SV124 @ SV479 ) @ ( plus_plus_nat @ SV124 @ SV756 ) )
              | ( ord_less_nat @ SV479 @ SV756 ) ) )
        = $true )
      | ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV124 @ SV479 ) @ ( plus_plus_nat @ SV124 @ SV756 ) )
              | ~ ( ord_less_nat @ SV479 @ SV756 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12367]) ).

thf(12581,plain,
    ! [SV757: nat,SV480: nat,SV125: nat] :
      ( ( ( ~ ( ( ord_less_nat @ ( plus_plus_nat @ SV125 @ SV480 ) @ ( plus_plus_nat @ SV757 @ SV480 ) )
              | ( ord_less_nat @ SV125 @ SV757 ) ) )
        = $true )
      | ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV125 @ SV480 ) @ ( plus_plus_nat @ SV757 @ SV480 ) )
              | ~ ( ord_less_nat @ SV125 @ SV757 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12369]) ).

thf(12582,plain,
    ! [SV770: nat,SV493: nat,SV142: nat] :
      ( ( ( ~ ( ( ( times_times_nat @ SV142 @ SV493 )
                = ( times_times_nat @ SV770 @ SV493 ) )
              | ( SV493 = zero_zero_nat )
              | ( SV142 = SV770 ) ) )
        = $true )
      | ( ( ~ ( ( ( times_times_nat @ SV142 @ SV493 )
               != ( times_times_nat @ SV770 @ SV493 ) )
              | ~ ( ( SV493 = zero_zero_nat )
                  | ( SV142 = SV770 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12374]) ).

thf(12583,plain,
    ! [SV771: nat,SV494: nat,SV143: nat] :
      ( ( ( ~ ( ( ( times_times_nat @ SV143 @ SV494 )
                = ( times_times_nat @ SV143 @ SV771 ) )
              | ( SV143 = zero_zero_nat )
              | ( SV494 = SV771 ) ) )
        = $true )
      | ( ( ~ ( ( ( times_times_nat @ SV143 @ SV494 )
               != ( times_times_nat @ SV143 @ SV771 ) )
              | ~ ( ( SV143 = zero_zero_nat )
                  | ( SV494 = SV771 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12376]) ).

thf(12584,plain,
    ! [SV495: nat,SV144: nat] :
      ( ( ( ( ( times_times_nat @ SV144 @ SV495 )
            = zero_zero_nat )
          | ( SV144 = zero_zero_nat )
          | ( SV495 = zero_zero_nat ) )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV144 @ SV495 )
               != zero_zero_nat )
              | ~ ( ( SV144 = zero_zero_nat )
                  | ( SV495 = zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12378]) ).

thf(12585,plain,
    ! [SV496: nat,SV148: nat] :
      ( ( ( ( SV148
            = ( plus_plus_nat @ SV148 @ SV496 ) )
          | ( SV496 = zero_zero_nat ) )
        = $false )
      | ( ( ~ ( ( SV148
               != ( plus_plus_nat @ SV148 @ SV496 ) )
              | ( SV496 != zero_zero_nat ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12379]) ).

thf(12586,plain,
    ! [SV497: nat,SV149: nat] :
      ( ( ( ( SV149
            = ( plus_plus_nat @ SV497 @ SV149 ) )
          | ( SV497 = zero_zero_nat ) )
        = $false )
      | ( ( ~ ( ( SV149
               != ( plus_plus_nat @ SV497 @ SV149 ) )
              | ( SV497 != zero_zero_nat ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12380]) ).

thf(12587,plain,
    ! [SV498: nat,SV150: nat] :
      ( ( ( ( ( plus_plus_nat @ SV150 @ SV498 )
            = SV150 )
          | ( SV498 = zero_zero_nat ) )
        = $false )
      | ( ( ~ ( ( ( plus_plus_nat @ SV150 @ SV498 )
               != SV150 )
              | ( SV498 != zero_zero_nat ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12381]) ).

thf(12588,plain,
    ! [SV499: nat,SV151: nat] :
      ( ( ( ( ( plus_plus_nat @ SV151 @ SV499 )
            = SV499 )
          | ( SV151 = zero_zero_nat ) )
        = $false )
      | ( ( ~ ( ( ( plus_plus_nat @ SV151 @ SV499 )
               != SV499 )
              | ( SV151 != zero_zero_nat ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12382]) ).

thf(12589,plain,
    ! [SV772: nat,SV502: nat,SV160: nat] :
      ( ( ( ~ ( ( ( times_times_nat @ SV160 @ SV502 )
                = ( times_times_nat @ SV772 @ SV502 ) )
              | ( SV160 = SV772 )
              | ( SV502 = zero_zero_nat ) ) )
        = $true )
      | ( ( ~ ( ( ( times_times_nat @ SV160 @ SV502 )
               != ( times_times_nat @ SV772 @ SV502 ) )
              | ~ ( ( SV160 = SV772 )
                  | ( SV502 = zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12383]) ).

thf(12590,plain,
    ! [SV773: nat,SV503: nat,SV161: nat] :
      ( ( ( ~ ( ( ( times_times_nat @ SV161 @ SV503 )
                = ( times_times_nat @ SV161 @ SV773 ) )
              | ( SV503 = SV773 )
              | ( SV161 = zero_zero_nat ) ) )
        = $true )
      | ( ( ~ ( ( ( times_times_nat @ SV161 @ SV503 )
               != ( times_times_nat @ SV161 @ SV773 ) )
              | ~ ( ( SV503 = SV773 )
                  | ( SV161 = zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12385]) ).

thf(12591,plain,
    ! [SV504: nat,SV163: nat] :
      ( ( ( ( ( times_times_nat @ SV163 @ SV504 )
            = zero_zero_nat )
          | ( SV163 = zero_zero_nat )
          | ( SV504 = zero_zero_nat ) )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV163 @ SV504 )
               != zero_zero_nat )
              | ~ ( ( SV163 = zero_zero_nat )
                  | ( SV504 = zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12387]) ).

thf(12592,plain,
    ! [SV169: nat] :
      ( ( ( ( power_power_nat @ SV169 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = zero_zero_nat )
        = $false )
      | ( ( ~ ( ( ( power_power_nat @ SV169 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
               != zero_zero_nat )
              | ( SV169 != zero_zero_nat ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12388]) ).

thf(12593,plain,
    ! [SV169: nat] :
      ( ( ( SV169 = zero_zero_nat )
        = $false )
      | ( ( ~ ( ( ( power_power_nat @ SV169 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
               != zero_zero_nat )
              | ( SV169 != zero_zero_nat ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12388]) ).

thf(12594,plain,
    ! [SV787: num,SV518: num,SV179: num] :
      ( ( ( ~ ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV179 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) )
                = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV787 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) ) )
              | ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV179 ) @ ( numeral_numeral_nat @ SV518 ) )
                = ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV787 ) @ ( numeral_numeral_nat @ SV518 ) ) ) ) )
        = $true )
      | ( ( ~ ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV179 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) )
               != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV787 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) ) )
              | ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV179 ) @ ( numeral_numeral_nat @ SV518 ) )
               != ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV787 ) @ ( numeral_numeral_nat @ SV518 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12389]) ).

thf(12595,plain,
    ! [SV788: nat,SV520: nat,SV185: nat] :
      ( ( ( ~ ( ( ( times_times_nat @ SV185 @ SV520 )
                = ( times_times_nat @ SV185 @ SV788 ) )
              | ( SV185 = zero_zero_nat )
              | ( SV520 = SV788 ) ) )
        = $true )
      | ( ( ~ ( ( ( times_times_nat @ SV185 @ SV520 )
               != ( times_times_nat @ SV185 @ SV788 ) )
              | ~ ( ( SV185 = zero_zero_nat )
                  | ( SV520 = SV788 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12391]) ).

thf(12596,plain,
    ! [SV534: num,SV199: num] :
      ( ( ( ( ( bit0 @ SV199 )
            = ( bit0 @ SV534 ) )
          | ( SV199 = SV534 ) )
        = $false )
      | ( ( ~ ( ( ( bit0 @ SV199 )
               != ( bit0 @ SV534 ) )
              | ( SV199 != SV534 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12393]) ).

thf(12597,plain,
    ! [SV535: nat,SV201: nat] :
      ( ( ( ( dvd_dvd_nat @ SV201 @ ( plus_plus_nat @ SV535 @ SV201 ) )
          | ( dvd_dvd_nat @ SV201 @ SV535 ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ SV201 @ ( plus_plus_nat @ SV535 @ SV201 ) )
              | ~ ( dvd_dvd_nat @ SV201 @ SV535 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12394]) ).

thf(12598,plain,
    ! [SV536: nat,SV202: nat] :
      ( ( ( ( dvd_dvd_nat @ SV202 @ ( plus_plus_nat @ SV202 @ SV536 ) )
          | ( dvd_dvd_nat @ SV202 @ SV536 ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ SV202 @ ( plus_plus_nat @ SV202 @ SV536 ) )
              | ~ ( dvd_dvd_nat @ SV202 @ SV536 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12395]) ).

thf(12599,plain,
    ! [SV795: nat,SV537: nat,SV203: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ SV203 @ ( plus_plus_nat @ SV537 @ ( times_times_nat @ SV795 @ SV203 ) ) )
              | ( dvd_dvd_nat @ SV203 @ SV537 ) ) )
        = $true )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ SV203 @ ( plus_plus_nat @ SV537 @ ( times_times_nat @ SV795 @ SV203 ) ) )
              | ~ ( dvd_dvd_nat @ SV203 @ SV537 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12396]) ).

thf(12600,plain,
    ! [SV796: nat,SV538: nat,SV204: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ SV204 @ ( plus_plus_nat @ ( times_times_nat @ SV538 @ SV204 ) @ SV796 ) )
              | ( dvd_dvd_nat @ SV204 @ SV796 ) ) )
        = $true )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ SV204 @ ( plus_plus_nat @ ( times_times_nat @ SV538 @ SV204 ) @ SV796 ) )
              | ~ ( dvd_dvd_nat @ SV204 @ SV796 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12398]) ).

thf(12601,plain,
    ! [SV539: nat,SV205: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ SV205 @ SV539 ) )
          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ SV205 @ SV539 ) )
              | ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
                  | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12400]) ).

thf(12602,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
            = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
              | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
               != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12401]) ).

thf(12603,plain,
    ! [SV955: int,SV920: int,SV797: nat,SV543: int,SV209: nat] :
      ( ( ( bit_concat_bit @ SV209 @ SV543 @ ( bit_concat_bit @ SV797 @ SV920 @ SV955 ) )
        = ( bit_concat_bit @ ( plus_plus_nat @ SV797 @ SV209 ) @ ( bit_concat_bit @ SV209 @ SV543 @ SV920 ) @ SV955 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12402]) ).

thf(12604,plain,
    ! [SV548: nat,SV215: nat] :
      ( ( ( ( SV215
            = ( plus_plus_nat @ SV215 @ SV548 ) )
          | ( SV548 = zero_zero_nat ) )
        = $false )
      | ( ( ~ ( ( SV215
               != ( plus_plus_nat @ SV215 @ SV548 ) )
              | ( SV548 != zero_zero_nat ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12404]) ).

thf(12605,plain,
    ! [SV922: nat,SV802: nat,SV549: nat,SV216: nat] :
      ( ( ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV549 ) @ ( times_times_nat @ SV802 @ SV922 ) )
              = ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV922 ) @ ( times_times_nat @ SV802 @ SV549 ) ) )
            | ( SV216 = SV802 )
            | ( SV549 = SV922 ) )
        | ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV549 ) @ ( times_times_nat @ SV802 @ SV922 ) )
             != ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV922 ) @ ( times_times_nat @ SV802 @ SV549 ) ) )
            | ~ ( ( SV216 = SV802 )
                | ( SV549 = SV922 ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12405]) ).

thf(12606,plain,
    ! [SV922: nat,SV802: nat,SV549: nat,SV216: nat] :
      ( ( ( ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV549 ) @ ( times_times_nat @ SV802 @ SV922 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV922 ) @ ( times_times_nat @ SV802 @ SV549 ) ) )
        = ( ( SV216 = SV802 )
          | ( SV549 = SV922 ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12405]) ).

thf(12607,plain,
    ! [SV803: nat,SV554: nat,SV224: nat] :
      ( ( ( ~ ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV224 ) @ SV554 )
                = ( semiri1316708129612266289at_nat @ SV803 ) )
              | ( ( power_power_nat @ SV224 @ SV554 )
                = SV803 ) ) )
        = $true )
      | ( ( ~ ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV224 ) @ SV554 )
               != ( semiri1316708129612266289at_nat @ SV803 ) )
              | ( ( power_power_nat @ SV224 @ SV554 )
               != SV803 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12406]) ).

thf(12608,plain,
    ! [SV804: nat,SV555: nat,SV225: nat] :
      ( ( ( ~ ( ( ( semiri1316708129612266289at_nat @ SV225 )
                = ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV555 ) @ SV804 ) )
              | ( SV225
                = ( power_power_nat @ SV555 @ SV804 ) ) ) )
        = $true )
      | ( ( ~ ( ( ( semiri1316708129612266289at_nat @ SV225 )
               != ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV555 ) @ SV804 ) )
              | ( SV225
               != ( power_power_nat @ SV555 @ SV804 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12408]) ).

thf(12609,plain,
    ! [SV805: nat,SV556: nat,SV226: num] :
      ( ( ( ~ ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
                = ( semiri1316708129612266289at_nat @ SV805 ) )
              | ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
                = SV805 ) ) )
        = $true )
      | ( ( ~ ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
               != ( semiri1316708129612266289at_nat @ SV805 ) )
              | ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
               != SV805 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12410]) ).

thf(12610,plain,
    ! [SV806: nat,SV557: num,SV227: nat] :
      ( ( ( ~ ( ( ( semiri1316708129612266289at_nat @ SV227 )
                = ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
              | ( SV227
                = ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) ) ) )
        = $true )
      | ( ( ~ ( ( ( semiri1316708129612266289at_nat @ SV227 )
               != ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
              | ( SV227
               != ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12412]) ).

thf(12611,plain,
    ! [SV561: nat,SV231: nat > real] :
      ( ( ( ( summable_real
            @ ^ [SY1684: nat] : ( SV231 @ ( plus_plus_nat @ SY1684 @ SV561 ) ) )
          | ( summable_real @ SV231 ) )
        = $false )
      | ( ( ~ ( ~ ( summable_real
                  @ ^ [SY1684: nat] : ( SV231 @ ( plus_plus_nat @ SY1684 @ SV561 ) ) )
              | ~ ( summable_real @ SV231 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12414]) ).

thf(12612,plain,
    ! [SV562: nat,SV232: nat > complex] :
      ( ( ( ( summable_complex
            @ ^ [SY1685: nat] : ( SV232 @ ( plus_plus_nat @ SY1685 @ SV562 ) ) )
          | ( summable_complex @ SV232 ) )
        = $false )
      | ( ( ~ ( ~ ( summable_complex
                  @ ^ [SY1685: nat] : ( SV232 @ ( plus_plus_nat @ SY1685 @ SV562 ) ) )
              | ~ ( summable_complex @ SV232 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12415]) ).

thf(12613,plain,
    ! [SV243: $o] :
      ( ( ( SV243
          | $true )
        = $false )
      | ( ( ~ ( ~ SV243
              | ~ $true ) )
        = $true )
      | ( ( SV243 = $false )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12418]) ).

thf(12614,plain,
    ! [SV243: $o] :
      ( ( ( ~ ( SV243
              | $false ) )
        = $true )
      | ( ( ~ ( ~ SV243
              | ~ $false ) )
        = $true )
      | ( ( SV243 = $true )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12419]) ).

thf(12615,plain,
    ( ( ( $true
        | $true )
      = $false )
    | ( ( ~ ( ~ $true
            | ~ $true ) )
      = $true )
    | ( ( $true = $false )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12421]) ).

thf(12616,plain,
    ( ( ( ~ ( $true
            | $false ) )
      = $true )
    | ( ( ~ ( ~ $true
            | ~ $false ) )
      = $true )
    | ( ( $true = $true )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12422]) ).

thf(12617,plain,
    ( ( ( $false
        | $true )
      = $false )
    | ( ( ~ ( ~ $false
            | ~ $true ) )
      = $true )
    | ( ( $false = $false )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12424]) ).

thf(12618,plain,
    ( ( ( ~ ( $false
            | $false ) )
      = $true )
    | ( ( ~ ( ~ $false
            | ~ $false ) )
      = $true )
    | ( ( $false = $true )
      = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12425]) ).

thf(12619,plain,
    ! [SV815: nat,SV570: nat,SV244: nat] :
      ( ( ( SV244 != zero_zero_nat )
        = $false )
      | ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ SV244 @ SV570 ) @ SV815 ) @ SV244 )
          = ( plus_plus_nat @ SV570 @ ( divide_divide_nat @ SV815 @ SV244 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12427]) ).

thf(12620,plain,
    ! [SV816: nat,SV571: nat,SV245: nat] :
      ( ( ( ord_less_nat @ SV245 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV571 ) )
        = $false )
      | ( ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ SV816 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV571 ) ) @ SV245 ) @ SV571 )
          = SV245 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12428]) ).

thf(12621,plain,
    ! [SV817: nat,SV572: nat,SV246: nat] :
      ( ( ( dvd_dvd_nat @ SV246 @ SV572 )
        = $false )
      | ( ( ( divide_divide_nat @ ( plus_plus_nat @ SV572 @ SV817 ) @ SV246 )
          = ( plus_plus_nat @ ( divide_divide_nat @ SV572 @ SV246 ) @ ( divide_divide_nat @ SV817 @ SV246 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12429]) ).

thf(12622,plain,
    ! [SV818: nat,SV573: nat,SV247: nat] :
      ( ( ( ord_less_nat @ SV247 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV573 @ SV818 ) ) )
        = $false )
      | ( ( ord_less_nat @ ( vEBT_VEBT_high @ SV247 @ SV573 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV818 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12430]) ).

thf(12623,plain,
    ! [SV819: nat,SV575: nat,SV249: nat] :
      ( ( ( ord_less_nat @ ( plus_plus_nat @ SV249 @ SV575 ) @ SV819 )
        = $false )
      | ( ( ord_less_nat @ SV249 @ SV819 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12431]) ).

thf(12624,plain,
    ! [SV820: nat,SV576: nat,SV250: nat] :
      ( ( ( ( times_times_nat @ SV250 @ SV576 )
          = ( times_times_nat @ SV576 @ SV250 ) )
        = $false )
      | ( ( ( times_times_nat @ ( power_power_nat @ SV250 @ SV820 ) @ SV576 )
          = ( times_times_nat @ SV576 @ ( power_power_nat @ SV250 @ SV820 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12432]) ).

thf(12625,plain,
    ! [SV577: nat,SV251: nat] :
      ( ( ( SV251 = zero_zero_nat )
        = $true )
      | ( ( SV577 = zero_zero_nat )
        = $true )
      | ( ( ( times_times_nat @ SV251 @ SV577 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[12433]) ).

thf(12626,plain,
    ! [SV821: nat,SV578: nat,SV252: nat] :
      ( ( ( SV252 != zero_zero_nat )
        = $false )
      | ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ SV578 @ SV252 ) @ SV821 ) @ SV252 )
          = ( plus_plus_nat @ SV578 @ ( divide_divide_nat @ SV821 @ SV252 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12434]) ).

thf(12627,plain,
    ! [SV925: nat,SV822: nat,SV579: nat,SV253: nat] :
      ( ( ( ~ ( ord_less_nat @ SV253 @ SV579 ) )
        = $true )
      | ( ( ( ( plus_plus_nat @ SV822 @ SV579 )
           != ( plus_plus_nat @ SV253 @ SV925 ) )
          | ( ord_less_nat @ SV822 @ SV925 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12435]) ).

thf(12628,plain,
    ! [SV823: nat,SV580: nat,SV254: nat] :
      ( ( ( dvd_dvd_nat @ ( times_times_nat @ SV254 @ SV580 ) @ SV823 )
        = $false )
      | ( ( dvd_dvd_nat @ SV254 @ ( divide_divide_nat @ SV823 @ SV580 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12436]) ).

thf(12629,plain,
    ! [SV824: nat,SV581: nat,SV255: nat] :
      ( ( ~ ( ( SV255 != zero_zero_nat )
            | ( ( divide_divide_nat @ ( times_times_nat @ SV255 @ SV581 ) @ ( times_times_nat @ SV255 @ SV824 ) )
              = zero_zero_nat ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[12437]) ).

thf(12630,plain,
    ! [SV824: nat,SV581: nat,SV255: nat] :
      ( ( ~ ( ~ ( ( SV255 != zero_zero_nat ) )
            | ( ( divide_divide_nat @ ( times_times_nat @ SV255 @ SV581 ) @ ( times_times_nat @ SV255 @ SV824 ) )
              = ( divide_divide_nat @ SV581 @ SV824 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[12437]) ).

thf(12631,plain,
    ! [SV582: nat,SV256: nat] :
      ( ( ( SV256 = zero_zero_nat )
        = $true )
      | ( ( ( divide_divide_nat @ ( times_times_nat @ SV256 @ SV582 ) @ SV256 )
          = SV582 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12438]) ).

thf(12632,plain,
    ! [SV825: nat,SV583: nat,SV257: nat] :
      ( ( ( SV257 != zero_zero_nat )
        = $false )
      | ( ( ( ( times_times_nat @ SV583 @ SV257 )
            = ( times_times_nat @ SV825 @ SV257 ) )
          = ( SV583 = SV825 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12439]) ).

thf(12633,plain,
    ! [SV826: nat,SV584: nat,SV258: nat] :
      ( ( ( dvd_dvd_nat @ SV258 @ ( times_times_nat @ SV584 @ SV826 ) )
        = $false )
      | ( ( ~ ! [SY1869: nat,SY1870: nat] :
                ( ( SV258
                 != ( times_times_nat @ SY1869 @ SY1870 ) )
                | ~ ( dvd_dvd_nat @ SY1869 @ SV584 )
                | ~ ( dvd_dvd_nat @ SY1870 @ SV826 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12440]) ).

thf(12634,plain,
    ! [SV585: nat,SV259: nat] :
      ( ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV259 @ SV585 ) )
          = zero_zero_nat )
        = $true )
      | ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV585 )
         != zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12441]) ).

thf(12635,plain,
    ! [SV926: nat,SV827: nat,SV586: nat,SV260: nat] :
      ( ( ( ~ ~ ( ( SV260 != SV586 )
                | ( SV827 != SV926 ) ) )
        = $true )
      | ( ( ( plus_plus_nat @ SV260 @ SV827 )
          = ( plus_plus_nat @ SV586 @ SV926 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12443]) ).

thf(12636,plain,
    ! [SV828: nat,SV587: nat,SV261: nat] :
      ( ( ( dvd_dvd_nat @ SV261 @ SV587 )
        = $false )
      | ( ( ~ ( dvd_dvd_nat @ SV261 @ SV828 )
          | ( ( divide_divide_nat @ ( plus_plus_nat @ SV587 @ SV828 ) @ SV261 )
            = ( plus_plus_nat @ ( divide_divide_nat @ SV587 @ SV261 ) @ ( divide_divide_nat @ SV828 @ SV261 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12444]) ).

thf(12637,plain,
    ! [SV829: nat,SV588: nat,SV262: nat] :
      ( ( ( dvd_dvd_nat @ SV262 @ SV588 )
        = $false )
      | ( ( ~ ( dvd_dvd_nat @ SV588 @ SV829 )
          | ( ( divide_divide_nat @ ( divide_divide_nat @ SV829 @ SV262 ) @ ( divide_divide_nat @ SV588 @ SV262 ) )
            = ( divide_divide_nat @ SV829 @ SV588 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12445]) ).

thf(12638,plain,
    ! [SV927: nat,SV830: nat,SV589: nat,SV263: nat] :
      ( ( ( SV263
         != ( plus_plus_nat @ SV589 @ SV830 ) )
        = $true )
      | ( ( ( plus_plus_nat @ SV263 @ SV927 )
          = ( plus_plus_nat @ SV589 @ ( plus_plus_nat @ SV830 @ SV927 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12446]) ).

thf(12639,plain,
    ! [SV831: nat,SV591: nat,SV265: nat] :
      ( ( ( ord_less_eq_nat @ SV265 @ SV591 )
        = $false )
      | ( ( ord_less_eq_nat @ ( times_times_nat @ SV265 @ SV831 ) @ ( times_times_nat @ SV591 @ SV831 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12448]) ).

thf(12640,plain,
    ! [SV832: nat,SV592: nat,SV266: nat] :
      ( ( ( SV266 != zero_zero_nat )
        = $false )
      | ( ( ( divide_divide_nat @ ( times_times_nat @ SV592 @ SV266 ) @ ( times_times_nat @ SV832 @ SV266 ) )
          = ( divide_divide_nat @ SV592 @ SV832 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12449]) ).

thf(12641,plain,
    ! [SV833: nat,SV593: nat,SV268: nat] :
      ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV268 @ SV593 ) @ SV833 )
        = $false )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ SV268 @ SV833 )
              | ~ ( ord_less_eq_nat @ SV593 @ SV833 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12450]) ).

thf(12642,plain,
    ! [SV834: nat,SV594: nat,SV269: nat] :
      ( ( ( SV269 != zero_zero_nat )
        = $false )
      | ( ( ( divide_divide_nat @ ( plus_plus_nat @ SV594 @ ( times_times_nat @ SV269 @ SV834 ) ) @ SV269 )
          = ( plus_plus_nat @ SV834 @ ( divide_divide_nat @ SV594 @ SV269 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12451]) ).

thf(12643,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ~ ( ( SV595 = SV928 )
            | ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                 != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
                | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                 != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
        | ~ ( ( SV595 != SV928 )
            | ~ ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                   != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
                  | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                   != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12452]) ).

thf(12644,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( SV595 = SV928 )
        = ( ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
               != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
              | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
               != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12452]) ).

thf(12645,plain,
    ! [SV929: nat,SV836: nat,SV596: nat,SV272: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV272 @ SV596 ) )
        = $true )
      | ( ( ~ ( dvd_dvd_nat @ SV836 @ SV929 )
          | ( dvd_dvd_nat @ ( times_times_nat @ SV272 @ SV836 ) @ ( times_times_nat @ SV596 @ SV929 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12453]) ).

thf(12646,plain,
    ! [SV837: nat,SV597: nat,SV273: nat] :
      ( ( ( ~ ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
                = ( modulo_modulo_nat @ SV837 @ SV597 ) )
              | ~ ! [SY1874: nat] :
                    ~ ~ ! [SY1875: nat] :
                          ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SY1874 ) )
                         != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1875 ) ) ) ) )
        = $true )
      | ( ( ~ ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
               != ( modulo_modulo_nat @ SV837 @ SV597 ) )
              | ~ ~ ! [SY1874: nat] :
                      ~ ~ ! [SY1875: nat] :
                            ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SY1874 ) )
                           != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1875 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12454]) ).

thf(12647,plain,
    ! [SV838: nat,SV598: nat,SV274: nat] :
      ( ( ( ( plus_plus_nat @ SV274 @ SV598 )
          = ( plus_plus_nat @ SV838 @ SV598 ) )
        = $false )
      | ( ( SV274 = SV838 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12456]) ).

thf(12648,plain,
    ! [SV839: nat,SV599: nat,SV275: nat] :
      ( ( ( SV275 != zero_zero_nat )
        = $false )
      | ( ( ( divide_divide_nat @ ( plus_plus_nat @ SV599 @ ( times_times_nat @ SV839 @ SV275 ) ) @ SV275 )
          = ( plus_plus_nat @ SV839 @ ( divide_divide_nat @ SV599 @ SV275 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12457]) ).

thf(12649,plain,
    ! [SV840: nat,SV600: nat,SV276: nat] :
      ( ( ( ord_less_eq_nat @ SV276 @ SV600 )
        = $false )
      | ( ( ord_less_eq_nat @ ( times_times_nat @ SV840 @ SV276 ) @ ( times_times_nat @ SV840 @ SV600 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12458]) ).

thf(12650,plain,
    ! [SV277: nat] :
      ( ( ( SV277
         != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( sK7_SY1343 @ SV277 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV277 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[12459]) ).

thf(12651,plain,
    ! [SV601: nat,SV280: nat] :
      ( ( ( ( times_times_nat @ SV280 @ SV601 )
          = zero_zero_nat )
        = $true )
      | ( ( ~ ( ~ ( ( SV280 != zero_zero_nat ) )
              | ~ ( ( SV601 != zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12460]) ).

thf(12652,plain,
    ! [SV841: nat,SV602: nat,SV281: nat] :
      ( ( ( ord_less_nat @ SV281 @ ( times_times_nat @ SV602 @ SV841 ) )
        = $false )
      | ( ( ord_less_nat @ ( divide_divide_nat @ SV281 @ SV841 ) @ SV602 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12461]) ).

thf(12653,plain,
    ! [SV930: nat,SV842: nat,SV603: nat,SV282: nat] :
      ( ( ( SV282
         != ( plus_plus_nat @ SV603 @ SV842 ) )
        = $true )
      | ( ( ( plus_plus_nat @ SV930 @ SV282 )
          = ( plus_plus_nat @ SV603 @ ( plus_plus_nat @ SV930 @ SV842 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12462]) ).

thf(12654,plain,
    ! [SV843: nat,SV604: nat,SV283: nat] :
      ( ( ( ( times_times_nat @ SV283 @ SV604 )
          = one_one_nat )
        = $false )
      | ( ( ( times_times_nat @ ( power_power_nat @ SV283 @ SV843 ) @ ( power_power_nat @ SV604 @ SV843 ) )
          = one_one_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12463]) ).

thf(12655,plain,
    ! [SV931: nat,SV844: nat,SV605: nat,SV284: nat] :
      ( ( ~ ( ~ ( ~ ( ( SV284 != SV605 ) )
                | ~ ( ( SV844 != SV931 ) ) )
            | ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
             != ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) ) )
        | ~ ( ~ ~ ( ~ ( ( SV284 != SV605 ) )
                  | ~ ( ( SV844 != SV931 ) ) )
            | ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
                 != ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12464]) ).

thf(12656,plain,
    ! [SV931: nat,SV844: nat,SV605: nat,SV284: nat] :
      ( ( ( ~ ( ~ ( ( SV284 != SV605 ) )
              | ~ ( ( SV844 != SV931 ) ) ) )
        = ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
         != ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12464]) ).

thf(12657,plain,
    ! [SV845: nat,SV606: nat,SV285: nat] :
      ( ( ( SV285 != zero_zero_nat )
        = $false )
      | ( ( ( ( times_times_nat @ SV285 @ SV606 )
            = ( times_times_nat @ SV285 @ SV845 ) )
          = ( SV606 = SV845 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12465]) ).

thf(12658,plain,
    ! [SV846: nat,SV607: nat,SV286: nat] :
      ( ( ( dvd_dvd_nat @ SV286 @ SV607 )
        = $false )
      | ( ( ( times_times_nat @ ( divide_divide_nat @ SV607 @ SV286 ) @ SV846 )
          = ( divide_divide_nat @ ( times_times_nat @ SV607 @ SV846 ) @ SV286 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12466]) ).

thf(12659,plain,
    ! [SV608: nat,SV287: nat] :
      ( ( ( SV287 = zero_zero_nat )
        = $true )
      | ( ( ~ ( ( SV608 != zero_zero_nat ) )
          | ( ( times_times_nat @ SV287 @ SV608 )
           != zero_zero_nat ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12467]) ).

thf(12660,plain,
    ! [SV609: nat,SV288: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV288 )
         != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV609 ) )
        = $true )
      | ( ( SV288 = SV609 )
        = $true )
      | ( ( ( divide_divide_nat @ SV288 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV609 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[12468]) ).

thf(12661,plain,
    ! [SV847: nat,SV610: nat,SV289: nat] :
      ( ( ( ord_less_eq_nat @ SV289 @ SV610 )
        = $false )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV289 @ SV847 ) @ ( plus_plus_nat @ SV610 @ SV847 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12469]) ).

thf(12662,plain,
    ! [SV932: nat,SV848: nat,SV611: nat,SV290: nat] :
      ( ( ( ~ ~ ( ~ ( ord_less_nat @ SV290 @ SV611 )
                | ~ ( ord_less_nat @ SV848 @ SV932 ) ) )
        = $true )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV290 @ SV848 ) @ ( plus_plus_nat @ SV611 @ SV932 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12470]) ).

thf(12663,plain,
    ! [SV614: nat,SV293: nat] :
      ( ( ( SV293 = zero_zero_nat )
        = $true )
      | ( ( ( divide_divide_nat @ ( times_times_nat @ SV614 @ SV293 ) @ SV293 )
          = SV614 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12472]) ).

thf(12664,plain,
    ! [SV933: nat,SV849: nat,SV615: nat,SV294: nat] :
      ( ( ( ~ ~ ( ( SV294 != SV615 )
                | ~ ( ord_less_nat @ SV849 @ SV933 ) ) )
        = $true )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV294 @ SV849 ) @ ( plus_plus_nat @ SV615 @ SV933 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12473]) ).

thf(12665,plain,
    ! [SV934: nat,SV850: nat,SV617: nat,SV296: nat] :
      ( ( ( ~ ( ord_less_nat @ SV296 @ SV617 ) )
        = $true )
      | ( ( ~ ( ord_less_nat @ SV850 @ SV934 )
          | ( ord_less_nat @ ( plus_plus_nat @ SV296 @ SV850 ) @ ( plus_plus_nat @ SV617 @ SV934 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12474]) ).

thf(12666,plain,
    ! [SV935: nat,SV851: nat,SV618: nat,SV297: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV297 @ SV618 ) )
        = $true )
      | ( ( ~ ( dvd_dvd_nat @ SV851 @ SV935 )
          | ( ( times_times_nat @ ( divide_divide_nat @ SV618 @ SV297 ) @ ( divide_divide_nat @ SV935 @ SV851 ) )
            = ( divide_divide_nat @ ( times_times_nat @ SV618 @ SV935 ) @ ( times_times_nat @ SV297 @ SV851 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12475]) ).

thf(12667,plain,
    ! [SV298: nat,SV619: nat] :
      ( ( ( ! [SY1748: nat] :
              ( SV619
             != ( plus_plus_nat @ SV298 @ SY1748 ) ) )
        = $false )
      | ( ( ord_less_eq_nat @ SV298 @ SV619 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12476]) ).

thf(12668,plain,
    ! [SV852: nat,SV620: nat,SV299: nat] :
      ( ( ( ord_less_eq_nat @ SV299 @ SV620 )
        = $false )
      | ( ( ord_less_eq_nat @ SV299 @ ( plus_plus_nat @ SV852 @ SV620 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12477]) ).

thf(12669,plain,
    ! [SV621: nat,SV300: nat] :
      ( ( ( ( ( times_times_nat @ SV300 @ SV621 )
            = one_one_nat )
          | ~ ( ( SV300 != one_one_nat )
              | ( SV621 != one_one_nat ) ) )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV300 @ SV621 )
               != one_one_nat )
              | ~ ~ ( ( SV300 != one_one_nat )
                    | ( SV621 != one_one_nat ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12478]) ).

thf(12670,plain,
    ! [SV936: nat,SV622: nat] :
      ( ( ~ ( ( dvd_dvd_nat @ SV622 @ SV936 )
            | ~ ! [SY1919: nat] :
                  ( SV936
                 != ( times_times_nat @ SV622 @ SY1919 ) ) )
        | ~ ( ~ ( dvd_dvd_nat @ SV622 @ SV936 )
            | ~ ~ ! [SY1919: nat] :
                    ( SV936
                   != ( times_times_nat @ SV622 @ SY1919 ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12479]) ).

thf(12671,plain,
    ! [SV936: nat,SV622: nat] :
      ( ( ( dvd_dvd_nat @ SV622 @ SV936 )
        = ( ~ ! [SY1919: nat] :
                ( SV936
               != ( times_times_nat @ SV622 @ SY1919 ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12479]) ).

thf(12672,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
          | ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
           != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) )
        = $false )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
              | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
                   != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12481]) ).

thf(12673,plain,
    ! [SV854: nat,SV625: nat,SV304: nat] :
      ( ( ( ord_less_nat @ SV304 @ SV625 )
        = $false )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV304 @ SV854 ) @ ( plus_plus_nat @ SV625 @ SV854 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12482]) ).

thf(12674,plain,
    ! [SV626: nat,SV305: nat] :
      ( ( ( ( ( plus_plus_nat @ SV305 @ SV626 )
            = zero_zero_nat )
          | ~ ( ( SV305 != zero_zero_nat )
              | ( SV626 != zero_zero_nat ) ) )
        = $false )
      | ( ( ~ ( ( ( plus_plus_nat @ SV305 @ SV626 )
               != zero_zero_nat )
              | ~ ~ ( ( SV305 != zero_zero_nat )
                    | ( SV626 != zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12483]) ).

thf(12675,plain,
    ! [SV855: nat,SV628: nat,SV308: nat] :
      ( ( ( ord_less_eq_nat @ SV308 @ SV628 )
        = $false )
      | ( ( ord_less_eq_nat @ ( divide_divide_nat @ SV308 @ SV855 ) @ ( divide_divide_nat @ SV628 @ SV855 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12485]) ).

thf(12676,plain,
    ! [SV309: nat,SV629: nat] :
      ( ( ( ! [SY1755: nat] :
              ( SV629
             != ( plus_plus_nat @ SV309 @ SY1755 ) ) )
        = $false )
      | ( ( ord_less_eq_nat @ SV309 @ SV629 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12486]) ).

thf(12677,plain,
    ! [SV630: nat,SV310: nat] :
      ( ( ( ( ( plus_plus_nat @ SV310 @ SV630 )
            = zero_zero_nat )
          | ~ ( ( SV310 != zero_zero_nat )
              | ( SV630 != zero_zero_nat ) ) )
        = $false )
      | ( ( ~ ( ( ( plus_plus_nat @ SV310 @ SV630 )
               != zero_zero_nat )
              | ~ ~ ( ( SV310 != zero_zero_nat )
                    | ( SV630 != zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12487]) ).

thf(12678,plain,
    ! [SV856: nat,SV631: nat,SV311: nat] :
      ( ( ( dvd_dvd_nat @ SV311 @ ( times_times_nat @ SV631 @ SV856 ) )
        = $false )
      | ( ( ~ ! [SY1883: nat] :
                ~ ~ ! [SY1884: nat] :
                      ~ ~ ( ~ ~ ( ( SV311
                                 != ( times_times_nat @ SY1883 @ SY1884 ) )
                                | ~ ( dvd_dvd_nat @ SY1883 @ SV631 ) )
                          | ~ ( dvd_dvd_nat @ SY1884 @ SV856 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12488]) ).

thf(12679,plain,
    ! [SV956: nat,SV937: nat,SV857: nat,SV632: nat,SV312: nat] :
      ( ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
        | ~ ( dvd_dvd_nat @ SV312 @ SV857 )
        | ~ ( ( ( times_times_nat @ SV632 @ SV937 )
              = ( plus_plus_nat @ ( times_times_nat @ SV857 @ SV956 ) @ SV312 ) )
            | ( ( times_times_nat @ SV857 @ SV937 )
              = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SV956 ) @ SV312 ) ) )
        | ~ ! [SY1887: nat] :
              ~ ~ ! [SY1888: nat] :
                    ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
                              | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) )
                        | ~ ( ( ( times_times_nat @ SV632 @ SY1887 )
                              = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1888 ) @ SV312 ) )
                            | ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1887 )
                              = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SY1888 ) @ SV312 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12489]) ).

thf(12680,plain,
    ! [SV858: nat,SV633: nat,SV313: nat] :
      ( ( ( ord_less_eq_nat @ SV313 @ SV633 )
        = $false )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV313 @ SV858 ) @ ( plus_plus_nat @ SV633 @ SV858 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12490]) ).

thf(12681,plain,
    ! [SV859: nat,SV634: nat,SV314: nat] :
      ( ( ( dvd_dvd_nat @ SV314 @ SV634 )
        = $false )
      | ( ( ~ ( dvd_dvd_nat @ SV634 @ SV859 )
          | ( ( divide_divide_nat @ SV859 @ ( divide_divide_nat @ SV634 @ SV314 ) )
            = ( times_times_nat @ ( divide_divide_nat @ SV859 @ SV634 ) @ SV314 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12491]) ).

thf(12682,plain,
    ! [SV636: num,SV316: num > $o] :
      ( ( ( ~ ! [SY1414: num] :
                ( ~ ( SV316 @ SY1414 )
                | ( SV316 @ ( inc @ SY1414 ) ) ) )
        = $true )
      | ( ( SV316 @ SV636 )
        = $true )
      | ( ( SV316 @ one )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[12492]) ).

thf(12683,plain,
    ! [SV637: nat,SV317: nat] :
      ( ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV317 @ SV637 ) )
          = zero_zero_nat )
        = $true )
      | ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV317 )
         != zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12493]) ).

thf(12684,plain,
    ! [SV860: nat,SV639: nat,SV319: nat > nat > $o] :
      ( ( ( ! [SY1419: nat,SY1420: nat] :
              ( ( SV319 @ SY1419 @ SY1420 )
              = ( SV319 @ SY1420 @ SY1419 ) ) )
        = $false )
      | ( ( ~ ! [SY1421: nat] : ( SV319 @ SY1421 @ zero_zero_nat )
          | ~ ! [SY1422: nat,SY1423: nat] :
                ( ~ ( SV319 @ SY1422 @ SY1423 )
                | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) )
          | ( SV319 @ SV639 @ SV860 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12494]) ).

thf(12685,plain,
    ! [SV861: nat,SV641: nat,SV321: nat] :
      ( ( ( ord_less_nat @ SV321 @ SV641 )
        = $false )
      | ( ( ord_less_nat @ SV321 @ ( plus_plus_nat @ SV861 @ SV641 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12495]) ).

thf(12686,plain,
    ! [SV642: nat,SV322: nat] :
      ( ( ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 )
          | ~ ( ~ ( ( SV322 != SV642 ) )
              | ~ ( vEBT_V8194947554948674370ptions @ summary @ SV642 ) ) )
        = $false )
      | ( ( ~ ( ~ ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 )
              | ~ ~ ( ~ ( ( SV322 != SV642 ) )
                    | ~ ( vEBT_V8194947554948674370ptions @ summary @ SV642 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12496]) ).

thf(12687,plain,
    ! [SV957: nat,SV938: nat,SV862: nat,SV643: nat,SV323: nat] :
      ( ( ( ( modulo_modulo_nat @ SV323 @ SV643 )
         != ( modulo_modulo_nat @ SV862 @ SV643 ) )
        | ( ( modulo_modulo_nat @ SV938 @ SV643 )
         != ( modulo_modulo_nat @ SV957 @ SV643 ) )
        | ( ( modulo_modulo_nat @ ( times_times_nat @ SV323 @ SV938 ) @ SV643 )
          = ( modulo_modulo_nat @ ( times_times_nat @ SV862 @ SV957 ) @ SV643 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12497]) ).

thf(12688,plain,
    ! [SV939: nat,SV644: nat] :
      ( ( ~ ( ( ord_less_eq_nat @ SV644 @ SV939 )
            | ~ ! [SY1924: nat] :
                  ( SV939
                 != ( plus_plus_nat @ SV644 @ SY1924 ) ) )
        | ~ ( ~ ( ord_less_eq_nat @ SV644 @ SV939 )
            | ~ ~ ! [SY1924: nat] :
                    ( SV939
                   != ( plus_plus_nat @ SV644 @ SY1924 ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12498]) ).

thf(12689,plain,
    ! [SV939: nat,SV644: nat] :
      ( ( ( ord_less_eq_nat @ SV644 @ SV939 )
        = ( ~ ! [SY1924: nat] :
                ( SV939
               != ( plus_plus_nat @ SV644 @ SY1924 ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12498]) ).

thf(12690,plain,
    ! [SV864: nat,SV645: nat,SV325: nat] :
      ( ( ( dvd_dvd_nat @ ( times_times_nat @ SV325 @ SV645 ) @ SV864 )
        = $false )
      | ( ( ( divide_divide_nat @ SV864 @ ( times_times_nat @ SV325 @ SV645 ) )
          = ( divide_divide_nat @ ( divide_divide_nat @ SV864 @ SV325 ) @ SV645 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12499]) ).

thf(12691,plain,
    ! [SV865: nat,SV646: nat,SV326: nat] :
      ( ( ( dvd_dvd_nat @ SV326 @ SV646 )
        = $false )
      | ( ( ( times_times_nat @ SV865 @ ( divide_divide_nat @ SV646 @ SV326 ) )
          = ( divide_divide_nat @ ( times_times_nat @ SV865 @ SV646 ) @ SV326 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12500]) ).

thf(12692,plain,
    ! [SV866: nat,SV647: nat,SV327: nat] :
      ( ( ( ord_less_nat @ SV327 @ SV647 )
        = $false )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV327 @ SV866 ) @ ( plus_plus_nat @ SV647 @ SV866 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12501]) ).

thf(12693,plain,
    ! [SV940: nat,SV867: nat,SV648: nat,SV328: nat] :
      ( ( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV328 @ SV648 )
                | ( SV867 != SV940 ) ) )
        = $true )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV328 @ SV867 ) @ ( plus_plus_nat @ SV648 @ SV940 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12502]) ).

thf(12694,plain,
    ! [SV649: nat,SV329: nat] :
      ( ( ( ( zero_zero_nat
            = ( plus_plus_nat @ SV329 @ SV649 ) )
          | ~ ( ( SV329 != zero_zero_nat )
              | ( SV649 != zero_zero_nat ) ) )
        = $false )
      | ( ( ~ ( ( zero_zero_nat
               != ( plus_plus_nat @ SV329 @ SV649 ) )
              | ~ ~ ( ( SV329 != zero_zero_nat )
                    | ( SV649 != zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12503]) ).

thf(12695,plain,
    ! [SV868: nat,SV650: nat,SV330: nat] :
      ( ( ( dvd_dvd_nat @ SV330 @ SV650 )
        = $false )
      | ( ( dvd_dvd_nat @ ( power_power_nat @ SV330 @ SV868 ) @ ( power_power_nat @ SV650 @ SV868 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12504]) ).

thf(12696,plain,
    ! [SV651: nat,SV331: nat] :
      ( ( ( SV331 = zero_zero_nat )
        = $true )
      | ( ( ( power_power_nat @ SV331 @ SV651 )
         != zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12505]) ).

thf(12697,plain,
    ! [SV958: vEBT_VEBT,SV941: vEBT_VEBT,SV869: list_VEBT_VEBT,SV652: nat,SV332: nat] :
      ( ( ~ ( ( SV332 != SV652 ) )
        | ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV869 @ SV332 @ SV941 ) @ SV652 @ SV958 )
          = ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV869 @ SV652 @ SV958 ) @ SV332 @ SV941 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12506]) ).

thf(12698,plain,
    ! [SV870: nat,SV656: nat,SV334: nat] :
      ( ( ( ord_less_nat @ ( plus_plus_nat @ SV334 @ SV656 ) @ ( plus_plus_nat @ SV870 @ SV656 ) )
        = $false )
      | ( ( ord_less_nat @ SV334 @ SV870 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12507]) ).

thf(12699,plain,
    ! [SV942: nat,SV871: nat,SV657: nat,SV335: nat] :
      ( ( ( ~ ~ ( ( SV335 != SV657 )
                | ~ ( ord_less_eq_nat @ SV871 @ SV942 ) ) )
        = $true )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV335 @ SV871 ) @ ( plus_plus_nat @ SV657 @ SV942 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12508]) ).

thf(12700,plain,
    ! [SV872: nat,SV658: nat,SV336: nat] :
      ( ( ( dvd_dvd_nat @ SV336 @ SV658 )
        = $false )
      | ( ( ( dvd_dvd_nat @ SV336 @ ( plus_plus_nat @ SV872 @ SV658 ) )
          = ( dvd_dvd_nat @ SV336 @ SV872 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12509]) ).

thf(12701,plain,
    ! [SV873: nat,SV659: nat,SV337: nat] :
      ( ( ( SV337
          = ( plus_plus_nat @ SV659 @ SV873 ) )
        = $false )
      | ( ( ( suc @ SV337 )
          = ( plus_plus_nat @ SV659 @ ( suc @ SV873 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12510]) ).

thf(12702,plain,
    ! [SV874: nat,SV660: nat,SV338: nat] :
      ( ( ( dvd_dvd_nat @ SV338 @ SV660 )
        = $false )
      | ( ( ~ ( dvd_dvd_nat @ SV338 @ SV874 )
          | ( dvd_dvd_nat @ SV338 @ ( plus_plus_nat @ SV660 @ SV874 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12511]) ).

thf(12703,plain,
    ! [SV875: nat,SV661: nat,SV339: nat] :
      ( ( ( ( plus_plus_nat @ SV339 @ SV661 )
          = ( plus_plus_nat @ SV339 @ SV875 ) )
        = $false )
      | ( ( SV661 = SV875 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12512]) ).

thf(12704,plain,
    ! [SV340: nat] :
      ( ( ( SV340
          = ( plus_plus_nat @ ( sK5_SY1465 @ SV340 ) @ ( sK5_SY1465 @ SV340 ) ) )
        = $true )
      | ( ( ~ ! [SY1466: nat] :
                ( SV340
               != ( plus_plus_nat @ SY1466 @ ( suc @ SY1466 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12513]) ).

thf(12705,plain,
    ! [SV943: nat,SV876: nat,SV662: nat,SV341: nat] :
      ( ( ( ~ ~ ( ~ ( ord_less_eq_nat @ SV341 @ SV662 )
                | ~ ( ord_less_eq_nat @ SV876 @ SV943 ) ) )
        = $true )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV341 @ SV876 ) @ ( plus_plus_nat @ SV662 @ SV943 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12514]) ).

thf(12706,plain,
    ! [SV877: nat,SV663: nat,SV342: nat] :
      ( ( ( SV342 != zero_zero_nat )
        = $false )
      | ( ( ( divide_divide_nat @ ( times_times_nat @ SV342 @ SV663 ) @ ( times_times_nat @ SV342 @ SV877 ) )
          = ( divide_divide_nat @ SV663 @ SV877 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12515]) ).

thf(12707,plain,
    ! [SV878: nat,SV664: nat,SV343: nat] :
      ( ( ( ord_less_nat @ SV343 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV664 ) )
        = $false )
      | ( ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ SV878 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV664 ) ) @ SV343 ) @ SV664 )
          = SV878 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12516]) ).

thf(12708,plain,
    ! [SV879: nat,SV665: nat,SV344: nat] :
      ( ( ( dvd_dvd_nat @ SV344 @ SV665 )
        = $false )
      | ( ( ( divide_divide_nat @ ( plus_plus_nat @ SV879 @ SV665 ) @ SV344 )
          = ( plus_plus_nat @ ( divide_divide_nat @ SV879 @ SV344 ) @ ( divide_divide_nat @ SV665 @ SV344 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12517]) ).

thf(12709,plain,
    ! [SV880: nat,SV666: nat,SV345: nat] :
      ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV345 @ SV666 ) @ SV880 )
        = $false )
      | ( ( ord_less_eq_nat @ SV666 @ SV880 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12518]) ).

thf(12710,plain,
    ! [SV881: nat,SV667: nat,SV346: nat] :
      ( ( ( dvd_dvd_nat @ ( times_times_nat @ SV346 @ SV667 ) @ SV881 )
        = $false )
      | ( ( dvd_dvd_nat @ SV667 @ SV881 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12519]) ).

thf(12711,plain,
    ! [SV882: nat,SV668: nat,SV347: nat] :
      ( ( ( dvd_dvd_nat @ SV347 @ SV668 )
        = $false )
      | ( ( ~ ( dvd_dvd_nat @ SV347 @ SV882 )
          | ( ( dvd_dvd_nat @ ( divide_divide_nat @ SV668 @ SV347 ) @ ( divide_divide_nat @ SV882 @ SV347 ) )
            = ( dvd_dvd_nat @ SV668 @ SV882 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12520]) ).

thf(12712,plain,
    ! [SV349: nat,SV669: nat] :
      ( ( ~ ! [SY1926: nat] :
              ~ ~ ! [SY1927: nat] :
                    ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ ( sK6_SY1803 @ SV669 @ SV349 ) @ SV349 )
                              | ~ ( dvd_dvd_nat @ ( sK6_SY1803 @ SV669 @ SV349 ) @ SV669 ) )
                        | ~ ( ( ( times_times_nat @ SV349 @ SY1926 )
                              = ( plus_plus_nat @ ( times_times_nat @ SV669 @ SY1927 ) @ ( sK6_SY1803 @ SV669 @ SV349 ) ) )
                            | ( ( times_times_nat @ SV669 @ SY1926 )
                              = ( plus_plus_nat @ ( times_times_nat @ SV349 @ SY1927 ) @ ( sK6_SY1803 @ SV669 @ SV349 ) ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[12521]) ).

thf(12713,plain,
    ! [SV671: nat,SV351: nat] :
      ( ( ( ( one_one_nat
            = ( times_times_nat @ SV351 @ SV671 ) )
          | ~ ( ( SV351 != one_one_nat )
              | ( SV671 != one_one_nat ) ) )
        = $false )
      | ( ( ~ ( ( one_one_nat
               != ( times_times_nat @ SV351 @ SV671 ) )
              | ~ ~ ( ( SV351 != one_one_nat )
                    | ( SV671 != one_one_nat ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12523]) ).

thf(12714,plain,
    ! [SV944: nat,SV883: nat,SV672: nat,SV352: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV352 @ SV672 ) )
        = $true )
      | ( ( ~ ( ord_less_eq_nat @ SV883 @ SV944 )
          | ( ord_less_eq_nat @ ( plus_plus_nat @ SV352 @ SV883 ) @ ( plus_plus_nat @ SV672 @ SV944 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12524]) ).

thf(12715,plain,
    ! [SV959: nat,SV945: nat,SV884: nat,SV673: nat,SV353: nat] :
      ( ( ~ ( ( SV353 != zero_zero_nat ) )
        | ~ ~ ( ( SV673 != SV884 )
              | ~ ( ( SV945 != SV959 ) ) )
        | ( ( plus_plus_nat @ SV673 @ ( times_times_nat @ SV353 @ SV945 ) )
         != ( plus_plus_nat @ SV884 @ ( times_times_nat @ SV353 @ SV959 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12525]) ).

thf(12716,plain,
    ! [SV885: nat,SV674: nat,SV354: nat] :
      ( ( ( dvd_dvd_nat @ SV354 @ SV674 )
        = $false )
      | ( ( ( dvd_dvd_nat @ SV354 @ ( plus_plus_nat @ SV674 @ SV885 ) )
          = ( dvd_dvd_nat @ SV354 @ SV885 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12526]) ).

thf(12717,plain,
    ! [SV355: nat > nat,SV675: nat > nat] :
      ( ( ( ~ ( summable_nat @ SV675 ) )
        = $true )
      | ( ( summable_nat
          @ ^ [SY1812: nat] : ( plus_plus_nat @ ( SV355 @ SY1812 ) @ ( SV675 @ SY1812 ) ) )
        = $true )
      | ( ( summable_nat @ SV355 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[12527]) ).

thf(12718,plain,
    ! [SV886: nat,SV676: nat,SV356: nat] :
      ( ( ~ ( ( SV356 != zero_zero_nat )
            | ( ( divide_divide_nat @ ( times_times_nat @ SV356 @ SV676 ) @ ( times_times_nat @ SV356 @ SV886 ) )
              = zero_zero_nat ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[12528]) ).

thf(12719,plain,
    ! [SV886: nat,SV676: nat,SV356: nat] :
      ( ( ~ ( ~ ( ( SV356 != zero_zero_nat ) )
            | ( ( divide_divide_nat @ ( times_times_nat @ SV356 @ SV676 ) @ ( times_times_nat @ SV356 @ SV886 ) )
              = ( divide_divide_nat @ SV676 @ SV886 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[12528]) ).

thf(12720,plain,
    ! [SV887: nat,SV677: nat,SV357: nat] :
      ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV357 @ SV677 ) @ ( plus_plus_nat @ SV887 @ SV677 ) )
        = $false )
      | ( ( ord_less_eq_nat @ SV357 @ SV887 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12529]) ).

thf(12721,plain,
    ! [SV678: nat,SV359: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV359 )
        = $true )
      | ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV678 )
          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV359 @ SV678 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12530]) ).

thf(12722,plain,
    ! [SV888: nat,SV680: nat,SV361: nat] :
      ( ( ( ( divide_divide_nat @ SV361 @ SV680 )
          = ( divide_divide_nat @ SV888 @ SV680 ) )
        = $false )
      | ( ( ~ ( dvd_dvd_nat @ SV680 @ SV361 )
          | ~ ( dvd_dvd_nat @ SV680 @ SV888 )
          | ( SV361 = SV888 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12532]) ).

thf(12723,plain,
    ! [SV889: nat,SV681: nat,SV362: nat] :
      ( ( ( dvd_dvd_nat @ SV362 @ SV681 )
        = $false )
      | ( ( ~ ( dvd_dvd_nat @ SV362 @ SV889 )
          | ( ( ( divide_divide_nat @ SV681 @ SV362 )
              = ( divide_divide_nat @ SV889 @ SV362 ) )
            = ( SV681 = SV889 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12533]) ).

thf(12724,plain,
    ! [SV363: nat,SV682: nat] :
      ( ( ( ! [SY1817: nat] :
              ( SV682
             != ( times_times_nat @ SV363 @ SY1817 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV363 @ SV682 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12534]) ).

thf(12725,plain,
    ! [SV946: nat,SV890: nat,SV683: nat,SV364: nat] :
      ( ( ( ~ ( ord_less_nat @ SV364 @ SV683 ) )
        = $true )
      | ( ( ~ ( ord_less_nat @ SV890 @ SV946 )
          | ( ord_less_nat @ ( plus_plus_nat @ SV364 @ SV890 ) @ ( plus_plus_nat @ SV683 @ SV946 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12535]) ).

thf(12726,plain,
    ! [SV947: nat,SV891: nat,SV684: nat,SV365: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV365 @ SV684 ) )
        = $true )
      | ( ( ~ ( ord_less_eq_nat @ SV891 @ SV947 )
          | ( ord_less_eq_nat @ ( plus_plus_nat @ SV365 @ SV891 ) @ ( plus_plus_nat @ SV684 @ SV947 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12536]) ).

thf(12727,plain,
    ! [SV892: nat,SV685: nat,SV366: nat] :
      ( ( ( dvd_dvd_nat @ ( times_times_nat @ SV366 @ SV685 ) @ SV892 )
        = $false )
      | ( ( dvd_dvd_nat @ SV366 @ SV892 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12537]) ).

thf(12728,plain,
    ! [SV893: nat,SV686: nat,SV367: nat] :
      ( ( ( SV367
          = ( times_times_nat @ SV686 @ SV893 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV686 @ SV367 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12538]) ).

thf(12729,plain,
    ! [SV894: nat,SV687: nat,SV368: nat] :
      ( ( ( ord_less_eq_nat @ SV368 @ SV687 )
        = $false )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV894 @ SV368 ) @ ( plus_plus_nat @ SV894 @ SV687 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12539]) ).

thf(12730,plain,
    ! [SV895: nat,SV688: nat,SV369: nat] :
      ( ( ( ( plus_plus_nat @ SV369 @ SV688 )
          = SV895 )
        = $false )
      | ( ( SV369
          = ( minus_minus_nat @ SV895 @ SV688 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12540]) ).

thf(12731,plain,
    ! [SV896: nat,SV689: nat,SV370: nat] :
      ( ( ( ord_less_nat @ SV370 @ SV689 )
        = $false )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV896 @ SV370 ) @ ( plus_plus_nat @ SV896 @ SV689 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12541]) ).

thf(12732,plain,
    ! [SV897: nat,SV690: nat,SV371: nat] :
      ( ( ( dvd_dvd_nat @ SV371 @ SV690 )
        = $false )
      | ( ( dvd_dvd_nat @ SV371 @ ( times_times_nat @ SV897 @ SV690 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12542]) ).

thf(12733,plain,
    ! [SV898: nat,SV691: nat,SV372: nat] :
      ( ( ( dvd_dvd_nat @ SV372 @ SV691 )
        = $false )
      | ( ( dvd_dvd_nat @ SV372 @ ( times_times_nat @ SV691 @ SV898 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12543]) ).

thf(12734,plain,
    ! [SV692: option_nat,SV373: option_nat] :
      ( ( ( ~ ( ( SV373 = none_nat )
              | ( SV692 = none_nat ) )
          | ~ ( ( SV373 != none_nat )
              | ( SV692 != none_nat ) ) )
        = $false )
      | ( ( ~ ( ~ ( ( SV373 != none_nat ) )
              | ~ ( ( SV692 != none_nat ) )
              | ( ( the_nat @ SV373 )
                = ( the_nat @ SV692 ) ) )
          | ( SV373 = SV692 ) )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[12544]) ).

thf(12735,plain,
    ! [SV692: option_nat,SV373: option_nat] :
      ( ( ( ( SV373 = none_nat )
          = ( SV692 = none_nat ) )
        = $false )
      | ( ( ~ ( ~ ( ( SV373 != none_nat ) )
              | ~ ( ( SV692 != none_nat ) )
              | ( ( the_nat @ SV373 )
                = ( the_nat @ SV692 ) ) )
          | ( SV373 = SV692 ) )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[12544]) ).

thf(12736,plain,
    ! [SV374: nat > $o,SV693: nat] :
      ( ( ( ( ( divide_divide_nat @ ( sK8_SY1533 @ SV693 @ SV374 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
           != ( sK8_SY1533 @ SV693 @ SV374 ) )
          | ( SV374 @ ( sK8_SY1533 @ SV693 @ SV374 ) ) )
        = $false )
      | ( ( ~ ! [SY1534: nat,SY1535: $o] :
                ( ~ ( SV374 @ SY1534 )
                | ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ SY1535 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1534 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                 != SY1534 )
                | ( SV374 @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ SY1535 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1534 ) ) ) )
          | ( SV374 @ SV693 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[12545]) ).

thf(12737,plain,
    ! [SV948: nat,SV694: nat] :
      ( ( ~ ( ( ord_less_eq_nat @ SV694 @ SV948 )
            | ~ ! [SY1929: nat] :
                  ( SV948
                 != ( plus_plus_nat @ SV694 @ SY1929 ) ) )
        | ~ ( ~ ( ord_less_eq_nat @ SV694 @ SV948 )
            | ~ ~ ! [SY1929: nat] :
                    ( SV948
                   != ( plus_plus_nat @ SV694 @ SY1929 ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12546]) ).

thf(12738,plain,
    ! [SV948: nat,SV694: nat] :
      ( ( ( ord_less_eq_nat @ SV694 @ SV948 )
        = ( ~ ! [SY1929: nat] :
                ( SV948
               != ( plus_plus_nat @ SV694 @ SY1929 ) ) ) )
      = $true ),
    inference(extcnf_equal_pos,[status(thm)],[12546]) ).

thf(12739,plain,
    ! [SV900: nat,SV696: nat,SV377: nat] :
      ( ( ( dvd_dvd_nat @ SV377 @ SV696 )
        = $false )
      | ( ( ( power_power_nat @ ( divide_divide_nat @ SV696 @ SV377 ) @ SV900 )
          = ( divide_divide_nat @ ( power_power_nat @ SV696 @ SV900 ) @ ( power_power_nat @ SV377 @ SV900 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12547]) ).

thf(12740,plain,
    ! [SV949: nat,SV901: nat,SV697: nat,SV378: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV378 @ SV697 ) )
        = $true )
      | ( ( ~ ( ord_less_eq_nat @ SV901 @ SV949 )
          | ( ord_less_eq_nat @ ( times_times_nat @ SV378 @ SV901 ) @ ( times_times_nat @ SV697 @ SV949 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12548]) ).

thf(12741,plain,
    ! [SV950: nat,SV902: nat,SV698: nat,SV379: nat] :
      ( ( ( ~ ~ ( ~ ( ord_less_nat @ SV379 @ SV698 )
                | ( SV902 != SV950 ) ) )
        = $true )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV379 @ SV902 ) @ ( plus_plus_nat @ SV698 @ SV950 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12549]) ).

thf(12742,plain,
    ! [SV903: nat,SV699: nat,SV380: nat] :
      ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV380 @ SV699 ) @ ( plus_plus_nat @ SV380 @ SV903 ) )
        = $false )
      | ( ( ord_less_eq_nat @ SV699 @ SV903 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12550]) ).

thf(12743,plain,
    ! [SV382: num] :
      ( ( ( ~ ! [SY1550: num] :
                ( SV382
               != ( bit0 @ SY1550 ) ) )
        = $true )
      | ( ( ~ ! [SY1551: num] :
                ( SV382
               != ( bit1 @ SY1551 ) ) )
        = $true )
      | ( ( SV382 = one )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12552]) ).

thf(12744,plain,
    ! [SV951: vEBT_VEBT,SV904: list_VEBT_VEBT,SV701: nat,SV383: nat] :
      ( ( ( ~ ( ( SV383 != SV701 ) ) )
        = $true )
      | ( ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ SV904 @ SV383 @ SV951 ) @ SV701 )
          = ( nth_VEBT_VEBT @ SV904 @ SV701 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12553]) ).

thf(12745,plain,
    ! [SV960: nat,SV952: nat,SV905: nat,SV702: nat,SV384: nat] :
      ( ( ( ( modulo_modulo_nat @ SV384 @ SV702 )
         != ( modulo_modulo_nat @ SV905 @ SV702 ) )
        | ( ( modulo_modulo_nat @ SV952 @ SV702 )
         != ( modulo_modulo_nat @ SV960 @ SV702 ) )
        | ( ( modulo_modulo_nat @ ( plus_plus_nat @ SV384 @ SV952 ) @ SV702 )
          = ( modulo_modulo_nat @ ( plus_plus_nat @ SV905 @ SV960 ) @ SV702 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12554]) ).

thf(12746,plain,
    ! [SV906: nat,SV703: nat,SV386: nat] :
      ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV386 @ SV703 ) @ SV906 )
        = $false )
      | ( ( ord_less_eq_nat @ SV386 @ SV906 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12555]) ).

thf(12747,plain,
    ! [SV907: nat,SV704: nat,SV387: nat] :
      ( ( ( ord_less_nat @ ( plus_plus_nat @ SV387 @ SV704 ) @ ( plus_plus_nat @ SV387 @ SV907 ) )
        = $false )
      | ( ( ord_less_nat @ SV704 @ SV907 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12556]) ).

thf(12748,plain,
    ! [SV953: nat,SV908: nat > nat,SV705: nat,SV388: nat > nat] :
      ( ( ( ~ ( sums_nat @ SV388 @ SV705 ) )
        = $true )
      | ( ( ~ ( sums_nat @ SV908 @ SV953 )
          | ( sums_nat
            @ ^ [SY1914: nat] : ( plus_plus_nat @ ( SV388 @ SY1914 ) @ ( SV908 @ SY1914 ) )
            @ ( plus_plus_nat @ SV705 @ SV953 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12557]) ).

thf(12749,plain,
    ! [SV909: nat,SV706: nat,SV389: nat] :
      ( ( ( ord_less_nat @ SV389 @ SV706 )
        = $false )
      | ( ( ord_less_nat @ SV389 @ ( plus_plus_nat @ SV706 @ SV909 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12558]) ).

thf(12750,plain,
    ! [SV910: nat,SV707: nat,SV390: nat] :
      ( ( ( ord_less_eq_nat @ SV390 @ SV707 )
        = $false )
      | ( ( ord_less_eq_nat @ SV390 @ ( plus_plus_nat @ SV707 @ SV910 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12559]) ).

thf(12751,plain,
    ! [SV961: nat,SV912: nat,SV394: nat] :
      ( ( ( vEBT_VEBT_bit_concat @ SV394 @ SV912 @ SV961 )
        = ( plus_plus_nat @ ( times_times_nat @ SV394 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV961 ) ) @ SV912 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[12560]) ).

thf(12752,plain,
    ! [SV399: num,SV10: num] :
      ( ( ( ( numeral_numeral_nat @ SV10 )
          = ( numeral_numeral_nat @ SV399 ) )
        = $false )
      | ( ( ~ ( ( ( numeral_numeral_nat @ SV10 )
               != ( numeral_numeral_nat @ SV399 ) )
              | ( SV10 != SV399 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12562]) ).

thf(12753,plain,
    ! [SV399: num,SV10: num] :
      ( ( ( SV10 = SV399 )
        = $false )
      | ( ( ~ ( ( ( numeral_numeral_nat @ SV10 )
               != ( numeral_numeral_nat @ SV399 ) )
              | ( SV10 != SV399 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12562]) ).

thf(12754,plain,
    ! [SV427: nat,SV49: nat] :
      ( ( ( ord_less_eq_nat @ ( power_power_nat @ SV49 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ SV427 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV49 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ SV427 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
              | ~ ( ord_less_eq_nat @ SV49 @ SV427 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12563]) ).

thf(12755,plain,
    ! [SV427: nat,SV49: nat] :
      ( ( ( ord_less_eq_nat @ SV49 @ SV427 )
        = $false )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV49 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ SV427 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
              | ~ ( ord_less_eq_nat @ SV49 @ SV427 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12563]) ).

thf(12756,plain,
    ! [SV428: num,SV53: num] :
      ( ( ( ord_less_num @ ( bit0 @ SV53 ) @ ( bit0 @ SV428 ) )
        = $false )
      | ( ( ~ ( ~ ( ord_less_num @ ( bit0 @ SV53 ) @ ( bit0 @ SV428 ) )
              | ~ ( ord_less_num @ SV53 @ SV428 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12564]) ).

thf(12757,plain,
    ! [SV428: num,SV53: num] :
      ( ( ( ord_less_num @ SV53 @ SV428 )
        = $false )
      | ( ( ~ ( ~ ( ord_less_num @ ( bit0 @ SV53 ) @ ( bit0 @ SV428 ) )
              | ~ ( ord_less_num @ SV53 @ SV428 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12564]) ).

thf(12758,plain,
    ! [SV429: num,SV54: num] :
      ( ( ( ( bit0 @ SV54 )
          = ( bit0 @ SV429 ) )
        = $false )
      | ( ( ~ ( ( ( bit0 @ SV54 )
               != ( bit0 @ SV429 ) )
              | ( SV54 != SV429 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12565]) ).

thf(12759,plain,
    ! [SV429: num,SV54: num] :
      ( ( ( SV54 = SV429 )
        = $false )
      | ( ( ~ ( ( ( bit0 @ SV54 )
               != ( bit0 @ SV429 ) )
              | ( SV54 != SV429 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12565]) ).

thf(12760,plain,
    ! [SV432: num,SV62: num] :
      ( ( ( ord_less_eq_num @ ( bit0 @ SV62 ) @ ( bit0 @ SV432 ) )
        = $false )
      | ( ( ~ ( ~ ( ord_less_eq_num @ ( bit0 @ SV62 ) @ ( bit0 @ SV432 ) )
              | ~ ( ord_less_eq_num @ SV62 @ SV432 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12566]) ).

thf(12761,plain,
    ! [SV432: num,SV62: num] :
      ( ( ( ord_less_eq_num @ SV62 @ SV432 )
        = $false )
      | ( ( ~ ( ~ ( ord_less_eq_num @ ( bit0 @ SV62 ) @ ( bit0 @ SV432 ) )
              | ~ ( ord_less_eq_num @ SV62 @ SV432 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12566]) ).

thf(12762,plain,
    ! [SV64: num] :
      ( ( ( ( one_one_nat
           != ( numeral_numeral_nat @ SV64 ) )
          | ( one != SV64 ) )
        = $false )
      | ( ( one_one_nat
          = ( numeral_numeral_nat @ SV64 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12567]) ).

thf(12763,plain,
    ! [SV64: num] :
      ( ( ( ( one_one_nat
           != ( numeral_numeral_nat @ SV64 ) )
          | ( one != SV64 ) )
        = $false )
      | ( ( one = SV64 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12568]) ).

thf(12764,plain,
    ! [SV65: num] :
      ( ( ( ( ( numeral_numeral_nat @ SV65 )
           != one_one_nat )
          | ( SV65 != one ) )
        = $false )
      | ( ( ( numeral_numeral_nat @ SV65 )
          = one_one_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12569]) ).

thf(12765,plain,
    ! [SV65: num] :
      ( ( ( ( ( numeral_numeral_nat @ SV65 )
           != one_one_nat )
          | ( SV65 != one ) )
        = $false )
      | ( ( SV65 = one )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12570]) ).

thf(12766,plain,
    ! [SV67: num] :
      ( ( ( ~ ( ord_less_eq_num @ SV67 @ one )
          | ( SV67 != one ) )
        = $false )
      | ( ( ord_less_eq_num @ SV67 @ one )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12571]) ).

thf(12767,plain,
    ! [SV67: num] :
      ( ( ( ~ ( ord_less_eq_num @ SV67 @ one )
          | ( SV67 != one ) )
        = $false )
      | ( ( SV67 = one )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12572]) ).

thf(12768,plain,
    ! [SV729: nat,SV435: nat,SV71: nat] :
      ( ( ( ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SV435 ) @ ( plus_plus_nat @ SV71 @ SV729 ) )
          | ( ord_less_nat @ SV435 @ SV729 ) )
        = $false )
      | ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SV435 ) @ ( plus_plus_nat @ SV71 @ SV729 ) )
              | ~ ( ord_less_nat @ SV435 @ SV729 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12573]) ).

thf(12769,plain,
    ! [SV730: nat,SV436: nat,SV72: nat] :
      ( ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV72 @ SV436 ) @ ( plus_plus_nat @ SV72 @ SV730 ) )
          | ( ord_less_eq_nat @ SV436 @ SV730 ) )
        = $false )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV72 @ SV436 ) @ ( plus_plus_nat @ SV72 @ SV730 ) )
              | ~ ( ord_less_eq_nat @ SV436 @ SV730 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12574]) ).

thf(12770,plain,
    ! [SV736: nat,SV447: nat,SV86: nat] :
      ( ( ( ( ( times_times_nat @ ( suc @ SV86 ) @ SV447 )
            = ( times_times_nat @ ( suc @ SV86 ) @ SV736 ) )
          | ( SV447 = SV736 ) )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ ( suc @ SV86 ) @ SV447 )
               != ( times_times_nat @ ( suc @ SV86 ) @ SV736 ) )
              | ( SV447 != SV736 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12575]) ).

thf(12771,plain,
    ! [SV752: nat,SV475: nat,SV120: nat] :
      ( ( ( ( ( plus_plus_nat @ SV120 @ SV475 )
            = ( plus_plus_nat @ SV120 @ SV752 ) )
          | ( SV475 = SV752 ) )
        = $false )
      | ( ( ~ ( ( ( plus_plus_nat @ SV120 @ SV475 )
               != ( plus_plus_nat @ SV120 @ SV752 ) )
              | ( SV475 != SV752 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12576]) ).

thf(12772,plain,
    ! [SV753: nat,SV476: nat,SV121: nat] :
      ( ( ( ( ( plus_plus_nat @ SV121 @ SV476 )
            = ( plus_plus_nat @ SV753 @ SV476 ) )
          | ( SV121 = SV753 ) )
        = $false )
      | ( ( ~ ( ( ( plus_plus_nat @ SV121 @ SV476 )
               != ( plus_plus_nat @ SV753 @ SV476 ) )
              | ( SV121 != SV753 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12577]) ).

thf(12773,plain,
    ! [SV754: nat,SV477: nat,SV122: nat] :
      ( ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ SV477 ) @ ( plus_plus_nat @ SV122 @ SV754 ) )
          | ( ord_less_eq_nat @ SV477 @ SV754 ) )
        = $false )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ SV477 ) @ ( plus_plus_nat @ SV122 @ SV754 ) )
              | ~ ( ord_less_eq_nat @ SV477 @ SV754 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12578]) ).

thf(12774,plain,
    ! [SV755: nat,SV478: nat,SV123: nat] :
      ( ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV123 @ SV478 ) @ ( plus_plus_nat @ SV755 @ SV478 ) )
          | ( ord_less_eq_nat @ SV123 @ SV755 ) )
        = $false )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV123 @ SV478 ) @ ( plus_plus_nat @ SV755 @ SV478 ) )
              | ~ ( ord_less_eq_nat @ SV123 @ SV755 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12579]) ).

thf(12775,plain,
    ! [SV756: nat,SV479: nat,SV124: nat] :
      ( ( ( ( ord_less_nat @ ( plus_plus_nat @ SV124 @ SV479 ) @ ( plus_plus_nat @ SV124 @ SV756 ) )
          | ( ord_less_nat @ SV479 @ SV756 ) )
        = $false )
      | ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV124 @ SV479 ) @ ( plus_plus_nat @ SV124 @ SV756 ) )
              | ~ ( ord_less_nat @ SV479 @ SV756 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12580]) ).

thf(12776,plain,
    ! [SV757: nat,SV480: nat,SV125: nat] :
      ( ( ( ( ord_less_nat @ ( plus_plus_nat @ SV125 @ SV480 ) @ ( plus_plus_nat @ SV757 @ SV480 ) )
          | ( ord_less_nat @ SV125 @ SV757 ) )
        = $false )
      | ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV125 @ SV480 ) @ ( plus_plus_nat @ SV757 @ SV480 ) )
              | ~ ( ord_less_nat @ SV125 @ SV757 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12581]) ).

thf(12777,plain,
    ! [SV770: nat,SV493: nat,SV142: nat] :
      ( ( ( ( ( times_times_nat @ SV142 @ SV493 )
            = ( times_times_nat @ SV770 @ SV493 ) )
          | ( SV493 = zero_zero_nat )
          | ( SV142 = SV770 ) )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV142 @ SV493 )
               != ( times_times_nat @ SV770 @ SV493 ) )
              | ~ ( ( SV493 = zero_zero_nat )
                  | ( SV142 = SV770 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12582]) ).

thf(12778,plain,
    ! [SV771: nat,SV494: nat,SV143: nat] :
      ( ( ( ( ( times_times_nat @ SV143 @ SV494 )
            = ( times_times_nat @ SV143 @ SV771 ) )
          | ( SV143 = zero_zero_nat )
          | ( SV494 = SV771 ) )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV143 @ SV494 )
               != ( times_times_nat @ SV143 @ SV771 ) )
              | ~ ( ( SV143 = zero_zero_nat )
                  | ( SV494 = SV771 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12583]) ).

thf(12779,plain,
    ! [SV495: nat,SV144: nat] :
      ( ( ( ( times_times_nat @ SV144 @ SV495 )
          = zero_zero_nat )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV144 @ SV495 )
               != zero_zero_nat )
              | ~ ( ( SV144 = zero_zero_nat )
                  | ( SV495 = zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12584]) ).

thf(12780,plain,
    ! [SV495: nat,SV144: nat] :
      ( ( ( ( SV144 = zero_zero_nat )
          | ( SV495 = zero_zero_nat ) )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV144 @ SV495 )
               != zero_zero_nat )
              | ~ ( ( SV144 = zero_zero_nat )
                  | ( SV495 = zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12584]) ).

thf(12781,plain,
    ! [SV496: nat,SV148: nat] :
      ( ( ( SV148
          = ( plus_plus_nat @ SV148 @ SV496 ) )
        = $false )
      | ( ( ~ ( ( SV148
               != ( plus_plus_nat @ SV148 @ SV496 ) )
              | ( SV496 != zero_zero_nat ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12585]) ).

thf(12782,plain,
    ! [SV148: nat,SV496: nat] :
      ( ( ( SV496 = zero_zero_nat )
        = $false )
      | ( ( ~ ( ( SV148
               != ( plus_plus_nat @ SV148 @ SV496 ) )
              | ( SV496 != zero_zero_nat ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12585]) ).

thf(12783,plain,
    ! [SV497: nat,SV149: nat] :
      ( ( ( SV149
          = ( plus_plus_nat @ SV497 @ SV149 ) )
        = $false )
      | ( ( ~ ( ( SV149
               != ( plus_plus_nat @ SV497 @ SV149 ) )
              | ( SV497 != zero_zero_nat ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12586]) ).

thf(12784,plain,
    ! [SV149: nat,SV497: nat] :
      ( ( ( SV497 = zero_zero_nat )
        = $false )
      | ( ( ~ ( ( SV149
               != ( plus_plus_nat @ SV497 @ SV149 ) )
              | ( SV497 != zero_zero_nat ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12586]) ).

thf(12785,plain,
    ! [SV498: nat,SV150: nat] :
      ( ( ( ( plus_plus_nat @ SV150 @ SV498 )
          = SV150 )
        = $false )
      | ( ( ~ ( ( ( plus_plus_nat @ SV150 @ SV498 )
               != SV150 )
              | ( SV498 != zero_zero_nat ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12587]) ).

thf(12786,plain,
    ! [SV150: nat,SV498: nat] :
      ( ( ( SV498 = zero_zero_nat )
        = $false )
      | ( ( ~ ( ( ( plus_plus_nat @ SV150 @ SV498 )
               != SV150 )
              | ( SV498 != zero_zero_nat ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12587]) ).

thf(12787,plain,
    ! [SV499: nat,SV151: nat] :
      ( ( ( ( plus_plus_nat @ SV151 @ SV499 )
          = SV499 )
        = $false )
      | ( ( ~ ( ( ( plus_plus_nat @ SV151 @ SV499 )
               != SV499 )
              | ( SV151 != zero_zero_nat ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12588]) ).

thf(12788,plain,
    ! [SV499: nat,SV151: nat] :
      ( ( ( SV151 = zero_zero_nat )
        = $false )
      | ( ( ~ ( ( ( plus_plus_nat @ SV151 @ SV499 )
               != SV499 )
              | ( SV151 != zero_zero_nat ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12588]) ).

thf(12789,plain,
    ! [SV772: nat,SV502: nat,SV160: nat] :
      ( ( ( ( ( times_times_nat @ SV160 @ SV502 )
            = ( times_times_nat @ SV772 @ SV502 ) )
          | ( SV160 = SV772 )
          | ( SV502 = zero_zero_nat ) )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV160 @ SV502 )
               != ( times_times_nat @ SV772 @ SV502 ) )
              | ~ ( ( SV160 = SV772 )
                  | ( SV502 = zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12589]) ).

thf(12790,plain,
    ! [SV773: nat,SV503: nat,SV161: nat] :
      ( ( ( ( ( times_times_nat @ SV161 @ SV503 )
            = ( times_times_nat @ SV161 @ SV773 ) )
          | ( SV503 = SV773 )
          | ( SV161 = zero_zero_nat ) )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV161 @ SV503 )
               != ( times_times_nat @ SV161 @ SV773 ) )
              | ~ ( ( SV503 = SV773 )
                  | ( SV161 = zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12590]) ).

thf(12791,plain,
    ! [SV504: nat,SV163: nat] :
      ( ( ( ( times_times_nat @ SV163 @ SV504 )
          = zero_zero_nat )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV163 @ SV504 )
               != zero_zero_nat )
              | ~ ( ( SV163 = zero_zero_nat )
                  | ( SV504 = zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12591]) ).

thf(12792,plain,
    ! [SV504: nat,SV163: nat] :
      ( ( ( ( SV163 = zero_zero_nat )
          | ( SV504 = zero_zero_nat ) )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV163 @ SV504 )
               != zero_zero_nat )
              | ~ ( ( SV163 = zero_zero_nat )
                  | ( SV504 = zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12591]) ).

thf(12793,plain,
    ! [SV169: nat] :
      ( ( ( ( ( power_power_nat @ SV169 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
           != zero_zero_nat )
          | ( SV169 != zero_zero_nat ) )
        = $false )
      | ( ( ( power_power_nat @ SV169 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12592]) ).

thf(12794,plain,
    ! [SV169: nat] :
      ( ( ( ( ( power_power_nat @ SV169 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
           != zero_zero_nat )
          | ( SV169 != zero_zero_nat ) )
        = $false )
      | ( ( SV169 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12593]) ).

thf(12795,plain,
    ! [SV787: num,SV518: num,SV179: num] :
      ( ( ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV179 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) )
            = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV787 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) ) )
          | ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV179 ) @ ( numeral_numeral_nat @ SV518 ) )
            = ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV787 ) @ ( numeral_numeral_nat @ SV518 ) ) ) )
        = $false )
      | ( ( ~ ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV179 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) )
               != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV787 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) ) )
              | ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV179 ) @ ( numeral_numeral_nat @ SV518 ) )
               != ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV787 ) @ ( numeral_numeral_nat @ SV518 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12594]) ).

thf(12796,plain,
    ! [SV788: nat,SV520: nat,SV185: nat] :
      ( ( ( ( ( times_times_nat @ SV185 @ SV520 )
            = ( times_times_nat @ SV185 @ SV788 ) )
          | ( SV185 = zero_zero_nat )
          | ( SV520 = SV788 ) )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV185 @ SV520 )
               != ( times_times_nat @ SV185 @ SV788 ) )
              | ~ ( ( SV185 = zero_zero_nat )
                  | ( SV520 = SV788 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12595]) ).

thf(12797,plain,
    ! [SV534: num,SV199: num] :
      ( ( ( ( bit0 @ SV199 )
          = ( bit0 @ SV534 ) )
        = $false )
      | ( ( ~ ( ( ( bit0 @ SV199 )
               != ( bit0 @ SV534 ) )
              | ( SV199 != SV534 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12596]) ).

thf(12798,plain,
    ! [SV534: num,SV199: num] :
      ( ( ( SV199 = SV534 )
        = $false )
      | ( ( ~ ( ( ( bit0 @ SV199 )
               != ( bit0 @ SV534 ) )
              | ( SV199 != SV534 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12596]) ).

thf(12799,plain,
    ! [SV535: nat,SV201: nat] :
      ( ( ( dvd_dvd_nat @ SV201 @ ( plus_plus_nat @ SV535 @ SV201 ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ SV201 @ ( plus_plus_nat @ SV535 @ SV201 ) )
              | ~ ( dvd_dvd_nat @ SV201 @ SV535 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12597]) ).

thf(12800,plain,
    ! [SV535: nat,SV201: nat] :
      ( ( ( dvd_dvd_nat @ SV201 @ SV535 )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ SV201 @ ( plus_plus_nat @ SV535 @ SV201 ) )
              | ~ ( dvd_dvd_nat @ SV201 @ SV535 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12597]) ).

thf(12801,plain,
    ! [SV536: nat,SV202: nat] :
      ( ( ( dvd_dvd_nat @ SV202 @ ( plus_plus_nat @ SV202 @ SV536 ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ SV202 @ ( plus_plus_nat @ SV202 @ SV536 ) )
              | ~ ( dvd_dvd_nat @ SV202 @ SV536 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12598]) ).

thf(12802,plain,
    ! [SV536: nat,SV202: nat] :
      ( ( ( dvd_dvd_nat @ SV202 @ SV536 )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ SV202 @ ( plus_plus_nat @ SV202 @ SV536 ) )
              | ~ ( dvd_dvd_nat @ SV202 @ SV536 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12598]) ).

thf(12803,plain,
    ! [SV795: nat,SV537: nat,SV203: nat] :
      ( ( ( ( dvd_dvd_nat @ SV203 @ ( plus_plus_nat @ SV537 @ ( times_times_nat @ SV795 @ SV203 ) ) )
          | ( dvd_dvd_nat @ SV203 @ SV537 ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ SV203 @ ( plus_plus_nat @ SV537 @ ( times_times_nat @ SV795 @ SV203 ) ) )
              | ~ ( dvd_dvd_nat @ SV203 @ SV537 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12599]) ).

thf(12804,plain,
    ! [SV796: nat,SV538: nat,SV204: nat] :
      ( ( ( ( dvd_dvd_nat @ SV204 @ ( plus_plus_nat @ ( times_times_nat @ SV538 @ SV204 ) @ SV796 ) )
          | ( dvd_dvd_nat @ SV204 @ SV796 ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ SV204 @ ( plus_plus_nat @ ( times_times_nat @ SV538 @ SV204 ) @ SV796 ) )
              | ~ ( dvd_dvd_nat @ SV204 @ SV796 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12600]) ).

thf(12805,plain,
    ! [SV539: nat,SV205: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ SV205 @ SV539 ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ SV205 @ SV539 ) )
              | ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
                  | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12601]) ).

thf(12806,plain,
    ! [SV539: nat,SV205: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ SV205 @ SV539 ) )
              | ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
                  | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12601]) ).

thf(12807,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
              | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
               != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12602]) ).

thf(12808,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
              | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
               != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12602]) ).

thf(12809,plain,
    ! [SV548: nat,SV215: nat] :
      ( ( ( SV215
          = ( plus_plus_nat @ SV215 @ SV548 ) )
        = $false )
      | ( ( ~ ( ( SV215
               != ( plus_plus_nat @ SV215 @ SV548 ) )
              | ( SV548 != zero_zero_nat ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12604]) ).

thf(12810,plain,
    ! [SV215: nat,SV548: nat] :
      ( ( ( SV548 = zero_zero_nat )
        = $false )
      | ( ( ~ ( ( SV215
               != ( plus_plus_nat @ SV215 @ SV548 ) )
              | ( SV548 != zero_zero_nat ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12604]) ).

thf(12811,plain,
    ! [SV922: nat,SV802: nat,SV549: nat,SV216: nat] :
      ( ( ( ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV549 ) @ ( times_times_nat @ SV802 @ SV922 ) )
                = ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV922 ) @ ( times_times_nat @ SV802 @ SV549 ) ) )
              | ( SV216 = SV802 )
              | ( SV549 = SV922 ) ) )
        = $true )
      | ( ( ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV549 ) @ ( times_times_nat @ SV802 @ SV922 ) )
               != ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV922 ) @ ( times_times_nat @ SV802 @ SV549 ) ) )
              | ~ ( ( SV216 = SV802 )
                  | ( SV549 = SV922 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12605]) ).

thf(12812,plain,
    ! [SV803: nat,SV554: nat,SV224: nat] :
      ( ( ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV224 ) @ SV554 )
            = ( semiri1316708129612266289at_nat @ SV803 ) )
          | ( ( power_power_nat @ SV224 @ SV554 )
            = SV803 ) )
        = $false )
      | ( ( ~ ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV224 ) @ SV554 )
               != ( semiri1316708129612266289at_nat @ SV803 ) )
              | ( ( power_power_nat @ SV224 @ SV554 )
               != SV803 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12607]) ).

thf(12813,plain,
    ! [SV804: nat,SV555: nat,SV225: nat] :
      ( ( ( ( ( semiri1316708129612266289at_nat @ SV225 )
            = ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV555 ) @ SV804 ) )
          | ( SV225
            = ( power_power_nat @ SV555 @ SV804 ) ) )
        = $false )
      | ( ( ~ ( ( ( semiri1316708129612266289at_nat @ SV225 )
               != ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV555 ) @ SV804 ) )
              | ( SV225
               != ( power_power_nat @ SV555 @ SV804 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12608]) ).

thf(12814,plain,
    ! [SV805: nat,SV556: nat,SV226: num] :
      ( ( ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
            = ( semiri1316708129612266289at_nat @ SV805 ) )
          | ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
            = SV805 ) )
        = $false )
      | ( ( ~ ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
               != ( semiri1316708129612266289at_nat @ SV805 ) )
              | ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
               != SV805 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12609]) ).

thf(12815,plain,
    ! [SV806: nat,SV557: num,SV227: nat] :
      ( ( ( ( ( semiri1316708129612266289at_nat @ SV227 )
            = ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
          | ( SV227
            = ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) ) )
        = $false )
      | ( ( ~ ( ( ( semiri1316708129612266289at_nat @ SV227 )
               != ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
              | ( SV227
               != ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12610]) ).

thf(12816,plain,
    ! [SV561: nat,SV231: nat > real] :
      ( ( ( summable_real
          @ ^ [SY1684: nat] : ( SV231 @ ( plus_plus_nat @ SY1684 @ SV561 ) ) )
        = $false )
      | ( ( ~ ( ~ ( summable_real
                  @ ^ [SY1684: nat] : ( SV231 @ ( plus_plus_nat @ SY1684 @ SV561 ) ) )
              | ~ ( summable_real @ SV231 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12611]) ).

thf(12817,plain,
    ! [SV561: nat,SV231: nat > real] :
      ( ( ( summable_real @ SV231 )
        = $false )
      | ( ( ~ ( ~ ( summable_real
                  @ ^ [SY1684: nat] : ( SV231 @ ( plus_plus_nat @ SY1684 @ SV561 ) ) )
              | ~ ( summable_real @ SV231 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12611]) ).

thf(12818,plain,
    ! [SV562: nat,SV232: nat > complex] :
      ( ( ( summable_complex
          @ ^ [SY1685: nat] : ( SV232 @ ( plus_plus_nat @ SY1685 @ SV562 ) ) )
        = $false )
      | ( ( ~ ( ~ ( summable_complex
                  @ ^ [SY1685: nat] : ( SV232 @ ( plus_plus_nat @ SY1685 @ SV562 ) ) )
              | ~ ( summable_complex @ SV232 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12612]) ).

thf(12819,plain,
    ! [SV562: nat,SV232: nat > complex] :
      ( ( ( summable_complex @ SV232 )
        = $false )
      | ( ( ~ ( ~ ( summable_complex
                  @ ^ [SY1685: nat] : ( SV232 @ ( plus_plus_nat @ SY1685 @ SV562 ) ) )
              | ~ ( summable_complex @ SV232 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12612]) ).

thf(12820,plain,
    ! [SV243: $o] :
      ( ( SV243 = $false )
      | ( ( ~ ( ~ SV243
              | ~ $true ) )
        = $true )
      | ( ( SV243 = $false )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12613]) ).

thf(12821,plain,
    ! [SV243: $o] :
      ( ( $true = $false )
      | ( ( ~ ( ~ SV243
              | ~ $true ) )
        = $true )
      | ( ( SV243 = $false )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12613]) ).

thf(12822,plain,
    ! [SV243: $o] :
      ( ( ( SV243
          | $false )
        = $false )
      | ( ( ~ ( ~ SV243
              | ~ $false ) )
        = $true )
      | ( ( SV243 = $true )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12614]) ).

thf(12823,plain,
    ( ( $true = $false )
    | ( ( ~ ( ~ $true
            | ~ $true ) )
      = $true )
    | ( ( $true = $false )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12615]) ).

thf(12824,plain,
    ( ( $true = $false )
    | ( ( ~ ( ~ $true
            | ~ $true ) )
      = $true )
    | ( ( $true = $false )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12615]) ).

thf(12825,plain,
    ( ( ( $true
        | $false )
      = $false )
    | ( ( ~ ( ~ $true
            | ~ $false ) )
      = $true )
    | ( ( $true = $true )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12616]) ).

thf(12826,plain,
    ( ( $false = $false )
    | ( ( ~ ( ~ $false
            | ~ $true ) )
      = $true )
    | ( ( $false = $false )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12617]) ).

thf(12827,plain,
    ( ( $true = $false )
    | ( ( ~ ( ~ $false
            | ~ $true ) )
      = $true )
    | ( ( $false = $false )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12617]) ).

thf(12828,plain,
    ( ( ( $false
        | $false )
      = $false )
    | ( ( ~ ( ~ $false
            | ~ $false ) )
      = $true )
    | ( ( $false = $true )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12618]) ).

thf(12829,plain,
    ! [SV815: nat,SV570: nat,SV244: nat] :
      ( ( ( SV244 = zero_zero_nat )
        = $true )
      | ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ SV244 @ SV570 ) @ SV815 ) @ SV244 )
          = ( plus_plus_nat @ SV570 @ ( divide_divide_nat @ SV815 @ SV244 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12619]) ).

thf(12830,plain,
    ! [SV821: nat,SV578: nat,SV252: nat] :
      ( ( ( SV252 = zero_zero_nat )
        = $true )
      | ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ SV578 @ SV252 ) @ SV821 ) @ SV252 )
          = ( plus_plus_nat @ SV578 @ ( divide_divide_nat @ SV821 @ SV252 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12626]) ).

thf(12831,plain,
    ! [SV925: nat,SV822: nat,SV579: nat,SV253: nat] :
      ( ( ( ord_less_nat @ SV253 @ SV579 )
        = $false )
      | ( ( ( ( plus_plus_nat @ SV822 @ SV579 )
           != ( plus_plus_nat @ SV253 @ SV925 ) )
          | ( ord_less_nat @ SV822 @ SV925 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12627]) ).

thf(12832,plain,
    ! [SV824: nat,SV581: nat,SV255: nat] :
      ( ( ( SV255 != zero_zero_nat )
        | ( ( divide_divide_nat @ ( times_times_nat @ SV255 @ SV581 ) @ ( times_times_nat @ SV255 @ SV824 ) )
          = zero_zero_nat ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[12629]) ).

thf(12833,plain,
    ! [SV824: nat,SV581: nat,SV255: nat] :
      ( ( ~ ( ( SV255 != zero_zero_nat ) )
        | ( ( divide_divide_nat @ ( times_times_nat @ SV255 @ SV581 ) @ ( times_times_nat @ SV255 @ SV824 ) )
          = ( divide_divide_nat @ SV581 @ SV824 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[12630]) ).

thf(12834,plain,
    ! [SV825: nat,SV583: nat,SV257: nat] :
      ( ( ( SV257 = zero_zero_nat )
        = $true )
      | ( ( ( ( times_times_nat @ SV583 @ SV257 )
            = ( times_times_nat @ SV825 @ SV257 ) )
          = ( SV583 = SV825 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12632]) ).

thf(12835,plain,
    ! [SV826: nat,SV584: nat,SV258: nat] :
      ( ( ( ! [SY1869: nat,SY1870: nat] :
              ( ( SV258
               != ( times_times_nat @ SY1869 @ SY1870 ) )
              | ~ ( dvd_dvd_nat @ SY1869 @ SV584 )
              | ~ ( dvd_dvd_nat @ SY1870 @ SV826 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV258 @ ( times_times_nat @ SV584 @ SV826 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12633]) ).

thf(12836,plain,
    ! [SV259: nat,SV585: nat] :
      ( ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV585 )
          = zero_zero_nat )
        = $false )
      | ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV259 @ SV585 ) )
          = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12634]) ).

thf(12837,plain,
    ! [SV926: nat,SV827: nat,SV586: nat,SV260: nat] :
      ( ( ( ~ ( ( SV260 != SV586 )
              | ( SV827 != SV926 ) ) )
        = $false )
      | ( ( ( plus_plus_nat @ SV260 @ SV827 )
          = ( plus_plus_nat @ SV586 @ SV926 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12635]) ).

thf(12838,plain,
    ! [SV587: nat,SV828: nat,SV261: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV261 @ SV828 ) )
        = $true )
      | ( ( ( divide_divide_nat @ ( plus_plus_nat @ SV587 @ SV828 ) @ SV261 )
          = ( plus_plus_nat @ ( divide_divide_nat @ SV587 @ SV261 ) @ ( divide_divide_nat @ SV828 @ SV261 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV261 @ SV587 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[12636]) ).

thf(12839,plain,
    ! [SV262: nat,SV829: nat,SV588: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV588 @ SV829 ) )
        = $true )
      | ( ( ( divide_divide_nat @ ( divide_divide_nat @ SV829 @ SV262 ) @ ( divide_divide_nat @ SV588 @ SV262 ) )
          = ( divide_divide_nat @ SV829 @ SV588 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV262 @ SV588 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[12637]) ).

thf(12840,plain,
    ! [SV927: nat,SV830: nat,SV589: nat,SV263: nat] :
      ( ( ( SV263
          = ( plus_plus_nat @ SV589 @ SV830 ) )
        = $false )
      | ( ( ( plus_plus_nat @ SV263 @ SV927 )
          = ( plus_plus_nat @ SV589 @ ( plus_plus_nat @ SV830 @ SV927 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12638]) ).

thf(12841,plain,
    ! [SV832: nat,SV592: nat,SV266: nat] :
      ( ( ( SV266 = zero_zero_nat )
        = $true )
      | ( ( ( divide_divide_nat @ ( times_times_nat @ SV592 @ SV266 ) @ ( times_times_nat @ SV832 @ SV266 ) )
          = ( divide_divide_nat @ SV592 @ SV832 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12640]) ).

thf(12842,plain,
    ! [SV593: nat,SV833: nat,SV268: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV268 @ SV833 )
          | ~ ( ord_less_eq_nat @ SV593 @ SV833 ) )
        = $false )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV268 @ SV593 ) @ SV833 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12641]) ).

thf(12843,plain,
    ! [SV834: nat,SV594: nat,SV269: nat] :
      ( ( ( SV269 = zero_zero_nat )
        = $true )
      | ( ( ( divide_divide_nat @ ( plus_plus_nat @ SV594 @ ( times_times_nat @ SV269 @ SV834 ) ) @ SV269 )
          = ( plus_plus_nat @ SV834 @ ( divide_divide_nat @ SV594 @ SV269 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12642]) ).

thf(12844,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( ( SV595 = SV928 )
              | ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                   != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
                  | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                   != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
        = $true )
      | ( ( ~ ( ( SV595 != SV928 )
              | ~ ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                     != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
                    | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                     != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12643]) ).

thf(12845,plain,
    ! [SV929: nat,SV836: nat,SV596: nat,SV272: nat] :
      ( ( ( dvd_dvd_nat @ SV272 @ SV596 )
        = $false )
      | ( ( ~ ( dvd_dvd_nat @ SV836 @ SV929 )
          | ( dvd_dvd_nat @ ( times_times_nat @ SV272 @ SV836 ) @ ( times_times_nat @ SV596 @ SV929 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12645]) ).

thf(12846,plain,
    ! [SV837: nat,SV597: nat,SV273: nat] :
      ( ( ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
            = ( modulo_modulo_nat @ SV837 @ SV597 ) )
          | ~ ! [SY1874: nat] :
                ~ ~ ! [SY1875: nat] :
                      ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SY1874 ) )
                     != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1875 ) ) ) )
        = $false )
      | ( ( ~ ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
               != ( modulo_modulo_nat @ SV837 @ SV597 ) )
              | ~ ~ ! [SY1874: nat] :
                      ~ ~ ! [SY1875: nat] :
                            ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SY1874 ) )
                           != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1875 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12646]) ).

thf(12847,plain,
    ! [SV839: nat,SV599: nat,SV275: nat] :
      ( ( ( SV275 = zero_zero_nat )
        = $true )
      | ( ( ( divide_divide_nat @ ( plus_plus_nat @ SV599 @ ( times_times_nat @ SV839 @ SV275 ) ) @ SV275 )
          = ( plus_plus_nat @ SV839 @ ( divide_divide_nat @ SV599 @ SV275 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12648]) ).

thf(12848,plain,
    ! [SV277: nat] :
      ( ( ( SV277
          = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( sK7_SY1343 @ SV277 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV277 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[12650]) ).

thf(12849,plain,
    ! [SV601: nat,SV280: nat] :
      ( ( ( ~ ( ( SV280 != zero_zero_nat ) )
          | ~ ( ( SV601 != zero_zero_nat ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV280 @ SV601 )
          = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12651]) ).

thf(12850,plain,
    ! [SV930: nat,SV842: nat,SV603: nat,SV282: nat] :
      ( ( ( SV282
          = ( plus_plus_nat @ SV603 @ SV842 ) )
        = $false )
      | ( ( ( plus_plus_nat @ SV930 @ SV282 )
          = ( plus_plus_nat @ SV603 @ ( plus_plus_nat @ SV930 @ SV842 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12653]) ).

thf(12851,plain,
    ! [SV931: nat,SV844: nat,SV605: nat,SV284: nat] :
      ( ( ( ~ ( ~ ( ~ ( ( SV284 != SV605 ) )
                  | ~ ( ( SV844 != SV931 ) ) )
              | ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
               != ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) ) ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( ( SV284 != SV605 ) )
                    | ~ ( ( SV844 != SV931 ) ) )
              | ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
                   != ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12655]) ).

thf(12852,plain,
    ! [SV845: nat,SV606: nat,SV285: nat] :
      ( ( ( SV285 = zero_zero_nat )
        = $true )
      | ( ( ( ( times_times_nat @ SV285 @ SV606 )
            = ( times_times_nat @ SV285 @ SV845 ) )
          = ( SV606 = SV845 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12657]) ).

thf(12853,plain,
    ! [SV287: nat,SV608: nat] :
      ( ( ( ~ ( ( SV608 != zero_zero_nat ) ) )
        = $true )
      | ( ( ( times_times_nat @ SV287 @ SV608 )
         != zero_zero_nat )
        = $true )
      | ( ( SV287 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12659]) ).

thf(12854,plain,
    ! [SV609: nat,SV288: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV288 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV609 ) )
        = $false )
      | ( ( SV288 = SV609 )
        = $true )
      | ( ( ( divide_divide_nat @ SV288 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV609 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12660]) ).

thf(12855,plain,
    ! [SV932: nat,SV848: nat,SV611: nat,SV290: nat] :
      ( ( ( ~ ( ~ ( ord_less_nat @ SV290 @ SV611 )
              | ~ ( ord_less_nat @ SV848 @ SV932 ) ) )
        = $false )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV290 @ SV848 ) @ ( plus_plus_nat @ SV611 @ SV932 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12662]) ).

thf(12856,plain,
    ! [SV933: nat,SV849: nat,SV615: nat,SV294: nat] :
      ( ( ( ~ ( ( SV294 != SV615 )
              | ~ ( ord_less_nat @ SV849 @ SV933 ) ) )
        = $false )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV294 @ SV849 ) @ ( plus_plus_nat @ SV615 @ SV933 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12664]) ).

thf(12857,plain,
    ! [SV934: nat,SV850: nat,SV617: nat,SV296: nat] :
      ( ( ( ord_less_nat @ SV296 @ SV617 )
        = $false )
      | ( ( ~ ( ord_less_nat @ SV850 @ SV934 )
          | ( ord_less_nat @ ( plus_plus_nat @ SV296 @ SV850 ) @ ( plus_plus_nat @ SV617 @ SV934 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12665]) ).

thf(12858,plain,
    ! [SV935: nat,SV851: nat,SV618: nat,SV297: nat] :
      ( ( ( dvd_dvd_nat @ SV297 @ SV618 )
        = $false )
      | ( ( ~ ( dvd_dvd_nat @ SV851 @ SV935 )
          | ( ( times_times_nat @ ( divide_divide_nat @ SV618 @ SV297 ) @ ( divide_divide_nat @ SV935 @ SV851 ) )
            = ( divide_divide_nat @ ( times_times_nat @ SV618 @ SV935 ) @ ( times_times_nat @ SV297 @ SV851 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12666]) ).

thf(12859,plain,
    ! [SV298: nat,SV619: nat] :
      ( ( ( SV619
         != ( plus_plus_nat @ SV298 @ ( sK9_SY1748 @ SV298 @ SV619 ) ) )
        = $false )
      | ( ( ord_less_eq_nat @ SV298 @ SV619 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[12667]) ).

thf(12860,plain,
    ! [SV621: nat,SV300: nat] :
      ( ( ( ( times_times_nat @ SV300 @ SV621 )
          = one_one_nat )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV300 @ SV621 )
               != one_one_nat )
              | ~ ~ ( ( SV300 != one_one_nat )
                    | ( SV621 != one_one_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12669]) ).

thf(12861,plain,
    ! [SV621: nat,SV300: nat] :
      ( ( ( ~ ( ( SV300 != one_one_nat )
              | ( SV621 != one_one_nat ) ) )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV300 @ SV621 )
               != one_one_nat )
              | ~ ~ ( ( SV300 != one_one_nat )
                    | ( SV621 != one_one_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12669]) ).

thf(12862,plain,
    ! [SV936: nat,SV622: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ SV622 @ SV936 )
              | ~ ! [SY1919: nat] :
                    ( SV936
                   != ( times_times_nat @ SV622 @ SY1919 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ SV622 @ SV936 )
              | ~ ~ ! [SY1919: nat] :
                      ( SV936
                     != ( times_times_nat @ SV622 @ SY1919 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12670]) ).

thf(12863,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) ) )
        = $false )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
              | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
                   != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12672]) ).

thf(12864,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
         != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $false )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
              | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
                   != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12672]) ).

thf(12865,plain,
    ! [SV626: nat,SV305: nat] :
      ( ( ( ( plus_plus_nat @ SV305 @ SV626 )
          = zero_zero_nat )
        = $false )
      | ( ( ~ ( ( ( plus_plus_nat @ SV305 @ SV626 )
               != zero_zero_nat )
              | ~ ~ ( ( SV305 != zero_zero_nat )
                    | ( SV626 != zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12674]) ).

thf(12866,plain,
    ! [SV626: nat,SV305: nat] :
      ( ( ( ~ ( ( SV305 != zero_zero_nat )
              | ( SV626 != zero_zero_nat ) ) )
        = $false )
      | ( ( ~ ( ( ( plus_plus_nat @ SV305 @ SV626 )
               != zero_zero_nat )
              | ~ ~ ( ( SV305 != zero_zero_nat )
                    | ( SV626 != zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12674]) ).

thf(12867,plain,
    ! [SV309: nat,SV629: nat] :
      ( ( ( SV629
         != ( plus_plus_nat @ SV309 @ ( sK10_SY1755 @ SV309 @ SV629 ) ) )
        = $false )
      | ( ( ord_less_eq_nat @ SV309 @ SV629 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[12676]) ).

thf(12868,plain,
    ! [SV630: nat,SV310: nat] :
      ( ( ( ( plus_plus_nat @ SV310 @ SV630 )
          = zero_zero_nat )
        = $false )
      | ( ( ~ ( ( ( plus_plus_nat @ SV310 @ SV630 )
               != zero_zero_nat )
              | ~ ~ ( ( SV310 != zero_zero_nat )
                    | ( SV630 != zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12677]) ).

thf(12869,plain,
    ! [SV630: nat,SV310: nat] :
      ( ( ( ~ ( ( SV310 != zero_zero_nat )
              | ( SV630 != zero_zero_nat ) ) )
        = $false )
      | ( ( ~ ( ( ( plus_plus_nat @ SV310 @ SV630 )
               != zero_zero_nat )
              | ~ ~ ( ( SV310 != zero_zero_nat )
                    | ( SV630 != zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12677]) ).

thf(12870,plain,
    ! [SV856: nat,SV631: nat,SV311: nat] :
      ( ( ( ! [SY1883: nat] :
              ~ ~ ! [SY1884: nat] :
                    ~ ~ ( ~ ~ ( ( SV311
                               != ( times_times_nat @ SY1883 @ SY1884 ) )
                              | ~ ( dvd_dvd_nat @ SY1883 @ SV631 ) )
                        | ~ ( dvd_dvd_nat @ SY1884 @ SV856 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV311 @ ( times_times_nat @ SV631 @ SV856 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12678]) ).

thf(12871,plain,
    ! [SV956: nat,SV937: nat,SV857: nat,SV632: nat,SV312: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV312 @ SV632 ) )
        = $true )
      | ( ( ~ ( dvd_dvd_nat @ SV312 @ SV857 )
          | ~ ( ( ( times_times_nat @ SV632 @ SV937 )
                = ( plus_plus_nat @ ( times_times_nat @ SV857 @ SV956 ) @ SV312 ) )
              | ( ( times_times_nat @ SV857 @ SV937 )
                = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SV956 ) @ SV312 ) ) )
          | ~ ! [SY1887: nat] :
                ~ ~ ! [SY1888: nat] :
                      ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
                                | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) )
                          | ~ ( ( ( times_times_nat @ SV632 @ SY1887 )
                                = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1888 ) @ SV312 ) )
                              | ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1887 )
                                = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SY1888 ) @ SV312 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12679]) ).

thf(12872,plain,
    ! [SV314: nat,SV859: nat,SV634: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV634 @ SV859 ) )
        = $true )
      | ( ( ( divide_divide_nat @ SV859 @ ( divide_divide_nat @ SV634 @ SV314 ) )
          = ( times_times_nat @ ( divide_divide_nat @ SV859 @ SV634 ) @ SV314 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV314 @ SV634 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[12681]) ).

thf(12873,plain,
    ! [SV636: num,SV316: num > $o] :
      ( ( ( ! [SY1414: num] :
              ( ~ ( SV316 @ SY1414 )
              | ( SV316 @ ( inc @ SY1414 ) ) ) )
        = $false )
      | ( ( SV316 @ SV636 )
        = $true )
      | ( ( SV316 @ one )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12682]) ).

thf(12874,plain,
    ! [SV637: nat,SV317: nat] :
      ( ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV317 )
          = zero_zero_nat )
        = $false )
      | ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV317 @ SV637 ) )
          = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12683]) ).

thf(12875,plain,
    ! [SV639: nat,SV860: nat,SV319: nat > nat > $o] :
      ( ( ( ! [SY1934: nat] :
              ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ SY1934 )
              = ( SV319 @ SY1934 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) ) ) )
        = $false )
      | ( ( ~ ! [SY1421: nat] : ( SV319 @ SY1421 @ zero_zero_nat )
          | ~ ! [SY1422: nat,SY1423: nat] :
                ( ~ ( SV319 @ SY1422 @ SY1423 )
                | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) )
          | ( SV319 @ SV639 @ SV860 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[12684]) ).

thf(12876,plain,
    ! [SV642: nat,SV322: nat] :
      ( ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 )
        = $false )
      | ( ( ~ ( ~ ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 )
              | ~ ~ ( ~ ( ( SV322 != SV642 ) )
                    | ~ ( vEBT_V8194947554948674370ptions @ summary @ SV642 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12686]) ).

thf(12877,plain,
    ! [SV642: nat,SV322: nat] :
      ( ( ( ~ ( ~ ( ( SV322 != SV642 ) )
              | ~ ( vEBT_V8194947554948674370ptions @ summary @ SV642 ) ) )
        = $false )
      | ( ( ~ ( ~ ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 )
              | ~ ~ ( ~ ( ( SV322 != SV642 ) )
                    | ~ ( vEBT_V8194947554948674370ptions @ summary @ SV642 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12686]) ).

thf(12878,plain,
    ! [SV957: nat,SV938: nat,SV862: nat,SV643: nat,SV323: nat] :
      ( ( ( ( modulo_modulo_nat @ SV323 @ SV643 )
         != ( modulo_modulo_nat @ SV862 @ SV643 ) )
        = $true )
      | ( ( ( ( modulo_modulo_nat @ SV938 @ SV643 )
           != ( modulo_modulo_nat @ SV957 @ SV643 ) )
          | ( ( modulo_modulo_nat @ ( times_times_nat @ SV323 @ SV938 ) @ SV643 )
            = ( modulo_modulo_nat @ ( times_times_nat @ SV862 @ SV957 ) @ SV643 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12687]) ).

thf(12879,plain,
    ! [SV939: nat,SV644: nat] :
      ( ( ( ~ ( ( ord_less_eq_nat @ SV644 @ SV939 )
              | ~ ! [SY1924: nat] :
                    ( SV939
                   != ( plus_plus_nat @ SV644 @ SY1924 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ SV644 @ SV939 )
              | ~ ~ ! [SY1924: nat] :
                      ( SV939
                     != ( plus_plus_nat @ SV644 @ SY1924 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12688]) ).

thf(12880,plain,
    ! [SV940: nat,SV867: nat,SV648: nat,SV328: nat] :
      ( ( ( ~ ( ~ ( ord_less_eq_nat @ SV328 @ SV648 )
              | ( SV867 != SV940 ) ) )
        = $false )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV328 @ SV867 ) @ ( plus_plus_nat @ SV648 @ SV940 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12693]) ).

thf(12881,plain,
    ! [SV649: nat,SV329: nat] :
      ( ( ( zero_zero_nat
          = ( plus_plus_nat @ SV329 @ SV649 ) )
        = $false )
      | ( ( ~ ( ( zero_zero_nat
               != ( plus_plus_nat @ SV329 @ SV649 ) )
              | ~ ~ ( ( SV329 != zero_zero_nat )
                    | ( SV649 != zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12694]) ).

thf(12882,plain,
    ! [SV649: nat,SV329: nat] :
      ( ( ( ~ ( ( SV329 != zero_zero_nat )
              | ( SV649 != zero_zero_nat ) ) )
        = $false )
      | ( ( ~ ( ( zero_zero_nat
               != ( plus_plus_nat @ SV329 @ SV649 ) )
              | ~ ~ ( ( SV329 != zero_zero_nat )
                    | ( SV649 != zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12694]) ).

thf(12883,plain,
    ! [SV651: nat,SV331: nat] :
      ( ( ( ( power_power_nat @ SV331 @ SV651 )
          = zero_zero_nat )
        = $false )
      | ( ( SV331 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12696]) ).

thf(12884,plain,
    ! [SV958: vEBT_VEBT,SV941: vEBT_VEBT,SV869: list_VEBT_VEBT,SV652: nat,SV332: nat] :
      ( ( ( ~ ( ( SV332 != SV652 ) ) )
        = $true )
      | ( ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV869 @ SV332 @ SV941 ) @ SV652 @ SV958 )
          = ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV869 @ SV652 @ SV958 ) @ SV332 @ SV941 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12697]) ).

thf(12885,plain,
    ! [SV942: nat,SV871: nat,SV657: nat,SV335: nat] :
      ( ( ( ~ ( ( SV335 != SV657 )
              | ~ ( ord_less_eq_nat @ SV871 @ SV942 ) ) )
        = $false )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV335 @ SV871 ) @ ( plus_plus_nat @ SV657 @ SV942 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12699]) ).

thf(12886,plain,
    ! [SV658: nat,SV872: nat,SV336: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ SV336 @ ( plus_plus_nat @ SV872 @ SV658 ) )
              | ( dvd_dvd_nat @ SV336 @ SV872 ) )
          | ~ ( ~ ( dvd_dvd_nat @ SV336 @ ( plus_plus_nat @ SV872 @ SV658 ) )
              | ~ ( dvd_dvd_nat @ SV336 @ SV872 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV336 @ SV658 )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[12700]) ).

thf(12887,plain,
    ! [SV658: nat,SV872: nat,SV336: nat] :
      ( ( ( ( dvd_dvd_nat @ SV336 @ ( plus_plus_nat @ SV872 @ SV658 ) )
          = ( dvd_dvd_nat @ SV336 @ SV872 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV336 @ SV658 )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[12700]) ).

thf(12888,plain,
    ! [SV660: nat,SV874: nat,SV338: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV338 @ SV874 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV338 @ ( plus_plus_nat @ SV660 @ SV874 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV338 @ SV660 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[12702]) ).

thf(12889,plain,
    ! [SV340: nat] :
      ( ( ( ! [SY1466: nat] :
              ( SV340
             != ( plus_plus_nat @ SY1466 @ ( suc @ SY1466 ) ) ) )
        = $false )
      | ( ( SV340
          = ( plus_plus_nat @ ( sK5_SY1465 @ SV340 ) @ ( sK5_SY1465 @ SV340 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12704]) ).

thf(12890,plain,
    ! [SV943: nat,SV876: nat,SV662: nat,SV341: nat] :
      ( ( ( ~ ( ~ ( ord_less_eq_nat @ SV341 @ SV662 )
              | ~ ( ord_less_eq_nat @ SV876 @ SV943 ) ) )
        = $false )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV341 @ SV876 ) @ ( plus_plus_nat @ SV662 @ SV943 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12705]) ).

thf(12891,plain,
    ! [SV877: nat,SV663: nat,SV342: nat] :
      ( ( ( SV342 = zero_zero_nat )
        = $true )
      | ( ( ( divide_divide_nat @ ( times_times_nat @ SV342 @ SV663 ) @ ( times_times_nat @ SV342 @ SV877 ) )
          = ( divide_divide_nat @ SV663 @ SV877 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12706]) ).

thf(12892,plain,
    ! [SV668: nat,SV882: nat,SV347: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV347 @ SV882 ) )
        = $true )
      | ( ( ( dvd_dvd_nat @ ( divide_divide_nat @ SV668 @ SV347 ) @ ( divide_divide_nat @ SV882 @ SV347 ) )
          = ( dvd_dvd_nat @ SV668 @ SV882 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV347 @ SV668 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[12711]) ).

thf(12893,plain,
    ! [SV349: nat,SV669: nat] :
      ( ( ! [SY1926: nat] :
            ~ ~ ! [SY1927: nat] :
                  ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ ( sK6_SY1803 @ SV669 @ SV349 ) @ SV349 )
                            | ~ ( dvd_dvd_nat @ ( sK6_SY1803 @ SV669 @ SV349 ) @ SV669 ) )
                      | ~ ( ( ( times_times_nat @ SV349 @ SY1926 )
                            = ( plus_plus_nat @ ( times_times_nat @ SV669 @ SY1927 ) @ ( sK6_SY1803 @ SV669 @ SV349 ) ) )
                          | ( ( times_times_nat @ SV669 @ SY1926 )
                            = ( plus_plus_nat @ ( times_times_nat @ SV349 @ SY1927 ) @ ( sK6_SY1803 @ SV669 @ SV349 ) ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[12712]) ).

thf(12894,plain,
    ! [SV671: nat,SV351: nat] :
      ( ( ( one_one_nat
          = ( times_times_nat @ SV351 @ SV671 ) )
        = $false )
      | ( ( ~ ( ( one_one_nat
               != ( times_times_nat @ SV351 @ SV671 ) )
              | ~ ~ ( ( SV351 != one_one_nat )
                    | ( SV671 != one_one_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12713]) ).

thf(12895,plain,
    ! [SV671: nat,SV351: nat] :
      ( ( ( ~ ( ( SV351 != one_one_nat )
              | ( SV671 != one_one_nat ) ) )
        = $false )
      | ( ( ~ ( ( one_one_nat
               != ( times_times_nat @ SV351 @ SV671 ) )
              | ~ ~ ( ( SV351 != one_one_nat )
                    | ( SV671 != one_one_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12713]) ).

thf(12896,plain,
    ! [SV944: nat,SV883: nat,SV672: nat,SV352: nat] :
      ( ( ( ord_less_eq_nat @ SV352 @ SV672 )
        = $false )
      | ( ( ~ ( ord_less_eq_nat @ SV883 @ SV944 )
          | ( ord_less_eq_nat @ ( plus_plus_nat @ SV352 @ SV883 ) @ ( plus_plus_nat @ SV672 @ SV944 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12714]) ).

thf(12897,plain,
    ! [SV959: nat,SV945: nat,SV884: nat,SV673: nat,SV353: nat] :
      ( ( ( ~ ( ( SV353 != zero_zero_nat ) ) )
        = $true )
      | ( ( ~ ~ ( ( SV673 != SV884 )
                | ~ ( ( SV945 != SV959 ) ) )
          | ( ( plus_plus_nat @ SV673 @ ( times_times_nat @ SV353 @ SV945 ) )
           != ( plus_plus_nat @ SV884 @ ( times_times_nat @ SV353 @ SV959 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12715]) ).

thf(12898,plain,
    ! [SV885: nat,SV674: nat,SV354: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ SV354 @ ( plus_plus_nat @ SV674 @ SV885 ) )
              | ( dvd_dvd_nat @ SV354 @ SV885 ) )
          | ~ ( ~ ( dvd_dvd_nat @ SV354 @ ( plus_plus_nat @ SV674 @ SV885 ) )
              | ~ ( dvd_dvd_nat @ SV354 @ SV885 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV354 @ SV674 )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[12716]) ).

thf(12899,plain,
    ! [SV885: nat,SV674: nat,SV354: nat] :
      ( ( ( ( dvd_dvd_nat @ SV354 @ ( plus_plus_nat @ SV674 @ SV885 ) )
          = ( dvd_dvd_nat @ SV354 @ SV885 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV354 @ SV674 )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[12716]) ).

thf(12900,plain,
    ! [SV355: nat > nat,SV675: nat > nat] :
      ( ( ( summable_nat @ SV675 )
        = $false )
      | ( ( summable_nat
          @ ^ [SY1812: nat] : ( plus_plus_nat @ ( SV355 @ SY1812 ) @ ( SV675 @ SY1812 ) ) )
        = $true )
      | ( ( summable_nat @ SV355 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12717]) ).

thf(12901,plain,
    ! [SV886: nat,SV676: nat,SV356: nat] :
      ( ( ( SV356 != zero_zero_nat )
        | ( ( divide_divide_nat @ ( times_times_nat @ SV356 @ SV676 ) @ ( times_times_nat @ SV356 @ SV886 ) )
          = zero_zero_nat ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[12718]) ).

thf(12902,plain,
    ! [SV886: nat,SV676: nat,SV356: nat] :
      ( ( ~ ( ( SV356 != zero_zero_nat ) )
        | ( ( divide_divide_nat @ ( times_times_nat @ SV356 @ SV676 ) @ ( times_times_nat @ SV356 @ SV886 ) )
          = ( divide_divide_nat @ SV676 @ SV886 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[12719]) ).

thf(12903,plain,
    ! [SV359: nat,SV678: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV678 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV359 @ SV678 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV359 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12721]) ).

thf(12904,plain,
    ! [SV888: nat,SV361: nat,SV680: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV680 @ SV361 ) )
        = $true )
      | ( ( ~ ( dvd_dvd_nat @ SV680 @ SV888 )
          | ( SV361 = SV888 ) )
        = $true )
      | ( ( ( divide_divide_nat @ SV361 @ SV680 )
          = ( divide_divide_nat @ SV888 @ SV680 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[12722]) ).

thf(12905,plain,
    ! [SV681: nat,SV889: nat,SV362: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV362 @ SV889 ) )
        = $true )
      | ( ( ( ( divide_divide_nat @ SV681 @ SV362 )
            = ( divide_divide_nat @ SV889 @ SV362 ) )
          = ( SV681 = SV889 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV362 @ SV681 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[12723]) ).

thf(12906,plain,
    ! [SV363: nat,SV682: nat] :
      ( ( ( SV682
         != ( times_times_nat @ SV363 @ ( sK12_SY1817 @ SV363 @ SV682 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV363 @ SV682 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[12724]) ).

thf(12907,plain,
    ! [SV946: nat,SV890: nat,SV683: nat,SV364: nat] :
      ( ( ( ord_less_nat @ SV364 @ SV683 )
        = $false )
      | ( ( ~ ( ord_less_nat @ SV890 @ SV946 )
          | ( ord_less_nat @ ( plus_plus_nat @ SV364 @ SV890 ) @ ( plus_plus_nat @ SV683 @ SV946 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12725]) ).

thf(12908,plain,
    ! [SV947: nat,SV891: nat,SV684: nat,SV365: nat] :
      ( ( ( ord_less_eq_nat @ SV365 @ SV684 )
        = $false )
      | ( ( ~ ( ord_less_eq_nat @ SV891 @ SV947 )
          | ( ord_less_eq_nat @ ( plus_plus_nat @ SV365 @ SV891 ) @ ( plus_plus_nat @ SV684 @ SV947 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12726]) ).

thf(12909,plain,
    ! [SV692: option_nat,SV373: option_nat] :
      ( ( ( ~ ( ( SV373 = none_nat )
              | ( SV692 = none_nat ) ) )
        = $false )
      | ( ( ~ ( ~ ( ( SV373 != none_nat ) )
              | ~ ( ( SV692 != none_nat ) )
              | ( ( the_nat @ SV373 )
                = ( the_nat @ SV692 ) ) )
          | ( SV373 = SV692 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12734]) ).

thf(12910,plain,
    ! [SV692: option_nat,SV373: option_nat] :
      ( ( ( ~ ( ( SV373 != none_nat )
              | ( SV692 != none_nat ) ) )
        = $false )
      | ( ( ~ ( ~ ( ( SV373 != none_nat ) )
              | ~ ( ( SV692 != none_nat ) )
              | ( ( the_nat @ SV373 )
                = ( the_nat @ SV692 ) ) )
          | ( SV373 = SV692 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12734]) ).

thf(12911,plain,
    ! [SV692: option_nat,SV373: option_nat] :
      ( ( ( ~ ( ~ ( ( SV373 != none_nat ) )
              | ~ ( ( SV692 != none_nat ) )
              | ( ( the_nat @ SV373 )
                = ( the_nat @ SV692 ) ) ) )
        = $true )
      | ( ( SV373 = SV692 )
        = $true )
      | ( ( ( SV373 = none_nat )
          = ( SV692 = none_nat ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[12735]) ).

thf(12912,plain,
    ! [SV374: nat > $o,SV693: nat] :
      ( ( ( ( divide_divide_nat @ ( sK8_SY1533 @ SV693 @ SV374 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
         != ( sK8_SY1533 @ SV693 @ SV374 ) )
        = $false )
      | ( ( ~ ! [SY1534: nat,SY1535: $o] :
                ( ~ ( SV374 @ SY1534 )
                | ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ SY1535 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1534 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                 != SY1534 )
                | ( SV374 @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ SY1535 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1534 ) ) ) )
          | ( SV374 @ SV693 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12736]) ).

thf(12913,plain,
    ! [SV693: nat,SV374: nat > $o] :
      ( ( ( SV374 @ ( sK8_SY1533 @ SV693 @ SV374 ) )
        = $false )
      | ( ( ~ ! [SY1534: nat,SY1535: $o] :
                ( ~ ( SV374 @ SY1534 )
                | ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ SY1535 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1534 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                 != SY1534 )
                | ( SV374 @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ SY1535 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1534 ) ) ) )
          | ( SV374 @ SV693 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12736]) ).

thf(12914,plain,
    ! [SV948: nat,SV694: nat] :
      ( ( ( ~ ( ( ord_less_eq_nat @ SV694 @ SV948 )
              | ~ ! [SY1929: nat] :
                    ( SV948
                   != ( plus_plus_nat @ SV694 @ SY1929 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ SV694 @ SV948 )
              | ~ ~ ! [SY1929: nat] :
                      ( SV948
                     != ( plus_plus_nat @ SV694 @ SY1929 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12737]) ).

thf(12915,plain,
    ! [SV949: nat,SV901: nat,SV697: nat,SV378: nat] :
      ( ( ( ord_less_eq_nat @ SV378 @ SV697 )
        = $false )
      | ( ( ~ ( ord_less_eq_nat @ SV901 @ SV949 )
          | ( ord_less_eq_nat @ ( times_times_nat @ SV378 @ SV901 ) @ ( times_times_nat @ SV697 @ SV949 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12740]) ).

thf(12916,plain,
    ! [SV950: nat,SV902: nat,SV698: nat,SV379: nat] :
      ( ( ( ~ ( ~ ( ord_less_nat @ SV379 @ SV698 )
              | ( SV902 != SV950 ) ) )
        = $false )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV379 @ SV902 ) @ ( plus_plus_nat @ SV698 @ SV950 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12741]) ).

thf(12917,plain,
    ! [SV382: num] :
      ( ( ( ! [SY1550: num] :
              ( SV382
             != ( bit0 @ SY1550 ) ) )
        = $false )
      | ( ( ~ ! [SY1551: num] :
                ( SV382
               != ( bit1 @ SY1551 ) ) )
        = $true )
      | ( ( SV382 = one )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12743]) ).

thf(12918,plain,
    ! [SV951: vEBT_VEBT,SV904: list_VEBT_VEBT,SV701: nat,SV383: nat] :
      ( ( ( SV383 != SV701 )
        = $false )
      | ( ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ SV904 @ SV383 @ SV951 ) @ SV701 )
          = ( nth_VEBT_VEBT @ SV904 @ SV701 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12744]) ).

thf(12919,plain,
    ! [SV960: nat,SV952: nat,SV905: nat,SV702: nat,SV384: nat] :
      ( ( ( ( modulo_modulo_nat @ SV384 @ SV702 )
         != ( modulo_modulo_nat @ SV905 @ SV702 ) )
        = $true )
      | ( ( ( ( modulo_modulo_nat @ SV952 @ SV702 )
           != ( modulo_modulo_nat @ SV960 @ SV702 ) )
          | ( ( modulo_modulo_nat @ ( plus_plus_nat @ SV384 @ SV952 ) @ SV702 )
            = ( modulo_modulo_nat @ ( plus_plus_nat @ SV905 @ SV960 ) @ SV702 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12745]) ).

thf(12920,plain,
    ! [SV953: nat,SV908: nat > nat,SV705: nat,SV388: nat > nat] :
      ( ( ( sums_nat @ SV388 @ SV705 )
        = $false )
      | ( ( ~ ( sums_nat @ SV908 @ SV953 )
          | ( sums_nat
            @ ^ [SY1914: nat] : ( plus_plus_nat @ ( SV388 @ SY1914 ) @ ( SV908 @ SY1914 ) )
            @ ( plus_plus_nat @ SV705 @ SV953 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12748]) ).

thf(12921,plain,
    ! [SV399: num,SV10: num] :
      ( ( ( ( ( numeral_numeral_nat @ SV10 )
           != ( numeral_numeral_nat @ SV399 ) )
          | ( SV10 != SV399 ) )
        = $false )
      | ( ( ( numeral_numeral_nat @ SV10 )
          = ( numeral_numeral_nat @ SV399 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12752]) ).

thf(12922,plain,
    ! [SV399: num,SV10: num] :
      ( ( ( ( ( numeral_numeral_nat @ SV10 )
           != ( numeral_numeral_nat @ SV399 ) )
          | ( SV10 != SV399 ) )
        = $false )
      | ( ( SV10 = SV399 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12753]) ).

thf(12923,plain,
    ! [SV427: nat,SV49: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV49 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ SV427 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
          | ~ ( ord_less_eq_nat @ SV49 @ SV427 ) )
        = $false )
      | ( ( ord_less_eq_nat @ ( power_power_nat @ SV49 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ SV427 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12754]) ).

thf(12924,plain,
    ! [SV427: nat,SV49: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV49 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ SV427 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
          | ~ ( ord_less_eq_nat @ SV49 @ SV427 ) )
        = $false )
      | ( ( ord_less_eq_nat @ SV49 @ SV427 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12755]) ).

thf(12925,plain,
    ! [SV428: num,SV53: num] :
      ( ( ( ~ ( ord_less_num @ ( bit0 @ SV53 ) @ ( bit0 @ SV428 ) )
          | ~ ( ord_less_num @ SV53 @ SV428 ) )
        = $false )
      | ( ( ord_less_num @ ( bit0 @ SV53 ) @ ( bit0 @ SV428 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12756]) ).

thf(12926,plain,
    ! [SV428: num,SV53: num] :
      ( ( ( ~ ( ord_less_num @ ( bit0 @ SV53 ) @ ( bit0 @ SV428 ) )
          | ~ ( ord_less_num @ SV53 @ SV428 ) )
        = $false )
      | ( ( ord_less_num @ SV53 @ SV428 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12757]) ).

thf(12927,plain,
    ! [SV429: num,SV54: num] :
      ( ( ( ( ( bit0 @ SV54 )
           != ( bit0 @ SV429 ) )
          | ( SV54 != SV429 ) )
        = $false )
      | ( ( ( bit0 @ SV54 )
          = ( bit0 @ SV429 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12758]) ).

thf(12928,plain,
    ! [SV429: num,SV54: num] :
      ( ( ( ( ( bit0 @ SV54 )
           != ( bit0 @ SV429 ) )
          | ( SV54 != SV429 ) )
        = $false )
      | ( ( SV54 = SV429 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12759]) ).

thf(12929,plain,
    ! [SV432: num,SV62: num] :
      ( ( ( ~ ( ord_less_eq_num @ ( bit0 @ SV62 ) @ ( bit0 @ SV432 ) )
          | ~ ( ord_less_eq_num @ SV62 @ SV432 ) )
        = $false )
      | ( ( ord_less_eq_num @ ( bit0 @ SV62 ) @ ( bit0 @ SV432 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12760]) ).

thf(12930,plain,
    ! [SV432: num,SV62: num] :
      ( ( ( ~ ( ord_less_eq_num @ ( bit0 @ SV62 ) @ ( bit0 @ SV432 ) )
          | ~ ( ord_less_eq_num @ SV62 @ SV432 ) )
        = $false )
      | ( ( ord_less_eq_num @ SV62 @ SV432 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12761]) ).

thf(12931,plain,
    ! [SV64: num] :
      ( ( ( one_one_nat
         != ( numeral_numeral_nat @ SV64 ) )
        = $false )
      | ( ( one_one_nat
          = ( numeral_numeral_nat @ SV64 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12762]) ).

thf(12932,plain,
    ! [SV64: num] :
      ( ( ( one != SV64 )
        = $false )
      | ( ( one_one_nat
          = ( numeral_numeral_nat @ SV64 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12762]) ).

thf(12933,plain,
    ! [SV64: num] :
      ( ( ( one_one_nat
         != ( numeral_numeral_nat @ SV64 ) )
        = $false )
      | ( ( one = SV64 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12763]) ).

thf(12934,plain,
    ! [SV64: num] :
      ( ( ( one != SV64 )
        = $false )
      | ( ( one = SV64 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12763]) ).

thf(12935,plain,
    ! [SV65: num] :
      ( ( ( ( numeral_numeral_nat @ SV65 )
         != one_one_nat )
        = $false )
      | ( ( ( numeral_numeral_nat @ SV65 )
          = one_one_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12764]) ).

thf(12936,plain,
    ! [SV65: num] :
      ( ( ( SV65 != one )
        = $false )
      | ( ( ( numeral_numeral_nat @ SV65 )
          = one_one_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12764]) ).

thf(12937,plain,
    ! [SV65: num] :
      ( ( ( ( numeral_numeral_nat @ SV65 )
         != one_one_nat )
        = $false )
      | ( ( SV65 = one )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12765]) ).

thf(12938,plain,
    ! [SV65: num] :
      ( ( ( SV65 != one )
        = $false )
      | ( ( SV65 = one )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12765]) ).

thf(12939,plain,
    ! [SV67: num] :
      ( ( ( ~ ( ord_less_eq_num @ SV67 @ one ) )
        = $false )
      | ( ( ord_less_eq_num @ SV67 @ one )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12766]) ).

thf(12940,plain,
    ! [SV67: num] :
      ( ( ( SV67 != one )
        = $false )
      | ( ( ord_less_eq_num @ SV67 @ one )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12766]) ).

thf(12941,plain,
    ! [SV67: num] :
      ( ( ( ~ ( ord_less_eq_num @ SV67 @ one ) )
        = $false )
      | ( ( SV67 = one )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12767]) ).

thf(12942,plain,
    ! [SV67: num] :
      ( ( ( SV67 != one )
        = $false )
      | ( ( SV67 = one )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12767]) ).

thf(12943,plain,
    ! [SV729: nat,SV435: nat,SV71: nat] :
      ( ( ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SV435 ) @ ( plus_plus_nat @ SV71 @ SV729 ) )
        = $false )
      | ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SV435 ) @ ( plus_plus_nat @ SV71 @ SV729 ) )
              | ~ ( ord_less_nat @ SV435 @ SV729 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12768]) ).

thf(12944,plain,
    ! [SV71: nat,SV729: nat,SV435: nat] :
      ( ( ( ord_less_nat @ SV435 @ SV729 )
        = $false )
      | ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SV435 ) @ ( plus_plus_nat @ SV71 @ SV729 ) )
              | ~ ( ord_less_nat @ SV435 @ SV729 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12768]) ).

thf(12945,plain,
    ! [SV730: nat,SV436: nat,SV72: nat] :
      ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV72 @ SV436 ) @ ( plus_plus_nat @ SV72 @ SV730 ) )
        = $false )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV72 @ SV436 ) @ ( plus_plus_nat @ SV72 @ SV730 ) )
              | ~ ( ord_less_eq_nat @ SV436 @ SV730 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12769]) ).

thf(12946,plain,
    ! [SV72: nat,SV730: nat,SV436: nat] :
      ( ( ( ord_less_eq_nat @ SV436 @ SV730 )
        = $false )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV72 @ SV436 ) @ ( plus_plus_nat @ SV72 @ SV730 ) )
              | ~ ( ord_less_eq_nat @ SV436 @ SV730 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12769]) ).

thf(12947,plain,
    ! [SV736: nat,SV447: nat,SV86: nat] :
      ( ( ( ( times_times_nat @ ( suc @ SV86 ) @ SV447 )
          = ( times_times_nat @ ( suc @ SV86 ) @ SV736 ) )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ ( suc @ SV86 ) @ SV447 )
               != ( times_times_nat @ ( suc @ SV86 ) @ SV736 ) )
              | ( SV447 != SV736 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12770]) ).

thf(12948,plain,
    ! [SV86: nat,SV736: nat,SV447: nat] :
      ( ( ( SV447 = SV736 )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ ( suc @ SV86 ) @ SV447 )
               != ( times_times_nat @ ( suc @ SV86 ) @ SV736 ) )
              | ( SV447 != SV736 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12770]) ).

thf(12949,plain,
    ! [SV752: nat,SV475: nat,SV120: nat] :
      ( ( ( ( plus_plus_nat @ SV120 @ SV475 )
          = ( plus_plus_nat @ SV120 @ SV752 ) )
        = $false )
      | ( ( ~ ( ( ( plus_plus_nat @ SV120 @ SV475 )
               != ( plus_plus_nat @ SV120 @ SV752 ) )
              | ( SV475 != SV752 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12771]) ).

thf(12950,plain,
    ! [SV120: nat,SV752: nat,SV475: nat] :
      ( ( ( SV475 = SV752 )
        = $false )
      | ( ( ~ ( ( ( plus_plus_nat @ SV120 @ SV475 )
               != ( plus_plus_nat @ SV120 @ SV752 ) )
              | ( SV475 != SV752 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12771]) ).

thf(12951,plain,
    ! [SV753: nat,SV476: nat,SV121: nat] :
      ( ( ( ( plus_plus_nat @ SV121 @ SV476 )
          = ( plus_plus_nat @ SV753 @ SV476 ) )
        = $false )
      | ( ( ~ ( ( ( plus_plus_nat @ SV121 @ SV476 )
               != ( plus_plus_nat @ SV753 @ SV476 ) )
              | ( SV121 != SV753 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12772]) ).

thf(12952,plain,
    ! [SV476: nat,SV753: nat,SV121: nat] :
      ( ( ( SV121 = SV753 )
        = $false )
      | ( ( ~ ( ( ( plus_plus_nat @ SV121 @ SV476 )
               != ( plus_plus_nat @ SV753 @ SV476 ) )
              | ( SV121 != SV753 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12772]) ).

thf(12953,plain,
    ! [SV754: nat,SV477: nat,SV122: nat] :
      ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ SV477 ) @ ( plus_plus_nat @ SV122 @ SV754 ) )
        = $false )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ SV477 ) @ ( plus_plus_nat @ SV122 @ SV754 ) )
              | ~ ( ord_less_eq_nat @ SV477 @ SV754 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12773]) ).

thf(12954,plain,
    ! [SV122: nat,SV754: nat,SV477: nat] :
      ( ( ( ord_less_eq_nat @ SV477 @ SV754 )
        = $false )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ SV477 ) @ ( plus_plus_nat @ SV122 @ SV754 ) )
              | ~ ( ord_less_eq_nat @ SV477 @ SV754 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12773]) ).

thf(12955,plain,
    ! [SV755: nat,SV478: nat,SV123: nat] :
      ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV123 @ SV478 ) @ ( plus_plus_nat @ SV755 @ SV478 ) )
        = $false )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV123 @ SV478 ) @ ( plus_plus_nat @ SV755 @ SV478 ) )
              | ~ ( ord_less_eq_nat @ SV123 @ SV755 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12774]) ).

thf(12956,plain,
    ! [SV478: nat,SV755: nat,SV123: nat] :
      ( ( ( ord_less_eq_nat @ SV123 @ SV755 )
        = $false )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV123 @ SV478 ) @ ( plus_plus_nat @ SV755 @ SV478 ) )
              | ~ ( ord_less_eq_nat @ SV123 @ SV755 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12774]) ).

thf(12957,plain,
    ! [SV756: nat,SV479: nat,SV124: nat] :
      ( ( ( ord_less_nat @ ( plus_plus_nat @ SV124 @ SV479 ) @ ( plus_plus_nat @ SV124 @ SV756 ) )
        = $false )
      | ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV124 @ SV479 ) @ ( plus_plus_nat @ SV124 @ SV756 ) )
              | ~ ( ord_less_nat @ SV479 @ SV756 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12775]) ).

thf(12958,plain,
    ! [SV124: nat,SV756: nat,SV479: nat] :
      ( ( ( ord_less_nat @ SV479 @ SV756 )
        = $false )
      | ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV124 @ SV479 ) @ ( plus_plus_nat @ SV124 @ SV756 ) )
              | ~ ( ord_less_nat @ SV479 @ SV756 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12775]) ).

thf(12959,plain,
    ! [SV757: nat,SV480: nat,SV125: nat] :
      ( ( ( ord_less_nat @ ( plus_plus_nat @ SV125 @ SV480 ) @ ( plus_plus_nat @ SV757 @ SV480 ) )
        = $false )
      | ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV125 @ SV480 ) @ ( plus_plus_nat @ SV757 @ SV480 ) )
              | ~ ( ord_less_nat @ SV125 @ SV757 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12776]) ).

thf(12960,plain,
    ! [SV480: nat,SV757: nat,SV125: nat] :
      ( ( ( ord_less_nat @ SV125 @ SV757 )
        = $false )
      | ( ( ~ ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV125 @ SV480 ) @ ( plus_plus_nat @ SV757 @ SV480 ) )
              | ~ ( ord_less_nat @ SV125 @ SV757 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12776]) ).

thf(12961,plain,
    ! [SV770: nat,SV493: nat,SV142: nat] :
      ( ( ( ( times_times_nat @ SV142 @ SV493 )
          = ( times_times_nat @ SV770 @ SV493 ) )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV142 @ SV493 )
               != ( times_times_nat @ SV770 @ SV493 ) )
              | ~ ( ( SV493 = zero_zero_nat )
                  | ( SV142 = SV770 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12777]) ).

thf(12962,plain,
    ! [SV770: nat,SV142: nat,SV493: nat] :
      ( ( ( ( SV493 = zero_zero_nat )
          | ( SV142 = SV770 ) )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV142 @ SV493 )
               != ( times_times_nat @ SV770 @ SV493 ) )
              | ~ ( ( SV493 = zero_zero_nat )
                  | ( SV142 = SV770 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12777]) ).

thf(12963,plain,
    ! [SV771: nat,SV494: nat,SV143: nat] :
      ( ( ( ( times_times_nat @ SV143 @ SV494 )
          = ( times_times_nat @ SV143 @ SV771 ) )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV143 @ SV494 )
               != ( times_times_nat @ SV143 @ SV771 ) )
              | ~ ( ( SV143 = zero_zero_nat )
                  | ( SV494 = SV771 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12778]) ).

thf(12964,plain,
    ! [SV771: nat,SV494: nat,SV143: nat] :
      ( ( ( ( SV143 = zero_zero_nat )
          | ( SV494 = SV771 ) )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV143 @ SV494 )
               != ( times_times_nat @ SV143 @ SV771 ) )
              | ~ ( ( SV143 = zero_zero_nat )
                  | ( SV494 = SV771 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12778]) ).

thf(12965,plain,
    ! [SV495: nat,SV144: nat] :
      ( ( ( ( ( times_times_nat @ SV144 @ SV495 )
           != zero_zero_nat )
          | ~ ( ( SV144 = zero_zero_nat )
              | ( SV495 = zero_zero_nat ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV144 @ SV495 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12779]) ).

thf(12966,plain,
    ! [SV495: nat,SV144: nat] :
      ( ( ( SV144 = zero_zero_nat )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV144 @ SV495 )
               != zero_zero_nat )
              | ~ ( ( SV144 = zero_zero_nat )
                  | ( SV495 = zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12780]) ).

thf(12967,plain,
    ! [SV144: nat,SV495: nat] :
      ( ( ( SV495 = zero_zero_nat )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV144 @ SV495 )
               != zero_zero_nat )
              | ~ ( ( SV144 = zero_zero_nat )
                  | ( SV495 = zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12780]) ).

thf(12968,plain,
    ! [SV496: nat,SV148: nat] :
      ( ( ( ( SV148
           != ( plus_plus_nat @ SV148 @ SV496 ) )
          | ( SV496 != zero_zero_nat ) )
        = $false )
      | ( ( SV148
          = ( plus_plus_nat @ SV148 @ SV496 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12781]) ).

thf(12969,plain,
    ! [SV496: nat,SV148: nat] :
      ( ( ( ( SV148
           != ( plus_plus_nat @ SV148 @ SV496 ) )
          | ( SV496 != zero_zero_nat ) )
        = $false )
      | ( ( SV496 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12782]) ).

thf(12970,plain,
    ! [SV497: nat,SV149: nat] :
      ( ( ( ( SV149
           != ( plus_plus_nat @ SV497 @ SV149 ) )
          | ( SV497 != zero_zero_nat ) )
        = $false )
      | ( ( SV149
          = ( plus_plus_nat @ SV497 @ SV149 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12783]) ).

thf(12971,plain,
    ! [SV497: nat,SV149: nat] :
      ( ( ( ( SV149
           != ( plus_plus_nat @ SV497 @ SV149 ) )
          | ( SV497 != zero_zero_nat ) )
        = $false )
      | ( ( SV497 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12784]) ).

thf(12972,plain,
    ! [SV498: nat,SV150: nat] :
      ( ( ( ( ( plus_plus_nat @ SV150 @ SV498 )
           != SV150 )
          | ( SV498 != zero_zero_nat ) )
        = $false )
      | ( ( ( plus_plus_nat @ SV150 @ SV498 )
          = SV150 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12785]) ).

thf(12973,plain,
    ! [SV498: nat,SV150: nat] :
      ( ( ( ( ( plus_plus_nat @ SV150 @ SV498 )
           != SV150 )
          | ( SV498 != zero_zero_nat ) )
        = $false )
      | ( ( SV498 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12786]) ).

thf(12974,plain,
    ! [SV499: nat,SV151: nat] :
      ( ( ( ( ( plus_plus_nat @ SV151 @ SV499 )
           != SV499 )
          | ( SV151 != zero_zero_nat ) )
        = $false )
      | ( ( ( plus_plus_nat @ SV151 @ SV499 )
          = SV499 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12787]) ).

thf(12975,plain,
    ! [SV499: nat,SV151: nat] :
      ( ( ( ( ( plus_plus_nat @ SV151 @ SV499 )
           != SV499 )
          | ( SV151 != zero_zero_nat ) )
        = $false )
      | ( ( SV151 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12788]) ).

thf(12976,plain,
    ! [SV772: nat,SV502: nat,SV160: nat] :
      ( ( ( ( times_times_nat @ SV160 @ SV502 )
          = ( times_times_nat @ SV772 @ SV502 ) )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV160 @ SV502 )
               != ( times_times_nat @ SV772 @ SV502 ) )
              | ~ ( ( SV160 = SV772 )
                  | ( SV502 = zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12789]) ).

thf(12977,plain,
    ! [SV502: nat,SV772: nat,SV160: nat] :
      ( ( ( ( SV160 = SV772 )
          | ( SV502 = zero_zero_nat ) )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV160 @ SV502 )
               != ( times_times_nat @ SV772 @ SV502 ) )
              | ~ ( ( SV160 = SV772 )
                  | ( SV502 = zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12789]) ).

thf(12978,plain,
    ! [SV773: nat,SV503: nat,SV161: nat] :
      ( ( ( ( times_times_nat @ SV161 @ SV503 )
          = ( times_times_nat @ SV161 @ SV773 ) )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV161 @ SV503 )
               != ( times_times_nat @ SV161 @ SV773 ) )
              | ~ ( ( SV503 = SV773 )
                  | ( SV161 = zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12790]) ).

thf(12979,plain,
    ! [SV161: nat,SV773: nat,SV503: nat] :
      ( ( ( ( SV503 = SV773 )
          | ( SV161 = zero_zero_nat ) )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV161 @ SV503 )
               != ( times_times_nat @ SV161 @ SV773 ) )
              | ~ ( ( SV503 = SV773 )
                  | ( SV161 = zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12790]) ).

thf(12980,plain,
    ! [SV504: nat,SV163: nat] :
      ( ( ( ( ( times_times_nat @ SV163 @ SV504 )
           != zero_zero_nat )
          | ~ ( ( SV163 = zero_zero_nat )
              | ( SV504 = zero_zero_nat ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV163 @ SV504 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12791]) ).

thf(12981,plain,
    ! [SV504: nat,SV163: nat] :
      ( ( ( SV163 = zero_zero_nat )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV163 @ SV504 )
               != zero_zero_nat )
              | ~ ( ( SV163 = zero_zero_nat )
                  | ( SV504 = zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12792]) ).

thf(12982,plain,
    ! [SV163: nat,SV504: nat] :
      ( ( ( SV504 = zero_zero_nat )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV163 @ SV504 )
               != zero_zero_nat )
              | ~ ( ( SV163 = zero_zero_nat )
                  | ( SV504 = zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12792]) ).

thf(12983,plain,
    ! [SV169: nat] :
      ( ( ( ( power_power_nat @ SV169 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
         != zero_zero_nat )
        = $false )
      | ( ( ( power_power_nat @ SV169 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12793]) ).

thf(12984,plain,
    ! [SV169: nat] :
      ( ( ( SV169 != zero_zero_nat )
        = $false )
      | ( ( ( power_power_nat @ SV169 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12793]) ).

thf(12985,plain,
    ! [SV169: nat] :
      ( ( ( ( power_power_nat @ SV169 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
         != zero_zero_nat )
        = $false )
      | ( ( SV169 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12794]) ).

thf(12986,plain,
    ! [SV169: nat] :
      ( ( ( SV169 != zero_zero_nat )
        = $false )
      | ( ( SV169 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12794]) ).

thf(12987,plain,
    ! [SV787: num,SV518: num,SV179: num] :
      ( ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV179 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) )
          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV787 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) ) )
        = $false )
      | ( ( ~ ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV179 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) )
               != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV787 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) ) )
              | ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV179 ) @ ( numeral_numeral_nat @ SV518 ) )
               != ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV787 ) @ ( numeral_numeral_nat @ SV518 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12795]) ).

thf(12988,plain,
    ! [SV787: num,SV518: num,SV179: num] :
      ( ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV179 ) @ ( numeral_numeral_nat @ SV518 ) )
          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV787 ) @ ( numeral_numeral_nat @ SV518 ) ) )
        = $false )
      | ( ( ~ ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV179 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) )
               != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV787 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) ) )
              | ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV179 ) @ ( numeral_numeral_nat @ SV518 ) )
               != ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV787 ) @ ( numeral_numeral_nat @ SV518 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12795]) ).

thf(12989,plain,
    ! [SV788: nat,SV520: nat,SV185: nat] :
      ( ( ( ( times_times_nat @ SV185 @ SV520 )
          = ( times_times_nat @ SV185 @ SV788 ) )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV185 @ SV520 )
               != ( times_times_nat @ SV185 @ SV788 ) )
              | ~ ( ( SV185 = zero_zero_nat )
                  | ( SV520 = SV788 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12796]) ).

thf(12990,plain,
    ! [SV788: nat,SV520: nat,SV185: nat] :
      ( ( ( ( SV185 = zero_zero_nat )
          | ( SV520 = SV788 ) )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV185 @ SV520 )
               != ( times_times_nat @ SV185 @ SV788 ) )
              | ~ ( ( SV185 = zero_zero_nat )
                  | ( SV520 = SV788 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12796]) ).

thf(12991,plain,
    ! [SV534: num,SV199: num] :
      ( ( ( ( ( bit0 @ SV199 )
           != ( bit0 @ SV534 ) )
          | ( SV199 != SV534 ) )
        = $false )
      | ( ( ( bit0 @ SV199 )
          = ( bit0 @ SV534 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12797]) ).

thf(12992,plain,
    ! [SV534: num,SV199: num] :
      ( ( ( ( ( bit0 @ SV199 )
           != ( bit0 @ SV534 ) )
          | ( SV199 != SV534 ) )
        = $false )
      | ( ( SV199 = SV534 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12798]) ).

thf(12993,plain,
    ! [SV535: nat,SV201: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV201 @ ( plus_plus_nat @ SV535 @ SV201 ) )
          | ~ ( dvd_dvd_nat @ SV201 @ SV535 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV201 @ ( plus_plus_nat @ SV535 @ SV201 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12799]) ).

thf(12994,plain,
    ! [SV535: nat,SV201: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV201 @ ( plus_plus_nat @ SV535 @ SV201 ) )
          | ~ ( dvd_dvd_nat @ SV201 @ SV535 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV201 @ SV535 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12800]) ).

thf(12995,plain,
    ! [SV536: nat,SV202: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV202 @ ( plus_plus_nat @ SV202 @ SV536 ) )
          | ~ ( dvd_dvd_nat @ SV202 @ SV536 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV202 @ ( plus_plus_nat @ SV202 @ SV536 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12801]) ).

thf(12996,plain,
    ! [SV536: nat,SV202: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV202 @ ( plus_plus_nat @ SV202 @ SV536 ) )
          | ~ ( dvd_dvd_nat @ SV202 @ SV536 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV202 @ SV536 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12802]) ).

thf(12997,plain,
    ! [SV795: nat,SV537: nat,SV203: nat] :
      ( ( ( dvd_dvd_nat @ SV203 @ ( plus_plus_nat @ SV537 @ ( times_times_nat @ SV795 @ SV203 ) ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ SV203 @ ( plus_plus_nat @ SV537 @ ( times_times_nat @ SV795 @ SV203 ) ) )
              | ~ ( dvd_dvd_nat @ SV203 @ SV537 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12803]) ).

thf(12998,plain,
    ! [SV795: nat,SV537: nat,SV203: nat] :
      ( ( ( dvd_dvd_nat @ SV203 @ SV537 )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ SV203 @ ( plus_plus_nat @ SV537 @ ( times_times_nat @ SV795 @ SV203 ) ) )
              | ~ ( dvd_dvd_nat @ SV203 @ SV537 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12803]) ).

thf(12999,plain,
    ! [SV796: nat,SV538: nat,SV204: nat] :
      ( ( ( dvd_dvd_nat @ SV204 @ ( plus_plus_nat @ ( times_times_nat @ SV538 @ SV204 ) @ SV796 ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ SV204 @ ( plus_plus_nat @ ( times_times_nat @ SV538 @ SV204 ) @ SV796 ) )
              | ~ ( dvd_dvd_nat @ SV204 @ SV796 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12804]) ).

thf(13000,plain,
    ! [SV538: nat,SV796: nat,SV204: nat] :
      ( ( ( dvd_dvd_nat @ SV204 @ SV796 )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ SV204 @ ( plus_plus_nat @ ( times_times_nat @ SV538 @ SV204 ) @ SV796 ) )
              | ~ ( dvd_dvd_nat @ SV204 @ SV796 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12804]) ).

thf(13001,plain,
    ! [SV539: nat,SV205: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ SV205 @ SV539 ) )
          | ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
              | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ SV205 @ SV539 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12805]) ).

thf(13002,plain,
    ! [SV539: nat,SV205: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ SV205 @ SV539 ) )
              | ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
                  | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12806]) ).

thf(13003,plain,
    ! [SV205: nat,SV539: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ SV205 @ SV539 ) )
              | ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
                  | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12806]) ).

thf(13004,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
           != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12807]) ).

thf(13005,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
          | ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
              | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
               != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) ) )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[12808]) ).

thf(13006,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
              | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
               != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) ) )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[12808]) ).

thf(13007,plain,
    ! [SV548: nat,SV215: nat] :
      ( ( ( ( SV215
           != ( plus_plus_nat @ SV215 @ SV548 ) )
          | ( SV548 != zero_zero_nat ) )
        = $false )
      | ( ( SV215
          = ( plus_plus_nat @ SV215 @ SV548 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12809]) ).

thf(13008,plain,
    ! [SV548: nat,SV215: nat] :
      ( ( ( ( SV215
           != ( plus_plus_nat @ SV215 @ SV548 ) )
          | ( SV548 != zero_zero_nat ) )
        = $false )
      | ( ( SV548 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12810]) ).

thf(13009,plain,
    ! [SV922: nat,SV802: nat,SV549: nat,SV216: nat] :
      ( ( ( ( ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV549 ) @ ( times_times_nat @ SV802 @ SV922 ) )
            = ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV922 ) @ ( times_times_nat @ SV802 @ SV549 ) ) )
          | ( SV216 = SV802 )
          | ( SV549 = SV922 ) )
        = $false )
      | ( ( ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV549 ) @ ( times_times_nat @ SV802 @ SV922 ) )
               != ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV922 ) @ ( times_times_nat @ SV802 @ SV549 ) ) )
              | ~ ( ( SV216 = SV802 )
                  | ( SV549 = SV922 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12811]) ).

thf(13010,plain,
    ! [SV803: nat,SV554: nat,SV224: nat] :
      ( ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV224 ) @ SV554 )
          = ( semiri1316708129612266289at_nat @ SV803 ) )
        = $false )
      | ( ( ~ ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV224 ) @ SV554 )
               != ( semiri1316708129612266289at_nat @ SV803 ) )
              | ( ( power_power_nat @ SV224 @ SV554 )
               != SV803 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12812]) ).

thf(13011,plain,
    ! [SV803: nat,SV554: nat,SV224: nat] :
      ( ( ( ( power_power_nat @ SV224 @ SV554 )
          = SV803 )
        = $false )
      | ( ( ~ ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV224 ) @ SV554 )
               != ( semiri1316708129612266289at_nat @ SV803 ) )
              | ( ( power_power_nat @ SV224 @ SV554 )
               != SV803 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12812]) ).

thf(13012,plain,
    ! [SV804: nat,SV555: nat,SV225: nat] :
      ( ( ( ( semiri1316708129612266289at_nat @ SV225 )
          = ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV555 ) @ SV804 ) )
        = $false )
      | ( ( ~ ( ( ( semiri1316708129612266289at_nat @ SV225 )
               != ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV555 ) @ SV804 ) )
              | ( SV225
               != ( power_power_nat @ SV555 @ SV804 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12813]) ).

thf(13013,plain,
    ! [SV804: nat,SV555: nat,SV225: nat] :
      ( ( ( SV225
          = ( power_power_nat @ SV555 @ SV804 ) )
        = $false )
      | ( ( ~ ( ( ( semiri1316708129612266289at_nat @ SV225 )
               != ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV555 ) @ SV804 ) )
              | ( SV225
               != ( power_power_nat @ SV555 @ SV804 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12813]) ).

thf(13014,plain,
    ! [SV805: nat,SV556: nat,SV226: num] :
      ( ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
          = ( semiri1316708129612266289at_nat @ SV805 ) )
        = $false )
      | ( ( ~ ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
               != ( semiri1316708129612266289at_nat @ SV805 ) )
              | ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
               != SV805 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12814]) ).

thf(13015,plain,
    ! [SV805: nat,SV556: nat,SV226: num] :
      ( ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
          = SV805 )
        = $false )
      | ( ( ~ ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
               != ( semiri1316708129612266289at_nat @ SV805 ) )
              | ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
               != SV805 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12814]) ).

thf(13016,plain,
    ! [SV806: nat,SV557: num,SV227: nat] :
      ( ( ( ( semiri1316708129612266289at_nat @ SV227 )
          = ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
        = $false )
      | ( ( ~ ( ( ( semiri1316708129612266289at_nat @ SV227 )
               != ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
              | ( SV227
               != ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12815]) ).

thf(13017,plain,
    ! [SV806: nat,SV557: num,SV227: nat] :
      ( ( ( SV227
          = ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
        = $false )
      | ( ( ~ ( ( ( semiri1316708129612266289at_nat @ SV227 )
               != ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
              | ( SV227
               != ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12815]) ).

thf(13018,plain,
    ! [SV561: nat,SV231: nat > real] :
      ( ( ( ~ ( summable_real
              @ ^ [SY1684: nat] : ( SV231 @ ( plus_plus_nat @ SY1684 @ SV561 ) ) )
          | ~ ( summable_real @ SV231 ) )
        = $false )
      | ( ( summable_real
          @ ^ [SY1684: nat] : ( SV231 @ ( plus_plus_nat @ SY1684 @ SV561 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12816]) ).

thf(13019,plain,
    ! [SV561: nat,SV231: nat > real] :
      ( ( ( ~ ( summable_real
              @ ^ [SY1684: nat] : ( SV231 @ ( plus_plus_nat @ SY1684 @ SV561 ) ) )
          | ~ ( summable_real @ SV231 ) )
        = $false )
      | ( ( summable_real @ SV231 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12817]) ).

thf(13020,plain,
    ! [SV562: nat,SV232: nat > complex] :
      ( ( ( ~ ( summable_complex
              @ ^ [SY1685: nat] : ( SV232 @ ( plus_plus_nat @ SY1685 @ SV562 ) ) )
          | ~ ( summable_complex @ SV232 ) )
        = $false )
      | ( ( summable_complex
          @ ^ [SY1685: nat] : ( SV232 @ ( plus_plus_nat @ SY1685 @ SV562 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12818]) ).

thf(13021,plain,
    ! [SV562: nat,SV232: nat > complex] :
      ( ( ( ~ ( summable_complex
              @ ^ [SY1685: nat] : ( SV232 @ ( plus_plus_nat @ SY1685 @ SV562 ) ) )
          | ~ ( summable_complex @ SV232 ) )
        = $false )
      | ( ( summable_complex @ SV232 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12819]) ).

thf(13022,plain,
    ! [SV243: $o] :
      ( ( ( ~ SV243
          | ~ $true )
        = $false )
      | ( SV243 = $false )
      | ( ( SV243 = $false )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12820]) ).

thf(13023,plain,
    ! [SV243: $o] :
      ( ( ( ~ SV243
          | ~ $true )
        = $false )
      | ( $true = $false )
      | ( ( SV243 = $false )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12821]) ).

thf(13024,plain,
    ! [SV243: $o] :
      ( ( SV243 = $false )
      | ( ( ~ ( ~ SV243
              | ~ $false ) )
        = $true )
      | ( ( SV243 = $true )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12822]) ).

thf(13025,plain,
    ! [SV243: $o] :
      ( ( $false = $false )
      | ( ( ~ ( ~ SV243
              | ~ $false ) )
        = $true )
      | ( ( SV243 = $true )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12822]) ).

thf(13026,plain,
    ( ( ( ~ $true
        | ~ $true )
      = $false )
    | ( $true = $false )
    | ( ( $true = $false )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12823]) ).

thf(13027,plain,
    ( ( ( ~ $true
        | ~ $true )
      = $false )
    | ( $true = $false )
    | ( ( $true = $false )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12824]) ).

thf(13028,plain,
    ( ( $true = $false )
    | ( ( ~ ( ~ $true
            | ~ $false ) )
      = $true )
    | ( ( $true = $true )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12825]) ).

thf(13029,plain,
    ( ( $false = $false )
    | ( ( ~ ( ~ $true
            | ~ $false ) )
      = $true )
    | ( ( $true = $true )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12825]) ).

thf(13030,plain,
    ( ( ( ~ $false
        | ~ $true )
      = $false )
    | ( $false = $false )
    | ( ( $false = $false )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12826]) ).

thf(13031,plain,
    ( ( ( ~ $false
        | ~ $true )
      = $false )
    | ( $true = $false )
    | ( ( $false = $false )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12827]) ).

thf(13032,plain,
    ( ( $false = $false )
    | ( ( ~ ( ~ $false
            | ~ $false ) )
      = $true )
    | ( ( $false = $true )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12828]) ).

thf(13033,plain,
    ( ( $false = $false )
    | ( ( ~ ( ~ $false
            | ~ $false ) )
      = $true )
    | ( ( $false = $true )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12828]) ).

thf(13034,plain,
    ! [SV925: nat,SV253: nat,SV579: nat,SV822: nat] :
      ( ( ( ( plus_plus_nat @ SV822 @ SV579 )
         != ( plus_plus_nat @ SV253 @ SV925 ) )
        = $true )
      | ( ( ord_less_nat @ SV822 @ SV925 )
        = $true )
      | ( ( ord_less_nat @ SV253 @ SV579 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[12831]) ).

thf(13035,plain,
    ! [SV824: nat,SV581: nat,SV255: nat] :
      ( ( ( SV255 != zero_zero_nat )
        = $true )
      | ( ( ( divide_divide_nat @ ( times_times_nat @ SV255 @ SV581 ) @ ( times_times_nat @ SV255 @ SV824 ) )
          = zero_zero_nat )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12832]) ).

thf(13036,plain,
    ! [SV824: nat,SV581: nat,SV255: nat] :
      ( ( ( ~ ( ( SV255 != zero_zero_nat ) ) )
        = $true )
      | ( ( ( divide_divide_nat @ ( times_times_nat @ SV255 @ SV581 ) @ ( times_times_nat @ SV255 @ SV824 ) )
          = ( divide_divide_nat @ SV581 @ SV824 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12833]) ).

thf(13037,plain,
    ! [SV825: nat,SV257: nat,SV583: nat] :
      ( ( ( ~ ( ( ( times_times_nat @ SV583 @ SV257 )
                = ( times_times_nat @ SV825 @ SV257 ) )
              | ( SV583 = SV825 ) )
          | ~ ( ( ( times_times_nat @ SV583 @ SV257 )
               != ( times_times_nat @ SV825 @ SV257 ) )
              | ( SV583 != SV825 ) ) )
        = $true )
      | ( ( SV257 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[12834]) ).

thf(13038,plain,
    ! [SV825: nat,SV257: nat,SV583: nat] :
      ( ( ( ( ( times_times_nat @ SV583 @ SV257 )
            = ( times_times_nat @ SV825 @ SV257 ) )
          = ( SV583 = SV825 ) )
        = $true )
      | ( ( SV257 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[12834]) ).

thf(13039,plain,
    ! [SV584: nat,SV826: nat,SV258: nat] :
      ( ( ( ! [SY1935: nat] :
              ( ( SV258
               != ( times_times_nat @ ( sK13_SY1869 @ SV826 @ SV584 @ SV258 ) @ SY1935 ) )
              | ~ ( dvd_dvd_nat @ ( sK13_SY1869 @ SV826 @ SV584 @ SV258 ) @ SV584 )
              | ~ ( dvd_dvd_nat @ SY1935 @ SV826 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV258 @ ( times_times_nat @ SV584 @ SV826 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[12835]) ).

thf(13040,plain,
    ! [SV926: nat,SV827: nat,SV586: nat,SV260: nat] :
      ( ( ( ( SV260 != SV586 )
          | ( SV827 != SV926 ) )
        = $true )
      | ( ( ( plus_plus_nat @ SV260 @ SV827 )
          = ( plus_plus_nat @ SV586 @ SV926 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12837]) ).

thf(13041,plain,
    ! [SV587: nat,SV828: nat,SV261: nat] :
      ( ( ( dvd_dvd_nat @ SV261 @ SV828 )
        = $false )
      | ( ( ( divide_divide_nat @ ( plus_plus_nat @ SV587 @ SV828 ) @ SV261 )
          = ( plus_plus_nat @ ( divide_divide_nat @ SV587 @ SV261 ) @ ( divide_divide_nat @ SV828 @ SV261 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV261 @ SV587 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12838]) ).

thf(13042,plain,
    ! [SV262: nat,SV829: nat,SV588: nat] :
      ( ( ( dvd_dvd_nat @ SV588 @ SV829 )
        = $false )
      | ( ( ( divide_divide_nat @ ( divide_divide_nat @ SV829 @ SV262 ) @ ( divide_divide_nat @ SV588 @ SV262 ) )
          = ( divide_divide_nat @ SV829 @ SV588 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV262 @ SV588 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12839]) ).

thf(13043,plain,
    ! [SV593: nat,SV833: nat,SV268: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV268 @ SV833 ) )
        = $false )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV268 @ SV593 ) @ SV833 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12842]) ).

thf(13044,plain,
    ! [SV268: nat,SV833: nat,SV593: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV593 @ SV833 ) )
        = $false )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV268 @ SV593 ) @ SV833 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12842]) ).

thf(13045,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( SV595 = SV928 )
          | ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
               != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
              | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
               != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
        = $false )
      | ( ( ~ ( ( SV595 != SV928 )
              | ~ ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                     != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
                    | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                     != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12844]) ).

thf(13046,plain,
    ! [SV596: nat,SV272: nat,SV929: nat,SV836: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV836 @ SV929 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( times_times_nat @ SV272 @ SV836 ) @ ( times_times_nat @ SV596 @ SV929 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV272 @ SV596 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[12845]) ).

thf(13047,plain,
    ! [SV837: nat,SV597: nat,SV273: nat] :
      ( ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
          = ( modulo_modulo_nat @ SV837 @ SV597 ) )
        = $false )
      | ( ( ~ ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
               != ( modulo_modulo_nat @ SV837 @ SV597 ) )
              | ~ ~ ! [SY1874: nat] :
                      ~ ~ ! [SY1875: nat] :
                            ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SY1874 ) )
                           != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1875 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12846]) ).

thf(13048,plain,
    ! [SV837: nat,SV597: nat,SV273: nat] :
      ( ( ( ~ ! [SY1874: nat] :
                ~ ~ ! [SY1875: nat] :
                      ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SY1874 ) )
                     != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1875 ) ) ) )
        = $false )
      | ( ( ~ ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
               != ( modulo_modulo_nat @ SV837 @ SV597 ) )
              | ~ ~ ! [SY1874: nat] :
                      ~ ~ ! [SY1875: nat] :
                            ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SY1874 ) )
                           != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1875 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12846]) ).

thf(13049,plain,
    ! [SV601: nat,SV280: nat] :
      ( ( ( ~ ( ( SV280 != zero_zero_nat ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV280 @ SV601 )
          = zero_zero_nat )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12849]) ).

thf(13050,plain,
    ! [SV280: nat,SV601: nat] :
      ( ( ( ~ ( ( SV601 != zero_zero_nat ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV280 @ SV601 )
          = zero_zero_nat )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12849]) ).

thf(13051,plain,
    ! [SV931: nat,SV844: nat,SV605: nat,SV284: nat] :
      ( ( ( ~ ( ~ ( ( SV284 != SV605 ) )
              | ~ ( ( SV844 != SV931 ) ) )
          | ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
           != ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) ) )
        = $false )
      | ( ( ~ ( ~ ~ ( ~ ( ( SV284 != SV605 ) )
                    | ~ ( ( SV844 != SV931 ) ) )
              | ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
                   != ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12851]) ).

thf(13052,plain,
    ! [SV845: nat,SV606: nat,SV285: nat] :
      ( ( ( ~ ( ( ( times_times_nat @ SV285 @ SV606 )
                = ( times_times_nat @ SV285 @ SV845 ) )
              | ( SV606 = SV845 ) )
          | ~ ( ( ( times_times_nat @ SV285 @ SV606 )
               != ( times_times_nat @ SV285 @ SV845 ) )
              | ( SV606 != SV845 ) ) )
        = $true )
      | ( ( SV285 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[12852]) ).

thf(13053,plain,
    ! [SV845: nat,SV606: nat,SV285: nat] :
      ( ( ( ( ( times_times_nat @ SV285 @ SV606 )
            = ( times_times_nat @ SV285 @ SV845 ) )
          = ( SV606 = SV845 ) )
        = $true )
      | ( ( SV285 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[12852]) ).

thf(13054,plain,
    ! [SV287: nat,SV608: nat] :
      ( ( ( SV608 != zero_zero_nat )
        = $false )
      | ( ( ( times_times_nat @ SV287 @ SV608 )
         != zero_zero_nat )
        = $true )
      | ( ( SV287 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12853]) ).

thf(13055,plain,
    ! [SV609: nat,SV288: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV288 )
              | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV609 ) )
          | ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV288 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV609 ) ) )
        = $false )
      | ( ( SV288 = SV609 )
        = $true )
      | ( ( ( divide_divide_nat @ SV288 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV609 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_equal_neg,[status(thm)],[12854]) ).

thf(13056,plain,
    ! [SV609: nat,SV288: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV288 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV609 ) )
        = $false )
      | ( ( SV288 = SV609 )
        = $true )
      | ( ( ( divide_divide_nat @ SV288 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV609 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_equal_neg,[status(thm)],[12854]) ).

thf(13057,plain,
    ! [SV932: nat,SV848: nat,SV611: nat,SV290: nat] :
      ( ( ( ~ ( ord_less_nat @ SV290 @ SV611 )
          | ~ ( ord_less_nat @ SV848 @ SV932 ) )
        = $true )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV290 @ SV848 ) @ ( plus_plus_nat @ SV611 @ SV932 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12855]) ).

thf(13058,plain,
    ! [SV933: nat,SV849: nat,SV615: nat,SV294: nat] :
      ( ( ( ( SV294 != SV615 )
          | ~ ( ord_less_nat @ SV849 @ SV933 ) )
        = $true )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV294 @ SV849 ) @ ( plus_plus_nat @ SV615 @ SV933 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12856]) ).

thf(13059,plain,
    ! [SV617: nat,SV296: nat,SV934: nat,SV850: nat] :
      ( ( ( ~ ( ord_less_nat @ SV850 @ SV934 ) )
        = $true )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV296 @ SV850 ) @ ( plus_plus_nat @ SV617 @ SV934 ) )
        = $true )
      | ( ( ord_less_nat @ SV296 @ SV617 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[12857]) ).

thf(13060,plain,
    ! [SV297: nat,SV618: nat,SV935: nat,SV851: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV851 @ SV935 ) )
        = $true )
      | ( ( ( times_times_nat @ ( divide_divide_nat @ SV618 @ SV297 ) @ ( divide_divide_nat @ SV935 @ SV851 ) )
          = ( divide_divide_nat @ ( times_times_nat @ SV618 @ SV935 ) @ ( times_times_nat @ SV297 @ SV851 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV297 @ SV618 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[12858]) ).

thf(13061,plain,
    ! [SV298: nat,SV619: nat] :
      ( ( ( SV619
          = ( plus_plus_nat @ SV298 @ ( sK9_SY1748 @ SV298 @ SV619 ) ) )
        = $true )
      | ( ( ord_less_eq_nat @ SV298 @ SV619 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[12859]) ).

thf(13062,plain,
    ! [SV621: nat,SV300: nat] :
      ( ( ( ( ( times_times_nat @ SV300 @ SV621 )
           != one_one_nat )
          | ~ ~ ( ( SV300 != one_one_nat )
                | ( SV621 != one_one_nat ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV300 @ SV621 )
          = one_one_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12860]) ).

thf(13063,plain,
    ! [SV621: nat,SV300: nat] :
      ( ( ( ( SV300 != one_one_nat )
          | ( SV621 != one_one_nat ) )
        = $true )
      | ( ( ~ ( ( ( times_times_nat @ SV300 @ SV621 )
               != one_one_nat )
              | ~ ~ ( ( SV300 != one_one_nat )
                    | ( SV621 != one_one_nat ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12861]) ).

thf(13064,plain,
    ! [SV936: nat,SV622: nat] :
      ( ( ( ( dvd_dvd_nat @ SV622 @ SV936 )
          | ~ ! [SY1919: nat] :
                ( SV936
               != ( times_times_nat @ SV622 @ SY1919 ) ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ SV622 @ SV936 )
              | ~ ~ ! [SY1919: nat] :
                      ( SV936
                     != ( times_times_nat @ SV622 @ SY1919 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12862]) ).

thf(13065,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
        = $true )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
              | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
                   != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12863]) ).

thf(13066,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
              | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
                   != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12864]) ).

thf(13067,plain,
    ! [SV626: nat,SV305: nat] :
      ( ( ( ( ( plus_plus_nat @ SV305 @ SV626 )
           != zero_zero_nat )
          | ~ ~ ( ( SV305 != zero_zero_nat )
                | ( SV626 != zero_zero_nat ) ) )
        = $false )
      | ( ( ( plus_plus_nat @ SV305 @ SV626 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12865]) ).

thf(13068,plain,
    ! [SV626: nat,SV305: nat] :
      ( ( ( ( SV305 != zero_zero_nat )
          | ( SV626 != zero_zero_nat ) )
        = $true )
      | ( ( ~ ( ( ( plus_plus_nat @ SV305 @ SV626 )
               != zero_zero_nat )
              | ~ ~ ( ( SV305 != zero_zero_nat )
                    | ( SV626 != zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12866]) ).

thf(13069,plain,
    ! [SV309: nat,SV629: nat] :
      ( ( ( SV629
          = ( plus_plus_nat @ SV309 @ ( sK10_SY1755 @ SV309 @ SV629 ) ) )
        = $true )
      | ( ( ord_less_eq_nat @ SV309 @ SV629 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[12867]) ).

thf(13070,plain,
    ! [SV630: nat,SV310: nat] :
      ( ( ( ( ( plus_plus_nat @ SV310 @ SV630 )
           != zero_zero_nat )
          | ~ ~ ( ( SV310 != zero_zero_nat )
                | ( SV630 != zero_zero_nat ) ) )
        = $false )
      | ( ( ( plus_plus_nat @ SV310 @ SV630 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12868]) ).

thf(13071,plain,
    ! [SV630: nat,SV310: nat] :
      ( ( ( ( SV310 != zero_zero_nat )
          | ( SV630 != zero_zero_nat ) )
        = $true )
      | ( ( ~ ( ( ( plus_plus_nat @ SV310 @ SV630 )
               != zero_zero_nat )
              | ~ ~ ( ( SV310 != zero_zero_nat )
                    | ( SV630 != zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12869]) ).

thf(13072,plain,
    ! [SV631: nat,SV856: nat,SV311: nat] :
      ( ( ( ~ ~ ! [SY1936: nat] :
                  ~ ~ ( ~ ~ ( ( SV311
                             != ( times_times_nat @ ( sK14_SY1883 @ SV856 @ SV631 @ SV311 ) @ SY1936 ) )
                            | ~ ( dvd_dvd_nat @ ( sK14_SY1883 @ SV856 @ SV631 @ SV311 ) @ SV631 ) )
                      | ~ ( dvd_dvd_nat @ SY1936 @ SV856 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV311 @ ( times_times_nat @ SV631 @ SV856 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[12870]) ).

thf(13073,plain,
    ! [SV956: nat,SV937: nat,SV857: nat,SV632: nat,SV312: nat] :
      ( ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false )
      | ( ( ~ ( dvd_dvd_nat @ SV312 @ SV857 )
          | ~ ( ( ( times_times_nat @ SV632 @ SV937 )
                = ( plus_plus_nat @ ( times_times_nat @ SV857 @ SV956 ) @ SV312 ) )
              | ( ( times_times_nat @ SV857 @ SV937 )
                = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SV956 ) @ SV312 ) ) )
          | ~ ! [SY1887: nat] :
                ~ ~ ! [SY1888: nat] :
                      ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
                                | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) )
                          | ~ ( ( ( times_times_nat @ SV632 @ SY1887 )
                                = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1888 ) @ SV312 ) )
                              | ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1887 )
                                = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SY1888 ) @ SV312 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12871]) ).

thf(13074,plain,
    ! [SV314: nat,SV859: nat,SV634: nat] :
      ( ( ( dvd_dvd_nat @ SV634 @ SV859 )
        = $false )
      | ( ( ( divide_divide_nat @ SV859 @ ( divide_divide_nat @ SV634 @ SV314 ) )
          = ( times_times_nat @ ( divide_divide_nat @ SV859 @ SV634 ) @ SV314 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV314 @ SV634 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12872]) ).

thf(13075,plain,
    ! [SV636: num,SV316: num > $o] :
      ( ( ( ~ ( SV316 @ ( sK15_SY1414 @ SV636 @ SV316 ) )
          | ( SV316 @ ( inc @ ( sK15_SY1414 @ SV636 @ SV316 ) ) ) )
        = $false )
      | ( ( SV316 @ SV636 )
        = $true )
      | ( ( SV316 @ one )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[12873]) ).

thf(13076,plain,
    ! [SV639: nat,SV860: nat,SV319: nat > nat > $o] :
      ( ( ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
          = ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) ) )
        = $false )
      | ( ( ~ ! [SY1421: nat] : ( SV319 @ SY1421 @ zero_zero_nat )
          | ~ ! [SY1422: nat,SY1423: nat] :
                ( ~ ( SV319 @ SY1422 @ SY1423 )
                | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) )
          | ( SV319 @ SV639 @ SV860 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[12875]) ).

thf(13077,plain,
    ! [SV642: nat,SV322: nat] :
      ( ( ( ~ ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 )
          | ~ ~ ( ~ ( ( SV322 != SV642 ) )
                | ~ ( vEBT_V8194947554948674370ptions @ summary @ SV642 ) ) )
        = $false )
      | ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12876]) ).

thf(13078,plain,
    ! [SV642: nat,SV322: nat] :
      ( ( ( ~ ( ( SV322 != SV642 ) )
          | ~ ( vEBT_V8194947554948674370ptions @ summary @ SV642 ) )
        = $true )
      | ( ( ~ ( ~ ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 )
              | ~ ~ ( ~ ( ( SV322 != SV642 ) )
                    | ~ ( vEBT_V8194947554948674370ptions @ summary @ SV642 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12877]) ).

thf(13079,plain,
    ! [SV957: nat,SV938: nat,SV862: nat,SV643: nat,SV323: nat] :
      ( ( ( ( modulo_modulo_nat @ SV323 @ SV643 )
          = ( modulo_modulo_nat @ SV862 @ SV643 ) )
        = $false )
      | ( ( ( ( modulo_modulo_nat @ SV938 @ SV643 )
           != ( modulo_modulo_nat @ SV957 @ SV643 ) )
          | ( ( modulo_modulo_nat @ ( times_times_nat @ SV323 @ SV938 ) @ SV643 )
            = ( modulo_modulo_nat @ ( times_times_nat @ SV862 @ SV957 ) @ SV643 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12878]) ).

thf(13080,plain,
    ! [SV939: nat,SV644: nat] :
      ( ( ( ( ord_less_eq_nat @ SV644 @ SV939 )
          | ~ ! [SY1924: nat] :
                ( SV939
               != ( plus_plus_nat @ SV644 @ SY1924 ) ) )
        = $false )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ SV644 @ SV939 )
              | ~ ~ ! [SY1924: nat] :
                      ( SV939
                     != ( plus_plus_nat @ SV644 @ SY1924 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12879]) ).

thf(13081,plain,
    ! [SV940: nat,SV867: nat,SV648: nat,SV328: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV328 @ SV648 )
          | ( SV867 != SV940 ) )
        = $true )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV328 @ SV867 ) @ ( plus_plus_nat @ SV648 @ SV940 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12880]) ).

thf(13082,plain,
    ! [SV649: nat,SV329: nat] :
      ( ( ( ( zero_zero_nat
           != ( plus_plus_nat @ SV329 @ SV649 ) )
          | ~ ~ ( ( SV329 != zero_zero_nat )
                | ( SV649 != zero_zero_nat ) ) )
        = $false )
      | ( ( zero_zero_nat
          = ( plus_plus_nat @ SV329 @ SV649 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12881]) ).

thf(13083,plain,
    ! [SV649: nat,SV329: nat] :
      ( ( ( ( SV329 != zero_zero_nat )
          | ( SV649 != zero_zero_nat ) )
        = $true )
      | ( ( ~ ( ( zero_zero_nat
               != ( plus_plus_nat @ SV329 @ SV649 ) )
              | ~ ~ ( ( SV329 != zero_zero_nat )
                    | ( SV649 != zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12882]) ).

thf(13084,plain,
    ! [SV958: vEBT_VEBT,SV941: vEBT_VEBT,SV869: list_VEBT_VEBT,SV652: nat,SV332: nat] :
      ( ( ( SV332 != SV652 )
        = $false )
      | ( ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV869 @ SV332 @ SV941 ) @ SV652 @ SV958 )
          = ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV869 @ SV652 @ SV958 ) @ SV332 @ SV941 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12884]) ).

thf(13085,plain,
    ! [SV942: nat,SV871: nat,SV657: nat,SV335: nat] :
      ( ( ( ( SV335 != SV657 )
          | ~ ( ord_less_eq_nat @ SV871 @ SV942 ) )
        = $true )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV335 @ SV871 ) @ ( plus_plus_nat @ SV657 @ SV942 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12885]) ).

thf(13086,plain,
    ! [SV658: nat,SV872: nat,SV336: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ SV336 @ ( plus_plus_nat @ SV872 @ SV658 ) )
              | ( dvd_dvd_nat @ SV336 @ SV872 ) ) )
        = $true )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ SV336 @ ( plus_plus_nat @ SV872 @ SV658 ) )
              | ~ ( dvd_dvd_nat @ SV336 @ SV872 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV336 @ SV658 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[12886]) ).

thf(13087,plain,
    ! [SV660: nat,SV874: nat,SV338: nat] :
      ( ( ( dvd_dvd_nat @ SV338 @ SV874 )
        = $false )
      | ( ( dvd_dvd_nat @ SV338 @ ( plus_plus_nat @ SV660 @ SV874 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV338 @ SV660 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12888]) ).

thf(13088,plain,
    ! [SV340: nat] :
      ( ( ( SV340
         != ( plus_plus_nat @ ( sK17_SY1466 @ SV340 ) @ ( suc @ ( sK17_SY1466 @ SV340 ) ) ) )
        = $false )
      | ( ( SV340
          = ( plus_plus_nat @ ( sK5_SY1465 @ SV340 ) @ ( sK5_SY1465 @ SV340 ) ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[12889]) ).

thf(13089,plain,
    ! [SV943: nat,SV876: nat,SV662: nat,SV341: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV341 @ SV662 )
          | ~ ( ord_less_eq_nat @ SV876 @ SV943 ) )
        = $true )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV341 @ SV876 ) @ ( plus_plus_nat @ SV662 @ SV943 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12890]) ).

thf(13090,plain,
    ! [SV668: nat,SV882: nat,SV347: nat] :
      ( ( ( dvd_dvd_nat @ SV347 @ SV882 )
        = $false )
      | ( ( ( dvd_dvd_nat @ ( divide_divide_nat @ SV668 @ SV347 ) @ ( divide_divide_nat @ SV882 @ SV347 ) )
          = ( dvd_dvd_nat @ SV668 @ SV882 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV347 @ SV668 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12892]) ).

thf(13091,plain,
    ! [SV349: nat,SV669: nat] :
      ( ( ~ ~ ! [SY1937: nat] :
                ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ ( sK6_SY1803 @ SV669 @ SV349 ) @ SV349 )
                          | ~ ( dvd_dvd_nat @ ( sK6_SY1803 @ SV669 @ SV349 ) @ SV669 ) )
                    | ~ ( ( ( times_times_nat @ SV349 @ ( sK18_SY1926 @ SV349 @ SV669 ) )
                          = ( plus_plus_nat @ ( times_times_nat @ SV669 @ SY1937 ) @ ( sK6_SY1803 @ SV669 @ SV349 ) ) )
                        | ( ( times_times_nat @ SV669 @ ( sK18_SY1926 @ SV349 @ SV669 ) )
                          = ( plus_plus_nat @ ( times_times_nat @ SV349 @ SY1937 ) @ ( sK6_SY1803 @ SV669 @ SV349 ) ) ) ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[12893]) ).

thf(13092,plain,
    ! [SV671: nat,SV351: nat] :
      ( ( ( ( one_one_nat
           != ( times_times_nat @ SV351 @ SV671 ) )
          | ~ ~ ( ( SV351 != one_one_nat )
                | ( SV671 != one_one_nat ) ) )
        = $false )
      | ( ( one_one_nat
          = ( times_times_nat @ SV351 @ SV671 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12894]) ).

thf(13093,plain,
    ! [SV671: nat,SV351: nat] :
      ( ( ( ( SV351 != one_one_nat )
          | ( SV671 != one_one_nat ) )
        = $true )
      | ( ( ~ ( ( one_one_nat
               != ( times_times_nat @ SV351 @ SV671 ) )
              | ~ ~ ( ( SV351 != one_one_nat )
                    | ( SV671 != one_one_nat ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12895]) ).

thf(13094,plain,
    ! [SV672: nat,SV352: nat,SV944: nat,SV883: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV883 @ SV944 ) )
        = $true )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV352 @ SV883 ) @ ( plus_plus_nat @ SV672 @ SV944 ) )
        = $true )
      | ( ( ord_less_eq_nat @ SV352 @ SV672 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[12896]) ).

thf(13095,plain,
    ! [SV959: nat,SV945: nat,SV884: nat,SV673: nat,SV353: nat] :
      ( ( ( SV353 != zero_zero_nat )
        = $false )
      | ( ( ~ ~ ( ( SV673 != SV884 )
                | ~ ( ( SV945 != SV959 ) ) )
          | ( ( plus_plus_nat @ SV673 @ ( times_times_nat @ SV353 @ SV945 ) )
           != ( plus_plus_nat @ SV884 @ ( times_times_nat @ SV353 @ SV959 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12897]) ).

thf(13096,plain,
    ! [SV885: nat,SV674: nat,SV354: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ SV354 @ ( plus_plus_nat @ SV674 @ SV885 ) )
              | ( dvd_dvd_nat @ SV354 @ SV885 ) ) )
        = $true )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ SV354 @ ( plus_plus_nat @ SV674 @ SV885 ) )
              | ~ ( dvd_dvd_nat @ SV354 @ SV885 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV354 @ SV674 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[12898]) ).

thf(13097,plain,
    ! [SV886: nat,SV676: nat,SV356: nat] :
      ( ( ( SV356 != zero_zero_nat )
        = $true )
      | ( ( ( divide_divide_nat @ ( times_times_nat @ SV356 @ SV676 ) @ ( times_times_nat @ SV356 @ SV886 ) )
          = zero_zero_nat )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12901]) ).

thf(13098,plain,
    ! [SV886: nat,SV676: nat,SV356: nat] :
      ( ( ( ~ ( ( SV356 != zero_zero_nat ) ) )
        = $true )
      | ( ( ( divide_divide_nat @ ( times_times_nat @ SV356 @ SV676 ) @ ( times_times_nat @ SV356 @ SV886 ) )
          = ( divide_divide_nat @ SV676 @ SV886 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[12902]) ).

thf(13099,plain,
    ! [SV359: nat,SV678: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV678 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV359 @ SV678 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV359 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12903]) ).

thf(13100,plain,
    ! [SV888: nat,SV361: nat,SV680: nat] :
      ( ( ( dvd_dvd_nat @ SV680 @ SV361 )
        = $false )
      | ( ( ~ ( dvd_dvd_nat @ SV680 @ SV888 )
          | ( SV361 = SV888 ) )
        = $true )
      | ( ( ( divide_divide_nat @ SV361 @ SV680 )
          = ( divide_divide_nat @ SV888 @ SV680 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12904]) ).

thf(13101,plain,
    ! [SV681: nat,SV889: nat,SV362: nat] :
      ( ( ( dvd_dvd_nat @ SV362 @ SV889 )
        = $false )
      | ( ( ( ( divide_divide_nat @ SV681 @ SV362 )
            = ( divide_divide_nat @ SV889 @ SV362 ) )
          = ( SV681 = SV889 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV362 @ SV681 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12905]) ).

thf(13102,plain,
    ! [SV363: nat,SV682: nat] :
      ( ( ( SV682
          = ( times_times_nat @ SV363 @ ( sK12_SY1817 @ SV363 @ SV682 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV363 @ SV682 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[12906]) ).

thf(13103,plain,
    ! [SV683: nat,SV364: nat,SV946: nat,SV890: nat] :
      ( ( ( ~ ( ord_less_nat @ SV890 @ SV946 ) )
        = $true )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV364 @ SV890 ) @ ( plus_plus_nat @ SV683 @ SV946 ) )
        = $true )
      | ( ( ord_less_nat @ SV364 @ SV683 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[12907]) ).

thf(13104,plain,
    ! [SV684: nat,SV365: nat,SV947: nat,SV891: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV891 @ SV947 ) )
        = $true )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV365 @ SV891 ) @ ( plus_plus_nat @ SV684 @ SV947 ) )
        = $true )
      | ( ( ord_less_eq_nat @ SV365 @ SV684 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[12908]) ).

thf(13105,plain,
    ! [SV692: option_nat,SV373: option_nat] :
      ( ( ( ( SV373 = none_nat )
          | ( SV692 = none_nat ) )
        = $true )
      | ( ( ~ ( ~ ( ( SV373 != none_nat ) )
              | ~ ( ( SV692 != none_nat ) )
              | ( ( the_nat @ SV373 )
                = ( the_nat @ SV692 ) ) )
          | ( SV373 = SV692 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12909]) ).

thf(13106,plain,
    ! [SV692: option_nat,SV373: option_nat] :
      ( ( ( ( SV373 != none_nat )
          | ( SV692 != none_nat ) )
        = $true )
      | ( ( ~ ( ~ ( ( SV373 != none_nat ) )
              | ~ ( ( SV692 != none_nat ) )
              | ( ( the_nat @ SV373 )
                = ( the_nat @ SV692 ) ) )
          | ( SV373 = SV692 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12910]) ).

thf(13107,plain,
    ! [SV692: option_nat,SV373: option_nat] :
      ( ( ( ~ ( ( SV373 != none_nat ) )
          | ~ ( ( SV692 != none_nat ) )
          | ( ( the_nat @ SV373 )
            = ( the_nat @ SV692 ) ) )
        = $false )
      | ( ( SV373 = SV692 )
        = $true )
      | ( ( ( SV373 = none_nat )
          = ( SV692 = none_nat ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12911]) ).

thf(13108,plain,
    ! [SV374: nat > $o,SV693: nat] :
      ( ( ( ( divide_divide_nat @ ( sK8_SY1533 @ SV693 @ SV374 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( sK8_SY1533 @ SV693 @ SV374 ) )
        = $true )
      | ( ( ~ ! [SY1534: nat,SY1535: $o] :
                ( ~ ( SV374 @ SY1534 )
                | ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ SY1535 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1534 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                 != SY1534 )
                | ( SV374 @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ SY1535 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1534 ) ) ) )
          | ( SV374 @ SV693 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12912]) ).

thf(13109,plain,
    ! [SV693: nat,SV374: nat > $o] :
      ( ( ( ~ ! [SY1534: nat,SY1535: $o] :
                ( ~ ( SV374 @ SY1534 )
                | ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ SY1535 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1534 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                 != SY1534 )
                | ( SV374 @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ SY1535 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1534 ) ) ) ) )
        = $true )
      | ( ( SV374 @ SV693 )
        = $true )
      | ( ( SV374 @ ( sK8_SY1533 @ SV693 @ SV374 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[12913]) ).

thf(13110,plain,
    ! [SV948: nat,SV694: nat] :
      ( ( ( ( ord_less_eq_nat @ SV694 @ SV948 )
          | ~ ! [SY1929: nat] :
                ( SV948
               != ( plus_plus_nat @ SV694 @ SY1929 ) ) )
        = $false )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ SV694 @ SV948 )
              | ~ ~ ! [SY1929: nat] :
                      ( SV948
                     != ( plus_plus_nat @ SV694 @ SY1929 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12914]) ).

thf(13111,plain,
    ! [SV697: nat,SV378: nat,SV949: nat,SV901: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV901 @ SV949 ) )
        = $true )
      | ( ( ord_less_eq_nat @ ( times_times_nat @ SV378 @ SV901 ) @ ( times_times_nat @ SV697 @ SV949 ) )
        = $true )
      | ( ( ord_less_eq_nat @ SV378 @ SV697 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[12915]) ).

thf(13112,plain,
    ! [SV950: nat,SV902: nat,SV698: nat,SV379: nat] :
      ( ( ( ~ ( ord_less_nat @ SV379 @ SV698 )
          | ( SV902 != SV950 ) )
        = $true )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV379 @ SV902 ) @ ( plus_plus_nat @ SV698 @ SV950 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12916]) ).

thf(13113,plain,
    ! [SV382: num] :
      ( ( ( SV382
         != ( bit0 @ ( sK19_SY1550 @ SV382 ) ) )
        = $false )
      | ( ( ~ ! [SY1551: num] :
                ( SV382
               != ( bit1 @ SY1551 ) ) )
        = $true )
      | ( ( SV382 = one )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[12917]) ).

thf(13114,plain,
    ! [SV951: vEBT_VEBT,SV904: list_VEBT_VEBT,SV701: nat,SV383: nat] :
      ( ( ( SV383 = SV701 )
        = $true )
      | ( ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ SV904 @ SV383 @ SV951 ) @ SV701 )
          = ( nth_VEBT_VEBT @ SV904 @ SV701 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[12918]) ).

thf(13115,plain,
    ! [SV960: nat,SV952: nat,SV905: nat,SV702: nat,SV384: nat] :
      ( ( ( ( modulo_modulo_nat @ SV384 @ SV702 )
          = ( modulo_modulo_nat @ SV905 @ SV702 ) )
        = $false )
      | ( ( ( ( modulo_modulo_nat @ SV952 @ SV702 )
           != ( modulo_modulo_nat @ SV960 @ SV702 ) )
          | ( ( modulo_modulo_nat @ ( plus_plus_nat @ SV384 @ SV952 ) @ SV702 )
            = ( modulo_modulo_nat @ ( plus_plus_nat @ SV905 @ SV960 ) @ SV702 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[12919]) ).

thf(13116,plain,
    ! [SV705: nat,SV388: nat > nat,SV953: nat,SV908: nat > nat] :
      ( ( ( ~ ( sums_nat @ SV908 @ SV953 ) )
        = $true )
      | ( ( sums_nat
          @ ^ [SY1914: nat] : ( plus_plus_nat @ ( SV388 @ SY1914 ) @ ( SV908 @ SY1914 ) )
          @ ( plus_plus_nat @ SV705 @ SV953 ) )
        = $true )
      | ( ( sums_nat @ SV388 @ SV705 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[12920]) ).

thf(13117,plain,
    ! [SV399: num,SV10: num] :
      ( ( ( ( numeral_numeral_nat @ SV10 )
         != ( numeral_numeral_nat @ SV399 ) )
        = $false )
      | ( ( ( numeral_numeral_nat @ SV10 )
          = ( numeral_numeral_nat @ SV399 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12921]) ).

thf(13118,plain,
    ! [SV399: num,SV10: num] :
      ( ( ( SV10 != SV399 )
        = $false )
      | ( ( ( numeral_numeral_nat @ SV10 )
          = ( numeral_numeral_nat @ SV399 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12921]) ).

thf(13119,plain,
    ! [SV399: num,SV10: num] :
      ( ( ( ( numeral_numeral_nat @ SV10 )
         != ( numeral_numeral_nat @ SV399 ) )
        = $false )
      | ( ( SV10 = SV399 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12922]) ).

thf(13120,plain,
    ! [SV399: num,SV10: num] :
      ( ( ( SV10 != SV399 )
        = $false )
      | ( ( SV10 = SV399 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12922]) ).

thf(13121,plain,
    ! [SV427: nat,SV49: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV49 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ SV427 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
        = $false )
      | ( ( ord_less_eq_nat @ ( power_power_nat @ SV49 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ SV427 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12923]) ).

thf(13122,plain,
    ! [SV427: nat,SV49: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV49 @ SV427 ) )
        = $false )
      | ( ( ord_less_eq_nat @ ( power_power_nat @ SV49 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ SV427 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12923]) ).

thf(13123,plain,
    ! [SV427: nat,SV49: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ ( power_power_nat @ SV49 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ SV427 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
        = $false )
      | ( ( ord_less_eq_nat @ SV49 @ SV427 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12924]) ).

thf(13124,plain,
    ! [SV427: nat,SV49: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV49 @ SV427 ) )
        = $false )
      | ( ( ord_less_eq_nat @ SV49 @ SV427 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12924]) ).

thf(13125,plain,
    ! [SV428: num,SV53: num] :
      ( ( ( ~ ( ord_less_num @ ( bit0 @ SV53 ) @ ( bit0 @ SV428 ) ) )
        = $false )
      | ( ( ord_less_num @ ( bit0 @ SV53 ) @ ( bit0 @ SV428 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12925]) ).

thf(13126,plain,
    ! [SV428: num,SV53: num] :
      ( ( ( ~ ( ord_less_num @ SV53 @ SV428 ) )
        = $false )
      | ( ( ord_less_num @ ( bit0 @ SV53 ) @ ( bit0 @ SV428 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12925]) ).

thf(13127,plain,
    ! [SV428: num,SV53: num] :
      ( ( ( ~ ( ord_less_num @ ( bit0 @ SV53 ) @ ( bit0 @ SV428 ) ) )
        = $false )
      | ( ( ord_less_num @ SV53 @ SV428 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12926]) ).

thf(13128,plain,
    ! [SV428: num,SV53: num] :
      ( ( ( ~ ( ord_less_num @ SV53 @ SV428 ) )
        = $false )
      | ( ( ord_less_num @ SV53 @ SV428 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12926]) ).

thf(13129,plain,
    ! [SV429: num,SV54: num] :
      ( ( ( ( bit0 @ SV54 )
         != ( bit0 @ SV429 ) )
        = $false )
      | ( ( ( bit0 @ SV54 )
          = ( bit0 @ SV429 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12927]) ).

thf(13130,plain,
    ! [SV429: num,SV54: num] :
      ( ( ( SV54 != SV429 )
        = $false )
      | ( ( ( bit0 @ SV54 )
          = ( bit0 @ SV429 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12927]) ).

thf(13131,plain,
    ! [SV429: num,SV54: num] :
      ( ( ( ( bit0 @ SV54 )
         != ( bit0 @ SV429 ) )
        = $false )
      | ( ( SV54 = SV429 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12928]) ).

thf(13132,plain,
    ! [SV429: num,SV54: num] :
      ( ( ( SV54 != SV429 )
        = $false )
      | ( ( SV54 = SV429 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12928]) ).

thf(13133,plain,
    ! [SV432: num,SV62: num] :
      ( ( ( ~ ( ord_less_eq_num @ ( bit0 @ SV62 ) @ ( bit0 @ SV432 ) ) )
        = $false )
      | ( ( ord_less_eq_num @ ( bit0 @ SV62 ) @ ( bit0 @ SV432 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12929]) ).

thf(13134,plain,
    ! [SV432: num,SV62: num] :
      ( ( ( ~ ( ord_less_eq_num @ SV62 @ SV432 ) )
        = $false )
      | ( ( ord_less_eq_num @ ( bit0 @ SV62 ) @ ( bit0 @ SV432 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12929]) ).

thf(13135,plain,
    ! [SV432: num,SV62: num] :
      ( ( ( ~ ( ord_less_eq_num @ ( bit0 @ SV62 ) @ ( bit0 @ SV432 ) ) )
        = $false )
      | ( ( ord_less_eq_num @ SV62 @ SV432 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12930]) ).

thf(13136,plain,
    ! [SV432: num,SV62: num] :
      ( ( ( ~ ( ord_less_eq_num @ SV62 @ SV432 ) )
        = $false )
      | ( ( ord_less_eq_num @ SV62 @ SV432 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12930]) ).

thf(13137,plain,
    ! [SV64: num] :
      ( ( ( one_one_nat
          = ( numeral_numeral_nat @ SV64 ) )
        = $true )
      | ( ( one_one_nat
          = ( numeral_numeral_nat @ SV64 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[12931]) ).

thf(13138,plain,
    ! [SV64: num] :
      ( ( ( one = SV64 )
        = $true )
      | ( ( one_one_nat
          = ( numeral_numeral_nat @ SV64 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[12932]) ).

thf(13139,plain,
    ! [SV64: num] :
      ( ( ( one_one_nat
          = ( numeral_numeral_nat @ SV64 ) )
        = $true )
      | ( ( one = SV64 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[12933]) ).

thf(13140,plain,
    ! [SV64: num] :
      ( ( ( one = SV64 )
        = $true )
      | ( ( one = SV64 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[12934]) ).

thf(13141,plain,
    ! [SV65: num] :
      ( ( ( ( numeral_numeral_nat @ SV65 )
          = one_one_nat )
        = $true )
      | ( ( ( numeral_numeral_nat @ SV65 )
          = one_one_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[12935]) ).

thf(13142,plain,
    ! [SV65: num] :
      ( ( ( SV65 = one )
        = $true )
      | ( ( ( numeral_numeral_nat @ SV65 )
          = one_one_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[12936]) ).

thf(13143,plain,
    ! [SV65: num] :
      ( ( ( ( numeral_numeral_nat @ SV65 )
          = one_one_nat )
        = $true )
      | ( ( SV65 = one )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[12937]) ).

thf(13144,plain,
    ! [SV65: num] :
      ( ( ( SV65 = one )
        = $true )
      | ( ( SV65 = one )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[12938]) ).

thf(13145,plain,
    ! [SV67: num] :
      ( ( ( ord_less_eq_num @ SV67 @ one )
        = $true )
      | ( ( ord_less_eq_num @ SV67 @ one )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[12939]) ).

thf(13146,plain,
    ! [SV67: num] :
      ( ( ( SV67 = one )
        = $true )
      | ( ( ord_less_eq_num @ SV67 @ one )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[12940]) ).

thf(13147,plain,
    ! [SV67: num] :
      ( ( ( ord_less_eq_num @ SV67 @ one )
        = $true )
      | ( ( SV67 = one )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[12941]) ).

thf(13148,plain,
    ! [SV67: num] :
      ( ( ( SV67 = one )
        = $true )
      | ( ( SV67 = one )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[12942]) ).

thf(13149,plain,
    ! [SV729: nat,SV435: nat,SV71: nat] :
      ( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SV435 ) @ ( plus_plus_nat @ SV71 @ SV729 ) )
          | ~ ( ord_less_nat @ SV435 @ SV729 ) )
        = $false )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SV435 ) @ ( plus_plus_nat @ SV71 @ SV729 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12943]) ).

thf(13150,plain,
    ! [SV729: nat,SV435: nat,SV71: nat] :
      ( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SV435 ) @ ( plus_plus_nat @ SV71 @ SV729 ) )
          | ~ ( ord_less_nat @ SV435 @ SV729 ) )
        = $false )
      | ( ( ord_less_nat @ SV435 @ SV729 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12944]) ).

thf(13151,plain,
    ! [SV730: nat,SV436: nat,SV72: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV72 @ SV436 ) @ ( plus_plus_nat @ SV72 @ SV730 ) )
          | ~ ( ord_less_eq_nat @ SV436 @ SV730 ) )
        = $false )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV72 @ SV436 ) @ ( plus_plus_nat @ SV72 @ SV730 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12945]) ).

thf(13152,plain,
    ! [SV730: nat,SV436: nat,SV72: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV72 @ SV436 ) @ ( plus_plus_nat @ SV72 @ SV730 ) )
          | ~ ( ord_less_eq_nat @ SV436 @ SV730 ) )
        = $false )
      | ( ( ord_less_eq_nat @ SV436 @ SV730 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12946]) ).

thf(13153,plain,
    ! [SV736: nat,SV447: nat,SV86: nat] :
      ( ( ( ( ( times_times_nat @ ( suc @ SV86 ) @ SV447 )
           != ( times_times_nat @ ( suc @ SV86 ) @ SV736 ) )
          | ( SV447 != SV736 ) )
        = $false )
      | ( ( ( times_times_nat @ ( suc @ SV86 ) @ SV447 )
          = ( times_times_nat @ ( suc @ SV86 ) @ SV736 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12947]) ).

thf(13154,plain,
    ! [SV736: nat,SV447: nat,SV86: nat] :
      ( ( ( ( ( times_times_nat @ ( suc @ SV86 ) @ SV447 )
           != ( times_times_nat @ ( suc @ SV86 ) @ SV736 ) )
          | ( SV447 != SV736 ) )
        = $false )
      | ( ( SV447 = SV736 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12948]) ).

thf(13155,plain,
    ! [SV752: nat,SV475: nat,SV120: nat] :
      ( ( ( ( ( plus_plus_nat @ SV120 @ SV475 )
           != ( plus_plus_nat @ SV120 @ SV752 ) )
          | ( SV475 != SV752 ) )
        = $false )
      | ( ( ( plus_plus_nat @ SV120 @ SV475 )
          = ( plus_plus_nat @ SV120 @ SV752 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12949]) ).

thf(13156,plain,
    ! [SV752: nat,SV475: nat,SV120: nat] :
      ( ( ( ( ( plus_plus_nat @ SV120 @ SV475 )
           != ( plus_plus_nat @ SV120 @ SV752 ) )
          | ( SV475 != SV752 ) )
        = $false )
      | ( ( SV475 = SV752 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12950]) ).

thf(13157,plain,
    ! [SV753: nat,SV476: nat,SV121: nat] :
      ( ( ( ( ( plus_plus_nat @ SV121 @ SV476 )
           != ( plus_plus_nat @ SV753 @ SV476 ) )
          | ( SV121 != SV753 ) )
        = $false )
      | ( ( ( plus_plus_nat @ SV121 @ SV476 )
          = ( plus_plus_nat @ SV753 @ SV476 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12951]) ).

thf(13158,plain,
    ! [SV753: nat,SV476: nat,SV121: nat] :
      ( ( ( ( ( plus_plus_nat @ SV121 @ SV476 )
           != ( plus_plus_nat @ SV753 @ SV476 ) )
          | ( SV121 != SV753 ) )
        = $false )
      | ( ( SV121 = SV753 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12952]) ).

thf(13159,plain,
    ! [SV754: nat,SV477: nat,SV122: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ SV477 ) @ ( plus_plus_nat @ SV122 @ SV754 ) )
          | ~ ( ord_less_eq_nat @ SV477 @ SV754 ) )
        = $false )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ SV477 ) @ ( plus_plus_nat @ SV122 @ SV754 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12953]) ).

thf(13160,plain,
    ! [SV754: nat,SV477: nat,SV122: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ SV477 ) @ ( plus_plus_nat @ SV122 @ SV754 ) )
          | ~ ( ord_less_eq_nat @ SV477 @ SV754 ) )
        = $false )
      | ( ( ord_less_eq_nat @ SV477 @ SV754 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12954]) ).

thf(13161,plain,
    ! [SV755: nat,SV478: nat,SV123: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV123 @ SV478 ) @ ( plus_plus_nat @ SV755 @ SV478 ) )
          | ~ ( ord_less_eq_nat @ SV123 @ SV755 ) )
        = $false )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV123 @ SV478 ) @ ( plus_plus_nat @ SV755 @ SV478 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12955]) ).

thf(13162,plain,
    ! [SV755: nat,SV478: nat,SV123: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV123 @ SV478 ) @ ( plus_plus_nat @ SV755 @ SV478 ) )
          | ~ ( ord_less_eq_nat @ SV123 @ SV755 ) )
        = $false )
      | ( ( ord_less_eq_nat @ SV123 @ SV755 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12956]) ).

thf(13163,plain,
    ! [SV756: nat,SV479: nat,SV124: nat] :
      ( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV124 @ SV479 ) @ ( plus_plus_nat @ SV124 @ SV756 ) )
          | ~ ( ord_less_nat @ SV479 @ SV756 ) )
        = $false )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV124 @ SV479 ) @ ( plus_plus_nat @ SV124 @ SV756 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12957]) ).

thf(13164,plain,
    ! [SV756: nat,SV479: nat,SV124: nat] :
      ( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV124 @ SV479 ) @ ( plus_plus_nat @ SV124 @ SV756 ) )
          | ~ ( ord_less_nat @ SV479 @ SV756 ) )
        = $false )
      | ( ( ord_less_nat @ SV479 @ SV756 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12958]) ).

thf(13165,plain,
    ! [SV757: nat,SV480: nat,SV125: nat] :
      ( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV125 @ SV480 ) @ ( plus_plus_nat @ SV757 @ SV480 ) )
          | ~ ( ord_less_nat @ SV125 @ SV757 ) )
        = $false )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV125 @ SV480 ) @ ( plus_plus_nat @ SV757 @ SV480 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12959]) ).

thf(13166,plain,
    ! [SV757: nat,SV480: nat,SV125: nat] :
      ( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV125 @ SV480 ) @ ( plus_plus_nat @ SV757 @ SV480 ) )
          | ~ ( ord_less_nat @ SV125 @ SV757 ) )
        = $false )
      | ( ( ord_less_nat @ SV125 @ SV757 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12960]) ).

thf(13167,plain,
    ! [SV770: nat,SV493: nat,SV142: nat] :
      ( ( ( ( ( times_times_nat @ SV142 @ SV493 )
           != ( times_times_nat @ SV770 @ SV493 ) )
          | ~ ( ( SV493 = zero_zero_nat )
              | ( SV142 = SV770 ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV142 @ SV493 )
          = ( times_times_nat @ SV770 @ SV493 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12961]) ).

thf(13168,plain,
    ! [SV770: nat,SV142: nat,SV493: nat] :
      ( ( ( SV493 = zero_zero_nat )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV142 @ SV493 )
               != ( times_times_nat @ SV770 @ SV493 ) )
              | ~ ( ( SV493 = zero_zero_nat )
                  | ( SV142 = SV770 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12962]) ).

thf(13169,plain,
    ! [SV493: nat,SV770: nat,SV142: nat] :
      ( ( ( SV142 = SV770 )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV142 @ SV493 )
               != ( times_times_nat @ SV770 @ SV493 ) )
              | ~ ( ( SV493 = zero_zero_nat )
                  | ( SV142 = SV770 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12962]) ).

thf(13170,plain,
    ! [SV771: nat,SV494: nat,SV143: nat] :
      ( ( ( ( ( times_times_nat @ SV143 @ SV494 )
           != ( times_times_nat @ SV143 @ SV771 ) )
          | ~ ( ( SV143 = zero_zero_nat )
              | ( SV494 = SV771 ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV143 @ SV494 )
          = ( times_times_nat @ SV143 @ SV771 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12963]) ).

thf(13171,plain,
    ! [SV771: nat,SV494: nat,SV143: nat] :
      ( ( ( SV143 = zero_zero_nat )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV143 @ SV494 )
               != ( times_times_nat @ SV143 @ SV771 ) )
              | ~ ( ( SV143 = zero_zero_nat )
                  | ( SV494 = SV771 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12964]) ).

thf(13172,plain,
    ! [SV143: nat,SV771: nat,SV494: nat] :
      ( ( ( SV494 = SV771 )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV143 @ SV494 )
               != ( times_times_nat @ SV143 @ SV771 ) )
              | ~ ( ( SV143 = zero_zero_nat )
                  | ( SV494 = SV771 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12964]) ).

thf(13173,plain,
    ! [SV495: nat,SV144: nat] :
      ( ( ( ( times_times_nat @ SV144 @ SV495 )
         != zero_zero_nat )
        = $false )
      | ( ( ( times_times_nat @ SV144 @ SV495 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12965]) ).

thf(13174,plain,
    ! [SV495: nat,SV144: nat] :
      ( ( ( ~ ( ( SV144 = zero_zero_nat )
              | ( SV495 = zero_zero_nat ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV144 @ SV495 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12965]) ).

thf(13175,plain,
    ! [SV495: nat,SV144: nat] :
      ( ( ( ( ( times_times_nat @ SV144 @ SV495 )
           != zero_zero_nat )
          | ~ ( ( SV144 = zero_zero_nat )
              | ( SV495 = zero_zero_nat ) ) )
        = $false )
      | ( ( SV144 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12966]) ).

thf(13176,plain,
    ! [SV495: nat,SV144: nat] :
      ( ( ( ( ( times_times_nat @ SV144 @ SV495 )
           != zero_zero_nat )
          | ~ ( ( SV144 = zero_zero_nat )
              | ( SV495 = zero_zero_nat ) ) )
        = $false )
      | ( ( SV495 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12967]) ).

thf(13177,plain,
    ! [SV496: nat,SV148: nat] :
      ( ( ( SV148
         != ( plus_plus_nat @ SV148 @ SV496 ) )
        = $false )
      | ( ( SV148
          = ( plus_plus_nat @ SV148 @ SV496 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12968]) ).

thf(13178,plain,
    ! [SV148: nat,SV496: nat] :
      ( ( ( SV496 != zero_zero_nat )
        = $false )
      | ( ( SV148
          = ( plus_plus_nat @ SV148 @ SV496 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12968]) ).

thf(13179,plain,
    ! [SV496: nat,SV148: nat] :
      ( ( ( SV148
         != ( plus_plus_nat @ SV148 @ SV496 ) )
        = $false )
      | ( ( SV496 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12969]) ).

thf(13180,plain,
    ! [SV496: nat] :
      ( ( ( SV496 != zero_zero_nat )
        = $false )
      | ( ( SV496 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12969]) ).

thf(13181,plain,
    ! [SV497: nat,SV149: nat] :
      ( ( ( SV149
         != ( plus_plus_nat @ SV497 @ SV149 ) )
        = $false )
      | ( ( SV149
          = ( plus_plus_nat @ SV497 @ SV149 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12970]) ).

thf(13182,plain,
    ! [SV149: nat,SV497: nat] :
      ( ( ( SV497 != zero_zero_nat )
        = $false )
      | ( ( SV149
          = ( plus_plus_nat @ SV497 @ SV149 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12970]) ).

thf(13183,plain,
    ! [SV497: nat,SV149: nat] :
      ( ( ( SV149
         != ( plus_plus_nat @ SV497 @ SV149 ) )
        = $false )
      | ( ( SV497 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12971]) ).

thf(13184,plain,
    ! [SV497: nat] :
      ( ( ( SV497 != zero_zero_nat )
        = $false )
      | ( ( SV497 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12971]) ).

thf(13185,plain,
    ! [SV498: nat,SV150: nat] :
      ( ( ( ( plus_plus_nat @ SV150 @ SV498 )
         != SV150 )
        = $false )
      | ( ( ( plus_plus_nat @ SV150 @ SV498 )
          = SV150 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12972]) ).

thf(13186,plain,
    ! [SV150: nat,SV498: nat] :
      ( ( ( SV498 != zero_zero_nat )
        = $false )
      | ( ( ( plus_plus_nat @ SV150 @ SV498 )
          = SV150 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12972]) ).

thf(13187,plain,
    ! [SV498: nat,SV150: nat] :
      ( ( ( ( plus_plus_nat @ SV150 @ SV498 )
         != SV150 )
        = $false )
      | ( ( SV498 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12973]) ).

thf(13188,plain,
    ! [SV498: nat] :
      ( ( ( SV498 != zero_zero_nat )
        = $false )
      | ( ( SV498 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12973]) ).

thf(13189,plain,
    ! [SV499: nat,SV151: nat] :
      ( ( ( ( plus_plus_nat @ SV151 @ SV499 )
         != SV499 )
        = $false )
      | ( ( ( plus_plus_nat @ SV151 @ SV499 )
          = SV499 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12974]) ).

thf(13190,plain,
    ! [SV499: nat,SV151: nat] :
      ( ( ( SV151 != zero_zero_nat )
        = $false )
      | ( ( ( plus_plus_nat @ SV151 @ SV499 )
          = SV499 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12974]) ).

thf(13191,plain,
    ! [SV499: nat,SV151: nat] :
      ( ( ( ( plus_plus_nat @ SV151 @ SV499 )
         != SV499 )
        = $false )
      | ( ( SV151 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12975]) ).

thf(13192,plain,
    ! [SV151: nat] :
      ( ( ( SV151 != zero_zero_nat )
        = $false )
      | ( ( SV151 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12975]) ).

thf(13193,plain,
    ! [SV772: nat,SV502: nat,SV160: nat] :
      ( ( ( ( ( times_times_nat @ SV160 @ SV502 )
           != ( times_times_nat @ SV772 @ SV502 ) )
          | ~ ( ( SV160 = SV772 )
              | ( SV502 = zero_zero_nat ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV160 @ SV502 )
          = ( times_times_nat @ SV772 @ SV502 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12976]) ).

thf(13194,plain,
    ! [SV502: nat,SV772: nat,SV160: nat] :
      ( ( ( SV160 = SV772 )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV160 @ SV502 )
               != ( times_times_nat @ SV772 @ SV502 ) )
              | ~ ( ( SV160 = SV772 )
                  | ( SV502 = zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12977]) ).

thf(13195,plain,
    ! [SV772: nat,SV160: nat,SV502: nat] :
      ( ( ( SV502 = zero_zero_nat )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV160 @ SV502 )
               != ( times_times_nat @ SV772 @ SV502 ) )
              | ~ ( ( SV160 = SV772 )
                  | ( SV502 = zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12977]) ).

thf(13196,plain,
    ! [SV773: nat,SV503: nat,SV161: nat] :
      ( ( ( ( ( times_times_nat @ SV161 @ SV503 )
           != ( times_times_nat @ SV161 @ SV773 ) )
          | ~ ( ( SV503 = SV773 )
              | ( SV161 = zero_zero_nat ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV161 @ SV503 )
          = ( times_times_nat @ SV161 @ SV773 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12978]) ).

thf(13197,plain,
    ! [SV161: nat,SV773: nat,SV503: nat] :
      ( ( ( SV503 = SV773 )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV161 @ SV503 )
               != ( times_times_nat @ SV161 @ SV773 ) )
              | ~ ( ( SV503 = SV773 )
                  | ( SV161 = zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12979]) ).

thf(13198,plain,
    ! [SV773: nat,SV503: nat,SV161: nat] :
      ( ( ( SV161 = zero_zero_nat )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV161 @ SV503 )
               != ( times_times_nat @ SV161 @ SV773 ) )
              | ~ ( ( SV503 = SV773 )
                  | ( SV161 = zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12979]) ).

thf(13199,plain,
    ! [SV504: nat,SV163: nat] :
      ( ( ( ( times_times_nat @ SV163 @ SV504 )
         != zero_zero_nat )
        = $false )
      | ( ( ( times_times_nat @ SV163 @ SV504 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12980]) ).

thf(13200,plain,
    ! [SV504: nat,SV163: nat] :
      ( ( ( ~ ( ( SV163 = zero_zero_nat )
              | ( SV504 = zero_zero_nat ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV163 @ SV504 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12980]) ).

thf(13201,plain,
    ! [SV504: nat,SV163: nat] :
      ( ( ( ( ( times_times_nat @ SV163 @ SV504 )
           != zero_zero_nat )
          | ~ ( ( SV163 = zero_zero_nat )
              | ( SV504 = zero_zero_nat ) ) )
        = $false )
      | ( ( SV163 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12981]) ).

thf(13202,plain,
    ! [SV504: nat,SV163: nat] :
      ( ( ( ( ( times_times_nat @ SV163 @ SV504 )
           != zero_zero_nat )
          | ~ ( ( SV163 = zero_zero_nat )
              | ( SV504 = zero_zero_nat ) ) )
        = $false )
      | ( ( SV504 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12982]) ).

thf(13203,plain,
    ! [SV169: nat] :
      ( ( ( ( power_power_nat @ SV169 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = zero_zero_nat )
        = $true )
      | ( ( ( power_power_nat @ SV169 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[12983]) ).

thf(13204,plain,
    ! [SV169: nat] :
      ( ( ( SV169 = zero_zero_nat )
        = $true )
      | ( ( ( power_power_nat @ SV169 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[12984]) ).

thf(13205,plain,
    ! [SV169: nat] :
      ( ( ( ( power_power_nat @ SV169 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = zero_zero_nat )
        = $true )
      | ( ( SV169 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[12985]) ).

thf(13206,plain,
    ! [SV169: nat] :
      ( ( ( SV169 = zero_zero_nat )
        = $true )
      | ( ( SV169 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[12986]) ).

thf(13207,plain,
    ! [SV787: num,SV518: num,SV179: num] :
      ( ( ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV179 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) )
           != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV787 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) ) )
          | ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV179 ) @ ( numeral_numeral_nat @ SV518 ) )
           != ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV787 ) @ ( numeral_numeral_nat @ SV518 ) ) ) )
        = $false )
      | ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV179 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) )
          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV787 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12987]) ).

thf(13208,plain,
    ! [SV787: num,SV518: num,SV179: num] :
      ( ( ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV179 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) )
           != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV787 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) ) )
          | ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV179 ) @ ( numeral_numeral_nat @ SV518 ) )
           != ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV787 ) @ ( numeral_numeral_nat @ SV518 ) ) ) )
        = $false )
      | ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV179 ) @ ( numeral_numeral_nat @ SV518 ) )
          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV787 ) @ ( numeral_numeral_nat @ SV518 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12988]) ).

thf(13209,plain,
    ! [SV788: nat,SV520: nat,SV185: nat] :
      ( ( ( ( ( times_times_nat @ SV185 @ SV520 )
           != ( times_times_nat @ SV185 @ SV788 ) )
          | ~ ( ( SV185 = zero_zero_nat )
              | ( SV520 = SV788 ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV185 @ SV520 )
          = ( times_times_nat @ SV185 @ SV788 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12989]) ).

thf(13210,plain,
    ! [SV788: nat,SV520: nat,SV185: nat] :
      ( ( ( SV185 = zero_zero_nat )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV185 @ SV520 )
               != ( times_times_nat @ SV185 @ SV788 ) )
              | ~ ( ( SV185 = zero_zero_nat )
                  | ( SV520 = SV788 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12990]) ).

thf(13211,plain,
    ! [SV185: nat,SV788: nat,SV520: nat] :
      ( ( ( SV520 = SV788 )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV185 @ SV520 )
               != ( times_times_nat @ SV185 @ SV788 ) )
              | ~ ( ( SV185 = zero_zero_nat )
                  | ( SV520 = SV788 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[12990]) ).

thf(13212,plain,
    ! [SV534: num,SV199: num] :
      ( ( ( ( bit0 @ SV199 )
         != ( bit0 @ SV534 ) )
        = $false )
      | ( ( ( bit0 @ SV199 )
          = ( bit0 @ SV534 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12991]) ).

thf(13213,plain,
    ! [SV534: num,SV199: num] :
      ( ( ( SV199 != SV534 )
        = $false )
      | ( ( ( bit0 @ SV199 )
          = ( bit0 @ SV534 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12991]) ).

thf(13214,plain,
    ! [SV534: num,SV199: num] :
      ( ( ( ( bit0 @ SV199 )
         != ( bit0 @ SV534 ) )
        = $false )
      | ( ( SV199 = SV534 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12992]) ).

thf(13215,plain,
    ! [SV534: num,SV199: num] :
      ( ( ( SV199 != SV534 )
        = $false )
      | ( ( SV199 = SV534 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12992]) ).

thf(13216,plain,
    ! [SV535: nat,SV201: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV201 @ ( plus_plus_nat @ SV535 @ SV201 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV201 @ ( plus_plus_nat @ SV535 @ SV201 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12993]) ).

thf(13217,plain,
    ! [SV535: nat,SV201: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV201 @ SV535 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV201 @ ( plus_plus_nat @ SV535 @ SV201 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12993]) ).

thf(13218,plain,
    ! [SV535: nat,SV201: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV201 @ ( plus_plus_nat @ SV535 @ SV201 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV201 @ SV535 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12994]) ).

thf(13219,plain,
    ! [SV535: nat,SV201: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV201 @ SV535 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV201 @ SV535 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12994]) ).

thf(13220,plain,
    ! [SV536: nat,SV202: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV202 @ ( plus_plus_nat @ SV202 @ SV536 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV202 @ ( plus_plus_nat @ SV202 @ SV536 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12995]) ).

thf(13221,plain,
    ! [SV536: nat,SV202: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV202 @ SV536 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV202 @ ( plus_plus_nat @ SV202 @ SV536 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12995]) ).

thf(13222,plain,
    ! [SV536: nat,SV202: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV202 @ ( plus_plus_nat @ SV202 @ SV536 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV202 @ SV536 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12996]) ).

thf(13223,plain,
    ! [SV536: nat,SV202: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV202 @ SV536 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV202 @ SV536 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[12996]) ).

thf(13224,plain,
    ! [SV795: nat,SV537: nat,SV203: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV203 @ ( plus_plus_nat @ SV537 @ ( times_times_nat @ SV795 @ SV203 ) ) )
          | ~ ( dvd_dvd_nat @ SV203 @ SV537 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV203 @ ( plus_plus_nat @ SV537 @ ( times_times_nat @ SV795 @ SV203 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12997]) ).

thf(13225,plain,
    ! [SV795: nat,SV537: nat,SV203: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV203 @ ( plus_plus_nat @ SV537 @ ( times_times_nat @ SV795 @ SV203 ) ) )
          | ~ ( dvd_dvd_nat @ SV203 @ SV537 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV203 @ SV537 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12998]) ).

thf(13226,plain,
    ! [SV796: nat,SV538: nat,SV204: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV204 @ ( plus_plus_nat @ ( times_times_nat @ SV538 @ SV204 ) @ SV796 ) )
          | ~ ( dvd_dvd_nat @ SV204 @ SV796 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV204 @ ( plus_plus_nat @ ( times_times_nat @ SV538 @ SV204 ) @ SV796 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[12999]) ).

thf(13227,plain,
    ! [SV796: nat,SV538: nat,SV204: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV204 @ ( plus_plus_nat @ ( times_times_nat @ SV538 @ SV204 ) @ SV796 ) )
          | ~ ( dvd_dvd_nat @ SV204 @ SV796 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV204 @ SV796 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13000]) ).

thf(13228,plain,
    ! [SV539: nat,SV205: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ SV205 @ SV539 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ SV205 @ SV539 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13001]) ).

thf(13229,plain,
    ! [SV539: nat,SV205: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
              | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ SV205 @ SV539 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13001]) ).

thf(13230,plain,
    ! [SV539: nat,SV205: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ SV205 @ SV539 ) )
          | ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
              | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13002]) ).

thf(13231,plain,
    ! [SV539: nat,SV205: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ SV205 @ SV539 ) )
          | ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
              | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13003]) ).

thf(13232,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13004]) ).

thf(13233,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
         != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13004]) ).

thf(13234,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
              | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
               != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13005]) ).

thf(13235,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
              | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
               != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13005]) ).

thf(13236,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
           != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $false )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13006]) ).

thf(13237,plain,
    ! [SV548: nat,SV215: nat] :
      ( ( ( SV215
         != ( plus_plus_nat @ SV215 @ SV548 ) )
        = $false )
      | ( ( SV215
          = ( plus_plus_nat @ SV215 @ SV548 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13007]) ).

thf(13238,plain,
    ! [SV215: nat,SV548: nat] :
      ( ( ( SV548 != zero_zero_nat )
        = $false )
      | ( ( SV215
          = ( plus_plus_nat @ SV215 @ SV548 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13007]) ).

thf(13239,plain,
    ! [SV548: nat,SV215: nat] :
      ( ( ( SV215
         != ( plus_plus_nat @ SV215 @ SV548 ) )
        = $false )
      | ( ( SV548 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13008]) ).

thf(13240,plain,
    ! [SV548: nat] :
      ( ( ( SV548 != zero_zero_nat )
        = $false )
      | ( ( SV548 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13008]) ).

thf(13241,plain,
    ! [SV922: nat,SV802: nat,SV549: nat,SV216: nat] :
      ( ( ( ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV549 ) @ ( times_times_nat @ SV802 @ SV922 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV922 ) @ ( times_times_nat @ SV802 @ SV549 ) ) )
        = $false )
      | ( ( ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV549 ) @ ( times_times_nat @ SV802 @ SV922 ) )
               != ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV922 ) @ ( times_times_nat @ SV802 @ SV549 ) ) )
              | ~ ( ( SV216 = SV802 )
                  | ( SV549 = SV922 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13009]) ).

thf(13242,plain,
    ! [SV922: nat,SV549: nat,SV802: nat,SV216: nat] :
      ( ( ( ( SV216 = SV802 )
          | ( SV549 = SV922 ) )
        = $false )
      | ( ( ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV549 ) @ ( times_times_nat @ SV802 @ SV922 ) )
               != ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV922 ) @ ( times_times_nat @ SV802 @ SV549 ) ) )
              | ~ ( ( SV216 = SV802 )
                  | ( SV549 = SV922 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13009]) ).

thf(13243,plain,
    ! [SV803: nat,SV554: nat,SV224: nat] :
      ( ( ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV224 ) @ SV554 )
           != ( semiri1316708129612266289at_nat @ SV803 ) )
          | ( ( power_power_nat @ SV224 @ SV554 )
           != SV803 ) )
        = $false )
      | ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV224 ) @ SV554 )
          = ( semiri1316708129612266289at_nat @ SV803 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13010]) ).

thf(13244,plain,
    ! [SV803: nat,SV554: nat,SV224: nat] :
      ( ( ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV224 ) @ SV554 )
           != ( semiri1316708129612266289at_nat @ SV803 ) )
          | ( ( power_power_nat @ SV224 @ SV554 )
           != SV803 ) )
        = $false )
      | ( ( ( power_power_nat @ SV224 @ SV554 )
          = SV803 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13011]) ).

thf(13245,plain,
    ! [SV804: nat,SV555: nat,SV225: nat] :
      ( ( ( ( ( semiri1316708129612266289at_nat @ SV225 )
           != ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV555 ) @ SV804 ) )
          | ( SV225
           != ( power_power_nat @ SV555 @ SV804 ) ) )
        = $false )
      | ( ( ( semiri1316708129612266289at_nat @ SV225 )
          = ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV555 ) @ SV804 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13012]) ).

thf(13246,plain,
    ! [SV804: nat,SV555: nat,SV225: nat] :
      ( ( ( ( ( semiri1316708129612266289at_nat @ SV225 )
           != ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV555 ) @ SV804 ) )
          | ( SV225
           != ( power_power_nat @ SV555 @ SV804 ) ) )
        = $false )
      | ( ( SV225
          = ( power_power_nat @ SV555 @ SV804 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13013]) ).

thf(13247,plain,
    ! [SV805: nat,SV556: nat,SV226: num] :
      ( ( ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
           != ( semiri1316708129612266289at_nat @ SV805 ) )
          | ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
           != SV805 ) )
        = $false )
      | ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
          = ( semiri1316708129612266289at_nat @ SV805 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13014]) ).

thf(13248,plain,
    ! [SV805: nat,SV556: nat,SV226: num] :
      ( ( ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
           != ( semiri1316708129612266289at_nat @ SV805 ) )
          | ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
           != SV805 ) )
        = $false )
      | ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
          = SV805 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13015]) ).

thf(13249,plain,
    ! [SV806: nat,SV557: num,SV227: nat] :
      ( ( ( ( ( semiri1316708129612266289at_nat @ SV227 )
           != ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
          | ( SV227
           != ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) ) )
        = $false )
      | ( ( ( semiri1316708129612266289at_nat @ SV227 )
          = ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13016]) ).

thf(13250,plain,
    ! [SV806: nat,SV557: num,SV227: nat] :
      ( ( ( ( ( semiri1316708129612266289at_nat @ SV227 )
           != ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
          | ( SV227
           != ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) ) )
        = $false )
      | ( ( SV227
          = ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13017]) ).

thf(13251,plain,
    ! [SV561: nat,SV231: nat > real] :
      ( ( ( ~ ( summable_real
              @ ^ [SY1684: nat] : ( SV231 @ ( plus_plus_nat @ SY1684 @ SV561 ) ) ) )
        = $false )
      | ( ( summable_real
          @ ^ [SY1684: nat] : ( SV231 @ ( plus_plus_nat @ SY1684 @ SV561 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13018]) ).

thf(13252,plain,
    ! [SV561: nat,SV231: nat > real] :
      ( ( ( ~ ( summable_real @ SV231 ) )
        = $false )
      | ( ( summable_real
          @ ^ [SY1684: nat] : ( SV231 @ ( plus_plus_nat @ SY1684 @ SV561 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13018]) ).

thf(13253,plain,
    ! [SV561: nat,SV231: nat > real] :
      ( ( ( ~ ( summable_real
              @ ^ [SY1684: nat] : ( SV231 @ ( plus_plus_nat @ SY1684 @ SV561 ) ) ) )
        = $false )
      | ( ( summable_real @ SV231 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13019]) ).

thf(13254,plain,
    ! [SV231: nat > real] :
      ( ( ( ~ ( summable_real @ SV231 ) )
        = $false )
      | ( ( summable_real @ SV231 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13019]) ).

thf(13255,plain,
    ! [SV562: nat,SV232: nat > complex] :
      ( ( ( ~ ( summable_complex
              @ ^ [SY1685: nat] : ( SV232 @ ( plus_plus_nat @ SY1685 @ SV562 ) ) ) )
        = $false )
      | ( ( summable_complex
          @ ^ [SY1685: nat] : ( SV232 @ ( plus_plus_nat @ SY1685 @ SV562 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13020]) ).

thf(13256,plain,
    ! [SV562: nat,SV232: nat > complex] :
      ( ( ( ~ ( summable_complex @ SV232 ) )
        = $false )
      | ( ( summable_complex
          @ ^ [SY1685: nat] : ( SV232 @ ( plus_plus_nat @ SY1685 @ SV562 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13020]) ).

thf(13257,plain,
    ! [SV562: nat,SV232: nat > complex] :
      ( ( ( ~ ( summable_complex
              @ ^ [SY1685: nat] : ( SV232 @ ( plus_plus_nat @ SY1685 @ SV562 ) ) ) )
        = $false )
      | ( ( summable_complex @ SV232 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13021]) ).

thf(13258,plain,
    ! [SV232: nat > complex] :
      ( ( ( ~ ( summable_complex @ SV232 ) )
        = $false )
      | ( ( summable_complex @ SV232 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13021]) ).

thf(13259,plain,
    ! [SV243: $o] :
      ( ( ( ~ SV243 ) = $false )
      | ( SV243 = $false )
      | ( ( SV243 = $false )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13022]) ).

thf(13260,plain,
    ! [SV243: $o] :
      ( ( ( ~ $true ) = $false )
      | ( SV243 = $false )
      | ( ( SV243 = $false )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13022]) ).

thf(13261,plain,
    ! [SV243: $o] :
      ( ( ( ~ SV243 ) = $false )
      | ( $true = $false )
      | ( ( SV243 = $false )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13023]) ).

thf(13262,plain,
    ! [SV243: $o] :
      ( ( ( ~ $true ) = $false )
      | ( $true = $false )
      | ( ( SV243 = $false )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13023]) ).

thf(13263,plain,
    ! [SV243: $o] :
      ( ( ( ~ SV243
          | ~ $false )
        = $false )
      | ( SV243 = $false )
      | ( ( SV243 = $true )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13024]) ).

thf(13264,plain,
    ! [SV243: $o] :
      ( ( ( ~ SV243
          | ~ $false )
        = $false )
      | ( $false = $false )
      | ( ( SV243 = $true )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13025]) ).

thf(13265,plain,
    ( ( ( ~ $true ) = $false )
    | ( $true = $false )
    | ( ( $true = $false )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13026]) ).

thf(13266,plain,
    ( ( ( ~ $true ) = $false )
    | ( $true = $false )
    | ( ( $true = $false )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13026]) ).

thf(13267,plain,
    ( ( ( ~ $true ) = $false )
    | ( $true = $false )
    | ( ( $true = $false )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13027]) ).

thf(13268,plain,
    ( ( ( ~ $true ) = $false )
    | ( $true = $false )
    | ( ( $true = $false )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13027]) ).

thf(13269,plain,
    ( ( ( ~ $true
        | ~ $false )
      = $false )
    | ( $true = $false )
    | ( ( $true = $true )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13028]) ).

thf(13270,plain,
    ( ( ( ~ $true
        | ~ $false )
      = $false )
    | ( $false = $false )
    | ( ( $true = $true )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13029]) ).

thf(13271,plain,
    ( ( ( ~ $false ) = $false )
    | ( $false = $false )
    | ( ( $false = $false )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13030]) ).

thf(13272,plain,
    ( ( ( ~ $true ) = $false )
    | ( $false = $false )
    | ( ( $false = $false )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13030]) ).

thf(13273,plain,
    ( ( ( ~ $false ) = $false )
    | ( $true = $false )
    | ( ( $false = $false )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13031]) ).

thf(13274,plain,
    ( ( ( ~ $true ) = $false )
    | ( $true = $false )
    | ( ( $false = $false )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13031]) ).

thf(13275,plain,
    ( ( ( ~ $false
        | ~ $false )
      = $false )
    | ( $false = $false )
    | ( ( $false = $true )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13032]) ).

thf(13276,plain,
    ( ( ( ~ $false
        | ~ $false )
      = $false )
    | ( $false = $false )
    | ( ( $false = $true )
      = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13033]) ).

thf(13277,plain,
    ! [SV925: nat,SV253: nat,SV579: nat,SV822: nat] :
      ( ( ( ( plus_plus_nat @ SV822 @ SV579 )
          = ( plus_plus_nat @ SV253 @ SV925 ) )
        = $false )
      | ( ( ord_less_nat @ SV822 @ SV925 )
        = $true )
      | ( ( ord_less_nat @ SV253 @ SV579 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13034]) ).

thf(13278,plain,
    ! [SV824: nat,SV581: nat,SV255: nat] :
      ( ( ( SV255 = zero_zero_nat )
        = $false )
      | ( ( ( divide_divide_nat @ ( times_times_nat @ SV255 @ SV581 ) @ ( times_times_nat @ SV255 @ SV824 ) )
          = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13035]) ).

thf(13279,plain,
    ! [SV824: nat,SV581: nat,SV255: nat] :
      ( ( ( SV255 != zero_zero_nat )
        = $false )
      | ( ( ( divide_divide_nat @ ( times_times_nat @ SV255 @ SV581 ) @ ( times_times_nat @ SV255 @ SV824 ) )
          = ( divide_divide_nat @ SV581 @ SV824 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13036]) ).

thf(13280,plain,
    ! [SV825: nat,SV257: nat,SV583: nat] :
      ( ( ( ~ ( ( ( times_times_nat @ SV583 @ SV257 )
                = ( times_times_nat @ SV825 @ SV257 ) )
              | ( SV583 = SV825 ) ) )
        = $true )
      | ( ( ~ ( ( ( times_times_nat @ SV583 @ SV257 )
               != ( times_times_nat @ SV825 @ SV257 ) )
              | ( SV583 != SV825 ) ) )
        = $true )
      | ( ( SV257 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13037]) ).

thf(13281,plain,
    ! [SV584: nat,SV826: nat,SV258: nat] :
      ( ( ( ( SV258
           != ( times_times_nat @ ( sK13_SY1869 @ SV826 @ SV584 @ SV258 ) @ ( sK20_SY1935 @ SV584 @ SV826 @ SV258 ) ) )
          | ~ ( dvd_dvd_nat @ ( sK13_SY1869 @ SV826 @ SV584 @ SV258 ) @ SV584 )
          | ~ ( dvd_dvd_nat @ ( sK20_SY1935 @ SV584 @ SV826 @ SV258 ) @ SV826 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV258 @ ( times_times_nat @ SV584 @ SV826 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[13039]) ).

thf(13282,plain,
    ! [SV926: nat,SV827: nat,SV586: nat,SV260: nat] :
      ( ( ( SV260 != SV586 )
        = $true )
      | ( ( SV827 != SV926 )
        = $true )
      | ( ( ( plus_plus_nat @ SV260 @ SV827 )
          = ( plus_plus_nat @ SV586 @ SV926 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13040]) ).

thf(13283,plain,
    ! [SV593: nat,SV833: nat,SV268: nat] :
      ( ( ( ord_less_eq_nat @ SV268 @ SV833 )
        = $true )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV268 @ SV593 ) @ SV833 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13043]) ).

thf(13284,plain,
    ! [SV268: nat,SV833: nat,SV593: nat] :
      ( ( ( ord_less_eq_nat @ SV593 @ SV833 )
        = $true )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV268 @ SV593 ) @ SV833 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13044]) ).

thf(13285,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( SV595 = SV928 )
        = $false )
      | ( ( ~ ( ( SV595 != SV928 )
              | ~ ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                     != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
                    | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                     != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13045]) ).

thf(13286,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
               != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
              | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
               != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
        = $false )
      | ( ( ~ ( ( SV595 != SV928 )
              | ~ ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                     != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
                    | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                     != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13045]) ).

thf(13287,plain,
    ! [SV596: nat,SV272: nat,SV929: nat,SV836: nat] :
      ( ( ( dvd_dvd_nat @ SV836 @ SV929 )
        = $false )
      | ( ( dvd_dvd_nat @ ( times_times_nat @ SV272 @ SV836 ) @ ( times_times_nat @ SV596 @ SV929 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV272 @ SV596 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13046]) ).

thf(13288,plain,
    ! [SV837: nat,SV597: nat,SV273: nat] :
      ( ( ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
           != ( modulo_modulo_nat @ SV837 @ SV597 ) )
          | ~ ~ ! [SY1874: nat] :
                  ~ ~ ! [SY1875: nat] :
                        ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SY1874 ) )
                       != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1875 ) ) ) )
        = $false )
      | ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
          = ( modulo_modulo_nat @ SV837 @ SV597 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13047]) ).

thf(13289,plain,
    ! [SV837: nat,SV597: nat,SV273: nat] :
      ( ( ( ! [SY1874: nat] :
              ~ ~ ! [SY1875: nat] :
                    ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SY1874 ) )
                   != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1875 ) ) ) )
        = $true )
      | ( ( ~ ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
               != ( modulo_modulo_nat @ SV837 @ SV597 ) )
              | ~ ~ ! [SY1874: nat] :
                      ~ ~ ! [SY1875: nat] :
                            ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SY1874 ) )
                           != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1875 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13048]) ).

thf(13290,plain,
    ! [SV601: nat,SV280: nat] :
      ( ( ( SV280 != zero_zero_nat )
        = $true )
      | ( ( ( times_times_nat @ SV280 @ SV601 )
          = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13049]) ).

thf(13291,plain,
    ! [SV280: nat,SV601: nat] :
      ( ( ( SV601 != zero_zero_nat )
        = $true )
      | ( ( ( times_times_nat @ SV280 @ SV601 )
          = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13050]) ).

thf(13292,plain,
    ! [SV931: nat,SV844: nat,SV605: nat,SV284: nat] :
      ( ( ( ~ ( ~ ( ( SV284 != SV605 ) )
              | ~ ( ( SV844 != SV931 ) ) ) )
        = $false )
      | ( ( ~ ( ~ ~ ( ~ ( ( SV284 != SV605 ) )
                    | ~ ( ( SV844 != SV931 ) ) )
              | ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
                   != ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13051]) ).

thf(13293,plain,
    ! [SV931: nat,SV605: nat,SV844: nat,SV284: nat] :
      ( ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
         != ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) )
        = $false )
      | ( ( ~ ( ~ ~ ( ~ ( ( SV284 != SV605 ) )
                    | ~ ( ( SV844 != SV931 ) ) )
              | ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
                   != ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13051]) ).

thf(13294,plain,
    ! [SV845: nat,SV606: nat,SV285: nat] :
      ( ( ( ~ ( ( ( times_times_nat @ SV285 @ SV606 )
                = ( times_times_nat @ SV285 @ SV845 ) )
              | ( SV606 = SV845 ) ) )
        = $true )
      | ( ( ~ ( ( ( times_times_nat @ SV285 @ SV606 )
               != ( times_times_nat @ SV285 @ SV845 ) )
              | ( SV606 != SV845 ) ) )
        = $true )
      | ( ( SV285 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13052]) ).

thf(13295,plain,
    ! [SV287: nat,SV608: nat] :
      ( ( ( SV608 = zero_zero_nat )
        = $true )
      | ( ( ( times_times_nat @ SV287 @ SV608 )
         != zero_zero_nat )
        = $true )
      | ( ( SV287 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13054]) ).

thf(13296,plain,
    ! [SV609: nat,SV288: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV288 )
              | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV609 ) ) )
        = $false )
      | ( ( SV288 = SV609 )
        = $true )
      | ( ( ( divide_divide_nat @ SV288 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV609 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13055]) ).

thf(13297,plain,
    ! [SV609: nat,SV288: nat] :
      ( ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV288 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV609 ) ) )
        = $false )
      | ( ( SV288 = SV609 )
        = $true )
      | ( ( ( divide_divide_nat @ SV288 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV609 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13055]) ).

thf(13298,plain,
    ! [SV932: nat,SV848: nat,SV611: nat,SV290: nat] :
      ( ( ( ~ ( ord_less_nat @ SV290 @ SV611 ) )
        = $true )
      | ( ( ~ ( ord_less_nat @ SV848 @ SV932 ) )
        = $true )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV290 @ SV848 ) @ ( plus_plus_nat @ SV611 @ SV932 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13057]) ).

thf(13299,plain,
    ! [SV933: nat,SV849: nat,SV615: nat,SV294: nat] :
      ( ( ( SV294 != SV615 )
        = $true )
      | ( ( ~ ( ord_less_nat @ SV849 @ SV933 ) )
        = $true )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV294 @ SV849 ) @ ( plus_plus_nat @ SV615 @ SV933 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13058]) ).

thf(13300,plain,
    ! [SV617: nat,SV296: nat,SV934: nat,SV850: nat] :
      ( ( ( ord_less_nat @ SV850 @ SV934 )
        = $false )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV296 @ SV850 ) @ ( plus_plus_nat @ SV617 @ SV934 ) )
        = $true )
      | ( ( ord_less_nat @ SV296 @ SV617 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13059]) ).

thf(13301,plain,
    ! [SV297: nat,SV618: nat,SV935: nat,SV851: nat] :
      ( ( ( dvd_dvd_nat @ SV851 @ SV935 )
        = $false )
      | ( ( ( times_times_nat @ ( divide_divide_nat @ SV618 @ SV297 ) @ ( divide_divide_nat @ SV935 @ SV851 ) )
          = ( divide_divide_nat @ ( times_times_nat @ SV618 @ SV935 ) @ ( times_times_nat @ SV297 @ SV851 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV297 @ SV618 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13060]) ).

thf(13302,plain,
    ! [SV621: nat,SV300: nat] :
      ( ( ( ( times_times_nat @ SV300 @ SV621 )
         != one_one_nat )
        = $false )
      | ( ( ( times_times_nat @ SV300 @ SV621 )
          = one_one_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13062]) ).

thf(13303,plain,
    ! [SV621: nat,SV300: nat] :
      ( ( ( ~ ~ ( ( SV300 != one_one_nat )
                | ( SV621 != one_one_nat ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV300 @ SV621 )
          = one_one_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13062]) ).

thf(13304,plain,
    ! [SV621: nat,SV300: nat] :
      ( ( ( SV300 != one_one_nat )
        = $true )
      | ( ( SV621 != one_one_nat )
        = $true )
      | ( ( ~ ( ( ( times_times_nat @ SV300 @ SV621 )
               != one_one_nat )
              | ~ ~ ( ( SV300 != one_one_nat )
                    | ( SV621 != one_one_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13063]) ).

thf(13305,plain,
    ! [SV936: nat,SV622: nat] :
      ( ( ( dvd_dvd_nat @ SV622 @ SV936 )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ SV622 @ SV936 )
              | ~ ~ ! [SY1919: nat] :
                      ( SV936
                     != ( times_times_nat @ SV622 @ SY1919 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13064]) ).

thf(13306,plain,
    ! [SV622: nat,SV936: nat] :
      ( ( ( ~ ! [SY1919: nat] :
                ( SV936
               != ( times_times_nat @ SV622 @ SY1919 ) ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ SV622 @ SV936 )
              | ~ ~ ! [SY1919: nat] :
                      ( SV936
                     != ( times_times_nat @ SV622 @ SY1919 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13064]) ).

thf(13307,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
          | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
               != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13065]) ).

thf(13308,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
          | ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
              | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
                   != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[13066]) ).

thf(13309,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
              | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
                   != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[13066]) ).

thf(13310,plain,
    ! [SV626: nat,SV305: nat] :
      ( ( ( ( plus_plus_nat @ SV305 @ SV626 )
         != zero_zero_nat )
        = $false )
      | ( ( ( plus_plus_nat @ SV305 @ SV626 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13067]) ).

thf(13311,plain,
    ! [SV626: nat,SV305: nat] :
      ( ( ( ~ ~ ( ( SV305 != zero_zero_nat )
                | ( SV626 != zero_zero_nat ) ) )
        = $false )
      | ( ( ( plus_plus_nat @ SV305 @ SV626 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13067]) ).

thf(13312,plain,
    ! [SV626: nat,SV305: nat] :
      ( ( ( SV305 != zero_zero_nat )
        = $true )
      | ( ( SV626 != zero_zero_nat )
        = $true )
      | ( ( ~ ( ( ( plus_plus_nat @ SV305 @ SV626 )
               != zero_zero_nat )
              | ~ ~ ( ( SV305 != zero_zero_nat )
                    | ( SV626 != zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13068]) ).

thf(13313,plain,
    ! [SV630: nat,SV310: nat] :
      ( ( ( ( plus_plus_nat @ SV310 @ SV630 )
         != zero_zero_nat )
        = $false )
      | ( ( ( plus_plus_nat @ SV310 @ SV630 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13070]) ).

thf(13314,plain,
    ! [SV630: nat,SV310: nat] :
      ( ( ( ~ ~ ( ( SV310 != zero_zero_nat )
                | ( SV630 != zero_zero_nat ) ) )
        = $false )
      | ( ( ( plus_plus_nat @ SV310 @ SV630 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13070]) ).

thf(13315,plain,
    ! [SV630: nat,SV310: nat] :
      ( ( ( SV310 != zero_zero_nat )
        = $true )
      | ( ( SV630 != zero_zero_nat )
        = $true )
      | ( ( ~ ( ( ( plus_plus_nat @ SV310 @ SV630 )
               != zero_zero_nat )
              | ~ ~ ( ( SV310 != zero_zero_nat )
                    | ( SV630 != zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13071]) ).

thf(13316,plain,
    ! [SV631: nat,SV856: nat,SV311: nat] :
      ( ( ( ~ ! [SY1936: nat] :
                ~ ~ ( ~ ~ ( ( SV311
                           != ( times_times_nat @ ( sK14_SY1883 @ SV856 @ SV631 @ SV311 ) @ SY1936 ) )
                          | ~ ( dvd_dvd_nat @ ( sK14_SY1883 @ SV856 @ SV631 @ SV311 ) @ SV631 ) )
                    | ~ ( dvd_dvd_nat @ SY1936 @ SV856 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV311 @ ( times_times_nat @ SV631 @ SV856 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13072]) ).

thf(13317,plain,
    ! [SV956: nat,SV937: nat,SV632: nat,SV857: nat,SV312: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV312 @ SV857 ) )
        = $true )
      | ( ( ~ ( ( ( times_times_nat @ SV632 @ SV937 )
                = ( plus_plus_nat @ ( times_times_nat @ SV857 @ SV956 ) @ SV312 ) )
              | ( ( times_times_nat @ SV857 @ SV937 )
                = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SV956 ) @ SV312 ) ) )
          | ~ ! [SY1887: nat] :
                ~ ~ ! [SY1888: nat] :
                      ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
                                | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) )
                          | ~ ( ( ( times_times_nat @ SV632 @ SY1887 )
                                = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1888 ) @ SV312 ) )
                              | ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1887 )
                                = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SY1888 ) @ SV312 ) ) ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13073]) ).

thf(13318,plain,
    ! [SV636: num,SV316: num > $o] :
      ( ( ( ~ ( SV316 @ ( sK15_SY1414 @ SV636 @ SV316 ) ) )
        = $false )
      | ( ( SV316 @ SV636 )
        = $true )
      | ( ( SV316 @ one )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13075]) ).

thf(13319,plain,
    ! [SV636: num,SV316: num > $o] :
      ( ( ( SV316 @ ( inc @ ( sK15_SY1414 @ SV636 @ SV316 ) ) )
        = $false )
      | ( ( SV316 @ SV636 )
        = $true )
      | ( ( SV316 @ one )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13075]) ).

thf(13320,plain,
    ! [SV639: nat,SV860: nat,SV319: nat > nat > $o] :
      ( ( ( ~ ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
              | ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) ) )
          | ~ ( ~ ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
              | ~ ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) ) ) )
        = $false )
      | ( ( ~ ! [SY1421: nat] : ( SV319 @ SY1421 @ zero_zero_nat )
          | ~ ! [SY1422: nat,SY1423: nat] :
                ( ~ ( SV319 @ SY1422 @ SY1423 )
                | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) )
          | ( SV319 @ SV639 @ SV860 ) )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[13076]) ).

thf(13321,plain,
    ! [SV639: nat,SV860: nat,SV319: nat > nat > $o] :
      ( ( ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
          = ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) ) )
        = $false )
      | ( ( ~ ! [SY1421: nat] : ( SV319 @ SY1421 @ zero_zero_nat )
          | ~ ! [SY1422: nat,SY1423: nat] :
                ( ~ ( SV319 @ SY1422 @ SY1423 )
                | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) )
          | ( SV319 @ SV639 @ SV860 ) )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[13076]) ).

thf(13322,plain,
    ! [SV642: nat,SV322: nat] :
      ( ( ( ~ ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 ) )
        = $false )
      | ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13077]) ).

thf(13323,plain,
    ! [SV642: nat,SV322: nat] :
      ( ( ( ~ ~ ( ~ ( ( SV322 != SV642 ) )
                | ~ ( vEBT_V8194947554948674370ptions @ summary @ SV642 ) ) )
        = $false )
      | ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13077]) ).

thf(13324,plain,
    ! [SV642: nat,SV322: nat] :
      ( ( ( ~ ( ( SV322 != SV642 ) ) )
        = $true )
      | ( ( ~ ( vEBT_V8194947554948674370ptions @ summary @ SV642 ) )
        = $true )
      | ( ( ~ ( ~ ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 )
              | ~ ~ ( ~ ( ( SV322 != SV642 ) )
                    | ~ ( vEBT_V8194947554948674370ptions @ summary @ SV642 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13078]) ).

thf(13325,plain,
    ! [SV862: nat,SV323: nat,SV957: nat,SV643: nat,SV938: nat] :
      ( ( ( ( modulo_modulo_nat @ SV938 @ SV643 )
         != ( modulo_modulo_nat @ SV957 @ SV643 ) )
        = $true )
      | ( ( ( modulo_modulo_nat @ ( times_times_nat @ SV323 @ SV938 ) @ SV643 )
          = ( modulo_modulo_nat @ ( times_times_nat @ SV862 @ SV957 ) @ SV643 ) )
        = $true )
      | ( ( ( modulo_modulo_nat @ SV323 @ SV643 )
          = ( modulo_modulo_nat @ SV862 @ SV643 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13079]) ).

thf(13326,plain,
    ! [SV939: nat,SV644: nat] :
      ( ( ( ord_less_eq_nat @ SV644 @ SV939 )
        = $false )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ SV644 @ SV939 )
              | ~ ~ ! [SY1924: nat] :
                      ( SV939
                     != ( plus_plus_nat @ SV644 @ SY1924 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13080]) ).

thf(13327,plain,
    ! [SV644: nat,SV939: nat] :
      ( ( ( ~ ! [SY1924: nat] :
                ( SV939
               != ( plus_plus_nat @ SV644 @ SY1924 ) ) )
        = $false )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ SV644 @ SV939 )
              | ~ ~ ! [SY1924: nat] :
                      ( SV939
                     != ( plus_plus_nat @ SV644 @ SY1924 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13080]) ).

thf(13328,plain,
    ! [SV940: nat,SV867: nat,SV648: nat,SV328: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV328 @ SV648 ) )
        = $true )
      | ( ( SV867 != SV940 )
        = $true )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV328 @ SV867 ) @ ( plus_plus_nat @ SV648 @ SV940 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13081]) ).

thf(13329,plain,
    ! [SV649: nat,SV329: nat] :
      ( ( ( zero_zero_nat
         != ( plus_plus_nat @ SV329 @ SV649 ) )
        = $false )
      | ( ( zero_zero_nat
          = ( plus_plus_nat @ SV329 @ SV649 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13082]) ).

thf(13330,plain,
    ! [SV649: nat,SV329: nat] :
      ( ( ( ~ ~ ( ( SV329 != zero_zero_nat )
                | ( SV649 != zero_zero_nat ) ) )
        = $false )
      | ( ( zero_zero_nat
          = ( plus_plus_nat @ SV329 @ SV649 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13082]) ).

thf(13331,plain,
    ! [SV649: nat,SV329: nat] :
      ( ( ( SV329 != zero_zero_nat )
        = $true )
      | ( ( SV649 != zero_zero_nat )
        = $true )
      | ( ( ~ ( ( zero_zero_nat
               != ( plus_plus_nat @ SV329 @ SV649 ) )
              | ~ ~ ( ( SV329 != zero_zero_nat )
                    | ( SV649 != zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13083]) ).

thf(13332,plain,
    ! [SV958: vEBT_VEBT,SV941: vEBT_VEBT,SV869: list_VEBT_VEBT,SV652: nat,SV332: nat] :
      ( ( ( SV332 = SV652 )
        = $true )
      | ( ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV869 @ SV332 @ SV941 ) @ SV652 @ SV958 )
          = ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ SV869 @ SV652 @ SV958 ) @ SV332 @ SV941 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13084]) ).

thf(13333,plain,
    ! [SV942: nat,SV871: nat,SV657: nat,SV335: nat] :
      ( ( ( SV335 != SV657 )
        = $true )
      | ( ( ~ ( ord_less_eq_nat @ SV871 @ SV942 ) )
        = $true )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV335 @ SV871 ) @ ( plus_plus_nat @ SV657 @ SV942 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13085]) ).

thf(13334,plain,
    ! [SV658: nat,SV872: nat,SV336: nat] :
      ( ( ( ( dvd_dvd_nat @ SV336 @ ( plus_plus_nat @ SV872 @ SV658 ) )
          | ( dvd_dvd_nat @ SV336 @ SV872 ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ SV336 @ ( plus_plus_nat @ SV872 @ SV658 ) )
              | ~ ( dvd_dvd_nat @ SV336 @ SV872 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV336 @ SV658 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13086]) ).

thf(13335,plain,
    ! [SV340: nat] :
      ( ( ( SV340
          = ( plus_plus_nat @ ( sK17_SY1466 @ SV340 ) @ ( suc @ ( sK17_SY1466 @ SV340 ) ) ) )
        = $true )
      | ( ( SV340
          = ( plus_plus_nat @ ( sK5_SY1465 @ SV340 ) @ ( sK5_SY1465 @ SV340 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13088]) ).

thf(13336,plain,
    ! [SV943: nat,SV876: nat,SV662: nat,SV341: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV341 @ SV662 ) )
        = $true )
      | ( ( ~ ( ord_less_eq_nat @ SV876 @ SV943 ) )
        = $true )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV341 @ SV876 ) @ ( plus_plus_nat @ SV662 @ SV943 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13089]) ).

thf(13337,plain,
    ! [SV882: nat,SV347: nat,SV668: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ ( divide_divide_nat @ SV668 @ SV347 ) @ ( divide_divide_nat @ SV882 @ SV347 ) )
              | ( dvd_dvd_nat @ SV668 @ SV882 ) )
          | ~ ( ~ ( dvd_dvd_nat @ ( divide_divide_nat @ SV668 @ SV347 ) @ ( divide_divide_nat @ SV882 @ SV347 ) )
              | ~ ( dvd_dvd_nat @ SV668 @ SV882 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV347 @ SV882 )
        = $false )
      | ( ( dvd_dvd_nat @ SV347 @ SV668 )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[13090]) ).

thf(13338,plain,
    ! [SV882: nat,SV347: nat,SV668: nat] :
      ( ( ( ( dvd_dvd_nat @ ( divide_divide_nat @ SV668 @ SV347 ) @ ( divide_divide_nat @ SV882 @ SV347 ) )
          = ( dvd_dvd_nat @ SV668 @ SV882 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV347 @ SV882 )
        = $false )
      | ( ( dvd_dvd_nat @ SV347 @ SV668 )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[13090]) ).

thf(13339,plain,
    ! [SV349: nat,SV669: nat] :
      ( ( ~ ! [SY1937: nat] :
              ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ ( sK6_SY1803 @ SV669 @ SV349 ) @ SV349 )
                        | ~ ( dvd_dvd_nat @ ( sK6_SY1803 @ SV669 @ SV349 ) @ SV669 ) )
                  | ~ ( ( ( times_times_nat @ SV349 @ ( sK18_SY1926 @ SV349 @ SV669 ) )
                        = ( plus_plus_nat @ ( times_times_nat @ SV669 @ SY1937 ) @ ( sK6_SY1803 @ SV669 @ SV349 ) ) )
                      | ( ( times_times_nat @ SV669 @ ( sK18_SY1926 @ SV349 @ SV669 ) )
                        = ( plus_plus_nat @ ( times_times_nat @ SV349 @ SY1937 ) @ ( sK6_SY1803 @ SV669 @ SV349 ) ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[13091]) ).

thf(13340,plain,
    ! [SV671: nat,SV351: nat] :
      ( ( ( one_one_nat
         != ( times_times_nat @ SV351 @ SV671 ) )
        = $false )
      | ( ( one_one_nat
          = ( times_times_nat @ SV351 @ SV671 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13092]) ).

thf(13341,plain,
    ! [SV671: nat,SV351: nat] :
      ( ( ( ~ ~ ( ( SV351 != one_one_nat )
                | ( SV671 != one_one_nat ) ) )
        = $false )
      | ( ( one_one_nat
          = ( times_times_nat @ SV351 @ SV671 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13092]) ).

thf(13342,plain,
    ! [SV671: nat,SV351: nat] :
      ( ( ( SV351 != one_one_nat )
        = $true )
      | ( ( SV671 != one_one_nat )
        = $true )
      | ( ( ~ ( ( one_one_nat
               != ( times_times_nat @ SV351 @ SV671 ) )
              | ~ ~ ( ( SV351 != one_one_nat )
                    | ( SV671 != one_one_nat ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13093]) ).

thf(13343,plain,
    ! [SV672: nat,SV352: nat,SV944: nat,SV883: nat] :
      ( ( ( ord_less_eq_nat @ SV883 @ SV944 )
        = $false )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV352 @ SV883 ) @ ( plus_plus_nat @ SV672 @ SV944 ) )
        = $true )
      | ( ( ord_less_eq_nat @ SV352 @ SV672 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13094]) ).

thf(13344,plain,
    ! [SV959: nat,SV945: nat,SV884: nat,SV673: nat,SV353: nat] :
      ( ( ( SV353 = zero_zero_nat )
        = $true )
      | ( ( ~ ~ ( ( SV673 != SV884 )
                | ~ ( ( SV945 != SV959 ) ) )
          | ( ( plus_plus_nat @ SV673 @ ( times_times_nat @ SV353 @ SV945 ) )
           != ( plus_plus_nat @ SV884 @ ( times_times_nat @ SV353 @ SV959 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13095]) ).

thf(13345,plain,
    ! [SV885: nat,SV674: nat,SV354: nat] :
      ( ( ( ( dvd_dvd_nat @ SV354 @ ( plus_plus_nat @ SV674 @ SV885 ) )
          | ( dvd_dvd_nat @ SV354 @ SV885 ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ SV354 @ ( plus_plus_nat @ SV674 @ SV885 ) )
              | ~ ( dvd_dvd_nat @ SV354 @ SV885 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV354 @ SV674 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13096]) ).

thf(13346,plain,
    ! [SV886: nat,SV676: nat,SV356: nat] :
      ( ( ( SV356 = zero_zero_nat )
        = $false )
      | ( ( ( divide_divide_nat @ ( times_times_nat @ SV356 @ SV676 ) @ ( times_times_nat @ SV356 @ SV886 ) )
          = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13097]) ).

thf(13347,plain,
    ! [SV886: nat,SV676: nat,SV356: nat] :
      ( ( ( SV356 != zero_zero_nat )
        = $false )
      | ( ( ( divide_divide_nat @ ( times_times_nat @ SV356 @ SV676 ) @ ( times_times_nat @ SV356 @ SV886 ) )
          = ( divide_divide_nat @ SV676 @ SV886 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13098]) ).

thf(13348,plain,
    ! [SV359: nat,SV678: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV678 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV359 @ SV678 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV359 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13099]) ).

thf(13349,plain,
    ! [SV361: nat,SV888: nat,SV680: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV680 @ SV888 ) )
        = $true )
      | ( ( SV361 = SV888 )
        = $true )
      | ( ( dvd_dvd_nat @ SV680 @ SV361 )
        = $false )
      | ( ( ( divide_divide_nat @ SV361 @ SV680 )
          = ( divide_divide_nat @ SV888 @ SV680 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13100]) ).

thf(13350,plain,
    ! [SV889: nat,SV362: nat,SV681: nat] :
      ( ( ( ~ ( ( ( divide_divide_nat @ SV681 @ SV362 )
                = ( divide_divide_nat @ SV889 @ SV362 ) )
              | ( SV681 = SV889 ) )
          | ~ ( ( ( divide_divide_nat @ SV681 @ SV362 )
               != ( divide_divide_nat @ SV889 @ SV362 ) )
              | ( SV681 != SV889 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV362 @ SV889 )
        = $false )
      | ( ( dvd_dvd_nat @ SV362 @ SV681 )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[13101]) ).

thf(13351,plain,
    ! [SV889: nat,SV362: nat,SV681: nat] :
      ( ( ( ( ( divide_divide_nat @ SV681 @ SV362 )
            = ( divide_divide_nat @ SV889 @ SV362 ) )
          = ( SV681 = SV889 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV362 @ SV889 )
        = $false )
      | ( ( dvd_dvd_nat @ SV362 @ SV681 )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[13101]) ).

thf(13352,plain,
    ! [SV683: nat,SV364: nat,SV946: nat,SV890: nat] :
      ( ( ( ord_less_nat @ SV890 @ SV946 )
        = $false )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV364 @ SV890 ) @ ( plus_plus_nat @ SV683 @ SV946 ) )
        = $true )
      | ( ( ord_less_nat @ SV364 @ SV683 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13103]) ).

thf(13353,plain,
    ! [SV684: nat,SV365: nat,SV947: nat,SV891: nat] :
      ( ( ( ord_less_eq_nat @ SV891 @ SV947 )
        = $false )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV365 @ SV891 ) @ ( plus_plus_nat @ SV684 @ SV947 ) )
        = $true )
      | ( ( ord_less_eq_nat @ SV365 @ SV684 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13104]) ).

thf(13354,plain,
    ! [SV692: option_nat,SV373: option_nat] :
      ( ( ( SV373 = none_nat )
        = $true )
      | ( ( SV692 = none_nat )
        = $true )
      | ( ( ~ ( ~ ( ( SV373 != none_nat ) )
              | ~ ( ( SV692 != none_nat ) )
              | ( ( the_nat @ SV373 )
                = ( the_nat @ SV692 ) ) )
          | ( SV373 = SV692 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13105]) ).

thf(13355,plain,
    ! [SV692: option_nat,SV373: option_nat] :
      ( ( ( SV373 != none_nat )
        = $true )
      | ( ( SV692 != none_nat )
        = $true )
      | ( ( ~ ( ~ ( ( SV373 != none_nat ) )
              | ~ ( ( SV692 != none_nat ) )
              | ( ( the_nat @ SV373 )
                = ( the_nat @ SV692 ) ) )
          | ( SV373 = SV692 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13106]) ).

thf(13356,plain,
    ! [SV692: option_nat,SV373: option_nat] :
      ( ( ( ~ ( ( SV373 != none_nat ) ) )
        = $false )
      | ( ( SV373 = SV692 )
        = $true )
      | ( ( ( SV373 = none_nat )
          = ( SV692 = none_nat ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13107]) ).

thf(13357,plain,
    ! [SV373: option_nat,SV692: option_nat] :
      ( ( ( ~ ( ( SV692 != none_nat ) )
          | ( ( the_nat @ SV373 )
            = ( the_nat @ SV692 ) ) )
        = $false )
      | ( ( SV373 = SV692 )
        = $true )
      | ( ( ( SV373 = none_nat )
          = ( SV692 = none_nat ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13107]) ).

thf(13358,plain,
    ! [SV693: nat,SV374: nat > $o] :
      ( ( ( ~ ! [SY1534: nat,SY1535: $o] :
                ( ~ ( SV374 @ SY1534 )
                | ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ SY1535 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1534 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                 != SY1534 )
                | ( SV374 @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ SY1535 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1534 ) ) ) ) )
        = $true )
      | ( ( SV374 @ SV693 )
        = $true )
      | ( ( ( divide_divide_nat @ ( sK8_SY1533 @ SV693 @ SV374 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( sK8_SY1533 @ SV693 @ SV374 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13108]) ).

thf(13359,plain,
    ! [SV693: nat,SV374: nat > $o] :
      ( ( ( ! [SY1534: nat,SY1535: $o] :
              ( ~ ( SV374 @ SY1534 )
              | ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ SY1535 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1534 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
               != SY1534 )
              | ( SV374 @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ SY1535 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1534 ) ) ) ) )
        = $false )
      | ( ( SV374 @ SV693 )
        = $true )
      | ( ( SV374 @ ( sK8_SY1533 @ SV693 @ SV374 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13109]) ).

thf(13360,plain,
    ! [SV948: nat,SV694: nat] :
      ( ( ( ord_less_eq_nat @ SV694 @ SV948 )
        = $false )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ SV694 @ SV948 )
              | ~ ~ ! [SY1929: nat] :
                      ( SV948
                     != ( plus_plus_nat @ SV694 @ SY1929 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13110]) ).

thf(13361,plain,
    ! [SV694: nat,SV948: nat] :
      ( ( ( ~ ! [SY1929: nat] :
                ( SV948
               != ( plus_plus_nat @ SV694 @ SY1929 ) ) )
        = $false )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ SV694 @ SV948 )
              | ~ ~ ! [SY1929: nat] :
                      ( SV948
                     != ( plus_plus_nat @ SV694 @ SY1929 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13110]) ).

thf(13362,plain,
    ! [SV697: nat,SV378: nat,SV949: nat,SV901: nat] :
      ( ( ( ord_less_eq_nat @ SV901 @ SV949 )
        = $false )
      | ( ( ord_less_eq_nat @ ( times_times_nat @ SV378 @ SV901 ) @ ( times_times_nat @ SV697 @ SV949 ) )
        = $true )
      | ( ( ord_less_eq_nat @ SV378 @ SV697 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13111]) ).

thf(13363,plain,
    ! [SV950: nat,SV902: nat,SV698: nat,SV379: nat] :
      ( ( ( ~ ( ord_less_nat @ SV379 @ SV698 ) )
        = $true )
      | ( ( SV902 != SV950 )
        = $true )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV379 @ SV902 ) @ ( plus_plus_nat @ SV698 @ SV950 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13112]) ).

thf(13364,plain,
    ! [SV382: num] :
      ( ( ( SV382
          = ( bit0 @ ( sK19_SY1550 @ SV382 ) ) )
        = $true )
      | ( ( ~ ! [SY1551: num] :
                ( SV382
               != ( bit1 @ SY1551 ) ) )
        = $true )
      | ( ( SV382 = one )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13113]) ).

thf(13365,plain,
    ! [SV905: nat,SV384: nat,SV960: nat,SV702: nat,SV952: nat] :
      ( ( ( ( modulo_modulo_nat @ SV952 @ SV702 )
         != ( modulo_modulo_nat @ SV960 @ SV702 ) )
        = $true )
      | ( ( ( modulo_modulo_nat @ ( plus_plus_nat @ SV384 @ SV952 ) @ SV702 )
          = ( modulo_modulo_nat @ ( plus_plus_nat @ SV905 @ SV960 ) @ SV702 ) )
        = $true )
      | ( ( ( modulo_modulo_nat @ SV384 @ SV702 )
          = ( modulo_modulo_nat @ SV905 @ SV702 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13115]) ).

thf(13366,plain,
    ! [SV705: nat,SV388: nat > nat,SV953: nat,SV908: nat > nat] :
      ( ( ( sums_nat @ SV908 @ SV953 )
        = $false )
      | ( ( sums_nat
          @ ^ [SY1914: nat] : ( plus_plus_nat @ ( SV388 @ SY1914 ) @ ( SV908 @ SY1914 ) )
          @ ( plus_plus_nat @ SV705 @ SV953 ) )
        = $true )
      | ( ( sums_nat @ SV388 @ SV705 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13116]) ).

thf(13367,plain,
    ! [SV399: num,SV10: num] :
      ( ( ( ( numeral_numeral_nat @ SV10 )
          = ( numeral_numeral_nat @ SV399 ) )
        = $true )
      | ( ( ( numeral_numeral_nat @ SV10 )
          = ( numeral_numeral_nat @ SV399 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13117]) ).

thf(13368,plain,
    ! [SV399: num,SV10: num] :
      ( ( ( SV10 = SV399 )
        = $true )
      | ( ( ( numeral_numeral_nat @ SV10 )
          = ( numeral_numeral_nat @ SV399 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13118]) ).

thf(13369,plain,
    ! [SV399: num,SV10: num] :
      ( ( ( ( numeral_numeral_nat @ SV10 )
          = ( numeral_numeral_nat @ SV399 ) )
        = $true )
      | ( ( SV10 = SV399 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13119]) ).

thf(13370,plain,
    ! [SV399: num,SV10: num] :
      ( ( ( SV10 = SV399 )
        = $true )
      | ( ( SV10 = SV399 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13120]) ).

thf(13371,plain,
    ! [SV427: nat,SV49: nat] :
      ( ( ( ord_less_eq_nat @ ( power_power_nat @ SV49 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ SV427 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $true )
      | ( ( ord_less_eq_nat @ ( power_power_nat @ SV49 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ SV427 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13121]) ).

thf(13372,plain,
    ! [SV427: nat,SV49: nat] :
      ( ( ( ord_less_eq_nat @ SV49 @ SV427 )
        = $true )
      | ( ( ord_less_eq_nat @ ( power_power_nat @ SV49 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ SV427 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13122]) ).

thf(13373,plain,
    ! [SV427: nat,SV49: nat] :
      ( ( ( ord_less_eq_nat @ ( power_power_nat @ SV49 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ SV427 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $true )
      | ( ( ord_less_eq_nat @ SV49 @ SV427 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13123]) ).

thf(13374,plain,
    ! [SV427: nat,SV49: nat] :
      ( ( ( ord_less_eq_nat @ SV49 @ SV427 )
        = $true )
      | ( ( ord_less_eq_nat @ SV49 @ SV427 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13124]) ).

thf(13375,plain,
    ! [SV428: num,SV53: num] :
      ( ( ( ord_less_num @ ( bit0 @ SV53 ) @ ( bit0 @ SV428 ) )
        = $true )
      | ( ( ord_less_num @ ( bit0 @ SV53 ) @ ( bit0 @ SV428 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13125]) ).

thf(13376,plain,
    ! [SV428: num,SV53: num] :
      ( ( ( ord_less_num @ SV53 @ SV428 )
        = $true )
      | ( ( ord_less_num @ ( bit0 @ SV53 ) @ ( bit0 @ SV428 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13126]) ).

thf(13377,plain,
    ! [SV428: num,SV53: num] :
      ( ( ( ord_less_num @ ( bit0 @ SV53 ) @ ( bit0 @ SV428 ) )
        = $true )
      | ( ( ord_less_num @ SV53 @ SV428 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13127]) ).

thf(13378,plain,
    ! [SV428: num,SV53: num] :
      ( ( ( ord_less_num @ SV53 @ SV428 )
        = $true )
      | ( ( ord_less_num @ SV53 @ SV428 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13128]) ).

thf(13379,plain,
    ! [SV429: num,SV54: num] :
      ( ( ( ( bit0 @ SV54 )
          = ( bit0 @ SV429 ) )
        = $true )
      | ( ( ( bit0 @ SV54 )
          = ( bit0 @ SV429 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13129]) ).

thf(13380,plain,
    ! [SV429: num,SV54: num] :
      ( ( ( SV54 = SV429 )
        = $true )
      | ( ( ( bit0 @ SV54 )
          = ( bit0 @ SV429 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13130]) ).

thf(13381,plain,
    ! [SV429: num,SV54: num] :
      ( ( ( ( bit0 @ SV54 )
          = ( bit0 @ SV429 ) )
        = $true )
      | ( ( SV54 = SV429 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13131]) ).

thf(13382,plain,
    ! [SV429: num,SV54: num] :
      ( ( ( SV54 = SV429 )
        = $true )
      | ( ( SV54 = SV429 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13132]) ).

thf(13383,plain,
    ! [SV432: num,SV62: num] :
      ( ( ( ord_less_eq_num @ ( bit0 @ SV62 ) @ ( bit0 @ SV432 ) )
        = $true )
      | ( ( ord_less_eq_num @ ( bit0 @ SV62 ) @ ( bit0 @ SV432 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13133]) ).

thf(13384,plain,
    ! [SV432: num,SV62: num] :
      ( ( ( ord_less_eq_num @ SV62 @ SV432 )
        = $true )
      | ( ( ord_less_eq_num @ ( bit0 @ SV62 ) @ ( bit0 @ SV432 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13134]) ).

thf(13385,plain,
    ! [SV432: num,SV62: num] :
      ( ( ( ord_less_eq_num @ ( bit0 @ SV62 ) @ ( bit0 @ SV432 ) )
        = $true )
      | ( ( ord_less_eq_num @ SV62 @ SV432 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13135]) ).

thf(13386,plain,
    ! [SV432: num,SV62: num] :
      ( ( ( ord_less_eq_num @ SV62 @ SV432 )
        = $true )
      | ( ( ord_less_eq_num @ SV62 @ SV432 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13136]) ).

thf(13387,plain,
    ! [SV729: nat,SV435: nat,SV71: nat] :
      ( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SV435 ) @ ( plus_plus_nat @ SV71 @ SV729 ) ) )
        = $false )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SV435 ) @ ( plus_plus_nat @ SV71 @ SV729 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13149]) ).

thf(13388,plain,
    ! [SV71: nat,SV729: nat,SV435: nat] :
      ( ( ( ~ ( ord_less_nat @ SV435 @ SV729 ) )
        = $false )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SV435 ) @ ( plus_plus_nat @ SV71 @ SV729 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13149]) ).

thf(13389,plain,
    ! [SV729: nat,SV435: nat,SV71: nat] :
      ( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SV435 ) @ ( plus_plus_nat @ SV71 @ SV729 ) ) )
        = $false )
      | ( ( ord_less_nat @ SV435 @ SV729 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13150]) ).

thf(13390,plain,
    ! [SV729: nat,SV435: nat] :
      ( ( ( ~ ( ord_less_nat @ SV435 @ SV729 ) )
        = $false )
      | ( ( ord_less_nat @ SV435 @ SV729 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13150]) ).

thf(13391,plain,
    ! [SV730: nat,SV436: nat,SV72: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV72 @ SV436 ) @ ( plus_plus_nat @ SV72 @ SV730 ) ) )
        = $false )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV72 @ SV436 ) @ ( plus_plus_nat @ SV72 @ SV730 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13151]) ).

thf(13392,plain,
    ! [SV72: nat,SV730: nat,SV436: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV436 @ SV730 ) )
        = $false )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV72 @ SV436 ) @ ( plus_plus_nat @ SV72 @ SV730 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13151]) ).

thf(13393,plain,
    ! [SV730: nat,SV436: nat,SV72: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV72 @ SV436 ) @ ( plus_plus_nat @ SV72 @ SV730 ) ) )
        = $false )
      | ( ( ord_less_eq_nat @ SV436 @ SV730 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13152]) ).

thf(13394,plain,
    ! [SV730: nat,SV436: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV436 @ SV730 ) )
        = $false )
      | ( ( ord_less_eq_nat @ SV436 @ SV730 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13152]) ).

thf(13395,plain,
    ! [SV736: nat,SV447: nat,SV86: nat] :
      ( ( ( ( times_times_nat @ ( suc @ SV86 ) @ SV447 )
         != ( times_times_nat @ ( suc @ SV86 ) @ SV736 ) )
        = $false )
      | ( ( ( times_times_nat @ ( suc @ SV86 ) @ SV447 )
          = ( times_times_nat @ ( suc @ SV86 ) @ SV736 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13153]) ).

thf(13396,plain,
    ! [SV86: nat,SV736: nat,SV447: nat] :
      ( ( ( SV447 != SV736 )
        = $false )
      | ( ( ( times_times_nat @ ( suc @ SV86 ) @ SV447 )
          = ( times_times_nat @ ( suc @ SV86 ) @ SV736 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13153]) ).

thf(13397,plain,
    ! [SV736: nat,SV447: nat,SV86: nat] :
      ( ( ( ( times_times_nat @ ( suc @ SV86 ) @ SV447 )
         != ( times_times_nat @ ( suc @ SV86 ) @ SV736 ) )
        = $false )
      | ( ( SV447 = SV736 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13154]) ).

thf(13398,plain,
    ! [SV736: nat,SV447: nat] :
      ( ( ( SV447 != SV736 )
        = $false )
      | ( ( SV447 = SV736 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13154]) ).

thf(13399,plain,
    ! [SV752: nat,SV475: nat,SV120: nat] :
      ( ( ( ( plus_plus_nat @ SV120 @ SV475 )
         != ( plus_plus_nat @ SV120 @ SV752 ) )
        = $false )
      | ( ( ( plus_plus_nat @ SV120 @ SV475 )
          = ( plus_plus_nat @ SV120 @ SV752 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13155]) ).

thf(13400,plain,
    ! [SV120: nat,SV752: nat,SV475: nat] :
      ( ( ( SV475 != SV752 )
        = $false )
      | ( ( ( plus_plus_nat @ SV120 @ SV475 )
          = ( plus_plus_nat @ SV120 @ SV752 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13155]) ).

thf(13401,plain,
    ! [SV752: nat,SV475: nat,SV120: nat] :
      ( ( ( ( plus_plus_nat @ SV120 @ SV475 )
         != ( plus_plus_nat @ SV120 @ SV752 ) )
        = $false )
      | ( ( SV475 = SV752 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13156]) ).

thf(13402,plain,
    ! [SV752: nat,SV475: nat] :
      ( ( ( SV475 != SV752 )
        = $false )
      | ( ( SV475 = SV752 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13156]) ).

thf(13403,plain,
    ! [SV753: nat,SV476: nat,SV121: nat] :
      ( ( ( ( plus_plus_nat @ SV121 @ SV476 )
         != ( plus_plus_nat @ SV753 @ SV476 ) )
        = $false )
      | ( ( ( plus_plus_nat @ SV121 @ SV476 )
          = ( plus_plus_nat @ SV753 @ SV476 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13157]) ).

thf(13404,plain,
    ! [SV476: nat,SV753: nat,SV121: nat] :
      ( ( ( SV121 != SV753 )
        = $false )
      | ( ( ( plus_plus_nat @ SV121 @ SV476 )
          = ( plus_plus_nat @ SV753 @ SV476 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13157]) ).

thf(13405,plain,
    ! [SV753: nat,SV476: nat,SV121: nat] :
      ( ( ( ( plus_plus_nat @ SV121 @ SV476 )
         != ( plus_plus_nat @ SV753 @ SV476 ) )
        = $false )
      | ( ( SV121 = SV753 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13158]) ).

thf(13406,plain,
    ! [SV753: nat,SV121: nat] :
      ( ( ( SV121 != SV753 )
        = $false )
      | ( ( SV121 = SV753 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13158]) ).

thf(13407,plain,
    ! [SV754: nat,SV477: nat,SV122: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ SV477 ) @ ( plus_plus_nat @ SV122 @ SV754 ) ) )
        = $false )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ SV477 ) @ ( plus_plus_nat @ SV122 @ SV754 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13159]) ).

thf(13408,plain,
    ! [SV122: nat,SV754: nat,SV477: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV477 @ SV754 ) )
        = $false )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ SV477 ) @ ( plus_plus_nat @ SV122 @ SV754 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13159]) ).

thf(13409,plain,
    ! [SV754: nat,SV477: nat,SV122: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ SV477 ) @ ( plus_plus_nat @ SV122 @ SV754 ) ) )
        = $false )
      | ( ( ord_less_eq_nat @ SV477 @ SV754 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13160]) ).

thf(13410,plain,
    ! [SV754: nat,SV477: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV477 @ SV754 ) )
        = $false )
      | ( ( ord_less_eq_nat @ SV477 @ SV754 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13160]) ).

thf(13411,plain,
    ! [SV755: nat,SV478: nat,SV123: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV123 @ SV478 ) @ ( plus_plus_nat @ SV755 @ SV478 ) ) )
        = $false )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV123 @ SV478 ) @ ( plus_plus_nat @ SV755 @ SV478 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13161]) ).

thf(13412,plain,
    ! [SV478: nat,SV755: nat,SV123: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV123 @ SV755 ) )
        = $false )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV123 @ SV478 ) @ ( plus_plus_nat @ SV755 @ SV478 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13161]) ).

thf(13413,plain,
    ! [SV755: nat,SV478: nat,SV123: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ ( plus_plus_nat @ SV123 @ SV478 ) @ ( plus_plus_nat @ SV755 @ SV478 ) ) )
        = $false )
      | ( ( ord_less_eq_nat @ SV123 @ SV755 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13162]) ).

thf(13414,plain,
    ! [SV755: nat,SV123: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV123 @ SV755 ) )
        = $false )
      | ( ( ord_less_eq_nat @ SV123 @ SV755 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13162]) ).

thf(13415,plain,
    ! [SV756: nat,SV479: nat,SV124: nat] :
      ( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV124 @ SV479 ) @ ( plus_plus_nat @ SV124 @ SV756 ) ) )
        = $false )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV124 @ SV479 ) @ ( plus_plus_nat @ SV124 @ SV756 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13163]) ).

thf(13416,plain,
    ! [SV124: nat,SV756: nat,SV479: nat] :
      ( ( ( ~ ( ord_less_nat @ SV479 @ SV756 ) )
        = $false )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV124 @ SV479 ) @ ( plus_plus_nat @ SV124 @ SV756 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13163]) ).

thf(13417,plain,
    ! [SV756: nat,SV479: nat,SV124: nat] :
      ( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV124 @ SV479 ) @ ( plus_plus_nat @ SV124 @ SV756 ) ) )
        = $false )
      | ( ( ord_less_nat @ SV479 @ SV756 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13164]) ).

thf(13418,plain,
    ! [SV756: nat,SV479: nat] :
      ( ( ( ~ ( ord_less_nat @ SV479 @ SV756 ) )
        = $false )
      | ( ( ord_less_nat @ SV479 @ SV756 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13164]) ).

thf(13419,plain,
    ! [SV757: nat,SV480: nat,SV125: nat] :
      ( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV125 @ SV480 ) @ ( plus_plus_nat @ SV757 @ SV480 ) ) )
        = $false )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV125 @ SV480 ) @ ( plus_plus_nat @ SV757 @ SV480 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13165]) ).

thf(13420,plain,
    ! [SV480: nat,SV757: nat,SV125: nat] :
      ( ( ( ~ ( ord_less_nat @ SV125 @ SV757 ) )
        = $false )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV125 @ SV480 ) @ ( plus_plus_nat @ SV757 @ SV480 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13165]) ).

thf(13421,plain,
    ! [SV757: nat,SV480: nat,SV125: nat] :
      ( ( ( ~ ( ord_less_nat @ ( plus_plus_nat @ SV125 @ SV480 ) @ ( plus_plus_nat @ SV757 @ SV480 ) ) )
        = $false )
      | ( ( ord_less_nat @ SV125 @ SV757 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13166]) ).

thf(13422,plain,
    ! [SV757: nat,SV125: nat] :
      ( ( ( ~ ( ord_less_nat @ SV125 @ SV757 ) )
        = $false )
      | ( ( ord_less_nat @ SV125 @ SV757 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13166]) ).

thf(13423,plain,
    ! [SV770: nat,SV493: nat,SV142: nat] :
      ( ( ( ( times_times_nat @ SV142 @ SV493 )
         != ( times_times_nat @ SV770 @ SV493 ) )
        = $false )
      | ( ( ( times_times_nat @ SV142 @ SV493 )
          = ( times_times_nat @ SV770 @ SV493 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13167]) ).

thf(13424,plain,
    ! [SV770: nat,SV142: nat,SV493: nat] :
      ( ( ( ~ ( ( SV493 = zero_zero_nat )
              | ( SV142 = SV770 ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV142 @ SV493 )
          = ( times_times_nat @ SV770 @ SV493 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13167]) ).

thf(13425,plain,
    ! [SV770: nat,SV493: nat,SV142: nat] :
      ( ( ( ( ( times_times_nat @ SV142 @ SV493 )
           != ( times_times_nat @ SV770 @ SV493 ) )
          | ~ ( ( SV493 = zero_zero_nat )
              | ( SV142 = SV770 ) ) )
        = $false )
      | ( ( SV493 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13168]) ).

thf(13426,plain,
    ! [SV770: nat,SV493: nat,SV142: nat] :
      ( ( ( ( ( times_times_nat @ SV142 @ SV493 )
           != ( times_times_nat @ SV770 @ SV493 ) )
          | ~ ( ( SV493 = zero_zero_nat )
              | ( SV142 = SV770 ) ) )
        = $false )
      | ( ( SV142 = SV770 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13169]) ).

thf(13427,plain,
    ! [SV771: nat,SV494: nat,SV143: nat] :
      ( ( ( ( times_times_nat @ SV143 @ SV494 )
         != ( times_times_nat @ SV143 @ SV771 ) )
        = $false )
      | ( ( ( times_times_nat @ SV143 @ SV494 )
          = ( times_times_nat @ SV143 @ SV771 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13170]) ).

thf(13428,plain,
    ! [SV771: nat,SV494: nat,SV143: nat] :
      ( ( ( ~ ( ( SV143 = zero_zero_nat )
              | ( SV494 = SV771 ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV143 @ SV494 )
          = ( times_times_nat @ SV143 @ SV771 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13170]) ).

thf(13429,plain,
    ! [SV771: nat,SV494: nat,SV143: nat] :
      ( ( ( ( ( times_times_nat @ SV143 @ SV494 )
           != ( times_times_nat @ SV143 @ SV771 ) )
          | ~ ( ( SV143 = zero_zero_nat )
              | ( SV494 = SV771 ) ) )
        = $false )
      | ( ( SV143 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13171]) ).

thf(13430,plain,
    ! [SV771: nat,SV494: nat,SV143: nat] :
      ( ( ( ( ( times_times_nat @ SV143 @ SV494 )
           != ( times_times_nat @ SV143 @ SV771 ) )
          | ~ ( ( SV143 = zero_zero_nat )
              | ( SV494 = SV771 ) ) )
        = $false )
      | ( ( SV494 = SV771 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13172]) ).

thf(13431,plain,
    ! [SV495: nat,SV144: nat] :
      ( ( ( ( times_times_nat @ SV144 @ SV495 )
          = zero_zero_nat )
        = $true )
      | ( ( ( times_times_nat @ SV144 @ SV495 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13173]) ).

thf(13432,plain,
    ! [SV495: nat,SV144: nat] :
      ( ( ( ( SV144 = zero_zero_nat )
          | ( SV495 = zero_zero_nat ) )
        = $true )
      | ( ( ( times_times_nat @ SV144 @ SV495 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13174]) ).

thf(13433,plain,
    ! [SV495: nat,SV144: nat] :
      ( ( ( ( times_times_nat @ SV144 @ SV495 )
         != zero_zero_nat )
        = $false )
      | ( ( SV144 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13175]) ).

thf(13434,plain,
    ! [SV495: nat,SV144: nat] :
      ( ( ( ~ ( ( SV144 = zero_zero_nat )
              | ( SV495 = zero_zero_nat ) ) )
        = $false )
      | ( ( SV144 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13175]) ).

thf(13435,plain,
    ! [SV495: nat,SV144: nat] :
      ( ( ( ( times_times_nat @ SV144 @ SV495 )
         != zero_zero_nat )
        = $false )
      | ( ( SV495 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13176]) ).

thf(13436,plain,
    ! [SV495: nat,SV144: nat] :
      ( ( ( ~ ( ( SV144 = zero_zero_nat )
              | ( SV495 = zero_zero_nat ) ) )
        = $false )
      | ( ( SV495 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13176]) ).

thf(13437,plain,
    ! [SV496: nat,SV148: nat] :
      ( ( ( SV148
          = ( plus_plus_nat @ SV148 @ SV496 ) )
        = $true )
      | ( ( SV148
          = ( plus_plus_nat @ SV148 @ SV496 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13177]) ).

thf(13438,plain,
    ! [SV148: nat,SV496: nat] :
      ( ( ( SV496 = zero_zero_nat )
        = $true )
      | ( ( SV148
          = ( plus_plus_nat @ SV148 @ SV496 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13178]) ).

thf(13439,plain,
    ! [SV496: nat,SV148: nat] :
      ( ( ( SV148
          = ( plus_plus_nat @ SV148 @ SV496 ) )
        = $true )
      | ( ( SV496 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13179]) ).

thf(13440,plain,
    ! [SV496: nat] :
      ( ( ( SV496 = zero_zero_nat )
        = $true )
      | ( ( SV496 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13180]) ).

thf(13441,plain,
    ! [SV497: nat,SV149: nat] :
      ( ( ( SV149
          = ( plus_plus_nat @ SV497 @ SV149 ) )
        = $true )
      | ( ( SV149
          = ( plus_plus_nat @ SV497 @ SV149 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13181]) ).

thf(13442,plain,
    ! [SV149: nat,SV497: nat] :
      ( ( ( SV497 = zero_zero_nat )
        = $true )
      | ( ( SV149
          = ( plus_plus_nat @ SV497 @ SV149 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13182]) ).

thf(13443,plain,
    ! [SV497: nat,SV149: nat] :
      ( ( ( SV149
          = ( plus_plus_nat @ SV497 @ SV149 ) )
        = $true )
      | ( ( SV497 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13183]) ).

thf(13444,plain,
    ! [SV497: nat] :
      ( ( ( SV497 = zero_zero_nat )
        = $true )
      | ( ( SV497 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13184]) ).

thf(13445,plain,
    ! [SV498: nat,SV150: nat] :
      ( ( ( ( plus_plus_nat @ SV150 @ SV498 )
          = SV150 )
        = $true )
      | ( ( ( plus_plus_nat @ SV150 @ SV498 )
          = SV150 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13185]) ).

thf(13446,plain,
    ! [SV150: nat,SV498: nat] :
      ( ( ( SV498 = zero_zero_nat )
        = $true )
      | ( ( ( plus_plus_nat @ SV150 @ SV498 )
          = SV150 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13186]) ).

thf(13447,plain,
    ! [SV498: nat,SV150: nat] :
      ( ( ( ( plus_plus_nat @ SV150 @ SV498 )
          = SV150 )
        = $true )
      | ( ( SV498 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13187]) ).

thf(13448,plain,
    ! [SV498: nat] :
      ( ( ( SV498 = zero_zero_nat )
        = $true )
      | ( ( SV498 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13188]) ).

thf(13449,plain,
    ! [SV499: nat,SV151: nat] :
      ( ( ( ( plus_plus_nat @ SV151 @ SV499 )
          = SV499 )
        = $true )
      | ( ( ( plus_plus_nat @ SV151 @ SV499 )
          = SV499 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13189]) ).

thf(13450,plain,
    ! [SV499: nat,SV151: nat] :
      ( ( ( SV151 = zero_zero_nat )
        = $true )
      | ( ( ( plus_plus_nat @ SV151 @ SV499 )
          = SV499 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13190]) ).

thf(13451,plain,
    ! [SV499: nat,SV151: nat] :
      ( ( ( ( plus_plus_nat @ SV151 @ SV499 )
          = SV499 )
        = $true )
      | ( ( SV151 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13191]) ).

thf(13452,plain,
    ! [SV151: nat] :
      ( ( ( SV151 = zero_zero_nat )
        = $true )
      | ( ( SV151 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13192]) ).

thf(13453,plain,
    ! [SV772: nat,SV502: nat,SV160: nat] :
      ( ( ( ( times_times_nat @ SV160 @ SV502 )
         != ( times_times_nat @ SV772 @ SV502 ) )
        = $false )
      | ( ( ( times_times_nat @ SV160 @ SV502 )
          = ( times_times_nat @ SV772 @ SV502 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13193]) ).

thf(13454,plain,
    ! [SV502: nat,SV772: nat,SV160: nat] :
      ( ( ( ~ ( ( SV160 = SV772 )
              | ( SV502 = zero_zero_nat ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV160 @ SV502 )
          = ( times_times_nat @ SV772 @ SV502 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13193]) ).

thf(13455,plain,
    ! [SV772: nat,SV502: nat,SV160: nat] :
      ( ( ( ( ( times_times_nat @ SV160 @ SV502 )
           != ( times_times_nat @ SV772 @ SV502 ) )
          | ~ ( ( SV160 = SV772 )
              | ( SV502 = zero_zero_nat ) ) )
        = $false )
      | ( ( SV160 = SV772 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13194]) ).

thf(13456,plain,
    ! [SV772: nat,SV502: nat,SV160: nat] :
      ( ( ( ( ( times_times_nat @ SV160 @ SV502 )
           != ( times_times_nat @ SV772 @ SV502 ) )
          | ~ ( ( SV160 = SV772 )
              | ( SV502 = zero_zero_nat ) ) )
        = $false )
      | ( ( SV502 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13195]) ).

thf(13457,plain,
    ! [SV773: nat,SV503: nat,SV161: nat] :
      ( ( ( ( times_times_nat @ SV161 @ SV503 )
         != ( times_times_nat @ SV161 @ SV773 ) )
        = $false )
      | ( ( ( times_times_nat @ SV161 @ SV503 )
          = ( times_times_nat @ SV161 @ SV773 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13196]) ).

thf(13458,plain,
    ! [SV161: nat,SV773: nat,SV503: nat] :
      ( ( ( ~ ( ( SV503 = SV773 )
              | ( SV161 = zero_zero_nat ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV161 @ SV503 )
          = ( times_times_nat @ SV161 @ SV773 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13196]) ).

thf(13459,plain,
    ! [SV773: nat,SV503: nat,SV161: nat] :
      ( ( ( ( ( times_times_nat @ SV161 @ SV503 )
           != ( times_times_nat @ SV161 @ SV773 ) )
          | ~ ( ( SV503 = SV773 )
              | ( SV161 = zero_zero_nat ) ) )
        = $false )
      | ( ( SV503 = SV773 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13197]) ).

thf(13460,plain,
    ! [SV773: nat,SV503: nat,SV161: nat] :
      ( ( ( ( ( times_times_nat @ SV161 @ SV503 )
           != ( times_times_nat @ SV161 @ SV773 ) )
          | ~ ( ( SV503 = SV773 )
              | ( SV161 = zero_zero_nat ) ) )
        = $false )
      | ( ( SV161 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13198]) ).

thf(13461,plain,
    ! [SV504: nat,SV163: nat] :
      ( ( ( ( times_times_nat @ SV163 @ SV504 )
          = zero_zero_nat )
        = $true )
      | ( ( ( times_times_nat @ SV163 @ SV504 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13199]) ).

thf(13462,plain,
    ! [SV504: nat,SV163: nat] :
      ( ( ( ( SV163 = zero_zero_nat )
          | ( SV504 = zero_zero_nat ) )
        = $true )
      | ( ( ( times_times_nat @ SV163 @ SV504 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13200]) ).

thf(13463,plain,
    ! [SV504: nat,SV163: nat] :
      ( ( ( ( times_times_nat @ SV163 @ SV504 )
         != zero_zero_nat )
        = $false )
      | ( ( SV163 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13201]) ).

thf(13464,plain,
    ! [SV504: nat,SV163: nat] :
      ( ( ( ~ ( ( SV163 = zero_zero_nat )
              | ( SV504 = zero_zero_nat ) ) )
        = $false )
      | ( ( SV163 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13201]) ).

thf(13465,plain,
    ! [SV504: nat,SV163: nat] :
      ( ( ( ( times_times_nat @ SV163 @ SV504 )
         != zero_zero_nat )
        = $false )
      | ( ( SV504 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13202]) ).

thf(13466,plain,
    ! [SV504: nat,SV163: nat] :
      ( ( ( ~ ( ( SV163 = zero_zero_nat )
              | ( SV504 = zero_zero_nat ) ) )
        = $false )
      | ( ( SV504 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13202]) ).

thf(13467,plain,
    ! [SV787: num,SV518: num,SV179: num] :
      ( ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV179 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) )
         != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV787 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) ) )
        = $false )
      | ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV179 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) )
          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV787 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13207]) ).

thf(13468,plain,
    ! [SV787: num,SV518: num,SV179: num] :
      ( ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV179 ) @ ( numeral_numeral_nat @ SV518 ) )
         != ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV787 ) @ ( numeral_numeral_nat @ SV518 ) ) )
        = $false )
      | ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV179 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) )
          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV787 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13207]) ).

thf(13469,plain,
    ! [SV787: num,SV518: num,SV179: num] :
      ( ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV179 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) )
         != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV787 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) ) )
        = $false )
      | ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV179 ) @ ( numeral_numeral_nat @ SV518 ) )
          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV787 ) @ ( numeral_numeral_nat @ SV518 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13208]) ).

thf(13470,plain,
    ! [SV787: num,SV518: num,SV179: num] :
      ( ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV179 ) @ ( numeral_numeral_nat @ SV518 ) )
         != ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV787 ) @ ( numeral_numeral_nat @ SV518 ) ) )
        = $false )
      | ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV179 ) @ ( numeral_numeral_nat @ SV518 ) )
          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV787 ) @ ( numeral_numeral_nat @ SV518 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13208]) ).

thf(13471,plain,
    ! [SV788: nat,SV520: nat,SV185: nat] :
      ( ( ( ( times_times_nat @ SV185 @ SV520 )
         != ( times_times_nat @ SV185 @ SV788 ) )
        = $false )
      | ( ( ( times_times_nat @ SV185 @ SV520 )
          = ( times_times_nat @ SV185 @ SV788 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13209]) ).

thf(13472,plain,
    ! [SV788: nat,SV520: nat,SV185: nat] :
      ( ( ( ~ ( ( SV185 = zero_zero_nat )
              | ( SV520 = SV788 ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV185 @ SV520 )
          = ( times_times_nat @ SV185 @ SV788 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13209]) ).

thf(13473,plain,
    ! [SV788: nat,SV520: nat,SV185: nat] :
      ( ( ( ( ( times_times_nat @ SV185 @ SV520 )
           != ( times_times_nat @ SV185 @ SV788 ) )
          | ~ ( ( SV185 = zero_zero_nat )
              | ( SV520 = SV788 ) ) )
        = $false )
      | ( ( SV185 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13210]) ).

thf(13474,plain,
    ! [SV788: nat,SV520: nat,SV185: nat] :
      ( ( ( ( ( times_times_nat @ SV185 @ SV520 )
           != ( times_times_nat @ SV185 @ SV788 ) )
          | ~ ( ( SV185 = zero_zero_nat )
              | ( SV520 = SV788 ) ) )
        = $false )
      | ( ( SV520 = SV788 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13211]) ).

thf(13475,plain,
    ! [SV534: num,SV199: num] :
      ( ( ( ( bit0 @ SV199 )
          = ( bit0 @ SV534 ) )
        = $true )
      | ( ( ( bit0 @ SV199 )
          = ( bit0 @ SV534 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13212]) ).

thf(13476,plain,
    ! [SV534: num,SV199: num] :
      ( ( ( SV199 = SV534 )
        = $true )
      | ( ( ( bit0 @ SV199 )
          = ( bit0 @ SV534 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13213]) ).

thf(13477,plain,
    ! [SV534: num,SV199: num] :
      ( ( ( ( bit0 @ SV199 )
          = ( bit0 @ SV534 ) )
        = $true )
      | ( ( SV199 = SV534 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13214]) ).

thf(13478,plain,
    ! [SV534: num,SV199: num] :
      ( ( ( SV199 = SV534 )
        = $true )
      | ( ( SV199 = SV534 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13215]) ).

thf(13479,plain,
    ! [SV535: nat,SV201: nat] :
      ( ( ( dvd_dvd_nat @ SV201 @ ( plus_plus_nat @ SV535 @ SV201 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV201 @ ( plus_plus_nat @ SV535 @ SV201 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13216]) ).

thf(13480,plain,
    ! [SV535: nat,SV201: nat] :
      ( ( ( dvd_dvd_nat @ SV201 @ SV535 )
        = $true )
      | ( ( dvd_dvd_nat @ SV201 @ ( plus_plus_nat @ SV535 @ SV201 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13217]) ).

thf(13481,plain,
    ! [SV535: nat,SV201: nat] :
      ( ( ( dvd_dvd_nat @ SV201 @ ( plus_plus_nat @ SV535 @ SV201 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV201 @ SV535 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13218]) ).

thf(13482,plain,
    ! [SV535: nat,SV201: nat] :
      ( ( ( dvd_dvd_nat @ SV201 @ SV535 )
        = $true )
      | ( ( dvd_dvd_nat @ SV201 @ SV535 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13219]) ).

thf(13483,plain,
    ! [SV536: nat,SV202: nat] :
      ( ( ( dvd_dvd_nat @ SV202 @ ( plus_plus_nat @ SV202 @ SV536 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV202 @ ( plus_plus_nat @ SV202 @ SV536 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13220]) ).

thf(13484,plain,
    ! [SV536: nat,SV202: nat] :
      ( ( ( dvd_dvd_nat @ SV202 @ SV536 )
        = $true )
      | ( ( dvd_dvd_nat @ SV202 @ ( plus_plus_nat @ SV202 @ SV536 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13221]) ).

thf(13485,plain,
    ! [SV536: nat,SV202: nat] :
      ( ( ( dvd_dvd_nat @ SV202 @ ( plus_plus_nat @ SV202 @ SV536 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV202 @ SV536 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13222]) ).

thf(13486,plain,
    ! [SV536: nat,SV202: nat] :
      ( ( ( dvd_dvd_nat @ SV202 @ SV536 )
        = $true )
      | ( ( dvd_dvd_nat @ SV202 @ SV536 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13223]) ).

thf(13487,plain,
    ! [SV795: nat,SV537: nat,SV203: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV203 @ ( plus_plus_nat @ SV537 @ ( times_times_nat @ SV795 @ SV203 ) ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV203 @ ( plus_plus_nat @ SV537 @ ( times_times_nat @ SV795 @ SV203 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13224]) ).

thf(13488,plain,
    ! [SV795: nat,SV537: nat,SV203: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV203 @ SV537 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV203 @ ( plus_plus_nat @ SV537 @ ( times_times_nat @ SV795 @ SV203 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13224]) ).

thf(13489,plain,
    ! [SV795: nat,SV537: nat,SV203: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV203 @ ( plus_plus_nat @ SV537 @ ( times_times_nat @ SV795 @ SV203 ) ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV203 @ SV537 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13225]) ).

thf(13490,plain,
    ! [SV537: nat,SV203: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV203 @ SV537 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV203 @ SV537 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13225]) ).

thf(13491,plain,
    ! [SV796: nat,SV538: nat,SV204: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV204 @ ( plus_plus_nat @ ( times_times_nat @ SV538 @ SV204 ) @ SV796 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV204 @ ( plus_plus_nat @ ( times_times_nat @ SV538 @ SV204 ) @ SV796 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13226]) ).

thf(13492,plain,
    ! [SV538: nat,SV796: nat,SV204: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV204 @ SV796 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV204 @ ( plus_plus_nat @ ( times_times_nat @ SV538 @ SV204 ) @ SV796 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13226]) ).

thf(13493,plain,
    ! [SV796: nat,SV538: nat,SV204: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV204 @ ( plus_plus_nat @ ( times_times_nat @ SV538 @ SV204 ) @ SV796 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV204 @ SV796 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13227]) ).

thf(13494,plain,
    ! [SV796: nat,SV204: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV204 @ SV796 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV204 @ SV796 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13227]) ).

thf(13495,plain,
    ! [SV539: nat,SV205: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ SV205 @ SV539 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ SV205 @ SV539 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13228]) ).

thf(13496,plain,
    ! [SV539: nat,SV205: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ SV205 @ SV539 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13229]) ).

thf(13497,plain,
    ! [SV539: nat,SV205: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ SV205 @ SV539 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13230]) ).

thf(13498,plain,
    ! [SV539: nat,SV205: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
              | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13230]) ).

thf(13499,plain,
    ! [SV539: nat,SV205: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ SV205 @ SV539 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13231]) ).

thf(13500,plain,
    ! [SV539: nat,SV205: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
              | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13231]) ).

thf(13501,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13232]) ).

thf(13502,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13233]) ).

thf(13503,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $true )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
              | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
               != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13234]) ).

thf(13504,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $true )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
              | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
               != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13235]) ).

thf(13505,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) ) )
        = $false )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13236]) ).

thf(13506,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
         != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13236]) ).

thf(13507,plain,
    ! [SV548: nat,SV215: nat] :
      ( ( ( SV215
          = ( plus_plus_nat @ SV215 @ SV548 ) )
        = $true )
      | ( ( SV215
          = ( plus_plus_nat @ SV215 @ SV548 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13237]) ).

thf(13508,plain,
    ! [SV215: nat,SV548: nat] :
      ( ( ( SV548 = zero_zero_nat )
        = $true )
      | ( ( SV215
          = ( plus_plus_nat @ SV215 @ SV548 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13238]) ).

thf(13509,plain,
    ! [SV548: nat,SV215: nat] :
      ( ( ( SV215
          = ( plus_plus_nat @ SV215 @ SV548 ) )
        = $true )
      | ( ( SV548 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13239]) ).

thf(13510,plain,
    ! [SV548: nat] :
      ( ( ( SV548 = zero_zero_nat )
        = $true )
      | ( ( SV548 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13240]) ).

thf(13511,plain,
    ! [SV922: nat,SV802: nat,SV549: nat,SV216: nat] :
      ( ( ( ( ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV549 ) @ ( times_times_nat @ SV802 @ SV922 ) )
           != ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV922 ) @ ( times_times_nat @ SV802 @ SV549 ) ) )
          | ~ ( ( SV216 = SV802 )
              | ( SV549 = SV922 ) ) )
        = $false )
      | ( ( ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV549 ) @ ( times_times_nat @ SV802 @ SV922 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV922 ) @ ( times_times_nat @ SV802 @ SV549 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13241]) ).

thf(13512,plain,
    ! [SV922: nat,SV549: nat,SV802: nat,SV216: nat] :
      ( ( ( SV216 = SV802 )
        = $false )
      | ( ( ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV549 ) @ ( times_times_nat @ SV802 @ SV922 ) )
               != ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV922 ) @ ( times_times_nat @ SV802 @ SV549 ) ) )
              | ~ ( ( SV216 = SV802 )
                  | ( SV549 = SV922 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13242]) ).

thf(13513,plain,
    ! [SV802: nat,SV216: nat,SV922: nat,SV549: nat] :
      ( ( ( SV549 = SV922 )
        = $false )
      | ( ( ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV549 ) @ ( times_times_nat @ SV802 @ SV922 ) )
               != ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV922 ) @ ( times_times_nat @ SV802 @ SV549 ) ) )
              | ~ ( ( SV216 = SV802 )
                  | ( SV549 = SV922 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13242]) ).

thf(13514,plain,
    ! [SV803: nat,SV554: nat,SV224: nat] :
      ( ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV224 ) @ SV554 )
         != ( semiri1316708129612266289at_nat @ SV803 ) )
        = $false )
      | ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV224 ) @ SV554 )
          = ( semiri1316708129612266289at_nat @ SV803 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13243]) ).

thf(13515,plain,
    ! [SV803: nat,SV554: nat,SV224: nat] :
      ( ( ( ( power_power_nat @ SV224 @ SV554 )
         != SV803 )
        = $false )
      | ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV224 ) @ SV554 )
          = ( semiri1316708129612266289at_nat @ SV803 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13243]) ).

thf(13516,plain,
    ! [SV803: nat,SV554: nat,SV224: nat] :
      ( ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV224 ) @ SV554 )
         != ( semiri1316708129612266289at_nat @ SV803 ) )
        = $false )
      | ( ( ( power_power_nat @ SV224 @ SV554 )
          = SV803 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13244]) ).

thf(13517,plain,
    ! [SV803: nat,SV554: nat,SV224: nat] :
      ( ( ( ( power_power_nat @ SV224 @ SV554 )
         != SV803 )
        = $false )
      | ( ( ( power_power_nat @ SV224 @ SV554 )
          = SV803 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13244]) ).

thf(13518,plain,
    ! [SV804: nat,SV555: nat,SV225: nat] :
      ( ( ( ( semiri1316708129612266289at_nat @ SV225 )
         != ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV555 ) @ SV804 ) )
        = $false )
      | ( ( ( semiri1316708129612266289at_nat @ SV225 )
          = ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV555 ) @ SV804 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13245]) ).

thf(13519,plain,
    ! [SV804: nat,SV555: nat,SV225: nat] :
      ( ( ( SV225
         != ( power_power_nat @ SV555 @ SV804 ) )
        = $false )
      | ( ( ( semiri1316708129612266289at_nat @ SV225 )
          = ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV555 ) @ SV804 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13245]) ).

thf(13520,plain,
    ! [SV804: nat,SV555: nat,SV225: nat] :
      ( ( ( ( semiri1316708129612266289at_nat @ SV225 )
         != ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV555 ) @ SV804 ) )
        = $false )
      | ( ( SV225
          = ( power_power_nat @ SV555 @ SV804 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13246]) ).

thf(13521,plain,
    ! [SV804: nat,SV555: nat,SV225: nat] :
      ( ( ( SV225
         != ( power_power_nat @ SV555 @ SV804 ) )
        = $false )
      | ( ( SV225
          = ( power_power_nat @ SV555 @ SV804 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13246]) ).

thf(13522,plain,
    ! [SV805: nat,SV556: nat,SV226: num] :
      ( ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
         != ( semiri1316708129612266289at_nat @ SV805 ) )
        = $false )
      | ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
          = ( semiri1316708129612266289at_nat @ SV805 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13247]) ).

thf(13523,plain,
    ! [SV805: nat,SV556: nat,SV226: num] :
      ( ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
         != SV805 )
        = $false )
      | ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
          = ( semiri1316708129612266289at_nat @ SV805 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13247]) ).

thf(13524,plain,
    ! [SV805: nat,SV556: nat,SV226: num] :
      ( ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
         != ( semiri1316708129612266289at_nat @ SV805 ) )
        = $false )
      | ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
          = SV805 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13248]) ).

thf(13525,plain,
    ! [SV805: nat,SV556: nat,SV226: num] :
      ( ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
         != SV805 )
        = $false )
      | ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
          = SV805 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13248]) ).

thf(13526,plain,
    ! [SV806: nat,SV557: num,SV227: nat] :
      ( ( ( ( semiri1316708129612266289at_nat @ SV227 )
         != ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
        = $false )
      | ( ( ( semiri1316708129612266289at_nat @ SV227 )
          = ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13249]) ).

thf(13527,plain,
    ! [SV806: nat,SV557: num,SV227: nat] :
      ( ( ( SV227
         != ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
        = $false )
      | ( ( ( semiri1316708129612266289at_nat @ SV227 )
          = ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13249]) ).

thf(13528,plain,
    ! [SV806: nat,SV557: num,SV227: nat] :
      ( ( ( ( semiri1316708129612266289at_nat @ SV227 )
         != ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
        = $false )
      | ( ( SV227
          = ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13250]) ).

thf(13529,plain,
    ! [SV806: nat,SV557: num,SV227: nat] :
      ( ( ( SV227
         != ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
        = $false )
      | ( ( SV227
          = ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13250]) ).

thf(13530,plain,
    ! [SV561: nat,SV231: nat > real] :
      ( ( ( summable_real
          @ ^ [SY1684: nat] : ( SV231 @ ( plus_plus_nat @ SY1684 @ SV561 ) ) )
        = $true )
      | ( ( summable_real
          @ ^ [SY1684: nat] : ( SV231 @ ( plus_plus_nat @ SY1684 @ SV561 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13251]) ).

thf(13531,plain,
    ! [SV561: nat,SV231: nat > real] :
      ( ( ( summable_real @ SV231 )
        = $true )
      | ( ( summable_real
          @ ^ [SY1684: nat] : ( SV231 @ ( plus_plus_nat @ SY1684 @ SV561 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13252]) ).

thf(13532,plain,
    ! [SV561: nat,SV231: nat > real] :
      ( ( ( summable_real
          @ ^ [SY1684: nat] : ( SV231 @ ( plus_plus_nat @ SY1684 @ SV561 ) ) )
        = $true )
      | ( ( summable_real @ SV231 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13253]) ).

thf(13533,plain,
    ! [SV231: nat > real] :
      ( ( ( summable_real @ SV231 )
        = $true )
      | ( ( summable_real @ SV231 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13254]) ).

thf(13534,plain,
    ! [SV562: nat,SV232: nat > complex] :
      ( ( ( summable_complex
          @ ^ [SY1685: nat] : ( SV232 @ ( plus_plus_nat @ SY1685 @ SV562 ) ) )
        = $true )
      | ( ( summable_complex
          @ ^ [SY1685: nat] : ( SV232 @ ( plus_plus_nat @ SY1685 @ SV562 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13255]) ).

thf(13535,plain,
    ! [SV562: nat,SV232: nat > complex] :
      ( ( ( summable_complex @ SV232 )
        = $true )
      | ( ( summable_complex
          @ ^ [SY1685: nat] : ( SV232 @ ( plus_plus_nat @ SY1685 @ SV562 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13256]) ).

thf(13536,plain,
    ! [SV562: nat,SV232: nat > complex] :
      ( ( ( summable_complex
          @ ^ [SY1685: nat] : ( SV232 @ ( plus_plus_nat @ SY1685 @ SV562 ) ) )
        = $true )
      | ( ( summable_complex @ SV232 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13257]) ).

thf(13537,plain,
    ! [SV232: nat > complex] :
      ( ( ( summable_complex @ SV232 )
        = $true )
      | ( ( summable_complex @ SV232 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13258]) ).

thf(13538,plain,
    ! [SV243: $o] :
      ( ( SV243 = $true )
      | ( SV243 = $false )
      | ( ( SV243 = $false )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13259]) ).

thf(13539,plain,
    ! [SV243: $o] :
      ( ( $true = $true )
      | ( SV243 = $false )
      | ( ( SV243 = $false )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13260]) ).

thf(13540,plain,
    ! [SV243: $o] :
      ( ( SV243 = $true )
      | ( $true = $false )
      | ( ( SV243 = $false )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13261]) ).

thf(13541,plain,
    ! [SV243: $o] :
      ( ( $true = $true )
      | ( $true = $false )
      | ( ( SV243 = $false )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13262]) ).

thf(13542,plain,
    ! [SV243: $o] :
      ( ( ( ~ SV243 ) = $false )
      | ( SV243 = $false )
      | ( ( SV243 = $true )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13263]) ).

thf(13543,plain,
    ! [SV243: $o] :
      ( ( ( ~ $false ) = $false )
      | ( SV243 = $false )
      | ( ( SV243 = $true )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13263]) ).

thf(13544,plain,
    ! [SV243: $o] :
      ( ( ( ~ SV243 ) = $false )
      | ( $false = $false )
      | ( ( SV243 = $true )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13264]) ).

thf(13545,plain,
    ! [SV243: $o] :
      ( ( ( ~ $false ) = $false )
      | ( $false = $false )
      | ( ( SV243 = $true )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13264]) ).

thf(13546,plain,
    ( ( $true = $true )
    | ( $true = $false )
    | ( ( $true = $false )
      = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13265]) ).

thf(13547,plain,
    ( ( $true = $true )
    | ( $true = $false )
    | ( ( $true = $false )
      = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13266]) ).

thf(13548,plain,
    ( ( $true = $true )
    | ( $true = $false )
    | ( ( $true = $false )
      = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13267]) ).

thf(13549,plain,
    ( ( $true = $true )
    | ( $true = $false )
    | ( ( $true = $false )
      = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13268]) ).

thf(13550,plain,
    ( ( ( ~ $true ) = $false )
    | ( $true = $false )
    | ( ( $true = $true )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13269]) ).

thf(13551,plain,
    ( ( ( ~ $false ) = $false )
    | ( $true = $false )
    | ( ( $true = $true )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13269]) ).

thf(13552,plain,
    ( ( ( ~ $true ) = $false )
    | ( $false = $false )
    | ( ( $true = $true )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13270]) ).

thf(13553,plain,
    ( ( ( ~ $false ) = $false )
    | ( $false = $false )
    | ( ( $true = $true )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13270]) ).

thf(13554,plain,
    ( ( $false = $true )
    | ( $false = $false )
    | ( ( $false = $false )
      = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13271]) ).

thf(13555,plain,
    ( ( $true = $true )
    | ( $false = $false )
    | ( ( $false = $false )
      = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13272]) ).

thf(13556,plain,
    ( ( $false = $true )
    | ( $true = $false )
    | ( ( $false = $false )
      = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13273]) ).

thf(13557,plain,
    ( ( $true = $true )
    | ( $true = $false )
    | ( ( $false = $false )
      = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13274]) ).

thf(13558,plain,
    ( ( ( ~ $false ) = $false )
    | ( $false = $false )
    | ( ( $false = $true )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13275]) ).

thf(13559,plain,
    ( ( ( ~ $false ) = $false )
    | ( $false = $false )
    | ( ( $false = $true )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13275]) ).

thf(13560,plain,
    ( ( ( ~ $false ) = $false )
    | ( $false = $false )
    | ( ( $false = $true )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13276]) ).

thf(13561,plain,
    ( ( ( ~ $false ) = $false )
    | ( $false = $false )
    | ( ( $false = $true )
      = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13276]) ).

thf(13562,plain,
    ! [SV824: nat,SV581: nat,SV255: nat] :
      ( ( ( SV255 = zero_zero_nat )
        = $true )
      | ( ( ( divide_divide_nat @ ( times_times_nat @ SV255 @ SV581 ) @ ( times_times_nat @ SV255 @ SV824 ) )
          = ( divide_divide_nat @ SV581 @ SV824 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13279]) ).

thf(13563,plain,
    ! [SV825: nat,SV257: nat,SV583: nat] :
      ( ( ( ( ( times_times_nat @ SV583 @ SV257 )
            = ( times_times_nat @ SV825 @ SV257 ) )
          | ( SV583 = SV825 ) )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV583 @ SV257 )
               != ( times_times_nat @ SV825 @ SV257 ) )
              | ( SV583 != SV825 ) ) )
        = $true )
      | ( ( SV257 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13280]) ).

thf(13564,plain,
    ! [SV584: nat,SV826: nat,SV258: nat] :
      ( ( ( SV258
         != ( times_times_nat @ ( sK13_SY1869 @ SV826 @ SV584 @ SV258 ) @ ( sK20_SY1935 @ SV584 @ SV826 @ SV258 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV258 @ ( times_times_nat @ SV584 @ SV826 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13281]) ).

thf(13565,plain,
    ! [SV258: nat,SV584: nat,SV826: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( sK13_SY1869 @ SV826 @ SV584 @ SV258 ) @ SV584 )
          | ~ ( dvd_dvd_nat @ ( sK20_SY1935 @ SV584 @ SV826 @ SV258 ) @ SV826 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV258 @ ( times_times_nat @ SV584 @ SV826 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13281]) ).

thf(13566,plain,
    ! [SV926: nat,SV827: nat,SV586: nat,SV260: nat] :
      ( ( ( SV260 = SV586 )
        = $false )
      | ( ( SV827 != SV926 )
        = $true )
      | ( ( ( plus_plus_nat @ SV260 @ SV827 )
          = ( plus_plus_nat @ SV586 @ SV926 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13282]) ).

thf(13567,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( SV595 != SV928 )
          | ~ ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                 != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
                | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                 != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
        = $false )
      | ( ( SV595 = SV928 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13285]) ).

thf(13568,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
           != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
          | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
           != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
        = $true )
      | ( ( ~ ( ( SV595 != SV928 )
              | ~ ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                     != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
                    | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                     != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13286]) ).

thf(13569,plain,
    ! [SV837: nat,SV597: nat,SV273: nat] :
      ( ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
         != ( modulo_modulo_nat @ SV837 @ SV597 ) )
        = $false )
      | ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
          = ( modulo_modulo_nat @ SV837 @ SV597 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13288]) ).

thf(13570,plain,
    ! [SV837: nat,SV597: nat,SV273: nat] :
      ( ( ( ~ ~ ! [SY1874: nat] :
                  ~ ~ ! [SY1875: nat] :
                        ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SY1874 ) )
                       != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1875 ) ) ) )
        = $false )
      | ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
          = ( modulo_modulo_nat @ SV837 @ SV597 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13288]) ).

thf(13571,plain,
    ! [SV837: nat,SV962: nat,SV597: nat,SV273: nat] :
      ( ( ( ~ ~ ! [SY1938: nat] :
                  ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SV962 ) )
                 != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1938 ) ) ) )
        = $true )
      | ( ( ~ ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
               != ( modulo_modulo_nat @ SV837 @ SV597 ) )
              | ~ ~ ! [SY1874: nat] :
                      ~ ~ ! [SY1875: nat] :
                            ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SY1874 ) )
                           != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1875 ) ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[13289]) ).

thf(13572,plain,
    ! [SV601: nat,SV280: nat] :
      ( ( ( SV280 = zero_zero_nat )
        = $false )
      | ( ( ( times_times_nat @ SV280 @ SV601 )
          = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13290]) ).

thf(13573,plain,
    ! [SV280: nat,SV601: nat] :
      ( ( ( SV601 = zero_zero_nat )
        = $false )
      | ( ( ( times_times_nat @ SV280 @ SV601 )
          = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13291]) ).

thf(13574,plain,
    ! [SV931: nat,SV844: nat,SV605: nat,SV284: nat] :
      ( ( ( ~ ( ( SV284 != SV605 ) )
          | ~ ( ( SV844 != SV931 ) ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( ( SV284 != SV605 ) )
                    | ~ ( ( SV844 != SV931 ) ) )
              | ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
                   != ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13292]) ).

thf(13575,plain,
    ! [SV931: nat,SV605: nat,SV844: nat,SV284: nat] :
      ( ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( ( SV284 != SV605 ) )
                    | ~ ( ( SV844 != SV931 ) ) )
              | ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
                   != ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13293]) ).

thf(13576,plain,
    ! [SV845: nat,SV606: nat,SV285: nat] :
      ( ( ( ( ( times_times_nat @ SV285 @ SV606 )
            = ( times_times_nat @ SV285 @ SV845 ) )
          | ( SV606 = SV845 ) )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV285 @ SV606 )
               != ( times_times_nat @ SV285 @ SV845 ) )
              | ( SV606 != SV845 ) ) )
        = $true )
      | ( ( SV285 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13294]) ).

thf(13577,plain,
    ! [SV608: nat,SV287: nat] :
      ( ( ( ( times_times_nat @ SV287 @ SV608 )
          = zero_zero_nat )
        = $false )
      | ( ( SV608 = zero_zero_nat )
        = $true )
      | ( ( SV287 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13295]) ).

thf(13578,plain,
    ! [SV609: nat,SV288: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV288 )
          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV609 ) )
        = $true )
      | ( ( SV288 = SV609 )
        = $true )
      | ( ( ( divide_divide_nat @ SV288 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV609 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13296]) ).

thf(13579,plain,
    ! [SV609: nat,SV288: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV288 )
          | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV609 ) )
        = $true )
      | ( ( SV288 = SV609 )
        = $true )
      | ( ( ( divide_divide_nat @ SV288 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV609 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13297]) ).

thf(13580,plain,
    ! [SV932: nat,SV848: nat,SV611: nat,SV290: nat] :
      ( ( ( ord_less_nat @ SV290 @ SV611 )
        = $false )
      | ( ( ~ ( ord_less_nat @ SV848 @ SV932 ) )
        = $true )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV290 @ SV848 ) @ ( plus_plus_nat @ SV611 @ SV932 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13298]) ).

thf(13581,plain,
    ! [SV933: nat,SV849: nat,SV615: nat,SV294: nat] :
      ( ( ( SV294 = SV615 )
        = $false )
      | ( ( ~ ( ord_less_nat @ SV849 @ SV933 ) )
        = $true )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV294 @ SV849 ) @ ( plus_plus_nat @ SV615 @ SV933 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13299]) ).

thf(13582,plain,
    ! [SV621: nat,SV300: nat] :
      ( ( ( ( times_times_nat @ SV300 @ SV621 )
          = one_one_nat )
        = $true )
      | ( ( ( times_times_nat @ SV300 @ SV621 )
          = one_one_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13302]) ).

thf(13583,plain,
    ! [SV621: nat,SV300: nat] :
      ( ( ( ~ ( ( SV300 != one_one_nat )
              | ( SV621 != one_one_nat ) ) )
        = $true )
      | ( ( ( times_times_nat @ SV300 @ SV621 )
          = one_one_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13303]) ).

thf(13584,plain,
    ! [SV621: nat,SV300: nat] :
      ( ( ( SV300 = one_one_nat )
        = $false )
      | ( ( SV621 != one_one_nat )
        = $true )
      | ( ( ~ ( ( ( times_times_nat @ SV300 @ SV621 )
               != one_one_nat )
              | ~ ~ ( ( SV300 != one_one_nat )
                    | ( SV621 != one_one_nat ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13304]) ).

thf(13585,plain,
    ! [SV936: nat,SV622: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV622 @ SV936 )
          | ~ ~ ! [SY1919: nat] :
                  ( SV936
                 != ( times_times_nat @ SV622 @ SY1919 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV622 @ SV936 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13305]) ).

thf(13586,plain,
    ! [SV622: nat,SV936: nat] :
      ( ( ( ! [SY1919: nat] :
              ( SV936
             != ( times_times_nat @ SV622 @ SY1919 ) ) )
        = $true )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ SV622 @ SV936 )
              | ~ ~ ! [SY1919: nat] :
                      ( SV936
                     != ( times_times_nat @ SV622 @ SY1919 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13306]) ).

thf(13587,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13307]) ).

thf(13588,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
               != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13307]) ).

thf(13589,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
              | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
                   != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13308]) ).

thf(13590,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
          | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
               != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) )
        = $false )
      | ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13309]) ).

thf(13591,plain,
    ! [SV626: nat,SV305: nat] :
      ( ( ( ( plus_plus_nat @ SV305 @ SV626 )
          = zero_zero_nat )
        = $true )
      | ( ( ( plus_plus_nat @ SV305 @ SV626 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13310]) ).

thf(13592,plain,
    ! [SV626: nat,SV305: nat] :
      ( ( ( ~ ( ( SV305 != zero_zero_nat )
              | ( SV626 != zero_zero_nat ) ) )
        = $true )
      | ( ( ( plus_plus_nat @ SV305 @ SV626 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13311]) ).

thf(13593,plain,
    ! [SV626: nat,SV305: nat] :
      ( ( ( SV305 = zero_zero_nat )
        = $false )
      | ( ( SV626 != zero_zero_nat )
        = $true )
      | ( ( ~ ( ( ( plus_plus_nat @ SV305 @ SV626 )
               != zero_zero_nat )
              | ~ ~ ( ( SV305 != zero_zero_nat )
                    | ( SV626 != zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13312]) ).

thf(13594,plain,
    ! [SV630: nat,SV310: nat] :
      ( ( ( ( plus_plus_nat @ SV310 @ SV630 )
          = zero_zero_nat )
        = $true )
      | ( ( ( plus_plus_nat @ SV310 @ SV630 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13313]) ).

thf(13595,plain,
    ! [SV630: nat,SV310: nat] :
      ( ( ( ~ ( ( SV310 != zero_zero_nat )
              | ( SV630 != zero_zero_nat ) ) )
        = $true )
      | ( ( ( plus_plus_nat @ SV310 @ SV630 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13314]) ).

thf(13596,plain,
    ! [SV630: nat,SV310: nat] :
      ( ( ( SV310 = zero_zero_nat )
        = $false )
      | ( ( SV630 != zero_zero_nat )
        = $true )
      | ( ( ~ ( ( ( plus_plus_nat @ SV310 @ SV630 )
               != zero_zero_nat )
              | ~ ~ ( ( SV310 != zero_zero_nat )
                    | ( SV630 != zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13315]) ).

thf(13597,plain,
    ! [SV631: nat,SV856: nat,SV311: nat] :
      ( ( ( ! [SY1936: nat] :
              ~ ~ ( ~ ~ ( ( SV311
                         != ( times_times_nat @ ( sK14_SY1883 @ SV856 @ SV631 @ SV311 ) @ SY1936 ) )
                        | ~ ( dvd_dvd_nat @ ( sK14_SY1883 @ SV856 @ SV631 @ SV311 ) @ SV631 ) )
                  | ~ ( dvd_dvd_nat @ SY1936 @ SV856 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV311 @ ( times_times_nat @ SV631 @ SV856 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13316]) ).

thf(13598,plain,
    ! [SV956: nat,SV937: nat,SV632: nat,SV857: nat,SV312: nat] :
      ( ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV632 @ SV937 )
                = ( plus_plus_nat @ ( times_times_nat @ SV857 @ SV956 ) @ SV312 ) )
              | ( ( times_times_nat @ SV857 @ SV937 )
                = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SV956 ) @ SV312 ) ) )
          | ~ ! [SY1887: nat] :
                ~ ~ ! [SY1888: nat] :
                      ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
                                | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) )
                          | ~ ( ( ( times_times_nat @ SV632 @ SY1887 )
                                = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1888 ) @ SV312 ) )
                              | ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1887 )
                                = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SY1888 ) @ SV312 ) ) ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13317]) ).

thf(13599,plain,
    ! [SV636: num,SV316: num > $o] :
      ( ( ( SV316 @ ( sK15_SY1414 @ SV636 @ SV316 ) )
        = $true )
      | ( ( SV316 @ SV636 )
        = $true )
      | ( ( SV316 @ one )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13318]) ).

thf(13600,plain,
    ! [SV639: nat,SV860: nat,SV319: nat > nat > $o] :
      ( ( ( ~ ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
              | ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) ) ) )
        = $false )
      | ( ( ~ ! [SY1421: nat] : ( SV319 @ SY1421 @ zero_zero_nat )
          | ~ ! [SY1422: nat,SY1423: nat] :
                ( ~ ( SV319 @ SY1422 @ SY1423 )
                | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) )
          | ( SV319 @ SV639 @ SV860 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13320]) ).

thf(13601,plain,
    ! [SV639: nat,SV860: nat,SV319: nat > nat > $o] :
      ( ( ( ~ ( ~ ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
              | ~ ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) ) ) )
        = $false )
      | ( ( ~ ! [SY1421: nat] : ( SV319 @ SY1421 @ zero_zero_nat )
          | ~ ! [SY1422: nat,SY1423: nat] :
                ( ~ ( SV319 @ SY1422 @ SY1423 )
                | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) )
          | ( SV319 @ SV639 @ SV860 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13320]) ).

thf(13602,plain,
    ! [SV860: nat,SV639: nat,SV319: nat > nat > $o] :
      ( ( ( ~ ! [SY1421: nat] : ( SV319 @ SY1421 @ zero_zero_nat ) )
        = $true )
      | ( ( ~ ! [SY1422: nat,SY1423: nat] :
                ( ~ ( SV319 @ SY1422 @ SY1423 )
                | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) )
          | ( SV319 @ SV639 @ SV860 ) )
        = $true )
      | ( ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
          = ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13321]) ).

thf(13603,plain,
    ! [SV642: nat,SV322: nat] :
      ( ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 )
        = $true )
      | ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13322]) ).

thf(13604,plain,
    ! [SV642: nat,SV322: nat] :
      ( ( ( ~ ( ~ ( ( SV322 != SV642 ) )
              | ~ ( vEBT_V8194947554948674370ptions @ summary @ SV642 ) ) )
        = $true )
      | ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13323]) ).

thf(13605,plain,
    ! [SV642: nat,SV322: nat] :
      ( ( ( SV322 != SV642 )
        = $false )
      | ( ( ~ ( vEBT_V8194947554948674370ptions @ summary @ SV642 ) )
        = $true )
      | ( ( ~ ( ~ ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 )
              | ~ ~ ( ~ ( ( SV322 != SV642 ) )
                    | ~ ( vEBT_V8194947554948674370ptions @ summary @ SV642 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13324]) ).

thf(13606,plain,
    ! [SV862: nat,SV323: nat,SV957: nat,SV643: nat,SV938: nat] :
      ( ( ( ( modulo_modulo_nat @ SV938 @ SV643 )
          = ( modulo_modulo_nat @ SV957 @ SV643 ) )
        = $false )
      | ( ( ( modulo_modulo_nat @ ( times_times_nat @ SV323 @ SV938 ) @ SV643 )
          = ( modulo_modulo_nat @ ( times_times_nat @ SV862 @ SV957 ) @ SV643 ) )
        = $true )
      | ( ( ( modulo_modulo_nat @ SV323 @ SV643 )
          = ( modulo_modulo_nat @ SV862 @ SV643 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13325]) ).

thf(13607,plain,
    ! [SV939: nat,SV644: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV644 @ SV939 )
          | ~ ~ ! [SY1924: nat] :
                  ( SV939
                 != ( plus_plus_nat @ SV644 @ SY1924 ) ) )
        = $false )
      | ( ( ord_less_eq_nat @ SV644 @ SV939 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13326]) ).

thf(13608,plain,
    ! [SV644: nat,SV939: nat] :
      ( ( ( ! [SY1924: nat] :
              ( SV939
             != ( plus_plus_nat @ SV644 @ SY1924 ) ) )
        = $true )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ SV644 @ SV939 )
              | ~ ~ ! [SY1924: nat] :
                      ( SV939
                     != ( plus_plus_nat @ SV644 @ SY1924 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13327]) ).

thf(13609,plain,
    ! [SV940: nat,SV867: nat,SV648: nat,SV328: nat] :
      ( ( ( ord_less_eq_nat @ SV328 @ SV648 )
        = $false )
      | ( ( SV867 != SV940 )
        = $true )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV328 @ SV867 ) @ ( plus_plus_nat @ SV648 @ SV940 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13328]) ).

thf(13610,plain,
    ! [SV649: nat,SV329: nat] :
      ( ( ( zero_zero_nat
          = ( plus_plus_nat @ SV329 @ SV649 ) )
        = $true )
      | ( ( zero_zero_nat
          = ( plus_plus_nat @ SV329 @ SV649 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13329]) ).

thf(13611,plain,
    ! [SV649: nat,SV329: nat] :
      ( ( ( ~ ( ( SV329 != zero_zero_nat )
              | ( SV649 != zero_zero_nat ) ) )
        = $true )
      | ( ( zero_zero_nat
          = ( plus_plus_nat @ SV329 @ SV649 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13330]) ).

thf(13612,plain,
    ! [SV649: nat,SV329: nat] :
      ( ( ( SV329 = zero_zero_nat )
        = $false )
      | ( ( SV649 != zero_zero_nat )
        = $true )
      | ( ( ~ ( ( zero_zero_nat
               != ( plus_plus_nat @ SV329 @ SV649 ) )
              | ~ ~ ( ( SV329 != zero_zero_nat )
                    | ( SV649 != zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13331]) ).

thf(13613,plain,
    ! [SV942: nat,SV871: nat,SV657: nat,SV335: nat] :
      ( ( ( SV335 = SV657 )
        = $false )
      | ( ( ~ ( ord_less_eq_nat @ SV871 @ SV942 ) )
        = $true )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV335 @ SV871 ) @ ( plus_plus_nat @ SV657 @ SV942 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13333]) ).

thf(13614,plain,
    ! [SV658: nat,SV872: nat,SV336: nat] :
      ( ( ( dvd_dvd_nat @ SV336 @ ( plus_plus_nat @ SV872 @ SV658 ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ SV336 @ ( plus_plus_nat @ SV872 @ SV658 ) )
              | ~ ( dvd_dvd_nat @ SV336 @ SV872 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV336 @ SV658 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13334]) ).

thf(13615,plain,
    ! [SV658: nat,SV872: nat,SV336: nat] :
      ( ( ( dvd_dvd_nat @ SV336 @ SV872 )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ SV336 @ ( plus_plus_nat @ SV872 @ SV658 ) )
              | ~ ( dvd_dvd_nat @ SV336 @ SV872 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV336 @ SV658 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13334]) ).

thf(13616,plain,
    ! [SV943: nat,SV876: nat,SV662: nat,SV341: nat] :
      ( ( ( ord_less_eq_nat @ SV341 @ SV662 )
        = $false )
      | ( ( ~ ( ord_less_eq_nat @ SV876 @ SV943 ) )
        = $true )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV341 @ SV876 ) @ ( plus_plus_nat @ SV662 @ SV943 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13336]) ).

thf(13617,plain,
    ! [SV882: nat,SV347: nat,SV668: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ ( divide_divide_nat @ SV668 @ SV347 ) @ ( divide_divide_nat @ SV882 @ SV347 ) )
              | ( dvd_dvd_nat @ SV668 @ SV882 ) ) )
        = $true )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( divide_divide_nat @ SV668 @ SV347 ) @ ( divide_divide_nat @ SV882 @ SV347 ) )
              | ~ ( dvd_dvd_nat @ SV668 @ SV882 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV347 @ SV882 )
        = $false )
      | ( ( dvd_dvd_nat @ SV347 @ SV668 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13337]) ).

thf(13618,plain,
    ! [SV349: nat,SV669: nat] :
      ( ( ! [SY1937: nat] :
            ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ ( sK6_SY1803 @ SV669 @ SV349 ) @ SV349 )
                      | ~ ( dvd_dvd_nat @ ( sK6_SY1803 @ SV669 @ SV349 ) @ SV669 ) )
                | ~ ( ( ( times_times_nat @ SV349 @ ( sK18_SY1926 @ SV349 @ SV669 ) )
                      = ( plus_plus_nat @ ( times_times_nat @ SV669 @ SY1937 ) @ ( sK6_SY1803 @ SV669 @ SV349 ) ) )
                    | ( ( times_times_nat @ SV669 @ ( sK18_SY1926 @ SV349 @ SV669 ) )
                      = ( plus_plus_nat @ ( times_times_nat @ SV349 @ SY1937 ) @ ( sK6_SY1803 @ SV669 @ SV349 ) ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[13339]) ).

thf(13619,plain,
    ! [SV671: nat,SV351: nat] :
      ( ( ( one_one_nat
          = ( times_times_nat @ SV351 @ SV671 ) )
        = $true )
      | ( ( one_one_nat
          = ( times_times_nat @ SV351 @ SV671 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13340]) ).

thf(13620,plain,
    ! [SV671: nat,SV351: nat] :
      ( ( ( ~ ( ( SV351 != one_one_nat )
              | ( SV671 != one_one_nat ) ) )
        = $true )
      | ( ( one_one_nat
          = ( times_times_nat @ SV351 @ SV671 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13341]) ).

thf(13621,plain,
    ! [SV671: nat,SV351: nat] :
      ( ( ( SV351 = one_one_nat )
        = $false )
      | ( ( SV671 != one_one_nat )
        = $true )
      | ( ( ~ ( ( one_one_nat
               != ( times_times_nat @ SV351 @ SV671 ) )
              | ~ ~ ( ( SV351 != one_one_nat )
                    | ( SV671 != one_one_nat ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13342]) ).

thf(13622,plain,
    ! [SV353: nat,SV959: nat,SV945: nat,SV884: nat,SV673: nat] :
      ( ( ( ~ ~ ( ( SV673 != SV884 )
                | ~ ( ( SV945 != SV959 ) ) ) )
        = $true )
      | ( ( ( plus_plus_nat @ SV673 @ ( times_times_nat @ SV353 @ SV945 ) )
         != ( plus_plus_nat @ SV884 @ ( times_times_nat @ SV353 @ SV959 ) ) )
        = $true )
      | ( ( SV353 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13344]) ).

thf(13623,plain,
    ! [SV885: nat,SV674: nat,SV354: nat] :
      ( ( ( dvd_dvd_nat @ SV354 @ ( plus_plus_nat @ SV674 @ SV885 ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ SV354 @ ( plus_plus_nat @ SV674 @ SV885 ) )
              | ~ ( dvd_dvd_nat @ SV354 @ SV885 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV354 @ SV674 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13345]) ).

thf(13624,plain,
    ! [SV674: nat,SV885: nat,SV354: nat] :
      ( ( ( dvd_dvd_nat @ SV354 @ SV885 )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ SV354 @ ( plus_plus_nat @ SV674 @ SV885 ) )
              | ~ ( dvd_dvd_nat @ SV354 @ SV885 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV354 @ SV674 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13345]) ).

thf(13625,plain,
    ! [SV886: nat,SV676: nat,SV356: nat] :
      ( ( ( SV356 = zero_zero_nat )
        = $true )
      | ( ( ( divide_divide_nat @ ( times_times_nat @ SV356 @ SV676 ) @ ( times_times_nat @ SV356 @ SV886 ) )
          = ( divide_divide_nat @ SV676 @ SV886 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13347]) ).

thf(13626,plain,
    ! [SV361: nat,SV888: nat,SV680: nat] :
      ( ( ( dvd_dvd_nat @ SV680 @ SV888 )
        = $false )
      | ( ( SV361 = SV888 )
        = $true )
      | ( ( dvd_dvd_nat @ SV680 @ SV361 )
        = $false )
      | ( ( ( divide_divide_nat @ SV361 @ SV680 )
          = ( divide_divide_nat @ SV888 @ SV680 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13349]) ).

thf(13627,plain,
    ! [SV889: nat,SV362: nat,SV681: nat] :
      ( ( ( ~ ( ( ( divide_divide_nat @ SV681 @ SV362 )
                = ( divide_divide_nat @ SV889 @ SV362 ) )
              | ( SV681 = SV889 ) ) )
        = $true )
      | ( ( ~ ( ( ( divide_divide_nat @ SV681 @ SV362 )
               != ( divide_divide_nat @ SV889 @ SV362 ) )
              | ( SV681 != SV889 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV362 @ SV889 )
        = $false )
      | ( ( dvd_dvd_nat @ SV362 @ SV681 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13350]) ).

thf(13628,plain,
    ! [SV692: option_nat,SV373: option_nat] :
      ( ( ( ~ ( ~ ( ( SV373 != none_nat ) )
              | ~ ( ( SV692 != none_nat ) )
              | ( ( the_nat @ SV373 )
                = ( the_nat @ SV692 ) ) ) )
        = $true )
      | ( ( SV373 = SV692 )
        = $true )
      | ( ( SV692 = none_nat )
        = $true )
      | ( ( SV373 = none_nat )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13354]) ).

thf(13629,plain,
    ! [SV692: option_nat,SV373: option_nat] :
      ( ( ( SV373 = none_nat )
        = $false )
      | ( ( SV692 != none_nat )
        = $true )
      | ( ( ~ ( ~ ( ( SV373 != none_nat ) )
              | ~ ( ( SV692 != none_nat ) )
              | ( ( the_nat @ SV373 )
                = ( the_nat @ SV692 ) ) )
          | ( SV373 = SV692 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13355]) ).

thf(13630,plain,
    ! [SV692: option_nat,SV373: option_nat] :
      ( ( ( SV373 != none_nat )
        = $true )
      | ( ( SV373 = SV692 )
        = $true )
      | ( ( ( SV373 = none_nat )
          = ( SV692 = none_nat ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13356]) ).

thf(13631,plain,
    ! [SV373: option_nat,SV692: option_nat] :
      ( ( ( ~ ( ( SV692 != none_nat ) ) )
        = $false )
      | ( ( SV373 = SV692 )
        = $true )
      | ( ( ( SV373 = none_nat )
          = ( SV692 = none_nat ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13357]) ).

thf(13632,plain,
    ! [SV692: option_nat,SV373: option_nat] :
      ( ( ( ( the_nat @ SV373 )
          = ( the_nat @ SV692 ) )
        = $false )
      | ( ( SV373 = SV692 )
        = $true )
      | ( ( ( SV373 = none_nat )
          = ( SV692 = none_nat ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13357]) ).

thf(13633,plain,
    ! [SV693: nat,SV374: nat > $o] :
      ( ( ( ! [SY1534: nat,SY1535: $o] :
              ( ~ ( SV374 @ SY1534 )
              | ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ SY1535 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1534 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
               != SY1534 )
              | ( SV374 @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ SY1535 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SY1534 ) ) ) ) )
        = $false )
      | ( ( SV374 @ SV693 )
        = $true )
      | ( ( ( divide_divide_nat @ ( sK8_SY1533 @ SV693 @ SV374 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( sK8_SY1533 @ SV693 @ SV374 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13358]) ).

thf(13634,plain,
    ! [SV693: nat,SV374: nat > $o] :
      ( ( ( ! [SY1939: $o] :
              ( ~ ( SV374 @ ( sK21_SY1534 @ SV693 @ SV374 ) )
              | ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ SY1939 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( sK21_SY1534 @ SV693 @ SV374 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
               != ( sK21_SY1534 @ SV693 @ SV374 ) )
              | ( SV374 @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ SY1939 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( sK21_SY1534 @ SV693 @ SV374 ) ) ) ) ) )
        = $false )
      | ( ( SV374 @ SV693 )
        = $true )
      | ( ( SV374 @ ( sK8_SY1533 @ SV693 @ SV374 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[13359]) ).

thf(13635,plain,
    ! [SV948: nat,SV694: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV694 @ SV948 )
          | ~ ~ ! [SY1929: nat] :
                  ( SV948
                 != ( plus_plus_nat @ SV694 @ SY1929 ) ) )
        = $false )
      | ( ( ord_less_eq_nat @ SV694 @ SV948 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13360]) ).

thf(13636,plain,
    ! [SV694: nat,SV948: nat] :
      ( ( ( ! [SY1929: nat] :
              ( SV948
             != ( plus_plus_nat @ SV694 @ SY1929 ) ) )
        = $true )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ SV694 @ SV948 )
              | ~ ~ ! [SY1929: nat] :
                      ( SV948
                     != ( plus_plus_nat @ SV694 @ SY1929 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13361]) ).

thf(13637,plain,
    ! [SV950: nat,SV902: nat,SV698: nat,SV379: nat] :
      ( ( ( ord_less_nat @ SV379 @ SV698 )
        = $false )
      | ( ( SV902 != SV950 )
        = $true )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV379 @ SV902 ) @ ( plus_plus_nat @ SV698 @ SV950 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13363]) ).

thf(13638,plain,
    ! [SV382: num] :
      ( ( ( ! [SY1551: num] :
              ( SV382
             != ( bit1 @ SY1551 ) ) )
        = $false )
      | ( ( SV382
          = ( bit0 @ ( sK19_SY1550 @ SV382 ) ) )
        = $true )
      | ( ( SV382 = one )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13364]) ).

thf(13639,plain,
    ! [SV905: nat,SV384: nat,SV960: nat,SV702: nat,SV952: nat] :
      ( ( ( ( modulo_modulo_nat @ SV952 @ SV702 )
          = ( modulo_modulo_nat @ SV960 @ SV702 ) )
        = $false )
      | ( ( ( modulo_modulo_nat @ ( plus_plus_nat @ SV384 @ SV952 ) @ SV702 )
          = ( modulo_modulo_nat @ ( plus_plus_nat @ SV905 @ SV960 ) @ SV702 ) )
        = $true )
      | ( ( ( modulo_modulo_nat @ SV384 @ SV702 )
          = ( modulo_modulo_nat @ SV905 @ SV702 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13365]) ).

thf(13640,plain,
    ! [SV729: nat,SV435: nat,SV71: nat] :
      ( ( ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SV435 ) @ ( plus_plus_nat @ SV71 @ SV729 ) )
        = $true )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SV435 ) @ ( plus_plus_nat @ SV71 @ SV729 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13387]) ).

thf(13641,plain,
    ! [SV71: nat,SV729: nat,SV435: nat] :
      ( ( ( ord_less_nat @ SV435 @ SV729 )
        = $true )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SV435 ) @ ( plus_plus_nat @ SV71 @ SV729 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13388]) ).

thf(13642,plain,
    ! [SV729: nat,SV435: nat,SV71: nat] :
      ( ( ( ord_less_nat @ ( plus_plus_nat @ SV71 @ SV435 ) @ ( plus_plus_nat @ SV71 @ SV729 ) )
        = $true )
      | ( ( ord_less_nat @ SV435 @ SV729 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13389]) ).

thf(13643,plain,
    ! [SV729: nat,SV435: nat] :
      ( ( ( ord_less_nat @ SV435 @ SV729 )
        = $true )
      | ( ( ord_less_nat @ SV435 @ SV729 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13390]) ).

thf(13644,plain,
    ! [SV730: nat,SV436: nat,SV72: nat] :
      ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV72 @ SV436 ) @ ( plus_plus_nat @ SV72 @ SV730 ) )
        = $true )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV72 @ SV436 ) @ ( plus_plus_nat @ SV72 @ SV730 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13391]) ).

thf(13645,plain,
    ! [SV72: nat,SV730: nat,SV436: nat] :
      ( ( ( ord_less_eq_nat @ SV436 @ SV730 )
        = $true )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV72 @ SV436 ) @ ( plus_plus_nat @ SV72 @ SV730 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13392]) ).

thf(13646,plain,
    ! [SV730: nat,SV436: nat,SV72: nat] :
      ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV72 @ SV436 ) @ ( plus_plus_nat @ SV72 @ SV730 ) )
        = $true )
      | ( ( ord_less_eq_nat @ SV436 @ SV730 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13393]) ).

thf(13647,plain,
    ! [SV730: nat,SV436: nat] :
      ( ( ( ord_less_eq_nat @ SV436 @ SV730 )
        = $true )
      | ( ( ord_less_eq_nat @ SV436 @ SV730 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13394]) ).

thf(13648,plain,
    ! [SV736: nat,SV447: nat,SV86: nat] :
      ( ( ( ( times_times_nat @ ( suc @ SV86 ) @ SV447 )
          = ( times_times_nat @ ( suc @ SV86 ) @ SV736 ) )
        = $true )
      | ( ( ( times_times_nat @ ( suc @ SV86 ) @ SV447 )
          = ( times_times_nat @ ( suc @ SV86 ) @ SV736 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13395]) ).

thf(13649,plain,
    ! [SV86: nat,SV736: nat,SV447: nat] :
      ( ( ( SV447 = SV736 )
        = $true )
      | ( ( ( times_times_nat @ ( suc @ SV86 ) @ SV447 )
          = ( times_times_nat @ ( suc @ SV86 ) @ SV736 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13396]) ).

thf(13650,plain,
    ! [SV736: nat,SV447: nat,SV86: nat] :
      ( ( ( ( times_times_nat @ ( suc @ SV86 ) @ SV447 )
          = ( times_times_nat @ ( suc @ SV86 ) @ SV736 ) )
        = $true )
      | ( ( SV447 = SV736 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13397]) ).

thf(13651,plain,
    ! [SV736: nat,SV447: nat] :
      ( ( ( SV447 = SV736 )
        = $true )
      | ( ( SV447 = SV736 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13398]) ).

thf(13652,plain,
    ! [SV752: nat,SV475: nat,SV120: nat] :
      ( ( ( ( plus_plus_nat @ SV120 @ SV475 )
          = ( plus_plus_nat @ SV120 @ SV752 ) )
        = $true )
      | ( ( ( plus_plus_nat @ SV120 @ SV475 )
          = ( plus_plus_nat @ SV120 @ SV752 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13399]) ).

thf(13653,plain,
    ! [SV120: nat,SV752: nat,SV475: nat] :
      ( ( ( SV475 = SV752 )
        = $true )
      | ( ( ( plus_plus_nat @ SV120 @ SV475 )
          = ( plus_plus_nat @ SV120 @ SV752 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13400]) ).

thf(13654,plain,
    ! [SV752: nat,SV475: nat,SV120: nat] :
      ( ( ( ( plus_plus_nat @ SV120 @ SV475 )
          = ( plus_plus_nat @ SV120 @ SV752 ) )
        = $true )
      | ( ( SV475 = SV752 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13401]) ).

thf(13655,plain,
    ! [SV752: nat,SV475: nat] :
      ( ( ( SV475 = SV752 )
        = $true )
      | ( ( SV475 = SV752 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13402]) ).

thf(13656,plain,
    ! [SV753: nat,SV476: nat,SV121: nat] :
      ( ( ( ( plus_plus_nat @ SV121 @ SV476 )
          = ( plus_plus_nat @ SV753 @ SV476 ) )
        = $true )
      | ( ( ( plus_plus_nat @ SV121 @ SV476 )
          = ( plus_plus_nat @ SV753 @ SV476 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13403]) ).

thf(13657,plain,
    ! [SV476: nat,SV753: nat,SV121: nat] :
      ( ( ( SV121 = SV753 )
        = $true )
      | ( ( ( plus_plus_nat @ SV121 @ SV476 )
          = ( plus_plus_nat @ SV753 @ SV476 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13404]) ).

thf(13658,plain,
    ! [SV753: nat,SV476: nat,SV121: nat] :
      ( ( ( ( plus_plus_nat @ SV121 @ SV476 )
          = ( plus_plus_nat @ SV753 @ SV476 ) )
        = $true )
      | ( ( SV121 = SV753 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13405]) ).

thf(13659,plain,
    ! [SV753: nat,SV121: nat] :
      ( ( ( SV121 = SV753 )
        = $true )
      | ( ( SV121 = SV753 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13406]) ).

thf(13660,plain,
    ! [SV754: nat,SV477: nat,SV122: nat] :
      ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ SV477 ) @ ( plus_plus_nat @ SV122 @ SV754 ) )
        = $true )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ SV477 ) @ ( plus_plus_nat @ SV122 @ SV754 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13407]) ).

thf(13661,plain,
    ! [SV122: nat,SV754: nat,SV477: nat] :
      ( ( ( ord_less_eq_nat @ SV477 @ SV754 )
        = $true )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ SV477 ) @ ( plus_plus_nat @ SV122 @ SV754 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13408]) ).

thf(13662,plain,
    ! [SV754: nat,SV477: nat,SV122: nat] :
      ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV122 @ SV477 ) @ ( plus_plus_nat @ SV122 @ SV754 ) )
        = $true )
      | ( ( ord_less_eq_nat @ SV477 @ SV754 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13409]) ).

thf(13663,plain,
    ! [SV754: nat,SV477: nat] :
      ( ( ( ord_less_eq_nat @ SV477 @ SV754 )
        = $true )
      | ( ( ord_less_eq_nat @ SV477 @ SV754 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13410]) ).

thf(13664,plain,
    ! [SV755: nat,SV478: nat,SV123: nat] :
      ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV123 @ SV478 ) @ ( plus_plus_nat @ SV755 @ SV478 ) )
        = $true )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV123 @ SV478 ) @ ( plus_plus_nat @ SV755 @ SV478 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13411]) ).

thf(13665,plain,
    ! [SV478: nat,SV755: nat,SV123: nat] :
      ( ( ( ord_less_eq_nat @ SV123 @ SV755 )
        = $true )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV123 @ SV478 ) @ ( plus_plus_nat @ SV755 @ SV478 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13412]) ).

thf(13666,plain,
    ! [SV755: nat,SV478: nat,SV123: nat] :
      ( ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV123 @ SV478 ) @ ( plus_plus_nat @ SV755 @ SV478 ) )
        = $true )
      | ( ( ord_less_eq_nat @ SV123 @ SV755 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13413]) ).

thf(13667,plain,
    ! [SV755: nat,SV123: nat] :
      ( ( ( ord_less_eq_nat @ SV123 @ SV755 )
        = $true )
      | ( ( ord_less_eq_nat @ SV123 @ SV755 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13414]) ).

thf(13668,plain,
    ! [SV756: nat,SV479: nat,SV124: nat] :
      ( ( ( ord_less_nat @ ( plus_plus_nat @ SV124 @ SV479 ) @ ( plus_plus_nat @ SV124 @ SV756 ) )
        = $true )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV124 @ SV479 ) @ ( plus_plus_nat @ SV124 @ SV756 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13415]) ).

thf(13669,plain,
    ! [SV124: nat,SV756: nat,SV479: nat] :
      ( ( ( ord_less_nat @ SV479 @ SV756 )
        = $true )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV124 @ SV479 ) @ ( plus_plus_nat @ SV124 @ SV756 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13416]) ).

thf(13670,plain,
    ! [SV756: nat,SV479: nat,SV124: nat] :
      ( ( ( ord_less_nat @ ( plus_plus_nat @ SV124 @ SV479 ) @ ( plus_plus_nat @ SV124 @ SV756 ) )
        = $true )
      | ( ( ord_less_nat @ SV479 @ SV756 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13417]) ).

thf(13671,plain,
    ! [SV756: nat,SV479: nat] :
      ( ( ( ord_less_nat @ SV479 @ SV756 )
        = $true )
      | ( ( ord_less_nat @ SV479 @ SV756 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13418]) ).

thf(13672,plain,
    ! [SV757: nat,SV480: nat,SV125: nat] :
      ( ( ( ord_less_nat @ ( plus_plus_nat @ SV125 @ SV480 ) @ ( plus_plus_nat @ SV757 @ SV480 ) )
        = $true )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV125 @ SV480 ) @ ( plus_plus_nat @ SV757 @ SV480 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13419]) ).

thf(13673,plain,
    ! [SV480: nat,SV757: nat,SV125: nat] :
      ( ( ( ord_less_nat @ SV125 @ SV757 )
        = $true )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV125 @ SV480 ) @ ( plus_plus_nat @ SV757 @ SV480 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13420]) ).

thf(13674,plain,
    ! [SV757: nat,SV480: nat,SV125: nat] :
      ( ( ( ord_less_nat @ ( plus_plus_nat @ SV125 @ SV480 ) @ ( plus_plus_nat @ SV757 @ SV480 ) )
        = $true )
      | ( ( ord_less_nat @ SV125 @ SV757 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13421]) ).

thf(13675,plain,
    ! [SV757: nat,SV125: nat] :
      ( ( ( ord_less_nat @ SV125 @ SV757 )
        = $true )
      | ( ( ord_less_nat @ SV125 @ SV757 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13422]) ).

thf(13676,plain,
    ! [SV770: nat,SV493: nat,SV142: nat] :
      ( ( ( ( times_times_nat @ SV142 @ SV493 )
          = ( times_times_nat @ SV770 @ SV493 ) )
        = $true )
      | ( ( ( times_times_nat @ SV142 @ SV493 )
          = ( times_times_nat @ SV770 @ SV493 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13423]) ).

thf(13677,plain,
    ! [SV770: nat,SV142: nat,SV493: nat] :
      ( ( ( ( SV493 = zero_zero_nat )
          | ( SV142 = SV770 ) )
        = $true )
      | ( ( ( times_times_nat @ SV142 @ SV493 )
          = ( times_times_nat @ SV770 @ SV493 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13424]) ).

thf(13678,plain,
    ! [SV770: nat,SV493: nat,SV142: nat] :
      ( ( ( ( times_times_nat @ SV142 @ SV493 )
         != ( times_times_nat @ SV770 @ SV493 ) )
        = $false )
      | ( ( SV493 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13425]) ).

thf(13679,plain,
    ! [SV770: nat,SV142: nat,SV493: nat] :
      ( ( ( ~ ( ( SV493 = zero_zero_nat )
              | ( SV142 = SV770 ) ) )
        = $false )
      | ( ( SV493 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13425]) ).

thf(13680,plain,
    ! [SV770: nat,SV493: nat,SV142: nat] :
      ( ( ( ( times_times_nat @ SV142 @ SV493 )
         != ( times_times_nat @ SV770 @ SV493 ) )
        = $false )
      | ( ( SV142 = SV770 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13426]) ).

thf(13681,plain,
    ! [SV770: nat,SV142: nat,SV493: nat] :
      ( ( ( ~ ( ( SV493 = zero_zero_nat )
              | ( SV142 = SV770 ) ) )
        = $false )
      | ( ( SV142 = SV770 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13426]) ).

thf(13682,plain,
    ! [SV771: nat,SV494: nat,SV143: nat] :
      ( ( ( ( times_times_nat @ SV143 @ SV494 )
          = ( times_times_nat @ SV143 @ SV771 ) )
        = $true )
      | ( ( ( times_times_nat @ SV143 @ SV494 )
          = ( times_times_nat @ SV143 @ SV771 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13427]) ).

thf(13683,plain,
    ! [SV771: nat,SV494: nat,SV143: nat] :
      ( ( ( ( SV143 = zero_zero_nat )
          | ( SV494 = SV771 ) )
        = $true )
      | ( ( ( times_times_nat @ SV143 @ SV494 )
          = ( times_times_nat @ SV143 @ SV771 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13428]) ).

thf(13684,plain,
    ! [SV771: nat,SV494: nat,SV143: nat] :
      ( ( ( ( times_times_nat @ SV143 @ SV494 )
         != ( times_times_nat @ SV143 @ SV771 ) )
        = $false )
      | ( ( SV143 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13429]) ).

thf(13685,plain,
    ! [SV771: nat,SV494: nat,SV143: nat] :
      ( ( ( ~ ( ( SV143 = zero_zero_nat )
              | ( SV494 = SV771 ) ) )
        = $false )
      | ( ( SV143 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13429]) ).

thf(13686,plain,
    ! [SV771: nat,SV494: nat,SV143: nat] :
      ( ( ( ( times_times_nat @ SV143 @ SV494 )
         != ( times_times_nat @ SV143 @ SV771 ) )
        = $false )
      | ( ( SV494 = SV771 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13430]) ).

thf(13687,plain,
    ! [SV771: nat,SV494: nat,SV143: nat] :
      ( ( ( ~ ( ( SV143 = zero_zero_nat )
              | ( SV494 = SV771 ) ) )
        = $false )
      | ( ( SV494 = SV771 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13430]) ).

thf(13688,plain,
    ! [SV495: nat,SV144: nat] :
      ( ( ( SV144 = zero_zero_nat )
        = $true )
      | ( ( SV495 = zero_zero_nat )
        = $true )
      | ( ( ( times_times_nat @ SV144 @ SV495 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13432]) ).

thf(13689,plain,
    ! [SV495: nat,SV144: nat] :
      ( ( ( ( times_times_nat @ SV144 @ SV495 )
          = zero_zero_nat )
        = $true )
      | ( ( SV144 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13433]) ).

thf(13690,plain,
    ! [SV495: nat,SV144: nat] :
      ( ( ( ( SV144 = zero_zero_nat )
          | ( SV495 = zero_zero_nat ) )
        = $true )
      | ( ( SV144 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13434]) ).

thf(13691,plain,
    ! [SV495: nat,SV144: nat] :
      ( ( ( ( times_times_nat @ SV144 @ SV495 )
          = zero_zero_nat )
        = $true )
      | ( ( SV495 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13435]) ).

thf(13692,plain,
    ! [SV495: nat,SV144: nat] :
      ( ( ( ( SV144 = zero_zero_nat )
          | ( SV495 = zero_zero_nat ) )
        = $true )
      | ( ( SV495 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13436]) ).

thf(13693,plain,
    ! [SV772: nat,SV502: nat,SV160: nat] :
      ( ( ( ( times_times_nat @ SV160 @ SV502 )
          = ( times_times_nat @ SV772 @ SV502 ) )
        = $true )
      | ( ( ( times_times_nat @ SV160 @ SV502 )
          = ( times_times_nat @ SV772 @ SV502 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13453]) ).

thf(13694,plain,
    ! [SV502: nat,SV772: nat,SV160: nat] :
      ( ( ( ( SV160 = SV772 )
          | ( SV502 = zero_zero_nat ) )
        = $true )
      | ( ( ( times_times_nat @ SV160 @ SV502 )
          = ( times_times_nat @ SV772 @ SV502 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13454]) ).

thf(13695,plain,
    ! [SV772: nat,SV502: nat,SV160: nat] :
      ( ( ( ( times_times_nat @ SV160 @ SV502 )
         != ( times_times_nat @ SV772 @ SV502 ) )
        = $false )
      | ( ( SV160 = SV772 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13455]) ).

thf(13696,plain,
    ! [SV502: nat,SV772: nat,SV160: nat] :
      ( ( ( ~ ( ( SV160 = SV772 )
              | ( SV502 = zero_zero_nat ) ) )
        = $false )
      | ( ( SV160 = SV772 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13455]) ).

thf(13697,plain,
    ! [SV772: nat,SV502: nat,SV160: nat] :
      ( ( ( ( times_times_nat @ SV160 @ SV502 )
         != ( times_times_nat @ SV772 @ SV502 ) )
        = $false )
      | ( ( SV502 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13456]) ).

thf(13698,plain,
    ! [SV502: nat,SV772: nat,SV160: nat] :
      ( ( ( ~ ( ( SV160 = SV772 )
              | ( SV502 = zero_zero_nat ) ) )
        = $false )
      | ( ( SV502 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13456]) ).

thf(13699,plain,
    ! [SV773: nat,SV503: nat,SV161: nat] :
      ( ( ( ( times_times_nat @ SV161 @ SV503 )
          = ( times_times_nat @ SV161 @ SV773 ) )
        = $true )
      | ( ( ( times_times_nat @ SV161 @ SV503 )
          = ( times_times_nat @ SV161 @ SV773 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13457]) ).

thf(13700,plain,
    ! [SV161: nat,SV773: nat,SV503: nat] :
      ( ( ( ( SV503 = SV773 )
          | ( SV161 = zero_zero_nat ) )
        = $true )
      | ( ( ( times_times_nat @ SV161 @ SV503 )
          = ( times_times_nat @ SV161 @ SV773 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13458]) ).

thf(13701,plain,
    ! [SV773: nat,SV503: nat,SV161: nat] :
      ( ( ( ( times_times_nat @ SV161 @ SV503 )
         != ( times_times_nat @ SV161 @ SV773 ) )
        = $false )
      | ( ( SV503 = SV773 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13459]) ).

thf(13702,plain,
    ! [SV161: nat,SV773: nat,SV503: nat] :
      ( ( ( ~ ( ( SV503 = SV773 )
              | ( SV161 = zero_zero_nat ) ) )
        = $false )
      | ( ( SV503 = SV773 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13459]) ).

thf(13703,plain,
    ! [SV773: nat,SV503: nat,SV161: nat] :
      ( ( ( ( times_times_nat @ SV161 @ SV503 )
         != ( times_times_nat @ SV161 @ SV773 ) )
        = $false )
      | ( ( SV161 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13460]) ).

thf(13704,plain,
    ! [SV161: nat,SV773: nat,SV503: nat] :
      ( ( ( ~ ( ( SV503 = SV773 )
              | ( SV161 = zero_zero_nat ) ) )
        = $false )
      | ( ( SV161 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13460]) ).

thf(13705,plain,
    ! [SV504: nat,SV163: nat] :
      ( ( ( SV163 = zero_zero_nat )
        = $true )
      | ( ( SV504 = zero_zero_nat )
        = $true )
      | ( ( ( times_times_nat @ SV163 @ SV504 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13462]) ).

thf(13706,plain,
    ! [SV504: nat,SV163: nat] :
      ( ( ( ( times_times_nat @ SV163 @ SV504 )
          = zero_zero_nat )
        = $true )
      | ( ( SV163 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13463]) ).

thf(13707,plain,
    ! [SV504: nat,SV163: nat] :
      ( ( ( ( SV163 = zero_zero_nat )
          | ( SV504 = zero_zero_nat ) )
        = $true )
      | ( ( SV163 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13464]) ).

thf(13708,plain,
    ! [SV504: nat,SV163: nat] :
      ( ( ( ( times_times_nat @ SV163 @ SV504 )
          = zero_zero_nat )
        = $true )
      | ( ( SV504 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13465]) ).

thf(13709,plain,
    ! [SV504: nat,SV163: nat] :
      ( ( ( ( SV163 = zero_zero_nat )
          | ( SV504 = zero_zero_nat ) )
        = $true )
      | ( ( SV504 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13466]) ).

thf(13710,plain,
    ! [SV787: num,SV518: num,SV179: num] :
      ( ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV179 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) )
          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV787 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) ) )
        = $true )
      | ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV179 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) )
          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV787 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13467]) ).

thf(13711,plain,
    ! [SV787: num,SV518: num,SV179: num] :
      ( ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV179 ) @ ( numeral_numeral_nat @ SV518 ) )
          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV787 ) @ ( numeral_numeral_nat @ SV518 ) ) )
        = $true )
      | ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV179 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) )
          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV787 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13468]) ).

thf(13712,plain,
    ! [SV787: num,SV518: num,SV179: num] :
      ( ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV179 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) )
          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ SV787 ) ) @ ( numeral_numeral_nat @ ( bit0 @ SV518 ) ) ) )
        = $true )
      | ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV179 ) @ ( numeral_numeral_nat @ SV518 ) )
          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV787 ) @ ( numeral_numeral_nat @ SV518 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13469]) ).

thf(13713,plain,
    ! [SV787: num,SV518: num,SV179: num] :
      ( ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV179 ) @ ( numeral_numeral_nat @ SV518 ) )
          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV787 ) @ ( numeral_numeral_nat @ SV518 ) ) )
        = $true )
      | ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV179 ) @ ( numeral_numeral_nat @ SV518 ) )
          = ( modulo_modulo_nat @ ( numeral_numeral_nat @ SV787 ) @ ( numeral_numeral_nat @ SV518 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13470]) ).

thf(13714,plain,
    ! [SV788: nat,SV520: nat,SV185: nat] :
      ( ( ( ( times_times_nat @ SV185 @ SV520 )
          = ( times_times_nat @ SV185 @ SV788 ) )
        = $true )
      | ( ( ( times_times_nat @ SV185 @ SV520 )
          = ( times_times_nat @ SV185 @ SV788 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13471]) ).

thf(13715,plain,
    ! [SV788: nat,SV520: nat,SV185: nat] :
      ( ( ( ( SV185 = zero_zero_nat )
          | ( SV520 = SV788 ) )
        = $true )
      | ( ( ( times_times_nat @ SV185 @ SV520 )
          = ( times_times_nat @ SV185 @ SV788 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13472]) ).

thf(13716,plain,
    ! [SV788: nat,SV520: nat,SV185: nat] :
      ( ( ( ( times_times_nat @ SV185 @ SV520 )
         != ( times_times_nat @ SV185 @ SV788 ) )
        = $false )
      | ( ( SV185 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13473]) ).

thf(13717,plain,
    ! [SV788: nat,SV520: nat,SV185: nat] :
      ( ( ( ~ ( ( SV185 = zero_zero_nat )
              | ( SV520 = SV788 ) ) )
        = $false )
      | ( ( SV185 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13473]) ).

thf(13718,plain,
    ! [SV788: nat,SV520: nat,SV185: nat] :
      ( ( ( ( times_times_nat @ SV185 @ SV520 )
         != ( times_times_nat @ SV185 @ SV788 ) )
        = $false )
      | ( ( SV520 = SV788 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13474]) ).

thf(13719,plain,
    ! [SV788: nat,SV520: nat,SV185: nat] :
      ( ( ( ~ ( ( SV185 = zero_zero_nat )
              | ( SV520 = SV788 ) ) )
        = $false )
      | ( ( SV520 = SV788 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13474]) ).

thf(13720,plain,
    ! [SV795: nat,SV537: nat,SV203: nat] :
      ( ( ( dvd_dvd_nat @ SV203 @ ( plus_plus_nat @ SV537 @ ( times_times_nat @ SV795 @ SV203 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV203 @ ( plus_plus_nat @ SV537 @ ( times_times_nat @ SV795 @ SV203 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13487]) ).

thf(13721,plain,
    ! [SV795: nat,SV537: nat,SV203: nat] :
      ( ( ( dvd_dvd_nat @ SV203 @ SV537 )
        = $true )
      | ( ( dvd_dvd_nat @ SV203 @ ( plus_plus_nat @ SV537 @ ( times_times_nat @ SV795 @ SV203 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13488]) ).

thf(13722,plain,
    ! [SV795: nat,SV537: nat,SV203: nat] :
      ( ( ( dvd_dvd_nat @ SV203 @ ( plus_plus_nat @ SV537 @ ( times_times_nat @ SV795 @ SV203 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV203 @ SV537 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13489]) ).

thf(13723,plain,
    ! [SV537: nat,SV203: nat] :
      ( ( ( dvd_dvd_nat @ SV203 @ SV537 )
        = $true )
      | ( ( dvd_dvd_nat @ SV203 @ SV537 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13490]) ).

thf(13724,plain,
    ! [SV796: nat,SV538: nat,SV204: nat] :
      ( ( ( dvd_dvd_nat @ SV204 @ ( plus_plus_nat @ ( times_times_nat @ SV538 @ SV204 ) @ SV796 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV204 @ ( plus_plus_nat @ ( times_times_nat @ SV538 @ SV204 ) @ SV796 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13491]) ).

thf(13725,plain,
    ! [SV538: nat,SV796: nat,SV204: nat] :
      ( ( ( dvd_dvd_nat @ SV204 @ SV796 )
        = $true )
      | ( ( dvd_dvd_nat @ SV204 @ ( plus_plus_nat @ ( times_times_nat @ SV538 @ SV204 ) @ SV796 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13492]) ).

thf(13726,plain,
    ! [SV796: nat,SV538: nat,SV204: nat] :
      ( ( ( dvd_dvd_nat @ SV204 @ ( plus_plus_nat @ ( times_times_nat @ SV538 @ SV204 ) @ SV796 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV204 @ SV796 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13493]) ).

thf(13727,plain,
    ! [SV796: nat,SV204: nat] :
      ( ( ( dvd_dvd_nat @ SV204 @ SV796 )
        = $true )
      | ( ( dvd_dvd_nat @ SV204 @ SV796 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13494]) ).

thf(13728,plain,
    ! [SV539: nat,SV205: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ SV205 @ SV539 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13496]) ).

thf(13729,plain,
    ! [SV539: nat,SV205: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ SV205 @ SV539 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13497]) ).

thf(13730,plain,
    ! [SV539: nat,SV205: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13498]) ).

thf(13731,plain,
    ! [SV539: nat,SV205: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ SV205 @ SV539 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13499]) ).

thf(13732,plain,
    ! [SV539: nat,SV205: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13500]) ).

thf(13733,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
          | ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[13502]) ).

thf(13734,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[13502]) ).

thf(13735,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $true )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
              | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
               != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13503]) ).

thf(13736,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 ) )
        = $true )
      | ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $true )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
              | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
               != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13504]) ).

thf(13737,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
        = $true )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13505]) ).

thf(13738,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $true )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13506]) ).

thf(13739,plain,
    ! [SV922: nat,SV802: nat,SV549: nat,SV216: nat] :
      ( ( ( ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV549 ) @ ( times_times_nat @ SV802 @ SV922 ) )
         != ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV922 ) @ ( times_times_nat @ SV802 @ SV549 ) ) )
        = $false )
      | ( ( ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV549 ) @ ( times_times_nat @ SV802 @ SV922 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV922 ) @ ( times_times_nat @ SV802 @ SV549 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13511]) ).

thf(13740,plain,
    ! [SV922: nat,SV549: nat,SV802: nat,SV216: nat] :
      ( ( ( ~ ( ( SV216 = SV802 )
              | ( SV549 = SV922 ) ) )
        = $false )
      | ( ( ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV549 ) @ ( times_times_nat @ SV802 @ SV922 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV922 ) @ ( times_times_nat @ SV802 @ SV549 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13511]) ).

thf(13741,plain,
    ! [SV922: nat,SV802: nat,SV549: nat,SV216: nat] :
      ( ( ( ( ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV549 ) @ ( times_times_nat @ SV802 @ SV922 ) )
           != ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV922 ) @ ( times_times_nat @ SV802 @ SV549 ) ) )
          | ~ ( ( SV216 = SV802 )
              | ( SV549 = SV922 ) ) )
        = $false )
      | ( ( SV216 = SV802 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13512]) ).

thf(13742,plain,
    ! [SV922: nat,SV802: nat,SV549: nat,SV216: nat] :
      ( ( ( ( ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV549 ) @ ( times_times_nat @ SV802 @ SV922 ) )
           != ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV922 ) @ ( times_times_nat @ SV802 @ SV549 ) ) )
          | ~ ( ( SV216 = SV802 )
              | ( SV549 = SV922 ) ) )
        = $false )
      | ( ( SV549 = SV922 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13513]) ).

thf(13743,plain,
    ! [SV803: nat,SV554: nat,SV224: nat] :
      ( ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV224 ) @ SV554 )
          = ( semiri1316708129612266289at_nat @ SV803 ) )
        = $true )
      | ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV224 ) @ SV554 )
          = ( semiri1316708129612266289at_nat @ SV803 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13514]) ).

thf(13744,plain,
    ! [SV803: nat,SV554: nat,SV224: nat] :
      ( ( ( ( power_power_nat @ SV224 @ SV554 )
          = SV803 )
        = $true )
      | ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV224 ) @ SV554 )
          = ( semiri1316708129612266289at_nat @ SV803 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13515]) ).

thf(13745,plain,
    ! [SV803: nat,SV554: nat,SV224: nat] :
      ( ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV224 ) @ SV554 )
          = ( semiri1316708129612266289at_nat @ SV803 ) )
        = $true )
      | ( ( ( power_power_nat @ SV224 @ SV554 )
          = SV803 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13516]) ).

thf(13746,plain,
    ! [SV803: nat,SV554: nat,SV224: nat] :
      ( ( ( ( power_power_nat @ SV224 @ SV554 )
          = SV803 )
        = $true )
      | ( ( ( power_power_nat @ SV224 @ SV554 )
          = SV803 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13517]) ).

thf(13747,plain,
    ! [SV804: nat,SV555: nat,SV225: nat] :
      ( ( ( ( semiri1316708129612266289at_nat @ SV225 )
          = ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV555 ) @ SV804 ) )
        = $true )
      | ( ( ( semiri1316708129612266289at_nat @ SV225 )
          = ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV555 ) @ SV804 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13518]) ).

thf(13748,plain,
    ! [SV804: nat,SV555: nat,SV225: nat] :
      ( ( ( SV225
          = ( power_power_nat @ SV555 @ SV804 ) )
        = $true )
      | ( ( ( semiri1316708129612266289at_nat @ SV225 )
          = ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV555 ) @ SV804 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13519]) ).

thf(13749,plain,
    ! [SV804: nat,SV555: nat,SV225: nat] :
      ( ( ( ( semiri1316708129612266289at_nat @ SV225 )
          = ( power_power_nat @ ( semiri1316708129612266289at_nat @ SV555 ) @ SV804 ) )
        = $true )
      | ( ( SV225
          = ( power_power_nat @ SV555 @ SV804 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13520]) ).

thf(13750,plain,
    ! [SV804: nat,SV555: nat,SV225: nat] :
      ( ( ( SV225
          = ( power_power_nat @ SV555 @ SV804 ) )
        = $true )
      | ( ( SV225
          = ( power_power_nat @ SV555 @ SV804 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13521]) ).

thf(13751,plain,
    ! [SV805: nat,SV556: nat,SV226: num] :
      ( ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
          = ( semiri1316708129612266289at_nat @ SV805 ) )
        = $true )
      | ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
          = ( semiri1316708129612266289at_nat @ SV805 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13522]) ).

thf(13752,plain,
    ! [SV805: nat,SV556: nat,SV226: num] :
      ( ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
          = SV805 )
        = $true )
      | ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
          = ( semiri1316708129612266289at_nat @ SV805 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13523]) ).

thf(13753,plain,
    ! [SV805: nat,SV556: nat,SV226: num] :
      ( ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
          = ( semiri1316708129612266289at_nat @ SV805 ) )
        = $true )
      | ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
          = SV805 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13524]) ).

thf(13754,plain,
    ! [SV805: nat,SV556: nat,SV226: num] :
      ( ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
          = SV805 )
        = $true )
      | ( ( ( power_power_nat @ ( numeral_numeral_nat @ SV226 ) @ SV556 )
          = SV805 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13525]) ).

thf(13755,plain,
    ! [SV806: nat,SV557: num,SV227: nat] :
      ( ( ( ( semiri1316708129612266289at_nat @ SV227 )
          = ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
        = $true )
      | ( ( ( semiri1316708129612266289at_nat @ SV227 )
          = ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13526]) ).

thf(13756,plain,
    ! [SV806: nat,SV557: num,SV227: nat] :
      ( ( ( SV227
          = ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
        = $true )
      | ( ( ( semiri1316708129612266289at_nat @ SV227 )
          = ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13527]) ).

thf(13757,plain,
    ! [SV806: nat,SV557: num,SV227: nat] :
      ( ( ( ( semiri1316708129612266289at_nat @ SV227 )
          = ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
        = $true )
      | ( ( SV227
          = ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13528]) ).

thf(13758,plain,
    ! [SV806: nat,SV557: num,SV227: nat] :
      ( ( ( SV227
          = ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
        = $true )
      | ( ( SV227
          = ( power_power_nat @ ( numeral_numeral_nat @ SV557 ) @ SV806 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13529]) ).

thf(13759,plain,
    ! [SV243: $o] :
      ( ( ( ~ ( SV243
              | $false )
          | ~ ( ~ SV243
              | ~ $false ) )
        = $true )
      | ( SV243 = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[13538]) ).

thf(13760,plain,
    ! [SV243: $o] :
      ( ( ( SV243 = $false )
        = $true )
      | ( SV243 = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[13538]) ).

thf(13761,plain,
    ! [SV243: $o] :
      ( ( ( ~ ( SV243
              | $false )
          | ~ ( ~ SV243
              | ~ $false ) )
        = $true )
      | ( SV243 = $false )
      | ( $true = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[13539]) ).

thf(13762,plain,
    ! [SV243: $o] :
      ( ( ( SV243 = $false )
        = $true )
      | ( SV243 = $false )
      | ( $true = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[13539]) ).

thf(13763,plain,
    ! [SV243: $o] :
      ( ( ( ~ ( SV243
              | $false )
          | ~ ( ~ SV243
              | ~ $false ) )
        = $true )
      | ( $true = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[13540]) ).

thf(13764,plain,
    ! [SV243: $o] :
      ( ( ( SV243 = $false )
        = $true )
      | ( $true = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[13540]) ).

thf(13765,plain,
    ! [SV243: $o] :
      ( ( ( ~ ( SV243
              | $false )
          | ~ ( ~ SV243
              | ~ $false ) )
        = $true )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[13541]) ).

thf(13766,plain,
    ! [SV243: $o] :
      ( ( ( SV243 = $false )
        = $true )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[13541]) ).

thf(13767,plain,
    ! [SV243: $o] :
      ( ( SV243 = $true )
      | ( SV243 = $false )
      | ( ( SV243 = $true )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13542]) ).

thf(13768,plain,
    ! [SV243: $o] :
      ( ( $false = $true )
      | ( SV243 = $false )
      | ( ( SV243 = $true )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13543]) ).

thf(13769,plain,
    ! [SV243: $o] :
      ( ( SV243 = $true )
      | ( $false = $false )
      | ( ( SV243 = $true )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13544]) ).

thf(13770,plain,
    ! [SV243: $o] :
      ( ( $false = $true )
      | ( $false = $false )
      | ( ( SV243 = $true )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13545]) ).

thf(13771,plain,
    ( ( ( ~ ( $true
            | $false )
        | ~ ( ~ $true
            | ~ $false ) )
      = $true )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[13546]) ).

thf(13772,plain,
    ( ( ( $true = $false )
      = $true )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[13546]) ).

thf(13773,plain,
    ( ( ( ~ ( $true
            | $false )
        | ~ ( ~ $true
            | ~ $false ) )
      = $true )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[13547]) ).

thf(13774,plain,
    ( ( ( $true = $false )
      = $true )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[13547]) ).

thf(13775,plain,
    ( ( ( ~ ( $true
            | $false )
        | ~ ( ~ $true
            | ~ $false ) )
      = $true )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[13548]) ).

thf(13776,plain,
    ( ( ( $true = $false )
      = $true )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[13548]) ).

thf(13777,plain,
    ( ( ( ~ ( $true
            | $false )
        | ~ ( ~ $true
            | ~ $false ) )
      = $true )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[13549]) ).

thf(13778,plain,
    ( ( ( $true = $false )
      = $true )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[13549]) ).

thf(13779,plain,
    ( ( $true = $true )
    | ( $true = $false )
    | ( ( $true = $true )
      = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13550]) ).

thf(13780,plain,
    ( ( $false = $true )
    | ( $true = $false )
    | ( ( $true = $true )
      = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13551]) ).

thf(13781,plain,
    ( ( $true = $true )
    | ( $false = $false )
    | ( ( $true = $true )
      = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13552]) ).

thf(13782,plain,
    ( ( $false = $true )
    | ( $false = $false )
    | ( ( $true = $true )
      = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13553]) ).

thf(13783,plain,
    ( ( ( ~ ( $false
            | $false )
        | ~ ( ~ $false
            | ~ $false ) )
      = $true )
    | ( $false = $false )
    | ( $false = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[13554]) ).

thf(13784,plain,
    ( ( ( $false = $false )
      = $true )
    | ( $false = $false )
    | ( $false = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[13554]) ).

thf(13785,plain,
    ( ( ( ~ ( $false
            | $false )
        | ~ ( ~ $false
            | ~ $false ) )
      = $true )
    | ( $false = $false )
    | ( $true = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[13555]) ).

thf(13786,plain,
    ( ( ( $false = $false )
      = $true )
    | ( $false = $false )
    | ( $true = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[13555]) ).

thf(13787,plain,
    ( ( ( ~ ( $false
            | $false )
        | ~ ( ~ $false
            | ~ $false ) )
      = $true )
    | ( $true = $false )
    | ( $false = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[13556]) ).

thf(13788,plain,
    ( ( ( $false = $false )
      = $true )
    | ( $true = $false )
    | ( $false = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[13556]) ).

thf(13789,plain,
    ( ( ( ~ ( $false
            | $false )
        | ~ ( ~ $false
            | ~ $false ) )
      = $true )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[13557]) ).

thf(13790,plain,
    ( ( ( $false = $false )
      = $true )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[13557]) ).

thf(13791,plain,
    ( ( $false = $true )
    | ( $false = $false )
    | ( ( $false = $true )
      = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13558]) ).

thf(13792,plain,
    ( ( $false = $true )
    | ( $false = $false )
    | ( ( $false = $true )
      = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13559]) ).

thf(13793,plain,
    ( ( $false = $true )
    | ( $false = $false )
    | ( ( $false = $true )
      = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13560]) ).

thf(13794,plain,
    ( ( $false = $true )
    | ( $false = $false )
    | ( ( $false = $true )
      = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13561]) ).

thf(13795,plain,
    ! [SV825: nat,SV257: nat,SV583: nat] :
      ( ( ( ( times_times_nat @ SV583 @ SV257 )
          = ( times_times_nat @ SV825 @ SV257 ) )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV583 @ SV257 )
               != ( times_times_nat @ SV825 @ SV257 ) )
              | ( SV583 != SV825 ) ) )
        = $true )
      | ( ( SV257 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13563]) ).

thf(13796,plain,
    ! [SV257: nat,SV825: nat,SV583: nat] :
      ( ( ( SV583 = SV825 )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV583 @ SV257 )
               != ( times_times_nat @ SV825 @ SV257 ) )
              | ( SV583 != SV825 ) ) )
        = $true )
      | ( ( SV257 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13563]) ).

thf(13797,plain,
    ! [SV584: nat,SV826: nat,SV258: nat] :
      ( ( ( SV258
          = ( times_times_nat @ ( sK13_SY1869 @ SV826 @ SV584 @ SV258 ) @ ( sK20_SY1935 @ SV584 @ SV826 @ SV258 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV258 @ ( times_times_nat @ SV584 @ SV826 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13564]) ).

thf(13798,plain,
    ! [SV258: nat,SV584: nat,SV826: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( sK13_SY1869 @ SV826 @ SV584 @ SV258 ) @ SV584 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV258 @ ( times_times_nat @ SV584 @ SV826 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13565]) ).

thf(13799,plain,
    ! [SV258: nat,SV826: nat,SV584: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( sK20_SY1935 @ SV584 @ SV826 @ SV258 ) @ SV826 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV258 @ ( times_times_nat @ SV584 @ SV826 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13565]) ).

thf(13800,plain,
    ! [SV586: nat,SV260: nat,SV926: nat,SV827: nat] :
      ( ( ( SV827 = SV926 )
        = $false )
      | ( ( SV260 = SV586 )
        = $false )
      | ( ( ( plus_plus_nat @ SV260 @ SV827 )
          = ( plus_plus_nat @ SV586 @ SV926 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13566]) ).

thf(13801,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( SV595 != SV928 )
        = $false )
      | ( ( SV595 = SV928 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13567]) ).

thf(13802,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                 != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
                | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                 != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
        = $false )
      | ( ( SV595 = SV928 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13567]) ).

thf(13803,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
         != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
         != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $true )
      | ( ( ~ ( ( SV595 != SV928 )
              | ~ ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                     != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
                    | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                     != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13568]) ).

thf(13804,plain,
    ! [SV837: nat,SV597: nat,SV273: nat] :
      ( ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
          = ( modulo_modulo_nat @ SV837 @ SV597 ) )
        = $true )
      | ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
          = ( modulo_modulo_nat @ SV837 @ SV597 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13569]) ).

thf(13805,plain,
    ! [SV837: nat,SV597: nat,SV273: nat] :
      ( ( ( ~ ! [SY1874: nat] :
                ~ ~ ! [SY1875: nat] :
                      ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SY1874 ) )
                     != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1875 ) ) ) )
        = $true )
      | ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
          = ( modulo_modulo_nat @ SV837 @ SV597 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13570]) ).

thf(13806,plain,
    ! [SV837: nat,SV962: nat,SV597: nat,SV273: nat] :
      ( ( ( ~ ! [SY1938: nat] :
                ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SV962 ) )
               != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1938 ) ) ) )
        = $false )
      | ( ( ~ ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
               != ( modulo_modulo_nat @ SV837 @ SV597 ) )
              | ~ ~ ! [SY1874: nat] :
                      ~ ~ ! [SY1875: nat] :
                            ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SY1874 ) )
                           != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1875 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13571]) ).

thf(13807,plain,
    ! [SV931: nat,SV844: nat,SV605: nat,SV284: nat] :
      ( ( ( ~ ( ( SV284 != SV605 ) ) )
        = $true )
      | ( ( ~ ( ( SV844 != SV931 ) ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( ( SV284 != SV605 ) )
                    | ~ ( ( SV844 != SV931 ) ) )
              | ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
                   != ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13574]) ).

thf(13808,plain,
    ! [SV931: nat,SV844: nat,SV605: nat,SV284: nat] :
      ( ( ( ~ ~ ( ~ ( ( SV284 != SV605 ) )
                | ~ ( ( SV844 != SV931 ) ) )
          | ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
               != ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) ) ) )
        = $false )
      | ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13575]) ).

thf(13809,plain,
    ! [SV845: nat,SV606: nat,SV285: nat] :
      ( ( ( ( times_times_nat @ SV285 @ SV606 )
          = ( times_times_nat @ SV285 @ SV845 ) )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV285 @ SV606 )
               != ( times_times_nat @ SV285 @ SV845 ) )
              | ( SV606 != SV845 ) ) )
        = $true )
      | ( ( SV285 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13576]) ).

thf(13810,plain,
    ! [SV285: nat,SV845: nat,SV606: nat] :
      ( ( ( SV606 = SV845 )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV285 @ SV606 )
               != ( times_times_nat @ SV285 @ SV845 ) )
              | ( SV606 != SV845 ) ) )
        = $true )
      | ( ( SV285 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13576]) ).

thf(13811,plain,
    ! [SV609: nat,SV288: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV288 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV609 )
        = $true )
      | ( ( SV288 = SV609 )
        = $true )
      | ( ( ( divide_divide_nat @ SV288 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV609 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13578]) ).

thf(13812,plain,
    ! [SV609: nat,SV288: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV288 ) )
        = $true )
      | ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV609 ) )
        = $true )
      | ( ( SV288 = SV609 )
        = $true )
      | ( ( ( divide_divide_nat @ SV288 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV609 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13579]) ).

thf(13813,plain,
    ! [SV611: nat,SV290: nat,SV932: nat,SV848: nat] :
      ( ( ( ord_less_nat @ SV848 @ SV932 )
        = $false )
      | ( ( ord_less_nat @ SV290 @ SV611 )
        = $false )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV290 @ SV848 ) @ ( plus_plus_nat @ SV611 @ SV932 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13580]) ).

thf(13814,plain,
    ! [SV615: nat,SV294: nat,SV933: nat,SV849: nat] :
      ( ( ( ord_less_nat @ SV849 @ SV933 )
        = $false )
      | ( ( SV294 = SV615 )
        = $false )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV294 @ SV849 ) @ ( plus_plus_nat @ SV615 @ SV933 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13581]) ).

thf(13815,plain,
    ! [SV621: nat,SV300: nat] :
      ( ( ( ( SV300 != one_one_nat )
          | ( SV621 != one_one_nat ) )
        = $false )
      | ( ( ( times_times_nat @ SV300 @ SV621 )
          = one_one_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13583]) ).

thf(13816,plain,
    ! [SV300: nat,SV621: nat] :
      ( ( ( SV621 = one_one_nat )
        = $false )
      | ( ( SV300 = one_one_nat )
        = $false )
      | ( ( ~ ( ( ( times_times_nat @ SV300 @ SV621 )
               != one_one_nat )
              | ~ ~ ( ( SV300 != one_one_nat )
                    | ( SV621 != one_one_nat ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13584]) ).

thf(13817,plain,
    ! [SV936: nat,SV622: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV622 @ SV936 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV622 @ SV936 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13585]) ).

thf(13818,plain,
    ! [SV622: nat,SV936: nat] :
      ( ( ( ~ ~ ! [SY1919: nat] :
                  ( SV936
                 != ( times_times_nat @ SV622 @ SY1919 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV622 @ SV936 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13585]) ).

thf(13819,plain,
    ! [SV963: nat,SV622: nat,SV936: nat] :
      ( ( ( SV936
         != ( times_times_nat @ SV622 @ SV963 ) )
        = $true )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ SV622 @ SV936 )
              | ~ ~ ! [SY1919: nat] :
                      ( SV936
                     != ( times_times_nat @ SV622 @ SY1919 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[13586]) ).

thf(13820,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13587]) ).

thf(13821,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
         != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13588]) ).

thf(13822,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
          | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $false )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
              | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
                   != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13589]) ).

thf(13823,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) ) )
        = $false )
      | ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13590]) ).

thf(13824,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
               != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) )
        = $false )
      | ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13590]) ).

thf(13825,plain,
    ! [SV626: nat,SV305: nat] :
      ( ( ( ( SV305 != zero_zero_nat )
          | ( SV626 != zero_zero_nat ) )
        = $false )
      | ( ( ( plus_plus_nat @ SV305 @ SV626 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13592]) ).

thf(13826,plain,
    ! [SV305: nat,SV626: nat] :
      ( ( ( SV626 = zero_zero_nat )
        = $false )
      | ( ( SV305 = zero_zero_nat )
        = $false )
      | ( ( ~ ( ( ( plus_plus_nat @ SV305 @ SV626 )
               != zero_zero_nat )
              | ~ ~ ( ( SV305 != zero_zero_nat )
                    | ( SV626 != zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13593]) ).

thf(13827,plain,
    ! [SV630: nat,SV310: nat] :
      ( ( ( ( SV310 != zero_zero_nat )
          | ( SV630 != zero_zero_nat ) )
        = $false )
      | ( ( ( plus_plus_nat @ SV310 @ SV630 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13595]) ).

thf(13828,plain,
    ! [SV310: nat,SV630: nat] :
      ( ( ( SV630 = zero_zero_nat )
        = $false )
      | ( ( SV310 = zero_zero_nat )
        = $false )
      | ( ( ~ ( ( ( plus_plus_nat @ SV310 @ SV630 )
               != zero_zero_nat )
              | ~ ~ ( ( SV310 != zero_zero_nat )
                    | ( SV630 != zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13596]) ).

thf(13829,plain,
    ! [SV631: nat,SV856: nat,SV311: nat] :
      ( ( ( ~ ~ ( ~ ~ ( ( SV311
                       != ( times_times_nat @ ( sK14_SY1883 @ SV856 @ SV631 @ SV311 ) @ ( sK22_SY1936 @ SV631 @ SV856 @ SV311 ) ) )
                      | ~ ( dvd_dvd_nat @ ( sK14_SY1883 @ SV856 @ SV631 @ SV311 ) @ SV631 ) )
                | ~ ( dvd_dvd_nat @ ( sK22_SY1936 @ SV631 @ SV856 @ SV311 ) @ SV856 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV311 @ ( times_times_nat @ SV631 @ SV856 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[13597]) ).

thf(13830,plain,
    ! [SV312: nat,SV956: nat,SV857: nat,SV937: nat,SV632: nat] :
      ( ( ( ~ ( ( ( times_times_nat @ SV632 @ SV937 )
                = ( plus_plus_nat @ ( times_times_nat @ SV857 @ SV956 ) @ SV312 ) )
              | ( ( times_times_nat @ SV857 @ SV937 )
                = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SV956 ) @ SV312 ) ) ) )
        = $true )
      | ( ( ~ ! [SY1887: nat] :
                ~ ~ ! [SY1888: nat] :
                      ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
                                | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) )
                          | ~ ( ( ( times_times_nat @ SV632 @ SY1887 )
                                = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1888 ) @ SV312 ) )
                              | ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1887 )
                                = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SY1888 ) @ SV312 ) ) ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13598]) ).

thf(13831,plain,
    ! [SV639: nat,SV860: nat,SV319: nat > nat > $o] :
      ( ( ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
          | ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) ) )
        = $true )
      | ( ( ~ ! [SY1421: nat] : ( SV319 @ SY1421 @ zero_zero_nat )
          | ~ ! [SY1422: nat,SY1423: nat] :
                ( ~ ( SV319 @ SY1422 @ SY1423 )
                | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) )
          | ( SV319 @ SV639 @ SV860 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13600]) ).

thf(13832,plain,
    ! [SV639: nat,SV860: nat,SV319: nat > nat > $o] :
      ( ( ( ~ ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
          | ~ ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) ) )
        = $true )
      | ( ( ~ ! [SY1421: nat] : ( SV319 @ SY1421 @ zero_zero_nat )
          | ~ ! [SY1422: nat,SY1423: nat] :
                ( ~ ( SV319 @ SY1422 @ SY1423 )
                | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) )
          | ( SV319 @ SV639 @ SV860 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13601]) ).

thf(13833,plain,
    ! [SV860: nat,SV639: nat,SV319: nat > nat > $o] :
      ( ( ( ! [SY1421: nat] : ( SV319 @ SY1421 @ zero_zero_nat ) )
        = $false )
      | ( ( ~ ! [SY1422: nat,SY1423: nat] :
                ( ~ ( SV319 @ SY1422 @ SY1423 )
                | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) )
          | ( SV319 @ SV639 @ SV860 ) )
        = $true )
      | ( ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
          = ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13602]) ).

thf(13834,plain,
    ! [SV642: nat,SV322: nat] :
      ( ( ( ~ ( ( SV322 != SV642 ) )
          | ~ ( vEBT_V8194947554948674370ptions @ summary @ SV642 ) )
        = $false )
      | ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13604]) ).

thf(13835,plain,
    ! [SV642: nat,SV322: nat] :
      ( ( ( SV322 = SV642 )
        = $true )
      | ( ( ~ ( vEBT_V8194947554948674370ptions @ summary @ SV642 ) )
        = $true )
      | ( ( ~ ( ~ ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 )
              | ~ ~ ( ~ ( ( SV322 != SV642 ) )
                    | ~ ( vEBT_V8194947554948674370ptions @ summary @ SV642 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13605]) ).

thf(13836,plain,
    ! [SV939: nat,SV644: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV644 @ SV939 ) )
        = $false )
      | ( ( ord_less_eq_nat @ SV644 @ SV939 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13607]) ).

thf(13837,plain,
    ! [SV644: nat,SV939: nat] :
      ( ( ( ~ ~ ! [SY1924: nat] :
                  ( SV939
                 != ( plus_plus_nat @ SV644 @ SY1924 ) ) )
        = $false )
      | ( ( ord_less_eq_nat @ SV644 @ SV939 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13607]) ).

thf(13838,plain,
    ! [SV964: nat,SV644: nat,SV939: nat] :
      ( ( ( SV939
         != ( plus_plus_nat @ SV644 @ SV964 ) )
        = $true )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ SV644 @ SV939 )
              | ~ ~ ! [SY1924: nat] :
                      ( SV939
                     != ( plus_plus_nat @ SV644 @ SY1924 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[13608]) ).

thf(13839,plain,
    ! [SV648: nat,SV328: nat,SV940: nat,SV867: nat] :
      ( ( ( SV867 = SV940 )
        = $false )
      | ( ( ord_less_eq_nat @ SV328 @ SV648 )
        = $false )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV328 @ SV867 ) @ ( plus_plus_nat @ SV648 @ SV940 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13609]) ).

thf(13840,plain,
    ! [SV649: nat,SV329: nat] :
      ( ( ( ( SV329 != zero_zero_nat )
          | ( SV649 != zero_zero_nat ) )
        = $false )
      | ( ( zero_zero_nat
          = ( plus_plus_nat @ SV329 @ SV649 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13611]) ).

thf(13841,plain,
    ! [SV329: nat,SV649: nat] :
      ( ( ( SV649 = zero_zero_nat )
        = $false )
      | ( ( SV329 = zero_zero_nat )
        = $false )
      | ( ( ~ ( ( zero_zero_nat
               != ( plus_plus_nat @ SV329 @ SV649 ) )
              | ~ ~ ( ( SV329 != zero_zero_nat )
                    | ( SV649 != zero_zero_nat ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13612]) ).

thf(13842,plain,
    ! [SV657: nat,SV335: nat,SV942: nat,SV871: nat] :
      ( ( ( ord_less_eq_nat @ SV871 @ SV942 )
        = $false )
      | ( ( SV335 = SV657 )
        = $false )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV335 @ SV871 ) @ ( plus_plus_nat @ SV657 @ SV942 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13613]) ).

thf(13843,plain,
    ! [SV658: nat,SV872: nat,SV336: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV336 @ ( plus_plus_nat @ SV872 @ SV658 ) )
          | ~ ( dvd_dvd_nat @ SV336 @ SV872 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV336 @ ( plus_plus_nat @ SV872 @ SV658 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV336 @ SV658 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13614]) ).

thf(13844,plain,
    ! [SV658: nat,SV872: nat,SV336: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV336 @ ( plus_plus_nat @ SV872 @ SV658 ) )
          | ~ ( dvd_dvd_nat @ SV336 @ SV872 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV336 @ SV872 )
        = $false )
      | ( ( dvd_dvd_nat @ SV336 @ SV658 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13615]) ).

thf(13845,plain,
    ! [SV662: nat,SV341: nat,SV943: nat,SV876: nat] :
      ( ( ( ord_less_eq_nat @ SV876 @ SV943 )
        = $false )
      | ( ( ord_less_eq_nat @ SV341 @ SV662 )
        = $false )
      | ( ( ord_less_eq_nat @ ( plus_plus_nat @ SV341 @ SV876 ) @ ( plus_plus_nat @ SV662 @ SV943 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13616]) ).

thf(13846,plain,
    ! [SV882: nat,SV347: nat,SV668: nat] :
      ( ( ( ( dvd_dvd_nat @ ( divide_divide_nat @ SV668 @ SV347 ) @ ( divide_divide_nat @ SV882 @ SV347 ) )
          | ( dvd_dvd_nat @ SV668 @ SV882 ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( divide_divide_nat @ SV668 @ SV347 ) @ ( divide_divide_nat @ SV882 @ SV347 ) )
              | ~ ( dvd_dvd_nat @ SV668 @ SV882 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV347 @ SV882 )
        = $false )
      | ( ( dvd_dvd_nat @ SV347 @ SV668 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13617]) ).

thf(13847,plain,
    ! [SV349: nat,SV669: nat] :
      ( ( ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ ( sK6_SY1803 @ SV669 @ SV349 ) @ SV349 )
                    | ~ ( dvd_dvd_nat @ ( sK6_SY1803 @ SV669 @ SV349 ) @ SV669 ) )
              | ~ ( ( ( times_times_nat @ SV349 @ ( sK18_SY1926 @ SV349 @ SV669 ) )
                    = ( plus_plus_nat @ ( times_times_nat @ SV669 @ ( sK23_SY1937 @ SV349 @ SV669 ) ) @ ( sK6_SY1803 @ SV669 @ SV349 ) ) )
                  | ( ( times_times_nat @ SV669 @ ( sK18_SY1926 @ SV349 @ SV669 ) )
                    = ( plus_plus_nat @ ( times_times_nat @ SV349 @ ( sK23_SY1937 @ SV349 @ SV669 ) ) @ ( sK6_SY1803 @ SV669 @ SV349 ) ) ) ) ) )
      = $false ),
    inference(extcnf_forall_neg,[status(esa)],[13618]) ).

thf(13848,plain,
    ! [SV671: nat,SV351: nat] :
      ( ( ( ( SV351 != one_one_nat )
          | ( SV671 != one_one_nat ) )
        = $false )
      | ( ( one_one_nat
          = ( times_times_nat @ SV351 @ SV671 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13620]) ).

thf(13849,plain,
    ! [SV351: nat,SV671: nat] :
      ( ( ( SV671 = one_one_nat )
        = $false )
      | ( ( SV351 = one_one_nat )
        = $false )
      | ( ( ~ ( ( one_one_nat
               != ( times_times_nat @ SV351 @ SV671 ) )
              | ~ ~ ( ( SV351 != one_one_nat )
                    | ( SV671 != one_one_nat ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13621]) ).

thf(13850,plain,
    ! [SV353: nat,SV959: nat,SV945: nat,SV884: nat,SV673: nat] :
      ( ( ( ~ ( ( SV673 != SV884 )
              | ~ ( ( SV945 != SV959 ) ) ) )
        = $false )
      | ( ( ( plus_plus_nat @ SV673 @ ( times_times_nat @ SV353 @ SV945 ) )
         != ( plus_plus_nat @ SV884 @ ( times_times_nat @ SV353 @ SV959 ) ) )
        = $true )
      | ( ( SV353 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13622]) ).

thf(13851,plain,
    ! [SV885: nat,SV674: nat,SV354: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV354 @ ( plus_plus_nat @ SV674 @ SV885 ) )
          | ~ ( dvd_dvd_nat @ SV354 @ SV885 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV354 @ ( plus_plus_nat @ SV674 @ SV885 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV354 @ SV674 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13623]) ).

thf(13852,plain,
    ! [SV885: nat,SV674: nat,SV354: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV354 @ ( plus_plus_nat @ SV674 @ SV885 ) )
          | ~ ( dvd_dvd_nat @ SV354 @ SV885 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV354 @ SV885 )
        = $false )
      | ( ( dvd_dvd_nat @ SV354 @ SV674 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13624]) ).

thf(13853,plain,
    ! [SV889: nat,SV362: nat,SV681: nat] :
      ( ( ( ( ( divide_divide_nat @ SV681 @ SV362 )
            = ( divide_divide_nat @ SV889 @ SV362 ) )
          | ( SV681 = SV889 ) )
        = $false )
      | ( ( ~ ( ( ( divide_divide_nat @ SV681 @ SV362 )
               != ( divide_divide_nat @ SV889 @ SV362 ) )
              | ( SV681 != SV889 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV362 @ SV889 )
        = $false )
      | ( ( dvd_dvd_nat @ SV362 @ SV681 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13627]) ).

thf(13854,plain,
    ! [SV692: option_nat,SV373: option_nat] :
      ( ( ( ~ ( ( SV373 != none_nat ) )
          | ~ ( ( SV692 != none_nat ) )
          | ( ( the_nat @ SV373 )
            = ( the_nat @ SV692 ) ) )
        = $false )
      | ( ( SV373 = SV692 )
        = $true )
      | ( ( SV692 = none_nat )
        = $true )
      | ( ( SV373 = none_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13628]) ).

thf(13855,plain,
    ! [SV373: option_nat,SV692: option_nat] :
      ( ( ( SV692 = none_nat )
        = $false )
      | ( ( SV373 = none_nat )
        = $false )
      | ( ( ~ ( ~ ( ( SV373 != none_nat ) )
              | ~ ( ( SV692 != none_nat ) )
              | ( ( the_nat @ SV373 )
                = ( the_nat @ SV692 ) ) )
          | ( SV373 = SV692 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13629]) ).

thf(13856,plain,
    ! [SV692: option_nat,SV373: option_nat] :
      ( ( ( SV373 = none_nat )
        = $false )
      | ( ( SV373 = SV692 )
        = $true )
      | ( ( ( SV373 = none_nat )
          = ( SV692 = none_nat ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13630]) ).

thf(13857,plain,
    ! [SV373: option_nat,SV692: option_nat] :
      ( ( ( SV692 != none_nat )
        = $true )
      | ( ( SV373 = SV692 )
        = $true )
      | ( ( ( SV373 = none_nat )
          = ( SV692 = none_nat ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13631]) ).

thf(13858,plain,
    ! [SV693: nat,SV374: nat > $o] :
      ( ( ( ! [SY1940: $o] :
              ( ~ ( SV374 @ ( sK24_SY1534 @ SV693 @ SV374 ) )
              | ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ SY1940 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( sK24_SY1534 @ SV693 @ SV374 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
               != ( sK24_SY1534 @ SV693 @ SV374 ) )
              | ( SV374 @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ SY1940 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( sK24_SY1534 @ SV693 @ SV374 ) ) ) ) ) )
        = $false )
      | ( ( SV374 @ SV693 )
        = $true )
      | ( ( ( divide_divide_nat @ ( sK8_SY1533 @ SV693 @ SV374 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( sK8_SY1533 @ SV693 @ SV374 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[13633]) ).

thf(13859,plain,
    ! [SV693: nat,SV374: nat > $o] :
      ( ( ( ~ ( SV374 @ ( sK21_SY1534 @ SV693 @ SV374 ) )
          | ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ ( sK25_SY1939 @ SV693 @ SV374 ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( sK21_SY1534 @ SV693 @ SV374 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
           != ( sK21_SY1534 @ SV693 @ SV374 ) )
          | ( SV374 @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ ( sK25_SY1939 @ SV693 @ SV374 ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( sK21_SY1534 @ SV693 @ SV374 ) ) ) ) )
        = $false )
      | ( ( SV374 @ SV693 )
        = $true )
      | ( ( SV374 @ ( sK8_SY1533 @ SV693 @ SV374 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[13634]) ).

thf(13860,plain,
    ! [SV948: nat,SV694: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV694 @ SV948 ) )
        = $false )
      | ( ( ord_less_eq_nat @ SV694 @ SV948 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13635]) ).

thf(13861,plain,
    ! [SV694: nat,SV948: nat] :
      ( ( ( ~ ~ ! [SY1929: nat] :
                  ( SV948
                 != ( plus_plus_nat @ SV694 @ SY1929 ) ) )
        = $false )
      | ( ( ord_less_eq_nat @ SV694 @ SV948 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13635]) ).

thf(13862,plain,
    ! [SV965: nat,SV694: nat,SV948: nat] :
      ( ( ( SV948
         != ( plus_plus_nat @ SV694 @ SV965 ) )
        = $true )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ SV694 @ SV948 )
              | ~ ~ ! [SY1929: nat] :
                      ( SV948
                     != ( plus_plus_nat @ SV694 @ SY1929 ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[13636]) ).

thf(13863,plain,
    ! [SV698: nat,SV379: nat,SV950: nat,SV902: nat] :
      ( ( ( SV902 = SV950 )
        = $false )
      | ( ( ord_less_nat @ SV379 @ SV698 )
        = $false )
      | ( ( ord_less_nat @ ( plus_plus_nat @ SV379 @ SV902 ) @ ( plus_plus_nat @ SV698 @ SV950 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13637]) ).

thf(13864,plain,
    ! [SV382: num] :
      ( ( ( SV382
         != ( bit1 @ ( sK26_SY1551 @ SV382 ) ) )
        = $false )
      | ( ( SV382
          = ( bit0 @ ( sK19_SY1550 @ SV382 ) ) )
        = $true )
      | ( ( SV382 = one )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[13638]) ).

thf(13865,plain,
    ! [SV770: nat,SV142: nat,SV493: nat] :
      ( ( ( SV493 = zero_zero_nat )
        = $true )
      | ( ( SV142 = SV770 )
        = $true )
      | ( ( ( times_times_nat @ SV142 @ SV493 )
          = ( times_times_nat @ SV770 @ SV493 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13677]) ).

thf(13866,plain,
    ! [SV770: nat,SV493: nat,SV142: nat] :
      ( ( ( ( times_times_nat @ SV142 @ SV493 )
          = ( times_times_nat @ SV770 @ SV493 ) )
        = $true )
      | ( ( SV493 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13678]) ).

thf(13867,plain,
    ! [SV770: nat,SV142: nat,SV493: nat] :
      ( ( ( ( SV493 = zero_zero_nat )
          | ( SV142 = SV770 ) )
        = $true )
      | ( ( SV493 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13679]) ).

thf(13868,plain,
    ! [SV770: nat,SV493: nat,SV142: nat] :
      ( ( ( ( times_times_nat @ SV142 @ SV493 )
          = ( times_times_nat @ SV770 @ SV493 ) )
        = $true )
      | ( ( SV142 = SV770 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13680]) ).

thf(13869,plain,
    ! [SV770: nat,SV142: nat,SV493: nat] :
      ( ( ( ( SV493 = zero_zero_nat )
          | ( SV142 = SV770 ) )
        = $true )
      | ( ( SV142 = SV770 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13681]) ).

thf(13870,plain,
    ! [SV771: nat,SV494: nat,SV143: nat] :
      ( ( ( SV143 = zero_zero_nat )
        = $true )
      | ( ( SV494 = SV771 )
        = $true )
      | ( ( ( times_times_nat @ SV143 @ SV494 )
          = ( times_times_nat @ SV143 @ SV771 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13683]) ).

thf(13871,plain,
    ! [SV771: nat,SV494: nat,SV143: nat] :
      ( ( ( ( times_times_nat @ SV143 @ SV494 )
          = ( times_times_nat @ SV143 @ SV771 ) )
        = $true )
      | ( ( SV143 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13684]) ).

thf(13872,plain,
    ! [SV771: nat,SV494: nat,SV143: nat] :
      ( ( ( ( SV143 = zero_zero_nat )
          | ( SV494 = SV771 ) )
        = $true )
      | ( ( SV143 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13685]) ).

thf(13873,plain,
    ! [SV771: nat,SV494: nat,SV143: nat] :
      ( ( ( ( times_times_nat @ SV143 @ SV494 )
          = ( times_times_nat @ SV143 @ SV771 ) )
        = $true )
      | ( ( SV494 = SV771 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13686]) ).

thf(13874,plain,
    ! [SV771: nat,SV494: nat,SV143: nat] :
      ( ( ( ( SV143 = zero_zero_nat )
          | ( SV494 = SV771 ) )
        = $true )
      | ( ( SV494 = SV771 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13687]) ).

thf(13875,plain,
    ! [SV495: nat,SV144: nat] :
      ( ( ( SV144 = zero_zero_nat )
        = $true )
      | ( ( SV495 = zero_zero_nat )
        = $true )
      | ( ( SV144 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13690]) ).

thf(13876,plain,
    ! [SV495: nat,SV144: nat] :
      ( ( ( SV144 = zero_zero_nat )
        = $true )
      | ( ( SV495 = zero_zero_nat )
        = $true )
      | ( ( SV495 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13692]) ).

thf(13877,plain,
    ! [SV502: nat,SV772: nat,SV160: nat] :
      ( ( ( SV160 = SV772 )
        = $true )
      | ( ( SV502 = zero_zero_nat )
        = $true )
      | ( ( ( times_times_nat @ SV160 @ SV502 )
          = ( times_times_nat @ SV772 @ SV502 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13694]) ).

thf(13878,plain,
    ! [SV772: nat,SV502: nat,SV160: nat] :
      ( ( ( ( times_times_nat @ SV160 @ SV502 )
          = ( times_times_nat @ SV772 @ SV502 ) )
        = $true )
      | ( ( SV160 = SV772 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13695]) ).

thf(13879,plain,
    ! [SV502: nat,SV772: nat,SV160: nat] :
      ( ( ( ( SV160 = SV772 )
          | ( SV502 = zero_zero_nat ) )
        = $true )
      | ( ( SV160 = SV772 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13696]) ).

thf(13880,plain,
    ! [SV772: nat,SV502: nat,SV160: nat] :
      ( ( ( ( times_times_nat @ SV160 @ SV502 )
          = ( times_times_nat @ SV772 @ SV502 ) )
        = $true )
      | ( ( SV502 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13697]) ).

thf(13881,plain,
    ! [SV502: nat,SV772: nat,SV160: nat] :
      ( ( ( ( SV160 = SV772 )
          | ( SV502 = zero_zero_nat ) )
        = $true )
      | ( ( SV502 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13698]) ).

thf(13882,plain,
    ! [SV161: nat,SV773: nat,SV503: nat] :
      ( ( ( SV503 = SV773 )
        = $true )
      | ( ( SV161 = zero_zero_nat )
        = $true )
      | ( ( ( times_times_nat @ SV161 @ SV503 )
          = ( times_times_nat @ SV161 @ SV773 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13700]) ).

thf(13883,plain,
    ! [SV773: nat,SV503: nat,SV161: nat] :
      ( ( ( ( times_times_nat @ SV161 @ SV503 )
          = ( times_times_nat @ SV161 @ SV773 ) )
        = $true )
      | ( ( SV503 = SV773 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13701]) ).

thf(13884,plain,
    ! [SV161: nat,SV773: nat,SV503: nat] :
      ( ( ( ( SV503 = SV773 )
          | ( SV161 = zero_zero_nat ) )
        = $true )
      | ( ( SV503 = SV773 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13702]) ).

thf(13885,plain,
    ! [SV773: nat,SV503: nat,SV161: nat] :
      ( ( ( ( times_times_nat @ SV161 @ SV503 )
          = ( times_times_nat @ SV161 @ SV773 ) )
        = $true )
      | ( ( SV161 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13703]) ).

thf(13886,plain,
    ! [SV161: nat,SV773: nat,SV503: nat] :
      ( ( ( ( SV503 = SV773 )
          | ( SV161 = zero_zero_nat ) )
        = $true )
      | ( ( SV161 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13704]) ).

thf(13887,plain,
    ! [SV504: nat,SV163: nat] :
      ( ( ( SV163 = zero_zero_nat )
        = $true )
      | ( ( SV504 = zero_zero_nat )
        = $true )
      | ( ( SV163 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13707]) ).

thf(13888,plain,
    ! [SV504: nat,SV163: nat] :
      ( ( ( SV163 = zero_zero_nat )
        = $true )
      | ( ( SV504 = zero_zero_nat )
        = $true )
      | ( ( SV504 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13709]) ).

thf(13889,plain,
    ! [SV788: nat,SV520: nat,SV185: nat] :
      ( ( ( SV185 = zero_zero_nat )
        = $true )
      | ( ( SV520 = SV788 )
        = $true )
      | ( ( ( times_times_nat @ SV185 @ SV520 )
          = ( times_times_nat @ SV185 @ SV788 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13715]) ).

thf(13890,plain,
    ! [SV788: nat,SV520: nat,SV185: nat] :
      ( ( ( ( times_times_nat @ SV185 @ SV520 )
          = ( times_times_nat @ SV185 @ SV788 ) )
        = $true )
      | ( ( SV185 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13716]) ).

thf(13891,plain,
    ! [SV788: nat,SV520: nat,SV185: nat] :
      ( ( ( ( SV185 = zero_zero_nat )
          | ( SV520 = SV788 ) )
        = $true )
      | ( ( SV185 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13717]) ).

thf(13892,plain,
    ! [SV788: nat,SV520: nat,SV185: nat] :
      ( ( ( ( times_times_nat @ SV185 @ SV520 )
          = ( times_times_nat @ SV185 @ SV788 ) )
        = $true )
      | ( ( SV520 = SV788 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13718]) ).

thf(13893,plain,
    ! [SV788: nat,SV520: nat,SV185: nat] :
      ( ( ( ( SV185 = zero_zero_nat )
          | ( SV520 = SV788 ) )
        = $true )
      | ( ( SV520 = SV788 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13719]) ).

thf(13894,plain,
    ! [SV539: nat,SV205: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13730]) ).

thf(13895,plain,
    ! [SV539: nat,SV205: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV205 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV539 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13732]) ).

thf(13896,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $true )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13733]) ).

thf(13897,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
           != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13735]) ).

thf(13898,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $true )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
              | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
               != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13736]) ).

thf(13899,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
          | ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $true )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[13738]) ).

thf(13900,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $true )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[13738]) ).

thf(13901,plain,
    ! [SV922: nat,SV802: nat,SV549: nat,SV216: nat] :
      ( ( ( ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV549 ) @ ( times_times_nat @ SV802 @ SV922 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV922 ) @ ( times_times_nat @ SV802 @ SV549 ) ) )
        = $true )
      | ( ( ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV549 ) @ ( times_times_nat @ SV802 @ SV922 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV922 ) @ ( times_times_nat @ SV802 @ SV549 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13739]) ).

thf(13902,plain,
    ! [SV922: nat,SV549: nat,SV802: nat,SV216: nat] :
      ( ( ( ( SV216 = SV802 )
          | ( SV549 = SV922 ) )
        = $true )
      | ( ( ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV549 ) @ ( times_times_nat @ SV802 @ SV922 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV922 ) @ ( times_times_nat @ SV802 @ SV549 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13740]) ).

thf(13903,plain,
    ! [SV922: nat,SV802: nat,SV549: nat,SV216: nat] :
      ( ( ( ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV549 ) @ ( times_times_nat @ SV802 @ SV922 ) )
         != ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV922 ) @ ( times_times_nat @ SV802 @ SV549 ) ) )
        = $false )
      | ( ( SV216 = SV802 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13741]) ).

thf(13904,plain,
    ! [SV922: nat,SV549: nat,SV802: nat,SV216: nat] :
      ( ( ( ~ ( ( SV216 = SV802 )
              | ( SV549 = SV922 ) ) )
        = $false )
      | ( ( SV216 = SV802 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13741]) ).

thf(13905,plain,
    ! [SV922: nat,SV802: nat,SV549: nat,SV216: nat] :
      ( ( ( ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV549 ) @ ( times_times_nat @ SV802 @ SV922 ) )
         != ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV922 ) @ ( times_times_nat @ SV802 @ SV549 ) ) )
        = $false )
      | ( ( SV549 = SV922 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13742]) ).

thf(13906,plain,
    ! [SV922: nat,SV549: nat,SV802: nat,SV216: nat] :
      ( ( ( ~ ( ( SV216 = SV802 )
              | ( SV549 = SV922 ) ) )
        = $false )
      | ( ( SV549 = SV922 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13742]) ).

thf(13907,plain,
    ! [SV243: $o] :
      ( ( ( ~ ( SV243
              | $false ) )
        = $true )
      | ( ( ~ ( ~ SV243
              | ~ $false ) )
        = $true )
      | ( SV243 = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13759]) ).

thf(13908,plain,
    ! [SV243: $o] :
      ( ( ( ~ ( SV243
              | $false ) )
        = $true )
      | ( ( ~ ( ~ SV243
              | ~ $false ) )
        = $true )
      | ( SV243 = $false )
      | ( $true = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13761]) ).

thf(13909,plain,
    ! [SV243: $o] :
      ( ( ( ~ ( SV243
              | $false ) )
        = $true )
      | ( ( ~ ( ~ SV243
              | ~ $false ) )
        = $true )
      | ( $true = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13763]) ).

thf(13910,plain,
    ! [SV243: $o] :
      ( ( ( ~ ( SV243
              | $false ) )
        = $true )
      | ( ( ~ ( ~ SV243
              | ~ $false ) )
        = $true )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13765]) ).

thf(13911,plain,
    ( ( ( ~ ( $true
            | $false ) )
      = $true )
    | ( ( ~ ( ~ $true
            | ~ $false ) )
      = $true )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13771]) ).

thf(13912,plain,
    ( ( ( ~ ( $true
            | $false ) )
      = $true )
    | ( ( ~ ( ~ $true
            | ~ $false ) )
      = $true )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13773]) ).

thf(13913,plain,
    ( ( ( ~ ( $true
            | $false ) )
      = $true )
    | ( ( ~ ( ~ $true
            | ~ $false ) )
      = $true )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13775]) ).

thf(13914,plain,
    ( ( ( ~ ( $true
            | $false ) )
      = $true )
    | ( ( ~ ( ~ $true
            | ~ $false ) )
      = $true )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13777]) ).

thf(13915,plain,
    ( ( ( ~ ( $false
            | $false ) )
      = $true )
    | ( ( ~ ( ~ $false
            | ~ $false ) )
      = $true )
    | ( $false = $false )
    | ( $false = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13783]) ).

thf(13916,plain,
    ( ( ( ~ ( $false
            | $false ) )
      = $true )
    | ( ( ~ ( ~ $false
            | ~ $false ) )
      = $true )
    | ( $false = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13785]) ).

thf(13917,plain,
    ( ( ( ~ ( $false
            | $false ) )
      = $true )
    | ( ( ~ ( ~ $false
            | ~ $false ) )
      = $true )
    | ( $true = $false )
    | ( $false = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13787]) ).

thf(13918,plain,
    ( ( ( ~ ( $false
            | $false ) )
      = $true )
    | ( ( ~ ( ~ $false
            | ~ $false ) )
      = $true )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13789]) ).

thf(13919,plain,
    ! [SV825: nat,SV257: nat,SV583: nat] :
      ( ( ( ( ( times_times_nat @ SV583 @ SV257 )
           != ( times_times_nat @ SV825 @ SV257 ) )
          | ( SV583 != SV825 ) )
        = $false )
      | ( ( ( times_times_nat @ SV583 @ SV257 )
          = ( times_times_nat @ SV825 @ SV257 ) )
        = $false )
      | ( ( SV257 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13795]) ).

thf(13920,plain,
    ! [SV825: nat,SV257: nat,SV583: nat] :
      ( ( ( ( ( times_times_nat @ SV583 @ SV257 )
           != ( times_times_nat @ SV825 @ SV257 ) )
          | ( SV583 != SV825 ) )
        = $false )
      | ( ( SV583 = SV825 )
        = $false )
      | ( ( SV257 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13796]) ).

thf(13921,plain,
    ! [SV258: nat,SV584: nat,SV826: nat] :
      ( ( ( dvd_dvd_nat @ ( sK13_SY1869 @ SV826 @ SV584 @ SV258 ) @ SV584 )
        = $true )
      | ( ( dvd_dvd_nat @ SV258 @ ( times_times_nat @ SV584 @ SV826 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13798]) ).

thf(13922,plain,
    ! [SV258: nat,SV826: nat,SV584: nat] :
      ( ( ( dvd_dvd_nat @ ( sK20_SY1935 @ SV584 @ SV826 @ SV258 ) @ SV826 )
        = $true )
      | ( ( dvd_dvd_nat @ SV258 @ ( times_times_nat @ SV584 @ SV826 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13799]) ).

thf(13923,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( SV595 = SV928 )
        = $true )
      | ( ( SV595 = SV928 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13801]) ).

thf(13924,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
               != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
              | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
               != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
        = $true )
      | ( ( SV595 = SV928 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13802]) ).

thf(13925,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
         != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $true )
      | ( ( ~ ( ( SV595 != SV928 )
              | ~ ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                     != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
                    | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                     != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13803]) ).

thf(13926,plain,
    ! [SV837: nat,SV597: nat,SV273: nat] :
      ( ( ( ! [SY1874: nat] :
              ~ ~ ! [SY1875: nat] :
                    ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SY1874 ) )
                   != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1875 ) ) ) )
        = $false )
      | ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
          = ( modulo_modulo_nat @ SV837 @ SV597 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13805]) ).

thf(13927,plain,
    ! [SV837: nat,SV962: nat,SV597: nat,SV273: nat] :
      ( ( ( ! [SY1938: nat] :
              ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SV962 ) )
             != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1938 ) ) ) )
        = $true )
      | ( ( ~ ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
               != ( modulo_modulo_nat @ SV837 @ SV597 ) )
              | ~ ~ ! [SY1874: nat] :
                      ~ ~ ! [SY1875: nat] :
                            ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SY1874 ) )
                           != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1875 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13806]) ).

thf(13928,plain,
    ! [SV931: nat,SV844: nat,SV605: nat,SV284: nat] :
      ( ( ( SV284 != SV605 )
        = $false )
      | ( ( ~ ( ( SV844 != SV931 ) ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( ( SV284 != SV605 ) )
                    | ~ ( ( SV844 != SV931 ) ) )
              | ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
                   != ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13807]) ).

thf(13929,plain,
    ! [SV931: nat,SV844: nat,SV605: nat,SV284: nat] :
      ( ( ( ~ ~ ( ~ ( ( SV284 != SV605 ) )
                | ~ ( ( SV844 != SV931 ) ) ) )
        = $false )
      | ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13808]) ).

thf(13930,plain,
    ! [SV931: nat,SV605: nat,SV844: nat,SV284: nat] :
      ( ( ( ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
               != ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) ) ) )
        = $false )
      | ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13808]) ).

thf(13931,plain,
    ! [SV845: nat,SV606: nat,SV285: nat] :
      ( ( ( ( ( times_times_nat @ SV285 @ SV606 )
           != ( times_times_nat @ SV285 @ SV845 ) )
          | ( SV606 != SV845 ) )
        = $false )
      | ( ( ( times_times_nat @ SV285 @ SV606 )
          = ( times_times_nat @ SV285 @ SV845 ) )
        = $false )
      | ( ( SV285 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13809]) ).

thf(13932,plain,
    ! [SV845: nat,SV606: nat,SV285: nat] :
      ( ( ( ( ( times_times_nat @ SV285 @ SV606 )
           != ( times_times_nat @ SV285 @ SV845 ) )
          | ( SV606 != SV845 ) )
        = $false )
      | ( ( SV606 = SV845 )
        = $false )
      | ( ( SV285 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13810]) ).

thf(13933,plain,
    ! [SV609: nat,SV288: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV288 )
        = $false )
      | ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV609 ) )
        = $true )
      | ( ( SV288 = SV609 )
        = $true )
      | ( ( ( divide_divide_nat @ SV288 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV609 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13812]) ).

thf(13934,plain,
    ! [SV621: nat,SV300: nat] :
      ( ( ( SV300 != one_one_nat )
        = $false )
      | ( ( ( times_times_nat @ SV300 @ SV621 )
          = one_one_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13815]) ).

thf(13935,plain,
    ! [SV300: nat,SV621: nat] :
      ( ( ( SV621 != one_one_nat )
        = $false )
      | ( ( ( times_times_nat @ SV300 @ SV621 )
          = one_one_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13815]) ).

thf(13936,plain,
    ! [SV621: nat,SV300: nat] :
      ( ( ( ( ( times_times_nat @ SV300 @ SV621 )
           != one_one_nat )
          | ~ ~ ( ( SV300 != one_one_nat )
                | ( SV621 != one_one_nat ) ) )
        = $false )
      | ( ( SV300 = one_one_nat )
        = $false )
      | ( ( SV621 = one_one_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13816]) ).

thf(13937,plain,
    ! [SV936: nat,SV622: nat] :
      ( ( ( dvd_dvd_nat @ SV622 @ SV936 )
        = $true )
      | ( ( dvd_dvd_nat @ SV622 @ SV936 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13817]) ).

thf(13938,plain,
    ! [SV622: nat,SV936: nat] :
      ( ( ( ~ ! [SY1919: nat] :
                ( SV936
               != ( times_times_nat @ SV622 @ SY1919 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV622 @ SV936 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13818]) ).

thf(13939,plain,
    ! [SV963: nat,SV622: nat,SV936: nat] :
      ( ( ( SV936
          = ( times_times_nat @ SV622 @ SV963 ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ SV622 @ SV936 )
              | ~ ~ ! [SY1919: nat] :
                      ( SV936
                     != ( times_times_nat @ SV622 @ SY1919 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13819]) ).

thf(13940,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13820]) ).

thf(13941,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13821]) ).

thf(13942,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
        = $false )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
              | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
                   != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13822]) ).

thf(13943,plain,
    ! [SV303: nat,SV624: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $false )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
              | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
                   != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13822]) ).

thf(13944,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) ) )
        = $true )
      | ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13823]) ).

thf(13945,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
         != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true )
      | ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13824]) ).

thf(13946,plain,
    ! [SV626: nat,SV305: nat] :
      ( ( ( SV305 != zero_zero_nat )
        = $false )
      | ( ( ( plus_plus_nat @ SV305 @ SV626 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13825]) ).

thf(13947,plain,
    ! [SV305: nat,SV626: nat] :
      ( ( ( SV626 != zero_zero_nat )
        = $false )
      | ( ( ( plus_plus_nat @ SV305 @ SV626 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13825]) ).

thf(13948,plain,
    ! [SV626: nat,SV305: nat] :
      ( ( ( ( ( plus_plus_nat @ SV305 @ SV626 )
           != zero_zero_nat )
          | ~ ~ ( ( SV305 != zero_zero_nat )
                | ( SV626 != zero_zero_nat ) ) )
        = $false )
      | ( ( SV305 = zero_zero_nat )
        = $false )
      | ( ( SV626 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13826]) ).

thf(13949,plain,
    ! [SV630: nat,SV310: nat] :
      ( ( ( SV310 != zero_zero_nat )
        = $false )
      | ( ( ( plus_plus_nat @ SV310 @ SV630 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13827]) ).

thf(13950,plain,
    ! [SV310: nat,SV630: nat] :
      ( ( ( SV630 != zero_zero_nat )
        = $false )
      | ( ( ( plus_plus_nat @ SV310 @ SV630 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13827]) ).

thf(13951,plain,
    ! [SV630: nat,SV310: nat] :
      ( ( ( ( ( plus_plus_nat @ SV310 @ SV630 )
           != zero_zero_nat )
          | ~ ~ ( ( SV310 != zero_zero_nat )
                | ( SV630 != zero_zero_nat ) ) )
        = $false )
      | ( ( SV310 = zero_zero_nat )
        = $false )
      | ( ( SV630 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13828]) ).

thf(13952,plain,
    ! [SV631: nat,SV856: nat,SV311: nat] :
      ( ( ( ~ ( ~ ~ ( ( SV311
                     != ( times_times_nat @ ( sK14_SY1883 @ SV856 @ SV631 @ SV311 ) @ ( sK22_SY1936 @ SV631 @ SV856 @ SV311 ) ) )
                    | ~ ( dvd_dvd_nat @ ( sK14_SY1883 @ SV856 @ SV631 @ SV311 ) @ SV631 ) )
              | ~ ( dvd_dvd_nat @ ( sK22_SY1936 @ SV631 @ SV856 @ SV311 ) @ SV856 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV311 @ ( times_times_nat @ SV631 @ SV856 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13829]) ).

thf(13953,plain,
    ! [SV312: nat,SV956: nat,SV857: nat,SV937: nat,SV632: nat] :
      ( ( ( ( ( times_times_nat @ SV632 @ SV937 )
            = ( plus_plus_nat @ ( times_times_nat @ SV857 @ SV956 ) @ SV312 ) )
          | ( ( times_times_nat @ SV857 @ SV937 )
            = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SV956 ) @ SV312 ) ) )
        = $false )
      | ( ( ~ ! [SY1887: nat] :
                ~ ~ ! [SY1888: nat] :
                      ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
                                | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) )
                          | ~ ( ( ( times_times_nat @ SV632 @ SY1887 )
                                = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1888 ) @ SV312 ) )
                              | ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1887 )
                                = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SY1888 ) @ SV312 ) ) ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13830]) ).

thf(13954,plain,
    ! [SV639: nat,SV860: nat,SV319: nat > nat > $o] :
      ( ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
        = $true )
      | ( ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) )
        = $true )
      | ( ( ~ ! [SY1421: nat] : ( SV319 @ SY1421 @ zero_zero_nat )
          | ~ ! [SY1422: nat,SY1423: nat] :
                ( ~ ( SV319 @ SY1422 @ SY1423 )
                | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) )
          | ( SV319 @ SV639 @ SV860 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13831]) ).

thf(13955,plain,
    ! [SV639: nat,SV860: nat,SV319: nat > nat > $o] :
      ( ( ( ~ ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) ) )
        = $true )
      | ( ( ~ ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) ) )
        = $true )
      | ( ( ~ ! [SY1421: nat] : ( SV319 @ SY1421 @ zero_zero_nat )
          | ~ ! [SY1422: nat,SY1423: nat] :
                ( ~ ( SV319 @ SY1422 @ SY1423 )
                | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) )
          | ( SV319 @ SV639 @ SV860 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13832]) ).

thf(13956,plain,
    ! [SV639: nat,SV860: nat,SV319: nat > nat > $o] :
      ( ( ( SV319 @ ( sK27_SY1421 @ SV860 @ SV639 @ SV319 ) @ zero_zero_nat )
        = $false )
      | ( ( ~ ! [SY1422: nat,SY1423: nat] :
                ( ~ ( SV319 @ SY1422 @ SY1423 )
                | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) )
          | ( SV319 @ SV639 @ SV860 ) )
        = $true )
      | ( ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
          = ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[13833]) ).

thf(13957,plain,
    ! [SV642: nat,SV322: nat] :
      ( ( ( ~ ( ( SV322 != SV642 ) ) )
        = $false )
      | ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13834]) ).

thf(13958,plain,
    ! [SV322: nat,SV642: nat] :
      ( ( ( ~ ( vEBT_V8194947554948674370ptions @ summary @ SV642 ) )
        = $false )
      | ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13834]) ).

thf(13959,plain,
    ! [SV322: nat,SV642: nat] :
      ( ( ( vEBT_V8194947554948674370ptions @ summary @ SV642 )
        = $false )
      | ( ( SV322 = SV642 )
        = $true )
      | ( ( ~ ( ~ ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 )
              | ~ ~ ( ~ ( ( SV322 != SV642 ) )
                    | ~ ( vEBT_V8194947554948674370ptions @ summary @ SV642 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13835]) ).

thf(13960,plain,
    ! [SV939: nat,SV644: nat] :
      ( ( ( ord_less_eq_nat @ SV644 @ SV939 )
        = $true )
      | ( ( ord_less_eq_nat @ SV644 @ SV939 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13836]) ).

thf(13961,plain,
    ! [SV644: nat,SV939: nat] :
      ( ( ( ~ ! [SY1924: nat] :
                ( SV939
               != ( plus_plus_nat @ SV644 @ SY1924 ) ) )
        = $true )
      | ( ( ord_less_eq_nat @ SV644 @ SV939 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13837]) ).

thf(13962,plain,
    ! [SV964: nat,SV644: nat,SV939: nat] :
      ( ( ( SV939
          = ( plus_plus_nat @ SV644 @ SV964 ) )
        = $false )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ SV644 @ SV939 )
              | ~ ~ ! [SY1924: nat] :
                      ( SV939
                     != ( plus_plus_nat @ SV644 @ SY1924 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13838]) ).

thf(13963,plain,
    ! [SV649: nat,SV329: nat] :
      ( ( ( SV329 != zero_zero_nat )
        = $false )
      | ( ( zero_zero_nat
          = ( plus_plus_nat @ SV329 @ SV649 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13840]) ).

thf(13964,plain,
    ! [SV329: nat,SV649: nat] :
      ( ( ( SV649 != zero_zero_nat )
        = $false )
      | ( ( zero_zero_nat
          = ( plus_plus_nat @ SV329 @ SV649 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13840]) ).

thf(13965,plain,
    ! [SV649: nat,SV329: nat] :
      ( ( ( ( zero_zero_nat
           != ( plus_plus_nat @ SV329 @ SV649 ) )
          | ~ ~ ( ( SV329 != zero_zero_nat )
                | ( SV649 != zero_zero_nat ) ) )
        = $false )
      | ( ( SV329 = zero_zero_nat )
        = $false )
      | ( ( SV649 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13841]) ).

thf(13966,plain,
    ! [SV658: nat,SV872: nat,SV336: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV336 @ ( plus_plus_nat @ SV872 @ SV658 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV336 @ ( plus_plus_nat @ SV872 @ SV658 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV336 @ SV658 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13843]) ).

thf(13967,plain,
    ! [SV658: nat,SV872: nat,SV336: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV336 @ SV872 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV336 @ ( plus_plus_nat @ SV872 @ SV658 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV336 @ SV658 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13843]) ).

thf(13968,plain,
    ! [SV658: nat,SV872: nat,SV336: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV336 @ ( plus_plus_nat @ SV872 @ SV658 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV336 @ SV872 )
        = $false )
      | ( ( dvd_dvd_nat @ SV336 @ SV658 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13844]) ).

thf(13969,plain,
    ! [SV658: nat,SV872: nat,SV336: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV336 @ SV872 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV336 @ SV872 )
        = $false )
      | ( ( dvd_dvd_nat @ SV336 @ SV658 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13844]) ).

thf(13970,plain,
    ! [SV882: nat,SV347: nat,SV668: nat] :
      ( ( ( dvd_dvd_nat @ ( divide_divide_nat @ SV668 @ SV347 ) @ ( divide_divide_nat @ SV882 @ SV347 ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( divide_divide_nat @ SV668 @ SV347 ) @ ( divide_divide_nat @ SV882 @ SV347 ) )
              | ~ ( dvd_dvd_nat @ SV668 @ SV882 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV347 @ SV882 )
        = $false )
      | ( ( dvd_dvd_nat @ SV347 @ SV668 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13846]) ).

thf(13971,plain,
    ! [SV347: nat,SV882: nat,SV668: nat] :
      ( ( ( dvd_dvd_nat @ SV668 @ SV882 )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( divide_divide_nat @ SV668 @ SV347 ) @ ( divide_divide_nat @ SV882 @ SV347 ) )
              | ~ ( dvd_dvd_nat @ SV668 @ SV882 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV347 @ SV882 )
        = $false )
      | ( ( dvd_dvd_nat @ SV347 @ SV668 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13846]) ).

thf(13972,plain,
    ! [SV349: nat,SV669: nat] :
      ( ( ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ ( sK6_SY1803 @ SV669 @ SV349 ) @ SV349 )
                  | ~ ( dvd_dvd_nat @ ( sK6_SY1803 @ SV669 @ SV349 ) @ SV669 ) )
            | ~ ( ( ( times_times_nat @ SV349 @ ( sK18_SY1926 @ SV349 @ SV669 ) )
                  = ( plus_plus_nat @ ( times_times_nat @ SV669 @ ( sK23_SY1937 @ SV349 @ SV669 ) ) @ ( sK6_SY1803 @ SV669 @ SV349 ) ) )
                | ( ( times_times_nat @ SV669 @ ( sK18_SY1926 @ SV349 @ SV669 ) )
                  = ( plus_plus_nat @ ( times_times_nat @ SV349 @ ( sK23_SY1937 @ SV349 @ SV669 ) ) @ ( sK6_SY1803 @ SV669 @ SV349 ) ) ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[13847]) ).

thf(13973,plain,
    ! [SV671: nat,SV351: nat] :
      ( ( ( SV351 != one_one_nat )
        = $false )
      | ( ( one_one_nat
          = ( times_times_nat @ SV351 @ SV671 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13848]) ).

thf(13974,plain,
    ! [SV351: nat,SV671: nat] :
      ( ( ( SV671 != one_one_nat )
        = $false )
      | ( ( one_one_nat
          = ( times_times_nat @ SV351 @ SV671 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13848]) ).

thf(13975,plain,
    ! [SV671: nat,SV351: nat] :
      ( ( ( ( one_one_nat
           != ( times_times_nat @ SV351 @ SV671 ) )
          | ~ ~ ( ( SV351 != one_one_nat )
                | ( SV671 != one_one_nat ) ) )
        = $false )
      | ( ( SV351 = one_one_nat )
        = $false )
      | ( ( SV671 = one_one_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13849]) ).

thf(13976,plain,
    ! [SV353: nat,SV959: nat,SV945: nat,SV884: nat,SV673: nat] :
      ( ( ( ( SV673 != SV884 )
          | ~ ( ( SV945 != SV959 ) ) )
        = $true )
      | ( ( ( plus_plus_nat @ SV673 @ ( times_times_nat @ SV353 @ SV945 ) )
         != ( plus_plus_nat @ SV884 @ ( times_times_nat @ SV353 @ SV959 ) ) )
        = $true )
      | ( ( SV353 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13850]) ).

thf(13977,plain,
    ! [SV885: nat,SV674: nat,SV354: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV354 @ ( plus_plus_nat @ SV674 @ SV885 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV354 @ ( plus_plus_nat @ SV674 @ SV885 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV354 @ SV674 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13851]) ).

thf(13978,plain,
    ! [SV674: nat,SV885: nat,SV354: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV354 @ SV885 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV354 @ ( plus_plus_nat @ SV674 @ SV885 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV354 @ SV674 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13851]) ).

thf(13979,plain,
    ! [SV885: nat,SV674: nat,SV354: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV354 @ ( plus_plus_nat @ SV674 @ SV885 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV354 @ SV885 )
        = $false )
      | ( ( dvd_dvd_nat @ SV354 @ SV674 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13852]) ).

thf(13980,plain,
    ! [SV674: nat,SV885: nat,SV354: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV354 @ SV885 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV354 @ SV885 )
        = $false )
      | ( ( dvd_dvd_nat @ SV354 @ SV674 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13852]) ).

thf(13981,plain,
    ! [SV889: nat,SV362: nat,SV681: nat] :
      ( ( ( ( divide_divide_nat @ SV681 @ SV362 )
          = ( divide_divide_nat @ SV889 @ SV362 ) )
        = $false )
      | ( ( ~ ( ( ( divide_divide_nat @ SV681 @ SV362 )
               != ( divide_divide_nat @ SV889 @ SV362 ) )
              | ( SV681 != SV889 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV362 @ SV889 )
        = $false )
      | ( ( dvd_dvd_nat @ SV362 @ SV681 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13853]) ).

thf(13982,plain,
    ! [SV362: nat,SV889: nat,SV681: nat] :
      ( ( ( SV681 = SV889 )
        = $false )
      | ( ( ~ ( ( ( divide_divide_nat @ SV681 @ SV362 )
               != ( divide_divide_nat @ SV889 @ SV362 ) )
              | ( SV681 != SV889 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV362 @ SV889 )
        = $false )
      | ( ( dvd_dvd_nat @ SV362 @ SV681 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13853]) ).

thf(13983,plain,
    ! [SV692: option_nat,SV373: option_nat] :
      ( ( ( ~ ( ( SV373 != none_nat ) ) )
        = $false )
      | ( ( SV373 = SV692 )
        = $true )
      | ( ( SV692 = none_nat )
        = $true )
      | ( ( SV373 = none_nat )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13854]) ).

thf(13984,plain,
    ! [SV373: option_nat,SV692: option_nat] :
      ( ( ( ~ ( ( SV692 != none_nat ) )
          | ( ( the_nat @ SV373 )
            = ( the_nat @ SV692 ) ) )
        = $false )
      | ( ( SV373 = SV692 )
        = $true )
      | ( ( SV692 = none_nat )
        = $true )
      | ( ( SV373 = none_nat )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13854]) ).

thf(13985,plain,
    ! [SV692: option_nat,SV373: option_nat] :
      ( ( ( ~ ( ~ ( ( SV373 != none_nat ) )
              | ~ ( ( SV692 != none_nat ) )
              | ( ( the_nat @ SV373 )
                = ( the_nat @ SV692 ) ) ) )
        = $true )
      | ( ( SV373 = SV692 )
        = $true )
      | ( ( SV373 = none_nat )
        = $false )
      | ( ( SV692 = none_nat )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13855]) ).

thf(13986,plain,
    ! [SV373: option_nat,SV692: option_nat] :
      ( ( ( SV692 = none_nat )
        = $false )
      | ( ( SV373 = SV692 )
        = $true )
      | ( ( ( SV373 = none_nat )
          = ( SV692 = none_nat ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13857]) ).

thf(13987,plain,
    ! [SV693: nat,SV374: nat > $o] :
      ( ( ( ~ ( SV374 @ ( sK24_SY1534 @ SV693 @ SV374 ) )
          | ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ ( sK28_SY1940 @ SV693 @ SV374 ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( sK24_SY1534 @ SV693 @ SV374 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
           != ( sK24_SY1534 @ SV693 @ SV374 ) )
          | ( SV374 @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ ( sK28_SY1940 @ SV693 @ SV374 ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( sK24_SY1534 @ SV693 @ SV374 ) ) ) ) )
        = $false )
      | ( ( SV374 @ SV693 )
        = $true )
      | ( ( ( divide_divide_nat @ ( sK8_SY1533 @ SV693 @ SV374 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( sK8_SY1533 @ SV693 @ SV374 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[13858]) ).

thf(13988,plain,
    ! [SV693: nat,SV374: nat > $o] :
      ( ( ( ~ ( SV374 @ ( sK21_SY1534 @ SV693 @ SV374 ) ) )
        = $false )
      | ( ( SV374 @ SV693 )
        = $true )
      | ( ( SV374 @ ( sK8_SY1533 @ SV693 @ SV374 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13859]) ).

thf(13989,plain,
    ! [SV374: nat > $o,SV693: nat] :
      ( ( ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ ( sK25_SY1939 @ SV693 @ SV374 ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( sK21_SY1534 @ SV693 @ SV374 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
           != ( sK21_SY1534 @ SV693 @ SV374 ) )
          | ( SV374 @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ ( sK25_SY1939 @ SV693 @ SV374 ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( sK21_SY1534 @ SV693 @ SV374 ) ) ) ) )
        = $false )
      | ( ( SV374 @ SV693 )
        = $true )
      | ( ( SV374 @ ( sK8_SY1533 @ SV693 @ SV374 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13859]) ).

thf(13990,plain,
    ! [SV948: nat,SV694: nat] :
      ( ( ( ord_less_eq_nat @ SV694 @ SV948 )
        = $true )
      | ( ( ord_less_eq_nat @ SV694 @ SV948 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13860]) ).

thf(13991,plain,
    ! [SV694: nat,SV948: nat] :
      ( ( ( ~ ! [SY1929: nat] :
                ( SV948
               != ( plus_plus_nat @ SV694 @ SY1929 ) ) )
        = $true )
      | ( ( ord_less_eq_nat @ SV694 @ SV948 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13861]) ).

thf(13992,plain,
    ! [SV965: nat,SV694: nat,SV948: nat] :
      ( ( ( SV948
          = ( plus_plus_nat @ SV694 @ SV965 ) )
        = $false )
      | ( ( ~ ( ~ ( ord_less_eq_nat @ SV694 @ SV948 )
              | ~ ~ ! [SY1929: nat] :
                      ( SV948
                     != ( plus_plus_nat @ SV694 @ SY1929 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13862]) ).

thf(13993,plain,
    ! [SV382: num] :
      ( ( ( SV382
          = ( bit1 @ ( sK26_SY1551 @ SV382 ) ) )
        = $true )
      | ( ( SV382
          = ( bit0 @ ( sK19_SY1550 @ SV382 ) ) )
        = $true )
      | ( ( SV382 = one )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13864]) ).

thf(13994,plain,
    ! [SV770: nat,SV142: nat,SV493: nat] :
      ( ( ( SV493 = zero_zero_nat )
        = $true )
      | ( ( SV142 = SV770 )
        = $true )
      | ( ( SV493 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13867]) ).

thf(13995,plain,
    ! [SV770: nat,SV142: nat,SV493: nat] :
      ( ( ( SV493 = zero_zero_nat )
        = $true )
      | ( ( SV142 = SV770 )
        = $true )
      | ( ( SV142 = SV770 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13869]) ).

thf(13996,plain,
    ! [SV771: nat,SV494: nat,SV143: nat] :
      ( ( ( SV143 = zero_zero_nat )
        = $true )
      | ( ( SV494 = SV771 )
        = $true )
      | ( ( SV143 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13872]) ).

thf(13997,plain,
    ! [SV771: nat,SV494: nat,SV143: nat] :
      ( ( ( SV143 = zero_zero_nat )
        = $true )
      | ( ( SV494 = SV771 )
        = $true )
      | ( ( SV494 = SV771 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13874]) ).

thf(13998,plain,
    ! [SV502: nat,SV772: nat,SV160: nat] :
      ( ( ( SV160 = SV772 )
        = $true )
      | ( ( SV502 = zero_zero_nat )
        = $true )
      | ( ( SV160 = SV772 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13879]) ).

thf(13999,plain,
    ! [SV502: nat,SV772: nat,SV160: nat] :
      ( ( ( SV160 = SV772 )
        = $true )
      | ( ( SV502 = zero_zero_nat )
        = $true )
      | ( ( SV502 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13881]) ).

thf(14000,plain,
    ! [SV161: nat,SV773: nat,SV503: nat] :
      ( ( ( SV503 = SV773 )
        = $true )
      | ( ( SV161 = zero_zero_nat )
        = $true )
      | ( ( SV503 = SV773 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13884]) ).

thf(14001,plain,
    ! [SV161: nat,SV773: nat,SV503: nat] :
      ( ( ( SV503 = SV773 )
        = $true )
      | ( ( SV161 = zero_zero_nat )
        = $true )
      | ( ( SV161 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13886]) ).

thf(14002,plain,
    ! [SV788: nat,SV520: nat,SV185: nat] :
      ( ( ( SV185 = zero_zero_nat )
        = $true )
      | ( ( SV520 = SV788 )
        = $true )
      | ( ( SV185 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13891]) ).

thf(14003,plain,
    ! [SV788: nat,SV520: nat,SV185: nat] :
      ( ( ( SV185 = zero_zero_nat )
        = $true )
      | ( ( SV520 = SV788 )
        = $true )
      | ( ( SV520 = SV788 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13893]) ).

thf(14004,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13896]) ).

thf(14005,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13897]) ).

thf(14006,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
         != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13897]) ).

thf(14007,plain,
    ! [SV206: nat,SV540: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
              | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
               != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13898]) ).

thf(14008,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $true )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $true )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13899]) ).

thf(14009,plain,
    ! [SV922: nat,SV549: nat,SV802: nat,SV216: nat] :
      ( ( ( SV216 = SV802 )
        = $true )
      | ( ( SV549 = SV922 )
        = $true )
      | ( ( ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV549 ) @ ( times_times_nat @ SV802 @ SV922 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV922 ) @ ( times_times_nat @ SV802 @ SV549 ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13902]) ).

thf(14010,plain,
    ! [SV922: nat,SV802: nat,SV549: nat,SV216: nat] :
      ( ( ( ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV549 ) @ ( times_times_nat @ SV802 @ SV922 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV922 ) @ ( times_times_nat @ SV802 @ SV549 ) ) )
        = $true )
      | ( ( SV216 = SV802 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13903]) ).

thf(14011,plain,
    ! [SV922: nat,SV549: nat,SV802: nat,SV216: nat] :
      ( ( ( ( SV216 = SV802 )
          | ( SV549 = SV922 ) )
        = $true )
      | ( ( SV216 = SV802 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13904]) ).

thf(14012,plain,
    ! [SV922: nat,SV802: nat,SV549: nat,SV216: nat] :
      ( ( ( ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV549 ) @ ( times_times_nat @ SV802 @ SV922 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV216 @ SV922 ) @ ( times_times_nat @ SV802 @ SV549 ) ) )
        = $true )
      | ( ( SV549 = SV922 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13905]) ).

thf(14013,plain,
    ! [SV922: nat,SV549: nat,SV802: nat,SV216: nat] :
      ( ( ( ( SV216 = SV802 )
          | ( SV549 = SV922 ) )
        = $true )
      | ( ( SV549 = SV922 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13906]) ).

thf(14014,plain,
    ! [SV243: $o] :
      ( ( ( SV243
          | $false )
        = $false )
      | ( ( ~ ( ~ SV243
              | ~ $false ) )
        = $true )
      | ( SV243 = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13907]) ).

thf(14015,plain,
    ! [SV243: $o] :
      ( ( ( SV243
          | $false )
        = $false )
      | ( ( ~ ( ~ SV243
              | ~ $false ) )
        = $true )
      | ( SV243 = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13908]) ).

thf(14016,plain,
    ! [SV243: $o] :
      ( ( ( SV243
          | $false )
        = $false )
      | ( ( ~ ( ~ SV243
              | ~ $false ) )
        = $true )
      | ( $true = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13909]) ).

thf(14017,plain,
    ! [SV243: $o] :
      ( ( ( SV243
          | $false )
        = $false )
      | ( ( ~ ( ~ SV243
              | ~ $false ) )
        = $true )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13910]) ).

thf(14018,plain,
    ( ( ( $true
        | $false )
      = $false )
    | ( ( ~ ( ~ $true
            | ~ $false ) )
      = $true )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13911]) ).

thf(14019,plain,
    ( ( ( $true
        | $false )
      = $false )
    | ( ( ~ ( ~ $true
            | ~ $false ) )
      = $true )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13912]) ).

thf(14020,plain,
    ( ( ( $true
        | $false )
      = $false )
    | ( ( ~ ( ~ $true
            | ~ $false ) )
      = $true )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13913]) ).

thf(14021,plain,
    ( ( ( $true
        | $false )
      = $false )
    | ( ( ~ ( ~ $true
            | ~ $false ) )
      = $true )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13914]) ).

thf(14022,plain,
    ( ( ( $false
        | $false )
      = $false )
    | ( ( ~ ( ~ $false
            | ~ $false ) )
      = $true )
    | ( $false = $false )
    | ( $false = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13915]) ).

thf(14023,plain,
    ( ( ( $false
        | $false )
      = $false )
    | ( ( ~ ( ~ $false
            | ~ $false ) )
      = $true )
    | ( $false = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13916]) ).

thf(14024,plain,
    ( ( ( $false
        | $false )
      = $false )
    | ( ( ~ ( ~ $false
            | ~ $false ) )
      = $true )
    | ( $true = $false )
    | ( $false = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13917]) ).

thf(14025,plain,
    ( ( ( $false
        | $false )
      = $false )
    | ( ( ~ ( ~ $false
            | ~ $false ) )
      = $true )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13918]) ).

thf(14026,plain,
    ! [SV825: nat,SV257: nat,SV583: nat] :
      ( ( ( ( times_times_nat @ SV583 @ SV257 )
         != ( times_times_nat @ SV825 @ SV257 ) )
        = $false )
      | ( ( ( times_times_nat @ SV583 @ SV257 )
          = ( times_times_nat @ SV825 @ SV257 ) )
        = $false )
      | ( ( SV257 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13919]) ).

thf(14027,plain,
    ! [SV257: nat,SV825: nat,SV583: nat] :
      ( ( ( SV583 != SV825 )
        = $false )
      | ( ( ( times_times_nat @ SV583 @ SV257 )
          = ( times_times_nat @ SV825 @ SV257 ) )
        = $false )
      | ( ( SV257 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13919]) ).

thf(14028,plain,
    ! [SV825: nat,SV257: nat,SV583: nat] :
      ( ( ( ( times_times_nat @ SV583 @ SV257 )
         != ( times_times_nat @ SV825 @ SV257 ) )
        = $false )
      | ( ( SV583 = SV825 )
        = $false )
      | ( ( SV257 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13920]) ).

thf(14029,plain,
    ! [SV257: nat,SV825: nat,SV583: nat] :
      ( ( ( SV583 != SV825 )
        = $false )
      | ( ( SV583 = SV825 )
        = $false )
      | ( ( SV257 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13920]) ).

thf(14030,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
           != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
          | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
           != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
        = $false )
      | ( ( SV595 = SV928 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13924]) ).

thf(14031,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
          | ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
         != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $true )
      | ( ( ~ ( ( SV595 != SV928 )
              | ~ ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                     != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
                    | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                     != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[13925]) ).

thf(14032,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
         != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $true )
      | ( ( ~ ( ( SV595 != SV928 )
              | ~ ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                     != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
                    | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                     != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[13925]) ).

thf(14033,plain,
    ! [SV837: nat,SV597: nat,SV273: nat] :
      ( ( ( ~ ~ ! [SY1941: nat] :
                  ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ ( sK29_SY1874 @ SV837 @ SV597 @ SV273 ) ) )
                 != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1941 ) ) ) )
        = $false )
      | ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
          = ( modulo_modulo_nat @ SV837 @ SV597 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[13926]) ).

thf(14034,plain,
    ! [SV966: nat,SV837: nat,SV962: nat,SV597: nat,SV273: nat] :
      ( ( ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SV962 ) )
         != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SV966 ) ) )
        = $true )
      | ( ( ~ ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
               != ( modulo_modulo_nat @ SV837 @ SV597 ) )
              | ~ ~ ! [SY1874: nat] :
                      ~ ~ ! [SY1875: nat] :
                            ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SY1874 ) )
                           != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1875 ) ) ) ) )
        = $true ) ),
    inference(extcnf_forall_pos,[status(thm)],[13927]) ).

thf(14035,plain,
    ! [SV931: nat,SV844: nat,SV605: nat,SV284: nat] :
      ( ( ( SV284 = SV605 )
        = $true )
      | ( ( ~ ( ( SV844 != SV931 ) ) )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( ( SV284 != SV605 ) )
                    | ~ ( ( SV844 != SV931 ) ) )
              | ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
                   != ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13928]) ).

thf(14036,plain,
    ! [SV931: nat,SV844: nat,SV605: nat,SV284: nat] :
      ( ( ( ~ ( ~ ( ( SV284 != SV605 ) )
              | ~ ( ( SV844 != SV931 ) ) ) )
        = $true )
      | ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13929]) ).

thf(14037,plain,
    ! [SV931: nat,SV605: nat,SV844: nat,SV284: nat] :
      ( ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
         != ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) )
        = $true )
      | ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13930]) ).

thf(14038,plain,
    ! [SV845: nat,SV606: nat,SV285: nat] :
      ( ( ( ( times_times_nat @ SV285 @ SV606 )
         != ( times_times_nat @ SV285 @ SV845 ) )
        = $false )
      | ( ( ( times_times_nat @ SV285 @ SV606 )
          = ( times_times_nat @ SV285 @ SV845 ) )
        = $false )
      | ( ( SV285 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13931]) ).

thf(14039,plain,
    ! [SV285: nat,SV845: nat,SV606: nat] :
      ( ( ( SV606 != SV845 )
        = $false )
      | ( ( ( times_times_nat @ SV285 @ SV606 )
          = ( times_times_nat @ SV285 @ SV845 ) )
        = $false )
      | ( ( SV285 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13931]) ).

thf(14040,plain,
    ! [SV845: nat,SV606: nat,SV285: nat] :
      ( ( ( ( times_times_nat @ SV285 @ SV606 )
         != ( times_times_nat @ SV285 @ SV845 ) )
        = $false )
      | ( ( SV606 = SV845 )
        = $false )
      | ( ( SV285 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13932]) ).

thf(14041,plain,
    ! [SV285: nat,SV845: nat,SV606: nat] :
      ( ( ( SV606 != SV845 )
        = $false )
      | ( ( SV606 = SV845 )
        = $false )
      | ( ( SV285 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13932]) ).

thf(14042,plain,
    ! [SV288: nat,SV609: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV609 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV288 )
        = $false )
      | ( ( SV288 = SV609 )
        = $true )
      | ( ( ( divide_divide_nat @ SV288 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV609 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13933]) ).

thf(14043,plain,
    ! [SV621: nat,SV300: nat] :
      ( ( ( SV300 = one_one_nat )
        = $true )
      | ( ( ( times_times_nat @ SV300 @ SV621 )
          = one_one_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13934]) ).

thf(14044,plain,
    ! [SV300: nat,SV621: nat] :
      ( ( ( SV621 = one_one_nat )
        = $true )
      | ( ( ( times_times_nat @ SV300 @ SV621 )
          = one_one_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13935]) ).

thf(14045,plain,
    ! [SV621: nat,SV300: nat] :
      ( ( ( ( times_times_nat @ SV300 @ SV621 )
         != one_one_nat )
        = $false )
      | ( ( SV300 = one_one_nat )
        = $false )
      | ( ( SV621 = one_one_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13936]) ).

thf(14046,plain,
    ! [SV621: nat,SV300: nat] :
      ( ( ( ~ ~ ( ( SV300 != one_one_nat )
                | ( SV621 != one_one_nat ) ) )
        = $false )
      | ( ( SV300 = one_one_nat )
        = $false )
      | ( ( SV621 = one_one_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13936]) ).

thf(14047,plain,
    ! [SV622: nat,SV936: nat] :
      ( ( ( ! [SY1919: nat] :
              ( SV936
             != ( times_times_nat @ SV622 @ SY1919 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV622 @ SV936 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13938]) ).

thf(14048,plain,
    ! [SV963: nat,SV936: nat,SV622: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV622 @ SV936 )
          | ~ ~ ! [SY1919: nat] :
                  ( SV936
                 != ( times_times_nat @ SV622 @ SY1919 ) ) )
        = $false )
      | ( ( SV936
          = ( times_times_nat @ SV622 @ SV963 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13939]) ).

thf(14049,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
          | ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[13941]) ).

thf(14050,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[13941]) ).

thf(14051,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
              | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
                   != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13942]) ).

thf(14052,plain,
    ! [SV303: nat,SV624: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
              | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
                   != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13943]) ).

thf(14053,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
        = $false )
      | ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13944]) ).

thf(14054,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $false )
      | ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13945]) ).

thf(14055,plain,
    ! [SV626: nat,SV305: nat] :
      ( ( ( SV305 = zero_zero_nat )
        = $true )
      | ( ( ( plus_plus_nat @ SV305 @ SV626 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13946]) ).

thf(14056,plain,
    ! [SV305: nat,SV626: nat] :
      ( ( ( SV626 = zero_zero_nat )
        = $true )
      | ( ( ( plus_plus_nat @ SV305 @ SV626 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13947]) ).

thf(14057,plain,
    ! [SV626: nat,SV305: nat] :
      ( ( ( ( plus_plus_nat @ SV305 @ SV626 )
         != zero_zero_nat )
        = $false )
      | ( ( SV305 = zero_zero_nat )
        = $false )
      | ( ( SV626 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13948]) ).

thf(14058,plain,
    ! [SV626: nat,SV305: nat] :
      ( ( ( ~ ~ ( ( SV305 != zero_zero_nat )
                | ( SV626 != zero_zero_nat ) ) )
        = $false )
      | ( ( SV305 = zero_zero_nat )
        = $false )
      | ( ( SV626 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13948]) ).

thf(14059,plain,
    ! [SV630: nat,SV310: nat] :
      ( ( ( SV310 = zero_zero_nat )
        = $true )
      | ( ( ( plus_plus_nat @ SV310 @ SV630 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13949]) ).

thf(14060,plain,
    ! [SV310: nat,SV630: nat] :
      ( ( ( SV630 = zero_zero_nat )
        = $true )
      | ( ( ( plus_plus_nat @ SV310 @ SV630 )
          = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13950]) ).

thf(14061,plain,
    ! [SV630: nat,SV310: nat] :
      ( ( ( ( plus_plus_nat @ SV310 @ SV630 )
         != zero_zero_nat )
        = $false )
      | ( ( SV310 = zero_zero_nat )
        = $false )
      | ( ( SV630 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13951]) ).

thf(14062,plain,
    ! [SV630: nat,SV310: nat] :
      ( ( ( ~ ~ ( ( SV310 != zero_zero_nat )
                | ( SV630 != zero_zero_nat ) ) )
        = $false )
      | ( ( SV310 = zero_zero_nat )
        = $false )
      | ( ( SV630 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13951]) ).

thf(14063,plain,
    ! [SV631: nat,SV856: nat,SV311: nat] :
      ( ( ( ~ ~ ( ( SV311
                 != ( times_times_nat @ ( sK14_SY1883 @ SV856 @ SV631 @ SV311 ) @ ( sK22_SY1936 @ SV631 @ SV856 @ SV311 ) ) )
                | ~ ( dvd_dvd_nat @ ( sK14_SY1883 @ SV856 @ SV631 @ SV311 ) @ SV631 ) )
          | ~ ( dvd_dvd_nat @ ( sK22_SY1936 @ SV631 @ SV856 @ SV311 ) @ SV856 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV311 @ ( times_times_nat @ SV631 @ SV856 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13952]) ).

thf(14064,plain,
    ! [SV312: nat,SV956: nat,SV857: nat,SV937: nat,SV632: nat] :
      ( ( ( ( times_times_nat @ SV632 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV857 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( ~ ! [SY1887: nat] :
                ~ ~ ! [SY1888: nat] :
                      ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
                                | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) )
                          | ~ ( ( ( times_times_nat @ SV632 @ SY1887 )
                                = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1888 ) @ SV312 ) )
                              | ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1887 )
                                = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SY1888 ) @ SV312 ) ) ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13953]) ).

thf(14065,plain,
    ! [SV312: nat,SV956: nat,SV632: nat,SV937: nat,SV857: nat] :
      ( ( ( ( times_times_nat @ SV857 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( ~ ! [SY1887: nat] :
                ~ ~ ! [SY1888: nat] :
                      ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
                                | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) )
                          | ~ ( ( ( times_times_nat @ SV632 @ SY1887 )
                                = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1888 ) @ SV312 ) )
                              | ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1887 )
                                = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SY1888 ) @ SV312 ) ) ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13953]) ).

thf(14066,plain,
    ! [SV860: nat,SV639: nat,SV319: nat > nat > $o] :
      ( ( ( ~ ! [SY1421: nat] : ( SV319 @ SY1421 @ zero_zero_nat ) )
        = $true )
      | ( ( ~ ! [SY1422: nat,SY1423: nat] :
                ( ~ ( SV319 @ SY1422 @ SY1423 )
                | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) )
          | ( SV319 @ SV639 @ SV860 ) )
        = $true )
      | ( ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) )
        = $true )
      | ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13954]) ).

thf(14067,plain,
    ! [SV639: nat,SV860: nat,SV319: nat > nat > $o] :
      ( ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
        = $false )
      | ( ( ~ ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) ) )
        = $true )
      | ( ( ~ ! [SY1421: nat] : ( SV319 @ SY1421 @ zero_zero_nat )
          | ~ ! [SY1422: nat,SY1423: nat] :
                ( ~ ( SV319 @ SY1422 @ SY1423 )
                | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) )
          | ( SV319 @ SV639 @ SV860 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[13955]) ).

thf(14068,plain,
    ! [SV860: nat,SV639: nat,SV319: nat > nat > $o] :
      ( ( ( ~ ! [SY1422: nat,SY1423: nat] :
                ( ~ ( SV319 @ SY1422 @ SY1423 )
                | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) ) )
        = $true )
      | ( ( SV319 @ SV639 @ SV860 )
        = $true )
      | ( ( SV319 @ ( sK27_SY1421 @ SV860 @ SV639 @ SV319 ) @ zero_zero_nat )
        = $false )
      | ( ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
          = ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[13956]) ).

thf(14069,plain,
    ! [SV642: nat,SV322: nat] :
      ( ( ( SV322 != SV642 )
        = $true )
      | ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13957]) ).

thf(14070,plain,
    ! [SV322: nat,SV642: nat] :
      ( ( ( vEBT_V8194947554948674370ptions @ summary @ SV642 )
        = $true )
      | ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13958]) ).

thf(14071,plain,
    ! [SV642: nat,SV322: nat] :
      ( ( ( ~ ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 )
          | ~ ~ ( ~ ( ( SV322 != SV642 ) )
                | ~ ( vEBT_V8194947554948674370ptions @ summary @ SV642 ) ) )
        = $false )
      | ( ( SV322 = SV642 )
        = $true )
      | ( ( vEBT_V8194947554948674370ptions @ summary @ SV642 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13959]) ).

thf(14072,plain,
    ! [SV644: nat,SV939: nat] :
      ( ( ( ! [SY1924: nat] :
              ( SV939
             != ( plus_plus_nat @ SV644 @ SY1924 ) ) )
        = $false )
      | ( ( ord_less_eq_nat @ SV644 @ SV939 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13961]) ).

thf(14073,plain,
    ! [SV964: nat,SV939: nat,SV644: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV644 @ SV939 )
          | ~ ~ ! [SY1924: nat] :
                  ( SV939
                 != ( plus_plus_nat @ SV644 @ SY1924 ) ) )
        = $false )
      | ( ( SV939
          = ( plus_plus_nat @ SV644 @ SV964 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13962]) ).

thf(14074,plain,
    ! [SV649: nat,SV329: nat] :
      ( ( ( SV329 = zero_zero_nat )
        = $true )
      | ( ( zero_zero_nat
          = ( plus_plus_nat @ SV329 @ SV649 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13963]) ).

thf(14075,plain,
    ! [SV329: nat,SV649: nat] :
      ( ( ( SV649 = zero_zero_nat )
        = $true )
      | ( ( zero_zero_nat
          = ( plus_plus_nat @ SV329 @ SV649 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13964]) ).

thf(14076,plain,
    ! [SV649: nat,SV329: nat] :
      ( ( ( zero_zero_nat
         != ( plus_plus_nat @ SV329 @ SV649 ) )
        = $false )
      | ( ( SV329 = zero_zero_nat )
        = $false )
      | ( ( SV649 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13965]) ).

thf(14077,plain,
    ! [SV649: nat,SV329: nat] :
      ( ( ( ~ ~ ( ( SV329 != zero_zero_nat )
                | ( SV649 != zero_zero_nat ) ) )
        = $false )
      | ( ( SV329 = zero_zero_nat )
        = $false )
      | ( ( SV649 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13965]) ).

thf(14078,plain,
    ! [SV658: nat,SV872: nat,SV336: nat] :
      ( ( ( dvd_dvd_nat @ SV336 @ ( plus_plus_nat @ SV872 @ SV658 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV336 @ ( plus_plus_nat @ SV872 @ SV658 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV336 @ SV658 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13966]) ).

thf(14079,plain,
    ! [SV658: nat,SV872: nat,SV336: nat] :
      ( ( ( dvd_dvd_nat @ SV336 @ SV872 )
        = $true )
      | ( ( dvd_dvd_nat @ SV336 @ ( plus_plus_nat @ SV872 @ SV658 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV336 @ SV658 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13967]) ).

thf(14080,plain,
    ! [SV658: nat,SV872: nat,SV336: nat] :
      ( ( ( dvd_dvd_nat @ SV336 @ ( plus_plus_nat @ SV872 @ SV658 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV336 @ SV872 )
        = $false )
      | ( ( dvd_dvd_nat @ SV336 @ SV658 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13968]) ).

thf(14081,plain,
    ! [SV658: nat,SV872: nat,SV336: nat] :
      ( ( ( dvd_dvd_nat @ SV336 @ SV872 )
        = $true )
      | ( ( dvd_dvd_nat @ SV336 @ SV872 )
        = $false )
      | ( ( dvd_dvd_nat @ SV336 @ SV658 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13969]) ).

thf(14082,plain,
    ! [SV882: nat,SV347: nat,SV668: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( divide_divide_nat @ SV668 @ SV347 ) @ ( divide_divide_nat @ SV882 @ SV347 ) )
          | ~ ( dvd_dvd_nat @ SV668 @ SV882 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( divide_divide_nat @ SV668 @ SV347 ) @ ( divide_divide_nat @ SV882 @ SV347 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV347 @ SV882 )
        = $false )
      | ( ( dvd_dvd_nat @ SV347 @ SV668 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13970]) ).

thf(14083,plain,
    ! [SV882: nat,SV347: nat,SV668: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( divide_divide_nat @ SV668 @ SV347 ) @ ( divide_divide_nat @ SV882 @ SV347 ) )
          | ~ ( dvd_dvd_nat @ SV668 @ SV882 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV668 @ SV882 )
        = $false )
      | ( ( dvd_dvd_nat @ SV347 @ SV882 )
        = $false )
      | ( ( dvd_dvd_nat @ SV347 @ SV668 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13971]) ).

thf(14084,plain,
    ! [SV349: nat,SV669: nat] :
      ( ( ~ ~ ( ~ ( dvd_dvd_nat @ ( sK6_SY1803 @ SV669 @ SV349 ) @ SV349 )
              | ~ ( dvd_dvd_nat @ ( sK6_SY1803 @ SV669 @ SV349 ) @ SV669 ) )
        | ~ ( ( ( times_times_nat @ SV349 @ ( sK18_SY1926 @ SV349 @ SV669 ) )
              = ( plus_plus_nat @ ( times_times_nat @ SV669 @ ( sK23_SY1937 @ SV349 @ SV669 ) ) @ ( sK6_SY1803 @ SV669 @ SV349 ) ) )
            | ( ( times_times_nat @ SV669 @ ( sK18_SY1926 @ SV349 @ SV669 ) )
              = ( plus_plus_nat @ ( times_times_nat @ SV349 @ ( sK23_SY1937 @ SV349 @ SV669 ) ) @ ( sK6_SY1803 @ SV669 @ SV349 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[13972]) ).

thf(14085,plain,
    ! [SV671: nat,SV351: nat] :
      ( ( ( SV351 = one_one_nat )
        = $true )
      | ( ( one_one_nat
          = ( times_times_nat @ SV351 @ SV671 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13973]) ).

thf(14086,plain,
    ! [SV351: nat,SV671: nat] :
      ( ( ( SV671 = one_one_nat )
        = $true )
      | ( ( one_one_nat
          = ( times_times_nat @ SV351 @ SV671 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13974]) ).

thf(14087,plain,
    ! [SV671: nat,SV351: nat] :
      ( ( ( one_one_nat
         != ( times_times_nat @ SV351 @ SV671 ) )
        = $false )
      | ( ( SV351 = one_one_nat )
        = $false )
      | ( ( SV671 = one_one_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13975]) ).

thf(14088,plain,
    ! [SV671: nat,SV351: nat] :
      ( ( ( ~ ~ ( ( SV351 != one_one_nat )
                | ( SV671 != one_one_nat ) ) )
        = $false )
      | ( ( SV351 = one_one_nat )
        = $false )
      | ( ( SV671 = one_one_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13975]) ).

thf(14089,plain,
    ! [SV353: nat,SV959: nat,SV945: nat,SV884: nat,SV673: nat] :
      ( ( ( SV673 != SV884 )
        = $true )
      | ( ( ~ ( ( SV945 != SV959 ) ) )
        = $true )
      | ( ( ( plus_plus_nat @ SV673 @ ( times_times_nat @ SV353 @ SV945 ) )
         != ( plus_plus_nat @ SV884 @ ( times_times_nat @ SV353 @ SV959 ) ) )
        = $true )
      | ( ( SV353 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[13976]) ).

thf(14090,plain,
    ! [SV885: nat,SV674: nat,SV354: nat] :
      ( ( ( dvd_dvd_nat @ SV354 @ ( plus_plus_nat @ SV674 @ SV885 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV354 @ ( plus_plus_nat @ SV674 @ SV885 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV354 @ SV674 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13977]) ).

thf(14091,plain,
    ! [SV674: nat,SV885: nat,SV354: nat] :
      ( ( ( dvd_dvd_nat @ SV354 @ SV885 )
        = $true )
      | ( ( dvd_dvd_nat @ SV354 @ ( plus_plus_nat @ SV674 @ SV885 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV354 @ SV674 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13978]) ).

thf(14092,plain,
    ! [SV885: nat,SV674: nat,SV354: nat] :
      ( ( ( dvd_dvd_nat @ SV354 @ ( plus_plus_nat @ SV674 @ SV885 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV354 @ SV885 )
        = $false )
      | ( ( dvd_dvd_nat @ SV354 @ SV674 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13979]) ).

thf(14093,plain,
    ! [SV674: nat,SV885: nat,SV354: nat] :
      ( ( ( dvd_dvd_nat @ SV354 @ SV885 )
        = $true )
      | ( ( dvd_dvd_nat @ SV354 @ SV885 )
        = $false )
      | ( ( dvd_dvd_nat @ SV354 @ SV674 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13980]) ).

thf(14094,plain,
    ! [SV889: nat,SV362: nat,SV681: nat] :
      ( ( ( ( ( divide_divide_nat @ SV681 @ SV362 )
           != ( divide_divide_nat @ SV889 @ SV362 ) )
          | ( SV681 != SV889 ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV681 @ SV362 )
          = ( divide_divide_nat @ SV889 @ SV362 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV362 @ SV889 )
        = $false )
      | ( ( dvd_dvd_nat @ SV362 @ SV681 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13981]) ).

thf(14095,plain,
    ! [SV889: nat,SV362: nat,SV681: nat] :
      ( ( ( ( ( divide_divide_nat @ SV681 @ SV362 )
           != ( divide_divide_nat @ SV889 @ SV362 ) )
          | ( SV681 != SV889 ) )
        = $false )
      | ( ( SV681 = SV889 )
        = $false )
      | ( ( dvd_dvd_nat @ SV362 @ SV889 )
        = $false )
      | ( ( dvd_dvd_nat @ SV362 @ SV681 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13982]) ).

thf(14096,plain,
    ! [SV692: option_nat,SV373: option_nat] :
      ( ( ( SV373 != none_nat )
        = $true )
      | ( ( SV373 = SV692 )
        = $true )
      | ( ( SV692 = none_nat )
        = $true )
      | ( ( SV373 = none_nat )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[13983]) ).

thf(14097,plain,
    ! [SV373: option_nat,SV692: option_nat] :
      ( ( ( ~ ( ( SV692 != none_nat ) ) )
        = $false )
      | ( ( SV373 = SV692 )
        = $true )
      | ( ( SV692 = none_nat )
        = $true )
      | ( ( SV373 = none_nat )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13984]) ).

thf(14098,plain,
    ! [SV692: option_nat,SV373: option_nat] :
      ( ( ( ( the_nat @ SV373 )
          = ( the_nat @ SV692 ) )
        = $false )
      | ( ( SV373 = SV692 )
        = $true )
      | ( ( SV692 = none_nat )
        = $true )
      | ( ( SV373 = none_nat )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13984]) ).

thf(14099,plain,
    ! [SV692: option_nat,SV373: option_nat] :
      ( ( ( ~ ( ( SV373 != none_nat ) )
          | ~ ( ( SV692 != none_nat ) )
          | ( ( the_nat @ SV373 )
            = ( the_nat @ SV692 ) ) )
        = $false )
      | ( ( SV373 = SV692 )
        = $true )
      | ( ( SV373 = none_nat )
        = $false )
      | ( ( SV692 = none_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13985]) ).

thf(14100,plain,
    ! [SV693: nat,SV374: nat > $o] :
      ( ( ( ~ ( SV374 @ ( sK24_SY1534 @ SV693 @ SV374 ) ) )
        = $false )
      | ( ( SV374 @ SV693 )
        = $true )
      | ( ( ( divide_divide_nat @ ( sK8_SY1533 @ SV693 @ SV374 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( sK8_SY1533 @ SV693 @ SV374 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13987]) ).

thf(14101,plain,
    ! [SV374: nat > $o,SV693: nat] :
      ( ( ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ ( sK28_SY1940 @ SV693 @ SV374 ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( sK24_SY1534 @ SV693 @ SV374 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
           != ( sK24_SY1534 @ SV693 @ SV374 ) )
          | ( SV374 @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ ( sK28_SY1940 @ SV693 @ SV374 ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( sK24_SY1534 @ SV693 @ SV374 ) ) ) ) )
        = $false )
      | ( ( SV374 @ SV693 )
        = $true )
      | ( ( ( divide_divide_nat @ ( sK8_SY1533 @ SV693 @ SV374 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( sK8_SY1533 @ SV693 @ SV374 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[13987]) ).

thf(14102,plain,
    ! [SV693: nat,SV374: nat > $o] :
      ( ( ( SV374 @ ( sK21_SY1534 @ SV693 @ SV374 ) )
        = $true )
      | ( ( SV374 @ SV693 )
        = $true )
      | ( ( SV374 @ ( sK8_SY1533 @ SV693 @ SV374 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[13988]) ).

thf(14103,plain,
    ! [SV374: nat > $o,SV693: nat] :
      ( ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ ( sK25_SY1939 @ SV693 @ SV374 ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( sK21_SY1534 @ SV693 @ SV374 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
         != ( sK21_SY1534 @ SV693 @ SV374 ) )
        = $false )
      | ( ( SV374 @ SV693 )
        = $true )
      | ( ( SV374 @ ( sK8_SY1533 @ SV693 @ SV374 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13989]) ).

thf(14104,plain,
    ! [SV693: nat,SV374: nat > $o] :
      ( ( ( SV374 @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ ( sK25_SY1939 @ SV693 @ SV374 ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( sK21_SY1534 @ SV693 @ SV374 ) ) ) )
        = $false )
      | ( ( SV374 @ SV693 )
        = $true )
      | ( ( SV374 @ ( sK8_SY1533 @ SV693 @ SV374 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[13989]) ).

thf(14105,plain,
    ! [SV694: nat,SV948: nat] :
      ( ( ( ! [SY1929: nat] :
              ( SV948
             != ( plus_plus_nat @ SV694 @ SY1929 ) ) )
        = $false )
      | ( ( ord_less_eq_nat @ SV694 @ SV948 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13991]) ).

thf(14106,plain,
    ! [SV965: nat,SV948: nat,SV694: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV694 @ SV948 )
          | ~ ~ ! [SY1929: nat] :
                  ( SV948
                 != ( plus_plus_nat @ SV694 @ SY1929 ) ) )
        = $false )
      | ( ( SV948
          = ( plus_plus_nat @ SV694 @ SV965 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[13992]) ).

thf(14107,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14004]) ).

thf(14108,plain,
    ! [SV206: nat,SV540: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14004]) ).

thf(14109,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14005]) ).

thf(14110,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14006]) ).

thf(14111,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
          | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
           != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14007]) ).

thf(14112,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $true )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14008]) ).

thf(14113,plain,
    ! [SV922: nat,SV549: nat,SV802: nat,SV216: nat] :
      ( ( ( SV216 = SV802 )
        = $true )
      | ( ( SV549 = SV922 )
        = $true )
      | ( ( SV216 = SV802 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[14011]) ).

thf(14114,plain,
    ! [SV922: nat,SV549: nat,SV802: nat,SV216: nat] :
      ( ( ( SV216 = SV802 )
        = $true )
      | ( ( SV549 = SV922 )
        = $true )
      | ( ( SV549 = SV922 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[14013]) ).

thf(14115,plain,
    ! [SV243: $o] :
      ( ( SV243 = $false )
      | ( ( ~ ( ~ SV243
              | ~ $false ) )
        = $true )
      | ( SV243 = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14014]) ).

thf(14116,plain,
    ! [SV243: $o] :
      ( ( $false = $false )
      | ( ( ~ ( ~ SV243
              | ~ $false ) )
        = $true )
      | ( SV243 = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14014]) ).

thf(14117,plain,
    ! [SV243: $o] :
      ( ( SV243 = $false )
      | ( ( ~ ( ~ SV243
              | ~ $false ) )
        = $true )
      | ( SV243 = $false )
      | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14015]) ).

thf(14118,plain,
    ! [SV243: $o] :
      ( ( $false = $false )
      | ( ( ~ ( ~ SV243
              | ~ $false ) )
        = $true )
      | ( SV243 = $false )
      | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14015]) ).

thf(14119,plain,
    ! [SV243: $o] :
      ( ( SV243 = $false )
      | ( ( ~ ( ~ SV243
              | ~ $false ) )
        = $true )
      | ( $true = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14016]) ).

thf(14120,plain,
    ! [SV243: $o] :
      ( ( $false = $false )
      | ( ( ~ ( ~ SV243
              | ~ $false ) )
        = $true )
      | ( $true = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14016]) ).

thf(14121,plain,
    ! [SV243: $o] :
      ( ( SV243 = $false )
      | ( ( ~ ( ~ SV243
              | ~ $false ) )
        = $true )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14017]) ).

thf(14122,plain,
    ! [SV243: $o] :
      ( ( $false = $false )
      | ( ( ~ ( ~ SV243
              | ~ $false ) )
        = $true )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14017]) ).

thf(14123,plain,
    ( ( $true = $false )
    | ( ( ~ ( ~ $true
            | ~ $false ) )
      = $true )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14018]) ).

thf(14124,plain,
    ( ( $false = $false )
    | ( ( ~ ( ~ $true
            | ~ $false ) )
      = $true )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14018]) ).

thf(14125,plain,
    ( ( $true = $false )
    | ( ( ~ ( ~ $true
            | ~ $false ) )
      = $true )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14019]) ).

thf(14126,plain,
    ( ( $false = $false )
    | ( ( ~ ( ~ $true
            | ~ $false ) )
      = $true )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14019]) ).

thf(14127,plain,
    ( ( $true = $false )
    | ( ( ~ ( ~ $true
            | ~ $false ) )
      = $true )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14020]) ).

thf(14128,plain,
    ( ( $false = $false )
    | ( ( ~ ( ~ $true
            | ~ $false ) )
      = $true )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14020]) ).

thf(14129,plain,
    ( ( $true = $false )
    | ( ( ~ ( ~ $true
            | ~ $false ) )
      = $true )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14021]) ).

thf(14130,plain,
    ( ( $false = $false )
    | ( ( ~ ( ~ $true
            | ~ $false ) )
      = $true )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14021]) ).

thf(14131,plain,
    ( ( $false = $false )
    | ( ( ~ ( ~ $false
            | ~ $false ) )
      = $true )
    | ( $false = $false )
    | ( $false = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14022]) ).

thf(14132,plain,
    ( ( $false = $false )
    | ( ( ~ ( ~ $false
            | ~ $false ) )
      = $true )
    | ( $false = $false )
    | ( $false = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14022]) ).

thf(14133,plain,
    ( ( $false = $false )
    | ( ( ~ ( ~ $false
            | ~ $false ) )
      = $true )
    | ( $false = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14023]) ).

thf(14134,plain,
    ( ( $false = $false )
    | ( ( ~ ( ~ $false
            | ~ $false ) )
      = $true )
    | ( $false = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14023]) ).

thf(14135,plain,
    ( ( $false = $false )
    | ( ( ~ ( ~ $false
            | ~ $false ) )
      = $true )
    | ( $true = $false )
    | ( $false = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14024]) ).

thf(14136,plain,
    ( ( $false = $false )
    | ( ( ~ ( ~ $false
            | ~ $false ) )
      = $true )
    | ( $true = $false )
    | ( $false = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14024]) ).

thf(14137,plain,
    ( ( $false = $false )
    | ( ( ~ ( ~ $false
            | ~ $false ) )
      = $true )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14025]) ).

thf(14138,plain,
    ( ( $false = $false )
    | ( ( ~ ( ~ $false
            | ~ $false ) )
      = $true )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14025]) ).

thf(14139,plain,
    ! [SV825: nat,SV257: nat,SV583: nat] :
      ( ( ( ( times_times_nat @ SV583 @ SV257 )
          = ( times_times_nat @ SV825 @ SV257 ) )
        = $true )
      | ( ( ( times_times_nat @ SV583 @ SV257 )
          = ( times_times_nat @ SV825 @ SV257 ) )
        = $false )
      | ( ( SV257 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14026]) ).

thf(14140,plain,
    ! [SV257: nat,SV825: nat,SV583: nat] :
      ( ( ( SV583 = SV825 )
        = $true )
      | ( ( ( times_times_nat @ SV583 @ SV257 )
          = ( times_times_nat @ SV825 @ SV257 ) )
        = $false )
      | ( ( SV257 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14027]) ).

thf(14141,plain,
    ! [SV825: nat,SV257: nat,SV583: nat] :
      ( ( ( ( times_times_nat @ SV583 @ SV257 )
          = ( times_times_nat @ SV825 @ SV257 ) )
        = $true )
      | ( ( SV583 = SV825 )
        = $false )
      | ( ( SV257 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14028]) ).

thf(14142,plain,
    ! [SV257: nat,SV825: nat,SV583: nat] :
      ( ( ( SV583 = SV825 )
        = $true )
      | ( ( SV583 = SV825 )
        = $false )
      | ( ( SV257 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14029]) ).

thf(14143,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
         != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( SV595 = SV928 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14030]) ).

thf(14144,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
         != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false )
      | ( ( SV595 = SV928 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14030]) ).

thf(14145,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
         != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $true )
      | ( ( ~ ( ( SV595 != SV928 )
              | ~ ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                     != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
                    | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                     != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14031]) ).

thf(14146,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
         != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $true )
      | ( ( ~ ( ( SV595 != SV928 )
              | ~ ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                     != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
                    | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                     != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14031]) ).

thf(14147,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ~ ( ( SV595 != SV928 )
              | ~ ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                     != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
                    | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                     != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14032]) ).

thf(14148,plain,
    ! [SV837: nat,SV597: nat,SV273: nat] :
      ( ( ( ~ ! [SY1941: nat] :
                ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ ( sK29_SY1874 @ SV837 @ SV597 @ SV273 ) ) )
               != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1941 ) ) ) )
        = $true )
      | ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
          = ( modulo_modulo_nat @ SV837 @ SV597 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14033]) ).

thf(14149,plain,
    ! [SV966: nat,SV837: nat,SV962: nat,SV597: nat,SV273: nat] :
      ( ( ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SV962 ) )
          = ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SV966 ) ) )
        = $false )
      | ( ( ~ ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
               != ( modulo_modulo_nat @ SV837 @ SV597 ) )
              | ~ ~ ! [SY1874: nat] :
                      ~ ~ ! [SY1875: nat] :
                            ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SY1874 ) )
                           != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1875 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14034]) ).

thf(14150,plain,
    ! [SV605: nat,SV284: nat,SV931: nat,SV844: nat] :
      ( ( ( SV844 != SV931 )
        = $false )
      | ( ( SV284 = SV605 )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( ( SV284 != SV605 ) )
                    | ~ ( ( SV844 != SV931 ) ) )
              | ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
                   != ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14035]) ).

thf(14151,plain,
    ! [SV931: nat,SV844: nat,SV605: nat,SV284: nat] :
      ( ( ( ~ ( ( SV284 != SV605 ) )
          | ~ ( ( SV844 != SV931 ) ) )
        = $false )
      | ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14036]) ).

thf(14152,plain,
    ! [SV931: nat,SV605: nat,SV844: nat,SV284: nat] :
      ( ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) )
        = $false )
      | ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14037]) ).

thf(14153,plain,
    ! [SV845: nat,SV606: nat,SV285: nat] :
      ( ( ( ( times_times_nat @ SV285 @ SV606 )
          = ( times_times_nat @ SV285 @ SV845 ) )
        = $true )
      | ( ( ( times_times_nat @ SV285 @ SV606 )
          = ( times_times_nat @ SV285 @ SV845 ) )
        = $false )
      | ( ( SV285 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14038]) ).

thf(14154,plain,
    ! [SV285: nat,SV845: nat,SV606: nat] :
      ( ( ( SV606 = SV845 )
        = $true )
      | ( ( ( times_times_nat @ SV285 @ SV606 )
          = ( times_times_nat @ SV285 @ SV845 ) )
        = $false )
      | ( ( SV285 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14039]) ).

thf(14155,plain,
    ! [SV845: nat,SV606: nat,SV285: nat] :
      ( ( ( ( times_times_nat @ SV285 @ SV606 )
          = ( times_times_nat @ SV285 @ SV845 ) )
        = $true )
      | ( ( SV606 = SV845 )
        = $false )
      | ( ( SV285 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14040]) ).

thf(14156,plain,
    ! [SV285: nat,SV845: nat,SV606: nat] :
      ( ( ( SV606 = SV845 )
        = $true )
      | ( ( SV606 = SV845 )
        = $false )
      | ( ( SV285 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14041]) ).

thf(14157,plain,
    ! [SV621: nat,SV300: nat] :
      ( ( ( ( times_times_nat @ SV300 @ SV621 )
          = one_one_nat )
        = $true )
      | ( ( SV300 = one_one_nat )
        = $false )
      | ( ( SV621 = one_one_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14045]) ).

thf(14158,plain,
    ! [SV621: nat,SV300: nat] :
      ( ( ( ~ ( ( SV300 != one_one_nat )
              | ( SV621 != one_one_nat ) ) )
        = $true )
      | ( ( SV300 = one_one_nat )
        = $false )
      | ( ( SV621 = one_one_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14046]) ).

thf(14159,plain,
    ! [SV622: nat,SV936: nat] :
      ( ( ( SV936
         != ( times_times_nat @ SV622 @ ( sK30_SY1919 @ SV622 @ SV936 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV622 @ SV936 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[14047]) ).

thf(14160,plain,
    ! [SV963: nat,SV936: nat,SV622: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV622 @ SV936 ) )
        = $false )
      | ( ( SV936
          = ( times_times_nat @ SV622 @ SV963 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14048]) ).

thf(14161,plain,
    ! [SV963: nat,SV622: nat,SV936: nat] :
      ( ( ( ~ ~ ! [SY1919: nat] :
                  ( SV936
                 != ( times_times_nat @ SV622 @ SY1919 ) ) )
        = $false )
      | ( ( SV936
          = ( times_times_nat @ SV622 @ SV963 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14048]) ).

thf(14162,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14049]) ).

thf(14163,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14049]) ).

thf(14164,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
          | ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
              | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
                   != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14051]) ).

thf(14165,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
          | ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
              | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
                   != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14052]) ).

thf(14166,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
          | ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $false )
      | ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[14054]) ).

thf(14167,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $false )
      | ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true ) ),
    inference(extcnf_equal_neg,[status(thm)],[14054]) ).

thf(14168,plain,
    ! [SV626: nat,SV305: nat] :
      ( ( ( ( plus_plus_nat @ SV305 @ SV626 )
          = zero_zero_nat )
        = $true )
      | ( ( SV305 = zero_zero_nat )
        = $false )
      | ( ( SV626 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14057]) ).

thf(14169,plain,
    ! [SV626: nat,SV305: nat] :
      ( ( ( ~ ( ( SV305 != zero_zero_nat )
              | ( SV626 != zero_zero_nat ) ) )
        = $true )
      | ( ( SV305 = zero_zero_nat )
        = $false )
      | ( ( SV626 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14058]) ).

thf(14170,plain,
    ! [SV630: nat,SV310: nat] :
      ( ( ( ( plus_plus_nat @ SV310 @ SV630 )
          = zero_zero_nat )
        = $true )
      | ( ( SV310 = zero_zero_nat )
        = $false )
      | ( ( SV630 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14061]) ).

thf(14171,plain,
    ! [SV630: nat,SV310: nat] :
      ( ( ( ~ ( ( SV310 != zero_zero_nat )
              | ( SV630 != zero_zero_nat ) ) )
        = $true )
      | ( ( SV310 = zero_zero_nat )
        = $false )
      | ( ( SV630 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14062]) ).

thf(14172,plain,
    ! [SV631: nat,SV856: nat,SV311: nat] :
      ( ( ( ~ ~ ( ( SV311
                 != ( times_times_nat @ ( sK14_SY1883 @ SV856 @ SV631 @ SV311 ) @ ( sK22_SY1936 @ SV631 @ SV856 @ SV311 ) ) )
                | ~ ( dvd_dvd_nat @ ( sK14_SY1883 @ SV856 @ SV631 @ SV311 ) @ SV631 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV311 @ ( times_times_nat @ SV631 @ SV856 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14063]) ).

thf(14173,plain,
    ! [SV311: nat,SV856: nat,SV631: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( sK22_SY1936 @ SV631 @ SV856 @ SV311 ) @ SV856 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV311 @ ( times_times_nat @ SV631 @ SV856 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14063]) ).

thf(14174,plain,
    ! [SV956: nat,SV937: nat,SV857: nat,SV632: nat,SV312: nat] :
      ( ( ( ! [SY1887: nat] :
              ~ ~ ! [SY1888: nat] :
                    ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
                              | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) )
                        | ~ ( ( ( times_times_nat @ SV632 @ SY1887 )
                              = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1888 ) @ SV312 ) )
                            | ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1887 )
                              = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SY1888 ) @ SV312 ) ) ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV632 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV857 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14064]) ).

thf(14175,plain,
    ! [SV956: nat,SV937: nat,SV857: nat,SV632: nat,SV312: nat] :
      ( ( ( ! [SY1887: nat] :
              ~ ~ ! [SY1888: nat] :
                    ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
                              | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) )
                        | ~ ( ( ( times_times_nat @ SV632 @ SY1887 )
                              = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1888 ) @ SV312 ) )
                            | ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1887 )
                              = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SY1888 ) @ SV312 ) ) ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV857 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14065]) ).

thf(14176,plain,
    ! [SV860: nat,SV639: nat,SV319: nat > nat > $o] :
      ( ( ( ! [SY1421: nat] : ( SV319 @ SY1421 @ zero_zero_nat ) )
        = $false )
      | ( ( ~ ! [SY1422: nat,SY1423: nat] :
                ( ~ ( SV319 @ SY1422 @ SY1423 )
                | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) )
          | ( SV319 @ SV639 @ SV860 ) )
        = $true )
      | ( ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) )
        = $true )
      | ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14066]) ).

thf(14177,plain,
    ! [SV860: nat,SV639: nat,SV319: nat > nat > $o] :
      ( ( ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) )
        = $false )
      | ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
        = $false )
      | ( ( ~ ! [SY1421: nat] : ( SV319 @ SY1421 @ zero_zero_nat )
          | ~ ! [SY1422: nat,SY1423: nat] :
                ( ~ ( SV319 @ SY1422 @ SY1423 )
                | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) )
          | ( SV319 @ SV639 @ SV860 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14067]) ).

thf(14178,plain,
    ! [SV860: nat,SV639: nat,SV319: nat > nat > $o] :
      ( ( ( ! [SY1422: nat,SY1423: nat] :
              ( ~ ( SV319 @ SY1422 @ SY1423 )
              | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) ) )
        = $false )
      | ( ( SV319 @ SV639 @ SV860 )
        = $true )
      | ( ( SV319 @ ( sK27_SY1421 @ SV860 @ SV639 @ SV319 ) @ zero_zero_nat )
        = $false )
      | ( ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
          = ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14068]) ).

thf(14179,plain,
    ! [SV642: nat,SV322: nat] :
      ( ( ( SV322 = SV642 )
        = $false )
      | ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14069]) ).

thf(14180,plain,
    ! [SV642: nat,SV322: nat] :
      ( ( ( ~ ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 ) )
        = $false )
      | ( ( SV322 = SV642 )
        = $true )
      | ( ( vEBT_V8194947554948674370ptions @ summary @ SV642 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14071]) ).

thf(14181,plain,
    ! [SV642: nat,SV322: nat] :
      ( ( ( ~ ~ ( ~ ( ( SV322 != SV642 ) )
                | ~ ( vEBT_V8194947554948674370ptions @ summary @ SV642 ) ) )
        = $false )
      | ( ( SV322 = SV642 )
        = $true )
      | ( ( vEBT_V8194947554948674370ptions @ summary @ SV642 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14071]) ).

thf(14182,plain,
    ! [SV644: nat,SV939: nat] :
      ( ( ( SV939
         != ( plus_plus_nat @ SV644 @ ( sK31_SY1924 @ SV644 @ SV939 ) ) )
        = $false )
      | ( ( ord_less_eq_nat @ SV644 @ SV939 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[14072]) ).

thf(14183,plain,
    ! [SV964: nat,SV939: nat,SV644: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV644 @ SV939 ) )
        = $false )
      | ( ( SV939
          = ( plus_plus_nat @ SV644 @ SV964 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14073]) ).

thf(14184,plain,
    ! [SV964: nat,SV644: nat,SV939: nat] :
      ( ( ( ~ ~ ! [SY1924: nat] :
                  ( SV939
                 != ( plus_plus_nat @ SV644 @ SY1924 ) ) )
        = $false )
      | ( ( SV939
          = ( plus_plus_nat @ SV644 @ SV964 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14073]) ).

thf(14185,plain,
    ! [SV649: nat,SV329: nat] :
      ( ( ( zero_zero_nat
          = ( plus_plus_nat @ SV329 @ SV649 ) )
        = $true )
      | ( ( SV329 = zero_zero_nat )
        = $false )
      | ( ( SV649 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14076]) ).

thf(14186,plain,
    ! [SV649: nat,SV329: nat] :
      ( ( ( ~ ( ( SV329 != zero_zero_nat )
              | ( SV649 != zero_zero_nat ) ) )
        = $true )
      | ( ( SV329 = zero_zero_nat )
        = $false )
      | ( ( SV649 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14077]) ).

thf(14187,plain,
    ! [SV882: nat,SV347: nat,SV668: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( divide_divide_nat @ SV668 @ SV347 ) @ ( divide_divide_nat @ SV882 @ SV347 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( divide_divide_nat @ SV668 @ SV347 ) @ ( divide_divide_nat @ SV882 @ SV347 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV347 @ SV882 )
        = $false )
      | ( ( dvd_dvd_nat @ SV347 @ SV668 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14082]) ).

thf(14188,plain,
    ! [SV347: nat,SV882: nat,SV668: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV668 @ SV882 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( divide_divide_nat @ SV668 @ SV347 ) @ ( divide_divide_nat @ SV882 @ SV347 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV347 @ SV882 )
        = $false )
      | ( ( dvd_dvd_nat @ SV347 @ SV668 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14082]) ).

thf(14189,plain,
    ! [SV882: nat,SV347: nat,SV668: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( divide_divide_nat @ SV668 @ SV347 ) @ ( divide_divide_nat @ SV882 @ SV347 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV668 @ SV882 )
        = $false )
      | ( ( dvd_dvd_nat @ SV347 @ SV882 )
        = $false )
      | ( ( dvd_dvd_nat @ SV347 @ SV668 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14083]) ).

thf(14190,plain,
    ! [SV347: nat,SV882: nat,SV668: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV668 @ SV882 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV668 @ SV882 )
        = $false )
      | ( ( dvd_dvd_nat @ SV347 @ SV882 )
        = $false )
      | ( ( dvd_dvd_nat @ SV347 @ SV668 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14083]) ).

thf(14191,plain,
    ! [SV349: nat,SV669: nat] :
      ( ( ~ ~ ( ~ ( dvd_dvd_nat @ ( sK6_SY1803 @ SV669 @ SV349 ) @ SV349 )
              | ~ ( dvd_dvd_nat @ ( sK6_SY1803 @ SV669 @ SV349 ) @ SV669 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[14084]) ).

thf(14192,plain,
    ! [SV669: nat,SV349: nat] :
      ( ( ~ ( ( ( times_times_nat @ SV349 @ ( sK18_SY1926 @ SV349 @ SV669 ) )
              = ( plus_plus_nat @ ( times_times_nat @ SV669 @ ( sK23_SY1937 @ SV349 @ SV669 ) ) @ ( sK6_SY1803 @ SV669 @ SV349 ) ) )
            | ( ( times_times_nat @ SV669 @ ( sK18_SY1926 @ SV349 @ SV669 ) )
              = ( plus_plus_nat @ ( times_times_nat @ SV349 @ ( sK23_SY1937 @ SV349 @ SV669 ) ) @ ( sK6_SY1803 @ SV669 @ SV349 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[14084]) ).

thf(14193,plain,
    ! [SV671: nat,SV351: nat] :
      ( ( ( one_one_nat
          = ( times_times_nat @ SV351 @ SV671 ) )
        = $true )
      | ( ( SV351 = one_one_nat )
        = $false )
      | ( ( SV671 = one_one_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14087]) ).

thf(14194,plain,
    ! [SV671: nat,SV351: nat] :
      ( ( ( ~ ( ( SV351 != one_one_nat )
              | ( SV671 != one_one_nat ) ) )
        = $true )
      | ( ( SV351 = one_one_nat )
        = $false )
      | ( ( SV671 = one_one_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14088]) ).

thf(14195,plain,
    ! [SV353: nat,SV959: nat,SV945: nat,SV884: nat,SV673: nat] :
      ( ( ( SV673 = SV884 )
        = $false )
      | ( ( ~ ( ( SV945 != SV959 ) ) )
        = $true )
      | ( ( ( plus_plus_nat @ SV673 @ ( times_times_nat @ SV353 @ SV945 ) )
         != ( plus_plus_nat @ SV884 @ ( times_times_nat @ SV353 @ SV959 ) ) )
        = $true )
      | ( ( SV353 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14089]) ).

thf(14196,plain,
    ! [SV889: nat,SV362: nat,SV681: nat] :
      ( ( ( ( divide_divide_nat @ SV681 @ SV362 )
         != ( divide_divide_nat @ SV889 @ SV362 ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV681 @ SV362 )
          = ( divide_divide_nat @ SV889 @ SV362 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV362 @ SV889 )
        = $false )
      | ( ( dvd_dvd_nat @ SV362 @ SV681 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14094]) ).

thf(14197,plain,
    ! [SV362: nat,SV889: nat,SV681: nat] :
      ( ( ( SV681 != SV889 )
        = $false )
      | ( ( ( divide_divide_nat @ SV681 @ SV362 )
          = ( divide_divide_nat @ SV889 @ SV362 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV362 @ SV889 )
        = $false )
      | ( ( dvd_dvd_nat @ SV362 @ SV681 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14094]) ).

thf(14198,plain,
    ! [SV889: nat,SV362: nat,SV681: nat] :
      ( ( ( ( divide_divide_nat @ SV681 @ SV362 )
         != ( divide_divide_nat @ SV889 @ SV362 ) )
        = $false )
      | ( ( SV681 = SV889 )
        = $false )
      | ( ( dvd_dvd_nat @ SV362 @ SV889 )
        = $false )
      | ( ( dvd_dvd_nat @ SV362 @ SV681 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14095]) ).

thf(14199,plain,
    ! [SV362: nat,SV889: nat,SV681: nat] :
      ( ( ( SV681 != SV889 )
        = $false )
      | ( ( SV681 = SV889 )
        = $false )
      | ( ( dvd_dvd_nat @ SV362 @ SV889 )
        = $false )
      | ( ( dvd_dvd_nat @ SV362 @ SV681 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14095]) ).

thf(14200,plain,
    ! [SV692: option_nat,SV373: option_nat] :
      ( ( ( SV373 = none_nat )
        = $false )
      | ( ( SV373 = SV692 )
        = $true )
      | ( ( SV692 = none_nat )
        = $true )
      | ( ( SV373 = none_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14096]) ).

thf(14201,plain,
    ! [SV373: option_nat,SV692: option_nat] :
      ( ( ( SV692 != none_nat )
        = $true )
      | ( ( SV373 = SV692 )
        = $true )
      | ( ( SV692 = none_nat )
        = $true )
      | ( ( SV373 = none_nat )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14097]) ).

thf(14202,plain,
    ! [SV692: option_nat,SV373: option_nat] :
      ( ( ( ~ ( ( SV373 != none_nat ) ) )
        = $false )
      | ( ( SV373 = SV692 )
        = $true )
      | ( ( SV373 = none_nat )
        = $false )
      | ( ( SV692 = none_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14099]) ).

thf(14203,plain,
    ! [SV373: option_nat,SV692: option_nat] :
      ( ( ( ~ ( ( SV692 != none_nat ) )
          | ( ( the_nat @ SV373 )
            = ( the_nat @ SV692 ) ) )
        = $false )
      | ( ( SV373 = SV692 )
        = $true )
      | ( ( SV373 = none_nat )
        = $false )
      | ( ( SV692 = none_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14099]) ).

thf(14204,plain,
    ! [SV693: nat,SV374: nat > $o] :
      ( ( ( SV374 @ ( sK24_SY1534 @ SV693 @ SV374 ) )
        = $true )
      | ( ( SV374 @ SV693 )
        = $true )
      | ( ( ( divide_divide_nat @ ( sK8_SY1533 @ SV693 @ SV374 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( sK8_SY1533 @ SV693 @ SV374 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14100]) ).

thf(14205,plain,
    ! [SV374: nat > $o,SV693: nat] :
      ( ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ ( sK28_SY1940 @ SV693 @ SV374 ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( sK24_SY1534 @ SV693 @ SV374 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
         != ( sK24_SY1534 @ SV693 @ SV374 ) )
        = $false )
      | ( ( SV374 @ SV693 )
        = $true )
      | ( ( ( divide_divide_nat @ ( sK8_SY1533 @ SV693 @ SV374 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( sK8_SY1533 @ SV693 @ SV374 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14101]) ).

thf(14206,plain,
    ! [SV693: nat,SV374: nat > $o] :
      ( ( ( SV374 @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ ( sK28_SY1940 @ SV693 @ SV374 ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( sK24_SY1534 @ SV693 @ SV374 ) ) ) )
        = $false )
      | ( ( SV374 @ SV693 )
        = $true )
      | ( ( ( divide_divide_nat @ ( sK8_SY1533 @ SV693 @ SV374 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( sK8_SY1533 @ SV693 @ SV374 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14101]) ).

thf(14207,plain,
    ! [SV374: nat > $o,SV693: nat] :
      ( ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ ( sK25_SY1939 @ SV693 @ SV374 ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( sK21_SY1534 @ SV693 @ SV374 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( sK21_SY1534 @ SV693 @ SV374 ) )
        = $true )
      | ( ( SV374 @ SV693 )
        = $true )
      | ( ( SV374 @ ( sK8_SY1533 @ SV693 @ SV374 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14103]) ).

thf(14208,plain,
    ! [SV694: nat,SV948: nat] :
      ( ( ( SV948
         != ( plus_plus_nat @ SV694 @ ( sK32_SY1929 @ SV694 @ SV948 ) ) )
        = $false )
      | ( ( ord_less_eq_nat @ SV694 @ SV948 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[14105]) ).

thf(14209,plain,
    ! [SV965: nat,SV948: nat,SV694: nat] :
      ( ( ( ~ ( ord_less_eq_nat @ SV694 @ SV948 ) )
        = $false )
      | ( ( SV948
          = ( plus_plus_nat @ SV694 @ SV965 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14106]) ).

thf(14210,plain,
    ! [SV965: nat,SV694: nat,SV948: nat] :
      ( ( ( ~ ~ ! [SY1929: nat] :
                  ( SV948
                 != ( plus_plus_nat @ SV694 @ SY1929 ) ) )
        = $false )
      | ( ( SV948
          = ( plus_plus_nat @ SV694 @ SV965 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14106]) ).

thf(14211,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14107]) ).

thf(14212,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14108]) ).

thf(14213,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
          | ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[14110]) ).

thf(14214,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $true ) ),
    inference(extcnf_equal_pos,[status(thm)],[14110]) ).

thf(14215,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14111]) ).

thf(14216,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
         != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14111]) ).

thf(14217,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $true )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14112]) ).

thf(14218,plain,
    ! [SV206: nat,SV540: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $true )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14112]) ).

thf(14219,plain,
    ! [SV243: $o] :
      ( ( ( ~ SV243
          | ~ $false )
        = $false )
      | ( SV243 = $false )
      | ( SV243 = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14115]) ).

thf(14220,plain,
    ! [SV243: $o] :
      ( ( ( ~ SV243
          | ~ $false )
        = $false )
      | ( $false = $false )
      | ( SV243 = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14116]) ).

thf(14221,plain,
    ! [SV243: $o] :
      ( ( ( ~ SV243
          | ~ $false )
        = $false )
      | ( SV243 = $false )
      | ( SV243 = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14117]) ).

thf(14222,plain,
    ! [SV243: $o] :
      ( ( ( ~ SV243
          | ~ $false )
        = $false )
      | ( $false = $false )
      | ( SV243 = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14118]) ).

thf(14223,plain,
    ! [SV243: $o] :
      ( ( ( ~ SV243
          | ~ $false )
        = $false )
      | ( SV243 = $false )
      | ( $true = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14119]) ).

thf(14224,plain,
    ! [SV243: $o] :
      ( ( ( ~ SV243
          | ~ $false )
        = $false )
      | ( $false = $false )
      | ( $true = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14120]) ).

thf(14225,plain,
    ! [SV243: $o] :
      ( ( ( ~ SV243
          | ~ $false )
        = $false )
      | ( SV243 = $false )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14121]) ).

thf(14226,plain,
    ! [SV243: $o] :
      ( ( ( ~ SV243
          | ~ $false )
        = $false )
      | ( $false = $false )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14122]) ).

thf(14227,plain,
    ( ( ( ~ $true
        | ~ $false )
      = $false )
    | ( $true = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14123]) ).

thf(14228,plain,
    ( ( ( ~ $true
        | ~ $false )
      = $false )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14124]) ).

thf(14229,plain,
    ( ( ( ~ $true
        | ~ $false )
      = $false )
    | ( $true = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14125]) ).

thf(14230,plain,
    ( ( ( ~ $true
        | ~ $false )
      = $false )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14126]) ).

thf(14231,plain,
    ( ( ( ~ $true
        | ~ $false )
      = $false )
    | ( $true = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14127]) ).

thf(14232,plain,
    ( ( ( ~ $true
        | ~ $false )
      = $false )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14128]) ).

thf(14233,plain,
    ( ( ( ~ $true
        | ~ $false )
      = $false )
    | ( $true = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14129]) ).

thf(14234,plain,
    ( ( ( ~ $true
        | ~ $false )
      = $false )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14130]) ).

thf(14235,plain,
    ( ( ( ~ $false
        | ~ $false )
      = $false )
    | ( $false = $false )
    | ( $false = $false )
    | ( $false = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14131]) ).

thf(14236,plain,
    ( ( ( ~ $false
        | ~ $false )
      = $false )
    | ( $false = $false )
    | ( $false = $false )
    | ( $false = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14132]) ).

thf(14237,plain,
    ( ( ( ~ $false
        | ~ $false )
      = $false )
    | ( $false = $false )
    | ( $false = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14133]) ).

thf(14238,plain,
    ( ( ( ~ $false
        | ~ $false )
      = $false )
    | ( $false = $false )
    | ( $false = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14134]) ).

thf(14239,plain,
    ( ( ( ~ $false
        | ~ $false )
      = $false )
    | ( $false = $false )
    | ( $true = $false )
    | ( $false = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14135]) ).

thf(14240,plain,
    ( ( ( ~ $false
        | ~ $false )
      = $false )
    | ( $false = $false )
    | ( $true = $false )
    | ( $false = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14136]) ).

thf(14241,plain,
    ( ( ( ~ $false
        | ~ $false )
      = $false )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14137]) ).

thf(14242,plain,
    ( ( ( ~ $false
        | ~ $false )
      = $false )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14138]) ).

thf(14243,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $true )
      | ( ( SV595 = SV928 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14143]) ).

thf(14244,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $true )
      | ( ( SV595 = SV928 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14144]) ).

thf(14245,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
         != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $true )
      | ( ( ~ ( ( SV595 != SV928 )
              | ~ ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                     != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
                    | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                     != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14145]) ).

thf(14246,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
         != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $true )
      | ( ( ~ ( ( SV595 != SV928 )
              | ~ ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                     != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
                    | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                     != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14146]) ).

thf(14247,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( SV595 != SV928 )
          | ~ ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                 != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
                | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                 != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
        = $false )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14147]) ).

thf(14248,plain,
    ! [SV837: nat,SV597: nat,SV273: nat] :
      ( ( ( ! [SY1941: nat] :
              ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ ( sK29_SY1874 @ SV837 @ SV597 @ SV273 ) ) )
             != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1941 ) ) ) )
        = $false )
      | ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
          = ( modulo_modulo_nat @ SV837 @ SV597 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14148]) ).

thf(14249,plain,
    ! [SV966: nat,SV962: nat,SV837: nat,SV597: nat,SV273: nat] :
      ( ( ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
           != ( modulo_modulo_nat @ SV837 @ SV597 ) )
          | ~ ~ ! [SY1874: nat] :
                  ~ ~ ! [SY1875: nat] :
                        ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SY1874 ) )
                       != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1875 ) ) ) )
        = $false )
      | ( ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SV962 ) )
          = ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SV966 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14149]) ).

thf(14250,plain,
    ! [SV605: nat,SV284: nat,SV931: nat,SV844: nat] :
      ( ( ( SV844 = SV931 )
        = $true )
      | ( ( SV284 = SV605 )
        = $true )
      | ( ( ~ ( ~ ~ ( ~ ( ( SV284 != SV605 ) )
                    | ~ ( ( SV844 != SV931 ) ) )
              | ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
                   != ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14150]) ).

thf(14251,plain,
    ! [SV931: nat,SV844: nat,SV605: nat,SV284: nat] :
      ( ( ( ~ ( ( SV284 != SV605 ) ) )
        = $false )
      | ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14151]) ).

thf(14252,plain,
    ! [SV605: nat,SV284: nat,SV931: nat,SV844: nat] :
      ( ( ( ~ ( ( SV844 != SV931 ) ) )
        = $false )
      | ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14151]) ).

thf(14253,plain,
    ! [SV621: nat,SV300: nat] :
      ( ( ( ( SV300 != one_one_nat )
          | ( SV621 != one_one_nat ) )
        = $false )
      | ( ( SV300 = one_one_nat )
        = $false )
      | ( ( SV621 = one_one_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14158]) ).

thf(14254,plain,
    ! [SV622: nat,SV936: nat] :
      ( ( ( SV936
          = ( times_times_nat @ SV622 @ ( sK30_SY1919 @ SV622 @ SV936 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV622 @ SV936 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14159]) ).

thf(14255,plain,
    ! [SV963: nat,SV936: nat,SV622: nat] :
      ( ( ( dvd_dvd_nat @ SV622 @ SV936 )
        = $true )
      | ( ( SV936
          = ( times_times_nat @ SV622 @ SV963 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14160]) ).

thf(14256,plain,
    ! [SV963: nat,SV622: nat,SV936: nat] :
      ( ( ( ~ ! [SY1919: nat] :
                ( SV936
               != ( times_times_nat @ SV622 @ SY1919 ) ) )
        = $true )
      | ( ( SV936
          = ( times_times_nat @ SV622 @ SV963 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14161]) ).

thf(14257,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
          | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14162]) ).

thf(14258,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
          | ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14163]) ).

thf(14259,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
              | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
                   != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14164]) ).

thf(14260,plain,
    ! [SV303: nat,SV624: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
              | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
                   != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14164]) ).

thf(14261,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
              | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
                   != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14165]) ).

thf(14262,plain,
    ! [SV303: nat,SV624: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
              | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
                   != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14165]) ).

thf(14263,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $false )
      | ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14166]) ).

thf(14264,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $false )
      | ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14166]) ).

thf(14265,plain,
    ! [SV626: nat,SV305: nat] :
      ( ( ( ( SV305 != zero_zero_nat )
          | ( SV626 != zero_zero_nat ) )
        = $false )
      | ( ( SV305 = zero_zero_nat )
        = $false )
      | ( ( SV626 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14169]) ).

thf(14266,plain,
    ! [SV630: nat,SV310: nat] :
      ( ( ( ( SV310 != zero_zero_nat )
          | ( SV630 != zero_zero_nat ) )
        = $false )
      | ( ( SV310 = zero_zero_nat )
        = $false )
      | ( ( SV630 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14171]) ).

thf(14267,plain,
    ! [SV631: nat,SV856: nat,SV311: nat] :
      ( ( ( ~ ( ( SV311
               != ( times_times_nat @ ( sK14_SY1883 @ SV856 @ SV631 @ SV311 ) @ ( sK22_SY1936 @ SV631 @ SV856 @ SV311 ) ) )
              | ~ ( dvd_dvd_nat @ ( sK14_SY1883 @ SV856 @ SV631 @ SV311 ) @ SV631 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV311 @ ( times_times_nat @ SV631 @ SV856 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14172]) ).

thf(14268,plain,
    ! [SV311: nat,SV856: nat,SV631: nat] :
      ( ( ( dvd_dvd_nat @ ( sK22_SY1936 @ SV631 @ SV856 @ SV311 ) @ SV856 )
        = $true )
      | ( ( dvd_dvd_nat @ SV311 @ ( times_times_nat @ SV631 @ SV856 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14173]) ).

thf(14269,plain,
    ! [SV937: nat,SV956: nat,SV857: nat,SV632: nat,SV312: nat] :
      ( ( ( ~ ~ ! [SY1942: nat] :
                  ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
                            | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) )
                      | ~ ( ( ( times_times_nat @ SV632 @ ( sK33_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
                            = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1942 ) @ SV312 ) )
                          | ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ ( sK33_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
                            = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SY1942 ) @ SV312 ) ) ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV632 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV857 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[14174]) ).

thf(14270,plain,
    ! [SV937: nat,SV956: nat,SV857: nat,SV632: nat,SV312: nat] :
      ( ( ( ~ ~ ! [SY1943: nat] :
                  ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
                            | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) )
                      | ~ ( ( ( times_times_nat @ SV632 @ ( sK34_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
                            = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1943 ) @ SV312 ) )
                          | ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ ( sK34_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
                            = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SY1943 ) @ SV312 ) ) ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV857 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[14175]) ).

thf(14271,plain,
    ! [SV639: nat,SV860: nat,SV319: nat > nat > $o] :
      ( ( ( SV319 @ ( sK35_SY1421 @ SV860 @ SV639 @ SV319 ) @ zero_zero_nat )
        = $false )
      | ( ( ~ ! [SY1422: nat,SY1423: nat] :
                ( ~ ( SV319 @ SY1422 @ SY1423 )
                | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) )
          | ( SV319 @ SV639 @ SV860 ) )
        = $true )
      | ( ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) )
        = $true )
      | ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[14176]) ).

thf(14272,plain,
    ! [SV860: nat,SV639: nat,SV319: nat > nat > $o] :
      ( ( ( ~ ! [SY1421: nat] : ( SV319 @ SY1421 @ zero_zero_nat ) )
        = $true )
      | ( ( ~ ! [SY1422: nat,SY1423: nat] :
                ( ~ ( SV319 @ SY1422 @ SY1423 )
                | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) )
          | ( SV319 @ SV639 @ SV860 ) )
        = $true )
      | ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
        = $false )
      | ( ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[14177]) ).

thf(14273,plain,
    ! [SV639: nat,SV860: nat,SV319: nat > nat > $o] :
      ( ( ( ! [SY1944: nat] :
              ( ~ ( SV319 @ ( sK36_SY1422 @ SV860 @ SV639 @ SV319 ) @ SY1944 )
              | ( SV319 @ ( sK36_SY1422 @ SV860 @ SV639 @ SV319 ) @ ( plus_plus_nat @ ( sK36_SY1422 @ SV860 @ SV639 @ SV319 ) @ SY1944 ) ) ) )
        = $false )
      | ( ( SV319 @ SV639 @ SV860 )
        = $true )
      | ( ( SV319 @ ( sK27_SY1421 @ SV860 @ SV639 @ SV319 ) @ zero_zero_nat )
        = $false )
      | ( ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
          = ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[14178]) ).

thf(14274,plain,
    ! [SV642: nat,SV322: nat] :
      ( ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ SV322 ) @ SV642 )
        = $true )
      | ( ( SV322 = SV642 )
        = $true )
      | ( ( vEBT_V8194947554948674370ptions @ summary @ SV642 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14180]) ).

thf(14275,plain,
    ! [SV642: nat,SV322: nat] :
      ( ( ( ~ ( ~ ( ( SV322 != SV642 ) )
              | ~ ( vEBT_V8194947554948674370ptions @ summary @ SV642 ) ) )
        = $true )
      | ( ( SV322 = SV642 )
        = $true )
      | ( ( vEBT_V8194947554948674370ptions @ summary @ SV642 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14181]) ).

thf(14276,plain,
    ! [SV644: nat,SV939: nat] :
      ( ( ( SV939
          = ( plus_plus_nat @ SV644 @ ( sK31_SY1924 @ SV644 @ SV939 ) ) )
        = $true )
      | ( ( ord_less_eq_nat @ SV644 @ SV939 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14182]) ).

thf(14277,plain,
    ! [SV964: nat,SV939: nat,SV644: nat] :
      ( ( ( ord_less_eq_nat @ SV644 @ SV939 )
        = $true )
      | ( ( SV939
          = ( plus_plus_nat @ SV644 @ SV964 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14183]) ).

thf(14278,plain,
    ! [SV964: nat,SV644: nat,SV939: nat] :
      ( ( ( ~ ! [SY1924: nat] :
                ( SV939
               != ( plus_plus_nat @ SV644 @ SY1924 ) ) )
        = $true )
      | ( ( SV939
          = ( plus_plus_nat @ SV644 @ SV964 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14184]) ).

thf(14279,plain,
    ! [SV649: nat,SV329: nat] :
      ( ( ( ( SV329 != zero_zero_nat )
          | ( SV649 != zero_zero_nat ) )
        = $false )
      | ( ( SV329 = zero_zero_nat )
        = $false )
      | ( ( SV649 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14186]) ).

thf(14280,plain,
    ! [SV882: nat,SV347: nat,SV668: nat] :
      ( ( ( dvd_dvd_nat @ ( divide_divide_nat @ SV668 @ SV347 ) @ ( divide_divide_nat @ SV882 @ SV347 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( divide_divide_nat @ SV668 @ SV347 ) @ ( divide_divide_nat @ SV882 @ SV347 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV347 @ SV882 )
        = $false )
      | ( ( dvd_dvd_nat @ SV347 @ SV668 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14187]) ).

thf(14281,plain,
    ! [SV347: nat,SV882: nat,SV668: nat] :
      ( ( ( dvd_dvd_nat @ SV668 @ SV882 )
        = $true )
      | ( ( dvd_dvd_nat @ ( divide_divide_nat @ SV668 @ SV347 ) @ ( divide_divide_nat @ SV882 @ SV347 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV347 @ SV882 )
        = $false )
      | ( ( dvd_dvd_nat @ SV347 @ SV668 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14188]) ).

thf(14282,plain,
    ! [SV882: nat,SV347: nat,SV668: nat] :
      ( ( ( dvd_dvd_nat @ ( divide_divide_nat @ SV668 @ SV347 ) @ ( divide_divide_nat @ SV882 @ SV347 ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV668 @ SV882 )
        = $false )
      | ( ( dvd_dvd_nat @ SV347 @ SV882 )
        = $false )
      | ( ( dvd_dvd_nat @ SV347 @ SV668 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14189]) ).

thf(14283,plain,
    ! [SV347: nat,SV882: nat,SV668: nat] :
      ( ( ( dvd_dvd_nat @ SV668 @ SV882 )
        = $true )
      | ( ( dvd_dvd_nat @ SV668 @ SV882 )
        = $false )
      | ( ( dvd_dvd_nat @ SV347 @ SV882 )
        = $false )
      | ( ( dvd_dvd_nat @ SV347 @ SV668 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14190]) ).

thf(14284,plain,
    ! [SV349: nat,SV669: nat] :
      ( ( ~ ( ~ ( dvd_dvd_nat @ ( sK6_SY1803 @ SV669 @ SV349 ) @ SV349 )
            | ~ ( dvd_dvd_nat @ ( sK6_SY1803 @ SV669 @ SV349 ) @ SV669 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[14191]) ).

thf(14285,plain,
    ! [SV669: nat,SV349: nat] :
      ( ( ( ( times_times_nat @ SV349 @ ( sK18_SY1926 @ SV349 @ SV669 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV669 @ ( sK23_SY1937 @ SV349 @ SV669 ) ) @ ( sK6_SY1803 @ SV669 @ SV349 ) ) )
        | ( ( times_times_nat @ SV669 @ ( sK18_SY1926 @ SV349 @ SV669 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV349 @ ( sK23_SY1937 @ SV349 @ SV669 ) ) @ ( sK6_SY1803 @ SV669 @ SV349 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[14192]) ).

thf(14286,plain,
    ! [SV671: nat,SV351: nat] :
      ( ( ( ( SV351 != one_one_nat )
          | ( SV671 != one_one_nat ) )
        = $false )
      | ( ( SV351 = one_one_nat )
        = $false )
      | ( ( SV671 = one_one_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14194]) ).

thf(14287,plain,
    ! [SV353: nat,SV884: nat,SV673: nat,SV959: nat,SV945: nat] :
      ( ( ( SV945 != SV959 )
        = $false )
      | ( ( SV673 = SV884 )
        = $false )
      | ( ( ( plus_plus_nat @ SV673 @ ( times_times_nat @ SV353 @ SV945 ) )
         != ( plus_plus_nat @ SV884 @ ( times_times_nat @ SV353 @ SV959 ) ) )
        = $true )
      | ( ( SV353 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14195]) ).

thf(14288,plain,
    ! [SV889: nat,SV362: nat,SV681: nat] :
      ( ( ( ( divide_divide_nat @ SV681 @ SV362 )
          = ( divide_divide_nat @ SV889 @ SV362 ) )
        = $true )
      | ( ( ( divide_divide_nat @ SV681 @ SV362 )
          = ( divide_divide_nat @ SV889 @ SV362 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV362 @ SV889 )
        = $false )
      | ( ( dvd_dvd_nat @ SV362 @ SV681 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14196]) ).

thf(14289,plain,
    ! [SV362: nat,SV889: nat,SV681: nat] :
      ( ( ( SV681 = SV889 )
        = $true )
      | ( ( ( divide_divide_nat @ SV681 @ SV362 )
          = ( divide_divide_nat @ SV889 @ SV362 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV362 @ SV889 )
        = $false )
      | ( ( dvd_dvd_nat @ SV362 @ SV681 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14197]) ).

thf(14290,plain,
    ! [SV889: nat,SV362: nat,SV681: nat] :
      ( ( ( ( divide_divide_nat @ SV681 @ SV362 )
          = ( divide_divide_nat @ SV889 @ SV362 ) )
        = $true )
      | ( ( SV681 = SV889 )
        = $false )
      | ( ( dvd_dvd_nat @ SV362 @ SV889 )
        = $false )
      | ( ( dvd_dvd_nat @ SV362 @ SV681 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14198]) ).

thf(14291,plain,
    ! [SV362: nat,SV889: nat,SV681: nat] :
      ( ( ( SV681 = SV889 )
        = $true )
      | ( ( SV681 = SV889 )
        = $false )
      | ( ( dvd_dvd_nat @ SV362 @ SV889 )
        = $false )
      | ( ( dvd_dvd_nat @ SV362 @ SV681 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14199]) ).

thf(14292,plain,
    ! [SV373: option_nat,SV692: option_nat] :
      ( ( ( SV692 = none_nat )
        = $false )
      | ( ( SV373 = SV692 )
        = $true )
      | ( ( SV692 = none_nat )
        = $true )
      | ( ( SV373 = none_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14201]) ).

thf(14293,plain,
    ! [SV692: option_nat,SV373: option_nat] :
      ( ( ( SV373 != none_nat )
        = $true )
      | ( ( SV373 = SV692 )
        = $true )
      | ( ( SV373 = none_nat )
        = $false )
      | ( ( SV692 = none_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14202]) ).

thf(14294,plain,
    ! [SV373: option_nat,SV692: option_nat] :
      ( ( ( ~ ( ( SV692 != none_nat ) ) )
        = $false )
      | ( ( SV373 = SV692 )
        = $true )
      | ( ( SV373 = none_nat )
        = $false )
      | ( ( SV692 = none_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14203]) ).

thf(14295,plain,
    ! [SV692: option_nat,SV373: option_nat] :
      ( ( ( ( the_nat @ SV373 )
          = ( the_nat @ SV692 ) )
        = $false )
      | ( ( SV373 = SV692 )
        = $true )
      | ( ( SV373 = none_nat )
        = $false )
      | ( ( SV692 = none_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14203]) ).

thf(14296,plain,
    ! [SV374: nat > $o,SV693: nat] :
      ( ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ ( sK28_SY1940 @ SV693 @ SV374 ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( sK24_SY1534 @ SV693 @ SV374 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( sK24_SY1534 @ SV693 @ SV374 ) )
        = $true )
      | ( ( SV374 @ SV693 )
        = $true )
      | ( ( ( divide_divide_nat @ ( sK8_SY1533 @ SV693 @ SV374 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( sK8_SY1533 @ SV693 @ SV374 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14205]) ).

thf(14297,plain,
    ! [SV694: nat,SV948: nat] :
      ( ( ( SV948
          = ( plus_plus_nat @ SV694 @ ( sK32_SY1929 @ SV694 @ SV948 ) ) )
        = $true )
      | ( ( ord_less_eq_nat @ SV694 @ SV948 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14208]) ).

thf(14298,plain,
    ! [SV965: nat,SV948: nat,SV694: nat] :
      ( ( ( ord_less_eq_nat @ SV694 @ SV948 )
        = $true )
      | ( ( SV948
          = ( plus_plus_nat @ SV694 @ SV965 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14209]) ).

thf(14299,plain,
    ! [SV965: nat,SV694: nat,SV948: nat] :
      ( ( ( ~ ! [SY1929: nat] :
                ( SV948
               != ( plus_plus_nat @ SV694 @ SY1929 ) ) )
        = $true )
      | ( ( SV948
          = ( plus_plus_nat @ SV694 @ SV965 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14210]) ).

thf(14300,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14211]) ).

thf(14301,plain,
    ! [SV206: nat,SV540: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14211]) ).

thf(14302,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14212]) ).

thf(14303,plain,
    ! [SV206: nat,SV540: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14212]) ).

thf(14304,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $true )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[14213]) ).

thf(14305,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14215]) ).

thf(14306,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14216]) ).

thf(14307,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14217]) ).

thf(14308,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14218]) ).

thf(14309,plain,
    ! [SV243: $o] :
      ( ( ( ~ SV243 ) = $false )
      | ( SV243 = $false )
      | ( SV243 = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14219]) ).

thf(14310,plain,
    ! [SV243: $o] :
      ( ( ( ~ $false ) = $false )
      | ( SV243 = $false )
      | ( SV243 = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14219]) ).

thf(14311,plain,
    ! [SV243: $o] :
      ( ( ( ~ SV243 ) = $false )
      | ( $false = $false )
      | ( SV243 = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14220]) ).

thf(14312,plain,
    ! [SV243: $o] :
      ( ( ( ~ $false ) = $false )
      | ( $false = $false )
      | ( SV243 = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14220]) ).

thf(14313,plain,
    ! [SV243: $o] :
      ( ( ( ~ SV243 ) = $false )
      | ( SV243 = $false )
      | ( SV243 = $false )
      | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14221]) ).

thf(14314,plain,
    ! [SV243: $o] :
      ( ( ( ~ $false ) = $false )
      | ( SV243 = $false )
      | ( SV243 = $false )
      | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14221]) ).

thf(14315,plain,
    ! [SV243: $o] :
      ( ( ( ~ SV243 ) = $false )
      | ( $false = $false )
      | ( SV243 = $false )
      | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14222]) ).

thf(14316,plain,
    ! [SV243: $o] :
      ( ( ( ~ $false ) = $false )
      | ( $false = $false )
      | ( SV243 = $false )
      | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14222]) ).

thf(14317,plain,
    ! [SV243: $o] :
      ( ( ( ~ SV243 ) = $false )
      | ( SV243 = $false )
      | ( $true = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14223]) ).

thf(14318,plain,
    ! [SV243: $o] :
      ( ( ( ~ $false ) = $false )
      | ( SV243 = $false )
      | ( $true = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14223]) ).

thf(14319,plain,
    ! [SV243: $o] :
      ( ( ( ~ SV243 ) = $false )
      | ( $false = $false )
      | ( $true = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14224]) ).

thf(14320,plain,
    ! [SV243: $o] :
      ( ( ( ~ $false ) = $false )
      | ( $false = $false )
      | ( $true = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14224]) ).

thf(14321,plain,
    ! [SV243: $o] :
      ( ( ( ~ SV243 ) = $false )
      | ( SV243 = $false )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14225]) ).

thf(14322,plain,
    ! [SV243: $o] :
      ( ( ( ~ $false ) = $false )
      | ( SV243 = $false )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14225]) ).

thf(14323,plain,
    ! [SV243: $o] :
      ( ( ( ~ SV243 ) = $false )
      | ( $false = $false )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14226]) ).

thf(14324,plain,
    ( ( ( ~ $false ) = $false )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14226]) ).

thf(14325,plain,
    ( ( ( ~ $true ) = $false )
    | ( $true = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14227]) ).

thf(14326,plain,
    ( ( ( ~ $false ) = $false )
    | ( $true = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14227]) ).

thf(14327,plain,
    ( ( ( ~ $true ) = $false )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14228]) ).

thf(14328,plain,
    ( ( ( ~ $false ) = $false )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14228]) ).

thf(14329,plain,
    ( ( ( ~ $true ) = $false )
    | ( $true = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14229]) ).

thf(14330,plain,
    ( ( ( ~ $false ) = $false )
    | ( $true = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14229]) ).

thf(14331,plain,
    ( ( ( ~ $true ) = $false )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14230]) ).

thf(14332,plain,
    ( ( ( ~ $false ) = $false )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14230]) ).

thf(14333,plain,
    ( ( ( ~ $true ) = $false )
    | ( $true = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14231]) ).

thf(14334,plain,
    ( ( ( ~ $false ) = $false )
    | ( $true = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14231]) ).

thf(14335,plain,
    ( ( ( ~ $true ) = $false )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14232]) ).

thf(14336,plain,
    ( ( ( ~ $false ) = $false )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14232]) ).

thf(14337,plain,
    ( ( ( ~ $true ) = $false )
    | ( $true = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14233]) ).

thf(14338,plain,
    ( ( ( ~ $false ) = $false )
    | ( $true = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14233]) ).

thf(14339,plain,
    ( ( ( ~ $true ) = $false )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14234]) ).

thf(14340,plain,
    ( ( ( ~ $false ) = $false )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14234]) ).

thf(14341,plain,
    ( ( ( ~ $false ) = $false )
    | ( $false = $false )
    | ( $false = $false )
    | ( $false = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14235]) ).

thf(14342,plain,
    ( ( ( ~ $false ) = $false )
    | ( $false = $false )
    | ( $false = $false )
    | ( $false = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14235]) ).

thf(14343,plain,
    ( ( ( ~ $false ) = $false )
    | ( $false = $false )
    | ( $false = $false )
    | ( $false = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14236]) ).

thf(14344,plain,
    ( ( ( ~ $false ) = $false )
    | ( $false = $false )
    | ( $false = $false )
    | ( $false = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14236]) ).

thf(14345,plain,
    ( ( ( ~ $false ) = $false )
    | ( $false = $false )
    | ( $false = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14237]) ).

thf(14346,plain,
    ( ( ( ~ $false ) = $false )
    | ( $false = $false )
    | ( $false = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14237]) ).

thf(14347,plain,
    ( ( ( ~ $false ) = $false )
    | ( $false = $false )
    | ( $false = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14238]) ).

thf(14348,plain,
    ( ( ( ~ $false ) = $false )
    | ( $false = $false )
    | ( $false = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14238]) ).

thf(14349,plain,
    ( ( ( ~ $false ) = $false )
    | ( $false = $false )
    | ( $true = $false )
    | ( $false = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14239]) ).

thf(14350,plain,
    ( ( ( ~ $false ) = $false )
    | ( $false = $false )
    | ( $true = $false )
    | ( $false = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14239]) ).

thf(14351,plain,
    ( ( ( ~ $false ) = $false )
    | ( $false = $false )
    | ( $true = $false )
    | ( $false = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14240]) ).

thf(14352,plain,
    ( ( ( ~ $false ) = $false )
    | ( $false = $false )
    | ( $true = $false )
    | ( $false = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14240]) ).

thf(14353,plain,
    ( ( ( ~ $false ) = $false )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14241]) ).

thf(14354,plain,
    ( ( ( ~ $false ) = $false )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14241]) ).

thf(14355,plain,
    ( ( ( ~ $false ) = $false )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14242]) ).

thf(14356,plain,
    ( ( ( ~ $false ) = $false )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14242]) ).

thf(14357,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
          | ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) ) )
        = $true )
      | ( ( SV595 = SV928 )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[14243]) ).

thf(14358,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $true )
      | ( ( SV595 = SV928 )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[14243]) ).

thf(14359,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
         != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $true )
      | ( ( ~ ( ( SV595 != SV928 )
              | ~ ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                     != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
                    | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                     != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[14245]) ).

thf(14360,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 ) )
        = $true )
      | ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
         != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $true )
      | ( ( ~ ( ( SV595 != SV928 )
              | ~ ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                     != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
                    | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                     != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[14246]) ).

thf(14361,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( SV595 != SV928 )
        = $false )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14247]) ).

thf(14362,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                 != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
                | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                 != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
        = $false )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14247]) ).

thf(14363,plain,
    ! [SV837: nat,SV597: nat,SV273: nat] :
      ( ( ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ ( sK29_SY1874 @ SV837 @ SV597 @ SV273 ) ) )
         != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ ( sK37_SY1941 @ SV837 @ SV597 @ SV273 ) ) ) )
        = $false )
      | ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
          = ( modulo_modulo_nat @ SV837 @ SV597 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[14248]) ).

thf(14364,plain,
    ! [SV966: nat,SV962: nat,SV837: nat,SV597: nat,SV273: nat] :
      ( ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
         != ( modulo_modulo_nat @ SV837 @ SV597 ) )
        = $false )
      | ( ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SV962 ) )
          = ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SV966 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14249]) ).

thf(14365,plain,
    ! [SV966: nat,SV962: nat,SV837: nat,SV597: nat,SV273: nat] :
      ( ( ( ~ ~ ! [SY1874: nat] :
                  ~ ~ ! [SY1875: nat] :
                        ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SY1874 ) )
                       != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1875 ) ) ) )
        = $false )
      | ( ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SV962 ) )
          = ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SV966 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14249]) ).

thf(14366,plain,
    ! [SV931: nat,SV844: nat,SV605: nat,SV284: nat] :
      ( ( ( ~ ~ ( ~ ( ( SV284 != SV605 ) )
                | ~ ( ( SV844 != SV931 ) ) )
          | ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
               != ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) ) ) )
        = $false )
      | ( ( SV284 = SV605 )
        = $true )
      | ( ( SV844 = SV931 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14250]) ).

thf(14367,plain,
    ! [SV931: nat,SV844: nat,SV605: nat,SV284: nat] :
      ( ( ( SV284 != SV605 )
        = $true )
      | ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14251]) ).

thf(14368,plain,
    ! [SV605: nat,SV284: nat,SV931: nat,SV844: nat] :
      ( ( ( SV844 != SV931 )
        = $true )
      | ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14252]) ).

thf(14369,plain,
    ! [SV621: nat,SV300: nat] :
      ( ( ( SV300 != one_one_nat )
        = $false )
      | ( ( SV300 = one_one_nat )
        = $false )
      | ( ( SV621 = one_one_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14253]) ).

thf(14370,plain,
    ! [SV300: nat,SV621: nat] :
      ( ( ( SV621 != one_one_nat )
        = $false )
      | ( ( SV300 = one_one_nat )
        = $false )
      | ( ( SV621 = one_one_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14253]) ).

thf(14371,plain,
    ! [SV963: nat,SV622: nat,SV936: nat] :
      ( ( ( ! [SY1919: nat] :
              ( SV936
             != ( times_times_nat @ SV622 @ SY1919 ) ) )
        = $false )
      | ( ( SV936
          = ( times_times_nat @ SV622 @ SV963 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14256]) ).

thf(14372,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
        = $true )
      | ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[14257]) ).

thf(14373,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
        = $true )
      | ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[14258]) ).

thf(14374,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
              | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
                   != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14259]) ).

thf(14375,plain,
    ! [SV303: nat,SV624: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
              | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
                   != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14260]) ).

thf(14376,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
              | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
                   != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14261]) ).

thf(14377,plain,
    ! [SV303: nat,SV624: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
              | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
                   != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14262]) ).

thf(14378,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
          | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14263]) ).

thf(14379,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
          | ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14264]) ).

thf(14380,plain,
    ! [SV626: nat,SV305: nat] :
      ( ( ( SV305 != zero_zero_nat )
        = $false )
      | ( ( SV305 = zero_zero_nat )
        = $false )
      | ( ( SV626 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14265]) ).

thf(14381,plain,
    ! [SV305: nat,SV626: nat] :
      ( ( ( SV626 != zero_zero_nat )
        = $false )
      | ( ( SV305 = zero_zero_nat )
        = $false )
      | ( ( SV626 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14265]) ).

thf(14382,plain,
    ! [SV630: nat,SV310: nat] :
      ( ( ( SV310 != zero_zero_nat )
        = $false )
      | ( ( SV310 = zero_zero_nat )
        = $false )
      | ( ( SV630 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14266]) ).

thf(14383,plain,
    ! [SV310: nat,SV630: nat] :
      ( ( ( SV630 != zero_zero_nat )
        = $false )
      | ( ( SV310 = zero_zero_nat )
        = $false )
      | ( ( SV630 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14266]) ).

thf(14384,plain,
    ! [SV631: nat,SV856: nat,SV311: nat] :
      ( ( ( ( SV311
           != ( times_times_nat @ ( sK14_SY1883 @ SV856 @ SV631 @ SV311 ) @ ( sK22_SY1936 @ SV631 @ SV856 @ SV311 ) ) )
          | ~ ( dvd_dvd_nat @ ( sK14_SY1883 @ SV856 @ SV631 @ SV311 ) @ SV631 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV311 @ ( times_times_nat @ SV631 @ SV856 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14267]) ).

thf(14385,plain,
    ! [SV937: nat,SV956: nat,SV857: nat,SV632: nat,SV312: nat] :
      ( ( ( ~ ! [SY1942: nat] :
                ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
                          | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) )
                    | ~ ( ( ( times_times_nat @ SV632 @ ( sK33_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
                          = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1942 ) @ SV312 ) )
                        | ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ ( sK33_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
                          = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SY1942 ) @ SV312 ) ) ) ) )
        = $true )
      | ( ( ( times_times_nat @ SV632 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV857 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14269]) ).

thf(14386,plain,
    ! [SV937: nat,SV956: nat,SV857: nat,SV632: nat,SV312: nat] :
      ( ( ( ~ ! [SY1943: nat] :
                ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
                          | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) )
                    | ~ ( ( ( times_times_nat @ SV632 @ ( sK34_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
                          = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1943 ) @ SV312 ) )
                        | ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ ( sK34_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
                          = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SY1943 ) @ SV312 ) ) ) ) )
        = $true )
      | ( ( ( times_times_nat @ SV857 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14270]) ).

thf(14387,plain,
    ! [SV860: nat,SV639: nat,SV319: nat > nat > $o] :
      ( ( ( ~ ! [SY1422: nat,SY1423: nat] :
                ( ~ ( SV319 @ SY1422 @ SY1423 )
                | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) ) )
        = $true )
      | ( ( SV319 @ SV639 @ SV860 )
        = $true )
      | ( ( SV319 @ ( sK35_SY1421 @ SV860 @ SV639 @ SV319 ) @ zero_zero_nat )
        = $false )
      | ( ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) )
        = $true )
      | ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[14271]) ).

thf(14388,plain,
    ! [SV860: nat,SV639: nat,SV319: nat > nat > $o] :
      ( ( ( ! [SY1421: nat] : ( SV319 @ SY1421 @ zero_zero_nat ) )
        = $false )
      | ( ( ~ ! [SY1422: nat,SY1423: nat] :
                ( ~ ( SV319 @ SY1422 @ SY1423 )
                | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) )
          | ( SV319 @ SV639 @ SV860 ) )
        = $true )
      | ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
        = $false )
      | ( ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14272]) ).

thf(14389,plain,
    ! [SV639: nat,SV860: nat,SV319: nat > nat > $o] :
      ( ( ( ~ ( SV319 @ ( sK36_SY1422 @ SV860 @ SV639 @ SV319 ) @ ( sK38_SY1944 @ SV639 @ SV860 @ SV319 ) )
          | ( SV319 @ ( sK36_SY1422 @ SV860 @ SV639 @ SV319 ) @ ( plus_plus_nat @ ( sK36_SY1422 @ SV860 @ SV639 @ SV319 ) @ ( sK38_SY1944 @ SV639 @ SV860 @ SV319 ) ) ) )
        = $false )
      | ( ( SV319 @ SV639 @ SV860 )
        = $true )
      | ( ( SV319 @ ( sK27_SY1421 @ SV860 @ SV639 @ SV319 ) @ zero_zero_nat )
        = $false )
      | ( ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
          = ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[14273]) ).

thf(14390,plain,
    ! [SV642: nat,SV322: nat] :
      ( ( ( ~ ( ( SV322 != SV642 ) )
          | ~ ( vEBT_V8194947554948674370ptions @ summary @ SV642 ) )
        = $false )
      | ( ( SV322 = SV642 )
        = $true )
      | ( ( vEBT_V8194947554948674370ptions @ summary @ SV642 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14275]) ).

thf(14391,plain,
    ! [SV964: nat,SV644: nat,SV939: nat] :
      ( ( ( ! [SY1924: nat] :
              ( SV939
             != ( plus_plus_nat @ SV644 @ SY1924 ) ) )
        = $false )
      | ( ( SV939
          = ( plus_plus_nat @ SV644 @ SV964 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14278]) ).

thf(14392,plain,
    ! [SV649: nat,SV329: nat] :
      ( ( ( SV329 != zero_zero_nat )
        = $false )
      | ( ( SV329 = zero_zero_nat )
        = $false )
      | ( ( SV649 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14279]) ).

thf(14393,plain,
    ! [SV329: nat,SV649: nat] :
      ( ( ( SV649 != zero_zero_nat )
        = $false )
      | ( ( SV329 = zero_zero_nat )
        = $false )
      | ( ( SV649 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14279]) ).

thf(14394,plain,
    ! [SV349: nat,SV669: nat] :
      ( ( ~ ( dvd_dvd_nat @ ( sK6_SY1803 @ SV669 @ SV349 ) @ SV349 )
        | ~ ( dvd_dvd_nat @ ( sK6_SY1803 @ SV669 @ SV349 ) @ SV669 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[14284]) ).

thf(14395,plain,
    ! [SV669: nat,SV349: nat] :
      ( ( ( ( times_times_nat @ SV349 @ ( sK18_SY1926 @ SV349 @ SV669 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV669 @ ( sK23_SY1937 @ SV349 @ SV669 ) ) @ ( sK6_SY1803 @ SV669 @ SV349 ) ) )
        = $true )
      | ( ( ( times_times_nat @ SV669 @ ( sK18_SY1926 @ SV349 @ SV669 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV349 @ ( sK23_SY1937 @ SV349 @ SV669 ) ) @ ( sK6_SY1803 @ SV669 @ SV349 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[14285]) ).

thf(14396,plain,
    ! [SV671: nat,SV351: nat] :
      ( ( ( SV351 != one_one_nat )
        = $false )
      | ( ( SV351 = one_one_nat )
        = $false )
      | ( ( SV671 = one_one_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14286]) ).

thf(14397,plain,
    ! [SV351: nat,SV671: nat] :
      ( ( ( SV671 != one_one_nat )
        = $false )
      | ( ( SV351 = one_one_nat )
        = $false )
      | ( ( SV671 = one_one_nat )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14286]) ).

thf(14398,plain,
    ! [SV353: nat,SV884: nat,SV673: nat,SV959: nat,SV945: nat] :
      ( ( ( SV945 = SV959 )
        = $true )
      | ( ( SV673 = SV884 )
        = $false )
      | ( ( ( plus_plus_nat @ SV673 @ ( times_times_nat @ SV353 @ SV945 ) )
         != ( plus_plus_nat @ SV884 @ ( times_times_nat @ SV353 @ SV959 ) ) )
        = $true )
      | ( ( SV353 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14287]) ).

thf(14399,plain,
    ! [SV692: option_nat,SV373: option_nat] :
      ( ( ( SV373 = none_nat )
        = $false )
      | ( ( SV373 = SV692 )
        = $true )
      | ( ( SV373 = none_nat )
        = $false )
      | ( ( SV692 = none_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14293]) ).

thf(14400,plain,
    ! [SV373: option_nat,SV692: option_nat] :
      ( ( ( SV692 != none_nat )
        = $true )
      | ( ( SV373 = SV692 )
        = $true )
      | ( ( SV373 = none_nat )
        = $false )
      | ( ( SV692 = none_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14294]) ).

thf(14401,plain,
    ! [SV965: nat,SV694: nat,SV948: nat] :
      ( ( ( ! [SY1929: nat] :
              ( SV948
             != ( plus_plus_nat @ SV694 @ SY1929 ) ) )
        = $false )
      | ( ( SV948
          = ( plus_plus_nat @ SV694 @ SV965 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14299]) ).

thf(14402,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14300]) ).

thf(14403,plain,
    ! [SV206: nat,SV540: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14301]) ).

thf(14404,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14302]) ).

thf(14405,plain,
    ! [SV206: nat,SV540: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV206 @ SV540 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14303]) ).

thf(14406,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14304]) ).

thf(14407,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
          | ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[14306]) ).

thf(14408,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[14306]) ).

thf(14409,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14307]) ).

thf(14410,plain,
    ! [SV206: nat,SV540: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14307]) ).

thf(14411,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14308]) ).

thf(14412,plain,
    ! [SV206: nat,SV540: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14308]) ).

thf(14413,plain,
    ! [SV243: $o] :
      ( ( SV243 = $true )
      | ( SV243 = $false )
      | ( SV243 = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14309]) ).

thf(14414,plain,
    ! [SV243: $o] :
      ( ( $false = $true )
      | ( SV243 = $false )
      | ( SV243 = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14310]) ).

thf(14415,plain,
    ! [SV243: $o] :
      ( ( SV243 = $true )
      | ( $false = $false )
      | ( SV243 = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14311]) ).

thf(14416,plain,
    ! [SV243: $o] :
      ( ( $false = $true )
      | ( $false = $false )
      | ( SV243 = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14312]) ).

thf(14417,plain,
    ! [SV243: $o] :
      ( ( SV243 = $true )
      | ( SV243 = $false )
      | ( SV243 = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14313]) ).

thf(14418,plain,
    ! [SV243: $o] :
      ( ( $false = $true )
      | ( SV243 = $false )
      | ( SV243 = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14314]) ).

thf(14419,plain,
    ! [SV243: $o] :
      ( ( SV243 = $true )
      | ( $false = $false )
      | ( SV243 = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14315]) ).

thf(14420,plain,
    ! [SV243: $o] :
      ( ( $false = $true )
      | ( $false = $false )
      | ( SV243 = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14316]) ).

thf(14421,plain,
    ! [SV243: $o] :
      ( ( SV243 = $true )
      | ( SV243 = $false )
      | ( $true = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14317]) ).

thf(14422,plain,
    ! [SV243: $o] :
      ( ( $false = $true )
      | ( SV243 = $false )
      | ( $true = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14318]) ).

thf(14423,plain,
    ! [SV243: $o] :
      ( ( SV243 = $true )
      | ( $false = $false )
      | ( $true = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14319]) ).

thf(14424,plain,
    ! [SV243: $o] :
      ( ( $false = $true )
      | ( $false = $false )
      | ( $true = $false )
      | ( SV243 = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14320]) ).

thf(14425,plain,
    ! [SV243: $o] :
      ( ( SV243 = $true )
      | ( SV243 = $false )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14321]) ).

thf(14426,plain,
    ! [SV243: $o] :
      ( ( $false = $true )
      | ( SV243 = $false )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14322]) ).

thf(14427,plain,
    ! [SV243: $o] :
      ( ( SV243 = $true )
      | ( $false = $false )
      | ( $true = $false )
      | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14323]) ).

thf(14428,plain,
    ( ( $false = $true )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14324]) ).

thf(14429,plain,
    ( ( $true = $true )
    | ( $true = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14325]) ).

thf(14430,plain,
    ( ( $false = $true )
    | ( $true = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14326]) ).

thf(14431,plain,
    ( ( $true = $true )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14327]) ).

thf(14432,plain,
    ( ( $false = $true )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14328]) ).

thf(14433,plain,
    ( ( $true = $true )
    | ( $true = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14329]) ).

thf(14434,plain,
    ( ( $false = $true )
    | ( $true = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14330]) ).

thf(14435,plain,
    ( ( $true = $true )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14331]) ).

thf(14436,plain,
    ( ( $false = $true )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14332]) ).

thf(14437,plain,
    ( ( $true = $true )
    | ( $true = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14333]) ).

thf(14438,plain,
    ( ( $false = $true )
    | ( $true = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14334]) ).

thf(14439,plain,
    ( ( $true = $true )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14335]) ).

thf(14440,plain,
    ( ( $false = $true )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14336]) ).

thf(14441,plain,
    ( ( $true = $true )
    | ( $true = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14337]) ).

thf(14442,plain,
    ( ( $false = $true )
    | ( $true = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14338]) ).

thf(14443,plain,
    ( ( $true = $true )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14339]) ).

thf(14444,plain,
    ( ( $false = $true )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14340]) ).

thf(14445,plain,
    ( ( $false = $true )
    | ( $false = $false )
    | ( $false = $false )
    | ( $false = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14341]) ).

thf(14446,plain,
    ( ( $false = $true )
    | ( $false = $false )
    | ( $false = $false )
    | ( $false = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14342]) ).

thf(14447,plain,
    ( ( $false = $true )
    | ( $false = $false )
    | ( $false = $false )
    | ( $false = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14343]) ).

thf(14448,plain,
    ( ( $false = $true )
    | ( $false = $false )
    | ( $false = $false )
    | ( $false = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14344]) ).

thf(14449,plain,
    ( ( $false = $true )
    | ( $false = $false )
    | ( $false = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14345]) ).

thf(14450,plain,
    ( ( $false = $true )
    | ( $false = $false )
    | ( $false = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14346]) ).

thf(14451,plain,
    ( ( $false = $true )
    | ( $false = $false )
    | ( $false = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14347]) ).

thf(14452,plain,
    ( ( $false = $true )
    | ( $false = $false )
    | ( $false = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14348]) ).

thf(14453,plain,
    ( ( $false = $true )
    | ( $false = $false )
    | ( $true = $false )
    | ( $false = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14349]) ).

thf(14454,plain,
    ( ( $false = $true )
    | ( $false = $false )
    | ( $true = $false )
    | ( $false = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14350]) ).

thf(14455,plain,
    ( ( $false = $true )
    | ( $false = $false )
    | ( $true = $false )
    | ( $false = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14351]) ).

thf(14456,plain,
    ( ( $false = $true )
    | ( $false = $false )
    | ( $true = $false )
    | ( $false = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14352]) ).

thf(14457,plain,
    ( ( $false = $true )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14353]) ).

thf(14458,plain,
    ( ( $false = $true )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14354]) ).

thf(14459,plain,
    ( ( $false = $true )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14355]) ).

thf(14460,plain,
    ( ( $false = $true )
    | ( $false = $false )
    | ( $true = $false )
    | ( $true = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14356]) ).

thf(14461,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) ) )
        = $true )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) ) )
        = $true )
      | ( ( SV595 = SV928 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[14357]) ).

thf(14462,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( ~ ( ( SV595 != SV928 )
              | ~ ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                     != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
                    | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                     != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14359]) ).

thf(14463,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
         != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $true )
      | ( ( ~ ( ( SV595 != SV928 )
              | ~ ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                     != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
                    | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                     != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14360]) ).

thf(14464,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( SV595 = SV928 )
        = $true )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14361]) ).

thf(14465,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
               != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
              | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
               != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
        = $true )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14362]) ).

thf(14466,plain,
    ! [SV837: nat,SV597: nat,SV273: nat] :
      ( ( ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ ( sK29_SY1874 @ SV837 @ SV597 @ SV273 ) ) )
          = ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ ( sK37_SY1941 @ SV837 @ SV597 @ SV273 ) ) ) )
        = $true )
      | ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
          = ( modulo_modulo_nat @ SV837 @ SV597 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14363]) ).

thf(14467,plain,
    ! [SV966: nat,SV962: nat,SV837: nat,SV597: nat,SV273: nat] :
      ( ( ( ( modulo_modulo_nat @ SV273 @ SV597 )
          = ( modulo_modulo_nat @ SV837 @ SV597 ) )
        = $true )
      | ( ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SV962 ) )
          = ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SV966 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14364]) ).

thf(14468,plain,
    ! [SV966: nat,SV962: nat,SV837: nat,SV597: nat,SV273: nat] :
      ( ( ( ~ ! [SY1874: nat] :
                ~ ~ ! [SY1875: nat] :
                      ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SY1874 ) )
                     != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1875 ) ) ) )
        = $true )
      | ( ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SV962 ) )
          = ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SV966 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14365]) ).

thf(14469,plain,
    ! [SV931: nat,SV844: nat,SV605: nat,SV284: nat] :
      ( ( ( ~ ~ ( ~ ( ( SV284 != SV605 ) )
                | ~ ( ( SV844 != SV931 ) ) ) )
        = $false )
      | ( ( SV284 = SV605 )
        = $true )
      | ( ( SV844 = SV931 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14366]) ).

thf(14470,plain,
    ! [SV931: nat,SV605: nat,SV844: nat,SV284: nat] :
      ( ( ( ~ ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
               != ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) ) ) )
        = $false )
      | ( ( SV284 = SV605 )
        = $true )
      | ( ( SV844 = SV931 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14366]) ).

thf(14471,plain,
    ! [SV931: nat,SV844: nat,SV605: nat,SV284: nat] :
      ( ( ( SV284 = SV605 )
        = $false )
      | ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14367]) ).

thf(14472,plain,
    ! [SV605: nat,SV284: nat,SV931: nat,SV844: nat] :
      ( ( ( SV844 = SV931 )
        = $false )
      | ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14368]) ).

thf(14473,plain,
    ! [SV621: nat,SV300: nat] :
      ( ( ( SV300 = one_one_nat )
        = $true )
      | ( ( SV300 = one_one_nat )
        = $false )
      | ( ( SV621 = one_one_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14369]) ).

thf(14474,plain,
    ! [SV300: nat,SV621: nat] :
      ( ( ( SV621 = one_one_nat )
        = $true )
      | ( ( SV300 = one_one_nat )
        = $false )
      | ( ( SV621 = one_one_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14370]) ).

thf(14475,plain,
    ! [SV963: nat,SV622: nat,SV936: nat] :
      ( ( ( SV936
         != ( times_times_nat @ SV622 @ ( sK39_SY1919 @ SV963 @ SV622 @ SV936 ) ) )
        = $false )
      | ( ( SV936
          = ( times_times_nat @ SV622 @ SV963 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[14371]) ).

thf(14476,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false )
      | ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14372]) ).

thf(14477,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
        = $false )
      | ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14373]) ).

thf(14478,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
              | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
                   != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14374]) ).

thf(14479,plain,
    ! [SV303: nat,SV624: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
              | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
                   != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14375]) ).

thf(14480,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
              | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
                   != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14376]) ).

thf(14481,plain,
    ! [SV303: nat,SV624: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
              | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
                   != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14377]) ).

thf(14482,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
        = $true )
      | ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[14378]) ).

thf(14483,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
        = $true )
      | ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[14379]) ).

thf(14484,plain,
    ! [SV626: nat,SV305: nat] :
      ( ( ( SV305 = zero_zero_nat )
        = $true )
      | ( ( SV305 = zero_zero_nat )
        = $false )
      | ( ( SV626 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14380]) ).

thf(14485,plain,
    ! [SV305: nat,SV626: nat] :
      ( ( ( SV626 = zero_zero_nat )
        = $true )
      | ( ( SV305 = zero_zero_nat )
        = $false )
      | ( ( SV626 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14381]) ).

thf(14486,plain,
    ! [SV630: nat,SV310: nat] :
      ( ( ( SV310 = zero_zero_nat )
        = $true )
      | ( ( SV310 = zero_zero_nat )
        = $false )
      | ( ( SV630 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14382]) ).

thf(14487,plain,
    ! [SV310: nat,SV630: nat] :
      ( ( ( SV630 = zero_zero_nat )
        = $true )
      | ( ( SV310 = zero_zero_nat )
        = $false )
      | ( ( SV630 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14383]) ).

thf(14488,plain,
    ! [SV631: nat,SV856: nat,SV311: nat] :
      ( ( ( SV311
         != ( times_times_nat @ ( sK14_SY1883 @ SV856 @ SV631 @ SV311 ) @ ( sK22_SY1936 @ SV631 @ SV856 @ SV311 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV311 @ ( times_times_nat @ SV631 @ SV856 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14384]) ).

thf(14489,plain,
    ! [SV311: nat,SV631: nat,SV856: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( sK14_SY1883 @ SV856 @ SV631 @ SV311 ) @ SV631 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV311 @ ( times_times_nat @ SV631 @ SV856 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14384]) ).

thf(14490,plain,
    ! [SV937: nat,SV956: nat,SV857: nat,SV632: nat,SV312: nat] :
      ( ( ( ! [SY1942: nat] :
              ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
                        | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) )
                  | ~ ( ( ( times_times_nat @ SV632 @ ( sK33_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
                        = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1942 ) @ SV312 ) )
                      | ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ ( sK33_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
                        = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SY1942 ) @ SV312 ) ) ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV632 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV857 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14385]) ).

thf(14491,plain,
    ! [SV937: nat,SV956: nat,SV857: nat,SV632: nat,SV312: nat] :
      ( ( ( ! [SY1943: nat] :
              ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
                        | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) )
                  | ~ ( ( ( times_times_nat @ SV632 @ ( sK34_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
                        = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ SY1943 ) @ SV312 ) )
                      | ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ ( sK34_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
                        = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SY1943 ) @ SV312 ) ) ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV857 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14386]) ).

thf(14492,plain,
    ! [SV860: nat,SV639: nat,SV319: nat > nat > $o] :
      ( ( ( ! [SY1422: nat,SY1423: nat] :
              ( ~ ( SV319 @ SY1422 @ SY1423 )
              | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) ) )
        = $false )
      | ( ( SV319 @ SV639 @ SV860 )
        = $true )
      | ( ( SV319 @ ( sK35_SY1421 @ SV860 @ SV639 @ SV319 ) @ zero_zero_nat )
        = $false )
      | ( ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) )
        = $true )
      | ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14387]) ).

thf(14493,plain,
    ! [SV639: nat,SV860: nat,SV319: nat > nat > $o] :
      ( ( ( SV319 @ ( sK40_SY1421 @ SV860 @ SV639 @ SV319 ) @ zero_zero_nat )
        = $false )
      | ( ( ~ ! [SY1422: nat,SY1423: nat] :
                ( ~ ( SV319 @ SY1422 @ SY1423 )
                | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) )
          | ( SV319 @ SV639 @ SV860 ) )
        = $true )
      | ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
        = $false )
      | ( ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[14388]) ).

thf(14494,plain,
    ! [SV639: nat,SV860: nat,SV319: nat > nat > $o] :
      ( ( ( ~ ( SV319 @ ( sK36_SY1422 @ SV860 @ SV639 @ SV319 ) @ ( sK38_SY1944 @ SV639 @ SV860 @ SV319 ) ) )
        = $false )
      | ( ( SV319 @ SV639 @ SV860 )
        = $true )
      | ( ( SV319 @ ( sK27_SY1421 @ SV860 @ SV639 @ SV319 ) @ zero_zero_nat )
        = $false )
      | ( ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
          = ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14389]) ).

thf(14495,plain,
    ! [SV639: nat,SV860: nat,SV319: nat > nat > $o] :
      ( ( ( SV319 @ ( sK36_SY1422 @ SV860 @ SV639 @ SV319 ) @ ( plus_plus_nat @ ( sK36_SY1422 @ SV860 @ SV639 @ SV319 ) @ ( sK38_SY1944 @ SV639 @ SV860 @ SV319 ) ) )
        = $false )
      | ( ( SV319 @ SV639 @ SV860 )
        = $true )
      | ( ( SV319 @ ( sK27_SY1421 @ SV860 @ SV639 @ SV319 ) @ zero_zero_nat )
        = $false )
      | ( ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
          = ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14389]) ).

thf(14496,plain,
    ! [SV642: nat,SV322: nat] :
      ( ( ( ~ ( ( SV322 != SV642 ) ) )
        = $false )
      | ( ( SV322 = SV642 )
        = $true )
      | ( ( vEBT_V8194947554948674370ptions @ summary @ SV642 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14390]) ).

thf(14497,plain,
    ! [SV322: nat,SV642: nat] :
      ( ( ( ~ ( vEBT_V8194947554948674370ptions @ summary @ SV642 ) )
        = $false )
      | ( ( SV322 = SV642 )
        = $true )
      | ( ( vEBT_V8194947554948674370ptions @ summary @ SV642 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14390]) ).

thf(14498,plain,
    ! [SV964: nat,SV644: nat,SV939: nat] :
      ( ( ( SV939
         != ( plus_plus_nat @ SV644 @ ( sK41_SY1924 @ SV964 @ SV644 @ SV939 ) ) )
        = $false )
      | ( ( SV939
          = ( plus_plus_nat @ SV644 @ SV964 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[14391]) ).

thf(14499,plain,
    ! [SV649: nat,SV329: nat] :
      ( ( ( SV329 = zero_zero_nat )
        = $true )
      | ( ( SV329 = zero_zero_nat )
        = $false )
      | ( ( SV649 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14392]) ).

thf(14500,plain,
    ! [SV329: nat,SV649: nat] :
      ( ( ( SV649 = zero_zero_nat )
        = $true )
      | ( ( SV329 = zero_zero_nat )
        = $false )
      | ( ( SV649 = zero_zero_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14393]) ).

thf(14501,plain,
    ! [SV349: nat,SV669: nat] :
      ( ( ~ ( dvd_dvd_nat @ ( sK6_SY1803 @ SV669 @ SV349 ) @ SV349 ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[14394]) ).

thf(14502,plain,
    ! [SV349: nat,SV669: nat] :
      ( ( ~ ( dvd_dvd_nat @ ( sK6_SY1803 @ SV669 @ SV349 ) @ SV669 ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[14394]) ).

thf(14503,plain,
    ! [SV671: nat,SV351: nat] :
      ( ( ( SV351 = one_one_nat )
        = $true )
      | ( ( SV351 = one_one_nat )
        = $false )
      | ( ( SV671 = one_one_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14396]) ).

thf(14504,plain,
    ! [SV351: nat,SV671: nat] :
      ( ( ( SV671 = one_one_nat )
        = $true )
      | ( ( SV351 = one_one_nat )
        = $false )
      | ( ( SV671 = one_one_nat )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14397]) ).

thf(14505,plain,
    ! [SV959: nat,SV884: nat,SV945: nat,SV353: nat,SV673: nat] :
      ( ( ( ( plus_plus_nat @ SV673 @ ( times_times_nat @ SV353 @ SV945 ) )
          = ( plus_plus_nat @ SV884 @ ( times_times_nat @ SV353 @ SV959 ) ) )
        = $false )
      | ( ( SV673 = SV884 )
        = $false )
      | ( ( SV945 = SV959 )
        = $true )
      | ( ( SV353 = zero_zero_nat )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14398]) ).

thf(14506,plain,
    ! [SV373: option_nat,SV692: option_nat] :
      ( ( ( SV692 = none_nat )
        = $false )
      | ( ( SV373 = SV692 )
        = $true )
      | ( ( SV373 = none_nat )
        = $false )
      | ( ( SV692 = none_nat )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14400]) ).

thf(14507,plain,
    ! [SV965: nat,SV694: nat,SV948: nat] :
      ( ( ( SV948
         != ( plus_plus_nat @ SV694 @ ( sK42_SY1929 @ SV965 @ SV694 @ SV948 ) ) )
        = $false )
      | ( ( SV948
          = ( plus_plus_nat @ SV694 @ SV965 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[14401]) ).

thf(14508,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14406]) ).

thf(14509,plain,
    ! [SV206: nat,SV540: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14406]) ).

thf(14510,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $true )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[14407]) ).

thf(14511,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14409]) ).

thf(14512,plain,
    ! [SV206: nat,SV540: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14410]) ).

thf(14513,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14411]) ).

thf(14514,plain,
    ! [SV206: nat,SV540: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14412]) ).

thf(14515,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) ) )
        = $true )
      | ( ( SV595 = SV928 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14461]) ).

thf(14516,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( SV595 != SV928 )
          | ~ ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                 != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
                | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                 != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14462]) ).

thf(14517,plain,
    ! [SV595: nat,SV928: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
         != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $true )
      | ( ( ~ ( ( SV595 != SV928 )
              | ~ ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                     != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
                    | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                     != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14463]) ).

thf(14518,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
           != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
          | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
           != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
        = $false )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14465]) ).

thf(14519,plain,
    ! [SV966: nat,SV962: nat,SV837: nat,SV597: nat,SV273: nat] :
      ( ( ( ! [SY1874: nat] :
              ~ ~ ! [SY1875: nat] :
                    ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SY1874 ) )
                   != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1875 ) ) ) )
        = $false )
      | ( ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SV962 ) )
          = ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SV966 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14468]) ).

thf(14520,plain,
    ! [SV931: nat,SV844: nat,SV605: nat,SV284: nat] :
      ( ( ( ~ ( ~ ( ( SV284 != SV605 ) )
              | ~ ( ( SV844 != SV931 ) ) ) )
        = $true )
      | ( ( SV284 = SV605 )
        = $true )
      | ( ( SV844 = SV931 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14469]) ).

thf(14521,plain,
    ! [SV931: nat,SV605: nat,SV844: nat,SV284: nat] :
      ( ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
         != ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) )
        = $true )
      | ( ( SV284 = SV605 )
        = $true )
      | ( ( SV844 = SV931 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14470]) ).

thf(14522,plain,
    ! [SV963: nat,SV622: nat,SV936: nat] :
      ( ( ( SV936
          = ( times_times_nat @ SV622 @ ( sK39_SY1919 @ SV963 @ SV622 @ SV936 ) ) )
        = $true )
      | ( ( SV936
          = ( times_times_nat @ SV622 @ SV963 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14475]) ).

thf(14523,plain,
    ! [SV303: nat,SV624: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14476]) ).

thf(14524,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14477]) ).

thf(14525,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
          | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
               != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14478]) ).

thf(14526,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
          | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
               != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14479]) ).

thf(14527,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
          | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
               != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14480]) ).

thf(14528,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
          | ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
               != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14481]) ).

thf(14529,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false )
      | ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14482]) ).

thf(14530,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
        = $false )
      | ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14483]) ).

thf(14531,plain,
    ! [SV631: nat,SV856: nat,SV311: nat] :
      ( ( ( SV311
          = ( times_times_nat @ ( sK14_SY1883 @ SV856 @ SV631 @ SV311 ) @ ( sK22_SY1936 @ SV631 @ SV856 @ SV311 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ SV311 @ ( times_times_nat @ SV631 @ SV856 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14488]) ).

thf(14532,plain,
    ! [SV311: nat,SV631: nat,SV856: nat] :
      ( ( ( dvd_dvd_nat @ ( sK14_SY1883 @ SV856 @ SV631 @ SV311 ) @ SV631 )
        = $true )
      | ( ( dvd_dvd_nat @ SV311 @ ( times_times_nat @ SV631 @ SV856 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14489]) ).

thf(14533,plain,
    ! [SV937: nat,SV956: nat,SV857: nat,SV632: nat,SV312: nat] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
                      | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) )
                | ~ ( ( ( times_times_nat @ SV632 @ ( sK33_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
                      = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ ( sK43_SY1942 @ SV937 @ SV956 @ SV857 @ SV632 @ SV312 ) ) @ SV312 ) )
                    | ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ ( sK33_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
                      = ( plus_plus_nat @ ( times_times_nat @ SV632 @ ( sK43_SY1942 @ SV937 @ SV956 @ SV857 @ SV632 @ SV312 ) ) @ SV312 ) ) ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV632 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV857 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[14490]) ).

thf(14534,plain,
    ! [SV937: nat,SV956: nat,SV857: nat,SV632: nat,SV312: nat] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
                      | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) )
                | ~ ( ( ( times_times_nat @ SV632 @ ( sK34_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
                      = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ ( sK44_SY1943 @ SV937 @ SV956 @ SV857 @ SV632 @ SV312 ) ) @ SV312 ) )
                    | ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ ( sK34_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
                      = ( plus_plus_nat @ ( times_times_nat @ SV632 @ ( sK44_SY1943 @ SV937 @ SV956 @ SV857 @ SV632 @ SV312 ) ) @ SV312 ) ) ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV857 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[14491]) ).

thf(14535,plain,
    ! [SV639: nat,SV860: nat,SV319: nat > nat > $o] :
      ( ( ( ! [SY1945: nat] :
              ( ~ ( SV319 @ ( sK45_SY1422 @ SV860 @ SV639 @ SV319 ) @ SY1945 )
              | ( SV319 @ ( sK45_SY1422 @ SV860 @ SV639 @ SV319 ) @ ( plus_plus_nat @ ( sK45_SY1422 @ SV860 @ SV639 @ SV319 ) @ SY1945 ) ) ) )
        = $false )
      | ( ( SV319 @ SV639 @ SV860 )
        = $true )
      | ( ( SV319 @ ( sK35_SY1421 @ SV860 @ SV639 @ SV319 ) @ zero_zero_nat )
        = $false )
      | ( ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) )
        = $true )
      | ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[14492]) ).

thf(14536,plain,
    ! [SV860: nat,SV639: nat,SV319: nat > nat > $o] :
      ( ( ( ~ ! [SY1422: nat,SY1423: nat] :
                ( ~ ( SV319 @ SY1422 @ SY1423 )
                | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) ) )
        = $true )
      | ( ( SV319 @ SV639 @ SV860 )
        = $true )
      | ( ( SV319 @ ( sK40_SY1421 @ SV860 @ SV639 @ SV319 ) @ zero_zero_nat )
        = $false )
      | ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
        = $false )
      | ( ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[14493]) ).

thf(14537,plain,
    ! [SV639: nat,SV860: nat,SV319: nat > nat > $o] :
      ( ( ( SV319 @ ( sK36_SY1422 @ SV860 @ SV639 @ SV319 ) @ ( sK38_SY1944 @ SV639 @ SV860 @ SV319 ) )
        = $true )
      | ( ( SV319 @ SV639 @ SV860 )
        = $true )
      | ( ( SV319 @ ( sK27_SY1421 @ SV860 @ SV639 @ SV319 ) @ zero_zero_nat )
        = $false )
      | ( ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
          = ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14494]) ).

thf(14538,plain,
    ! [SV642: nat,SV322: nat] :
      ( ( ( SV322 != SV642 )
        = $true )
      | ( ( SV322 = SV642 )
        = $true )
      | ( ( vEBT_V8194947554948674370ptions @ summary @ SV642 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14496]) ).

thf(14539,plain,
    ! [SV322: nat,SV642: nat] :
      ( ( ( vEBT_V8194947554948674370ptions @ summary @ SV642 )
        = $true )
      | ( ( SV322 = SV642 )
        = $true )
      | ( ( vEBT_V8194947554948674370ptions @ summary @ SV642 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14497]) ).

thf(14540,plain,
    ! [SV964: nat,SV644: nat,SV939: nat] :
      ( ( ( SV939
          = ( plus_plus_nat @ SV644 @ ( sK41_SY1924 @ SV964 @ SV644 @ SV939 ) ) )
        = $true )
      | ( ( SV939
          = ( plus_plus_nat @ SV644 @ SV964 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14498]) ).

thf(14541,plain,
    ! [SV349: nat,SV669: nat] :
      ( ( dvd_dvd_nat @ ( sK6_SY1803 @ SV669 @ SV349 ) @ SV349 )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[14501]) ).

thf(14542,plain,
    ! [SV349: nat,SV669: nat] :
      ( ( dvd_dvd_nat @ ( sK6_SY1803 @ SV669 @ SV349 ) @ SV669 )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[14502]) ).

thf(14543,plain,
    ! [SV965: nat,SV694: nat,SV948: nat] :
      ( ( ( SV948
          = ( plus_plus_nat @ SV694 @ ( sK42_SY1929 @ SV965 @ SV694 @ SV948 ) ) )
        = $true )
      | ( ( SV948
          = ( plus_plus_nat @ SV694 @ SV965 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14507]) ).

thf(14544,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14508]) ).

thf(14545,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14509]) ).

thf(14546,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14510]) ).

thf(14547,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) ) )
        = $true )
      | ( ( SV595 = SV928 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14515]) ).

thf(14548,plain,
    ! [SV595: nat,SV928: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) ) )
        = $true )
      | ( ( SV595 = SV928 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14515]) ).

thf(14549,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( SV595 != SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14516]) ).

thf(14550,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                 != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
                | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                 != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14516]) ).

thf(14551,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( ~ ( ( SV595 != SV928 )
              | ~ ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                     != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
                    | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                     != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14517]) ).

thf(14552,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
         != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14518]) ).

thf(14553,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
         != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14518]) ).

thf(14554,plain,
    ! [SV837: nat,SV962: nat,SV966: nat,SV597: nat,SV273: nat] :
      ( ( ( ~ ~ ! [SY1946: nat] :
                  ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ ( sK46_SY1874 @ SV966 @ SV962 @ SV837 @ SV597 @ SV273 ) ) )
                 != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1946 ) ) ) )
        = $false )
      | ( ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SV962 ) )
          = ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SV966 ) ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[14519]) ).

thf(14555,plain,
    ! [SV931: nat,SV844: nat,SV605: nat,SV284: nat] :
      ( ( ( ~ ( ( SV284 != SV605 ) )
          | ~ ( ( SV844 != SV931 ) ) )
        = $false )
      | ( ( SV284 = SV605 )
        = $true )
      | ( ( SV844 = SV931 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14520]) ).

thf(14556,plain,
    ! [SV931: nat,SV605: nat,SV844: nat,SV284: nat] :
      ( ( ( ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV844 ) @ ( times_times_nat @ SV605 @ SV931 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV284 @ SV931 ) @ ( times_times_nat @ SV605 @ SV844 ) ) )
        = $false )
      | ( ( SV284 = SV605 )
        = $true )
      | ( ( SV844 = SV931 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14521]) ).

thf(14557,plain,
    ! [SV303: nat,SV624: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14524]) ).

thf(14558,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14525]) ).

thf(14559,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
               != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14525]) ).

thf(14560,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14526]) ).

thf(14561,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
               != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14526]) ).

thf(14562,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14527]) ).

thf(14563,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
               != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14527]) ).

thf(14564,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14528]) ).

thf(14565,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
               != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14528]) ).

thf(14566,plain,
    ! [SV303: nat,SV624: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false )
      | ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14529]) ).

thf(14567,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14530]) ).

thf(14568,plain,
    ! [SV937: nat,SV956: nat,SV857: nat,SV632: nat,SV312: nat] :
      ( ( ( ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
                    | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) )
              | ~ ( ( ( times_times_nat @ SV632 @ ( sK33_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
                    = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ ( sK43_SY1942 @ SV937 @ SV956 @ SV857 @ SV632 @ SV312 ) ) @ SV312 ) )
                  | ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ ( sK33_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
                    = ( plus_plus_nat @ ( times_times_nat @ SV632 @ ( sK43_SY1942 @ SV937 @ SV956 @ SV857 @ SV632 @ SV312 ) ) @ SV312 ) ) ) ) )
        = $true )
      | ( ( ( times_times_nat @ SV632 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV857 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14533]) ).

thf(14569,plain,
    ! [SV937: nat,SV956: nat,SV857: nat,SV632: nat,SV312: nat] :
      ( ( ( ~ ( ~ ~ ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
                    | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) )
              | ~ ( ( ( times_times_nat @ SV632 @ ( sK34_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
                    = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ ( sK44_SY1943 @ SV937 @ SV956 @ SV857 @ SV632 @ SV312 ) ) @ SV312 ) )
                  | ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ ( sK34_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
                    = ( plus_plus_nat @ ( times_times_nat @ SV632 @ ( sK44_SY1943 @ SV937 @ SV956 @ SV857 @ SV632 @ SV312 ) ) @ SV312 ) ) ) ) )
        = $true )
      | ( ( ( times_times_nat @ SV857 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14534]) ).

thf(14570,plain,
    ! [SV639: nat,SV860: nat,SV319: nat > nat > $o] :
      ( ( ( ~ ( SV319 @ ( sK45_SY1422 @ SV860 @ SV639 @ SV319 ) @ ( sK47_SY1945 @ SV639 @ SV860 @ SV319 ) )
          | ( SV319 @ ( sK45_SY1422 @ SV860 @ SV639 @ SV319 ) @ ( plus_plus_nat @ ( sK45_SY1422 @ SV860 @ SV639 @ SV319 ) @ ( sK47_SY1945 @ SV639 @ SV860 @ SV319 ) ) ) )
        = $false )
      | ( ( SV319 @ SV639 @ SV860 )
        = $true )
      | ( ( SV319 @ ( sK35_SY1421 @ SV860 @ SV639 @ SV319 ) @ zero_zero_nat )
        = $false )
      | ( ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) )
        = $true )
      | ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[14535]) ).

thf(14571,plain,
    ! [SV860: nat,SV639: nat,SV319: nat > nat > $o] :
      ( ( ( ! [SY1422: nat,SY1423: nat] :
              ( ~ ( SV319 @ SY1422 @ SY1423 )
              | ( SV319 @ SY1422 @ ( plus_plus_nat @ SY1422 @ SY1423 ) ) ) )
        = $false )
      | ( ( SV319 @ SV639 @ SV860 )
        = $true )
      | ( ( SV319 @ ( sK40_SY1421 @ SV860 @ SV639 @ SV319 ) @ zero_zero_nat )
        = $false )
      | ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
        = $false )
      | ( ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14536]) ).

thf(14572,plain,
    ! [SV642: nat,SV322: nat] :
      ( ( ( SV322 = SV642 )
        = $false )
      | ( ( SV322 = SV642 )
        = $true )
      | ( ( vEBT_V8194947554948674370ptions @ summary @ SV642 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14538]) ).

thf(14573,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14544]) ).

thf(14574,plain,
    ! [SV206: nat,SV540: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14544]) ).

thf(14575,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14545]) ).

thf(14576,plain,
    ! [SV206: nat,SV540: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14545]) ).

thf(14577,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14546]) ).

thf(14578,plain,
    ! [SV206: nat,SV540: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14546]) ).

thf(14579,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( SV595 = SV928 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14547]) ).

thf(14580,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( SV595 = SV928 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14548]) ).

thf(14581,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( SV595 = SV928 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14549]) ).

thf(14582,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
               != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
              | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
               != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14550]) ).

thf(14583,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( SV595 != SV928 )
          | ~ ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                 != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
                | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                 != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14551]) ).

thf(14584,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $true )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14552]) ).

thf(14585,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $true )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14553]) ).

thf(14586,plain,
    ! [SV837: nat,SV962: nat,SV966: nat,SV597: nat,SV273: nat] :
      ( ( ( ~ ! [SY1946: nat] :
                ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ ( sK46_SY1874 @ SV966 @ SV962 @ SV837 @ SV597 @ SV273 ) ) )
               != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1946 ) ) ) )
        = $true )
      | ( ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SV962 ) )
          = ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SV966 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14554]) ).

thf(14587,plain,
    ! [SV931: nat,SV844: nat,SV605: nat,SV284: nat] :
      ( ( ( ~ ( ( SV284 != SV605 ) ) )
        = $false )
      | ( ( SV284 = SV605 )
        = $true )
      | ( ( SV844 = SV931 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14555]) ).

thf(14588,plain,
    ! [SV605: nat,SV284: nat,SV931: nat,SV844: nat] :
      ( ( ( ~ ( ( SV844 != SV931 ) ) )
        = $false )
      | ( ( SV284 = SV605 )
        = $true )
      | ( ( SV844 = SV931 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14555]) ).

thf(14589,plain,
    ! [SV303: nat,SV624: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14557]) ).

thf(14590,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14558]) ).

thf(14591,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
         != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14559]) ).

thf(14592,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14560]) ).

thf(14593,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
         != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14561]) ).

thf(14594,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14562]) ).

thf(14595,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
         != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14563]) ).

thf(14596,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14564]) ).

thf(14597,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
         != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14565]) ).

thf(14598,plain,
    ! [SV303: nat,SV624: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14567]) ).

thf(14599,plain,
    ! [SV937: nat,SV956: nat,SV857: nat,SV632: nat,SV312: nat] :
      ( ( ( ~ ~ ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
                | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) )
          | ~ ( ( ( times_times_nat @ SV632 @ ( sK33_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
                = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ ( sK43_SY1942 @ SV937 @ SV956 @ SV857 @ SV632 @ SV312 ) ) @ SV312 ) )
              | ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ ( sK33_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
                = ( plus_plus_nat @ ( times_times_nat @ SV632 @ ( sK43_SY1942 @ SV937 @ SV956 @ SV857 @ SV632 @ SV312 ) ) @ SV312 ) ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV632 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV857 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14568]) ).

thf(14600,plain,
    ! [SV937: nat,SV956: nat,SV857: nat,SV632: nat,SV312: nat] :
      ( ( ( ~ ~ ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
                | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) )
          | ~ ( ( ( times_times_nat @ SV632 @ ( sK34_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
                = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ ( sK44_SY1943 @ SV937 @ SV956 @ SV857 @ SV632 @ SV312 ) ) @ SV312 ) )
              | ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ ( sK34_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
                = ( plus_plus_nat @ ( times_times_nat @ SV632 @ ( sK44_SY1943 @ SV937 @ SV956 @ SV857 @ SV632 @ SV312 ) ) @ SV312 ) ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV857 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14569]) ).

thf(14601,plain,
    ! [SV639: nat,SV860: nat,SV319: nat > nat > $o] :
      ( ( ( ~ ( SV319 @ ( sK45_SY1422 @ SV860 @ SV639 @ SV319 ) @ ( sK47_SY1945 @ SV639 @ SV860 @ SV319 ) ) )
        = $false )
      | ( ( SV319 @ SV639 @ SV860 )
        = $true )
      | ( ( SV319 @ ( sK35_SY1421 @ SV860 @ SV639 @ SV319 ) @ zero_zero_nat )
        = $false )
      | ( ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) )
        = $true )
      | ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14570]) ).

thf(14602,plain,
    ! [SV639: nat,SV860: nat,SV319: nat > nat > $o] :
      ( ( ( SV319 @ ( sK45_SY1422 @ SV860 @ SV639 @ SV319 ) @ ( plus_plus_nat @ ( sK45_SY1422 @ SV860 @ SV639 @ SV319 ) @ ( sK47_SY1945 @ SV639 @ SV860 @ SV319 ) ) )
        = $false )
      | ( ( SV319 @ SV639 @ SV860 )
        = $true )
      | ( ( SV319 @ ( sK35_SY1421 @ SV860 @ SV639 @ SV319 ) @ zero_zero_nat )
        = $false )
      | ( ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) )
        = $true )
      | ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[14570]) ).

thf(14603,plain,
    ! [SV639: nat,SV860: nat,SV319: nat > nat > $o] :
      ( ( ( ! [SY1947: nat] :
              ( ~ ( SV319 @ ( sK48_SY1422 @ SV860 @ SV639 @ SV319 ) @ SY1947 )
              | ( SV319 @ ( sK48_SY1422 @ SV860 @ SV639 @ SV319 ) @ ( plus_plus_nat @ ( sK48_SY1422 @ SV860 @ SV639 @ SV319 ) @ SY1947 ) ) ) )
        = $false )
      | ( ( SV319 @ SV639 @ SV860 )
        = $true )
      | ( ( SV319 @ ( sK40_SY1421 @ SV860 @ SV639 @ SV319 ) @ zero_zero_nat )
        = $false )
      | ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
        = $false )
      | ( ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[14571]) ).

thf(14604,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14573]) ).

thf(14605,plain,
    ! [SV206: nat,SV540: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14574]) ).

thf(14606,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14575]) ).

thf(14607,plain,
    ! [SV206: nat,SV540: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14576]) ).

thf(14608,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14577]) ).

thf(14609,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
          | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14578]) ).

thf(14610,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( SV595 = SV928 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14579]) ).

thf(14611,plain,
    ! [SV595: nat,SV928: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( SV595 = SV928 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14579]) ).

thf(14612,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( SV595 = SV928 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14580]) ).

thf(14613,plain,
    ! [SV595: nat,SV928: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( SV595 = SV928 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14580]) ).

thf(14614,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
           != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
          | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
           != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14582]) ).

thf(14615,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( SV595 != SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14583]) ).

thf(14616,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
                 != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
                | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
                 != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14583]) ).

thf(14617,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
          | ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) ) )
        = $true )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[14584]) ).

thf(14618,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $true )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[14584]) ).

thf(14619,plain,
    ! [SV837: nat,SV962: nat,SV966: nat,SV597: nat,SV273: nat] :
      ( ( ( ! [SY1946: nat] :
              ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ ( sK46_SY1874 @ SV966 @ SV962 @ SV837 @ SV597 @ SV273 ) ) )
             != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SY1946 ) ) ) )
        = $false )
      | ( ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SV962 ) )
          = ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SV966 ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14586]) ).

thf(14620,plain,
    ! [SV931: nat,SV844: nat,SV605: nat,SV284: nat] :
      ( ( ( SV284 != SV605 )
        = $true )
      | ( ( SV284 = SV605 )
        = $true )
      | ( ( SV844 = SV931 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14587]) ).

thf(14621,plain,
    ! [SV605: nat,SV284: nat,SV931: nat,SV844: nat] :
      ( ( ( SV844 != SV931 )
        = $true )
      | ( ( SV284 = SV605 )
        = $true )
      | ( ( SV844 = SV931 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14588]) ).

thf(14622,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14590]) ).

thf(14623,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14591]) ).

thf(14624,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14592]) ).

thf(14625,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14593]) ).

thf(14626,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14594]) ).

thf(14627,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14595]) ).

thf(14628,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ SV303 @ SV624 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14596]) ).

thf(14629,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14597]) ).

thf(14630,plain,
    ! [SV303: nat,SV624: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14598]) ).

thf(14631,plain,
    ! [SV956: nat,SV937: nat,SV857: nat,SV632: nat,SV312: nat] :
      ( ( ( ~ ~ ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
                | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV632 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV857 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14599]) ).

thf(14632,plain,
    ! [SV312: nat,SV857: nat,SV937: nat,SV956: nat,SV632: nat] :
      ( ( ( ~ ( ( ( times_times_nat @ SV632 @ ( sK33_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
                = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ ( sK43_SY1942 @ SV937 @ SV956 @ SV857 @ SV632 @ SV312 ) ) @ SV312 ) )
              | ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ ( sK33_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
                = ( plus_plus_nat @ ( times_times_nat @ SV632 @ ( sK43_SY1942 @ SV937 @ SV956 @ SV857 @ SV632 @ SV312 ) ) @ SV312 ) ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV632 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV857 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14599]) ).

thf(14633,plain,
    ! [SV956: nat,SV937: nat,SV857: nat,SV632: nat,SV312: nat] :
      ( ( ( ~ ~ ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
                | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV857 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14600]) ).

thf(14634,plain,
    ! [SV312: nat,SV857: nat,SV937: nat,SV956: nat,SV632: nat] :
      ( ( ( ~ ( ( ( times_times_nat @ SV632 @ ( sK34_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
                = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ ( sK44_SY1943 @ SV937 @ SV956 @ SV857 @ SV632 @ SV312 ) ) @ SV312 ) )
              | ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ ( sK34_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
                = ( plus_plus_nat @ ( times_times_nat @ SV632 @ ( sK44_SY1943 @ SV937 @ SV956 @ SV857 @ SV632 @ SV312 ) ) @ SV312 ) ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV857 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14600]) ).

thf(14635,plain,
    ! [SV639: nat,SV860: nat,SV319: nat > nat > $o] :
      ( ( ( SV319 @ ( sK45_SY1422 @ SV860 @ SV639 @ SV319 ) @ ( sK47_SY1945 @ SV639 @ SV860 @ SV319 ) )
        = $true )
      | ( ( SV319 @ SV639 @ SV860 )
        = $true )
      | ( ( SV319 @ ( sK35_SY1421 @ SV860 @ SV639 @ SV319 ) @ zero_zero_nat )
        = $false )
      | ( ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) )
        = $true )
      | ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[14601]) ).

thf(14636,plain,
    ! [SV639: nat,SV860: nat,SV319: nat > nat > $o] :
      ( ( ( ~ ( SV319 @ ( sK48_SY1422 @ SV860 @ SV639 @ SV319 ) @ ( sK49_SY1947 @ SV639 @ SV860 @ SV319 ) )
          | ( SV319 @ ( sK48_SY1422 @ SV860 @ SV639 @ SV319 ) @ ( plus_plus_nat @ ( sK48_SY1422 @ SV860 @ SV639 @ SV319 ) @ ( sK49_SY1947 @ SV639 @ SV860 @ SV319 ) ) ) )
        = $false )
      | ( ( SV319 @ SV639 @ SV860 )
        = $true )
      | ( ( SV319 @ ( sK40_SY1421 @ SV860 @ SV639 @ SV319 ) @ zero_zero_nat )
        = $false )
      | ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
        = $false )
      | ( ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[14603]) ).

thf(14637,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14608]) ).

thf(14638,plain,
    ! [SV206: nat,SV540: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14608]) ).

thf(14639,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14609]) ).

thf(14640,plain,
    ! [SV206: nat,SV540: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14609]) ).

thf(14641,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( SV595 = SV928 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14610]) ).

thf(14642,plain,
    ! [SV595: nat,SV928: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( SV595 = SV928 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14611]) ).

thf(14643,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( SV595 = SV928 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14612]) ).

thf(14644,plain,
    ! [SV595: nat,SV928: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( SV595 = SV928 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14613]) ).

thf(14645,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
         != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14614]) ).

thf(14646,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
         != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14614]) ).

thf(14647,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( SV595 = SV928 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14615]) ).

thf(14648,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
               != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
              | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
               != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14616]) ).

thf(14649,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) ) )
        = $true )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) ) )
        = $true )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[14617]) ).

thf(14650,plain,
    ! [SV837: nat,SV962: nat,SV966: nat,SV597: nat,SV273: nat] :
      ( ( ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ ( sK46_SY1874 @ SV966 @ SV962 @ SV837 @ SV597 @ SV273 ) ) )
         != ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ ( sK50_SY1946 @ SV837 @ SV962 @ SV966 @ SV597 @ SV273 ) ) ) )
        = $false )
      | ( ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SV962 ) )
          = ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SV966 ) ) )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[14619]) ).

thf(14651,plain,
    ! [SV931: nat,SV844: nat,SV605: nat,SV284: nat] :
      ( ( ( SV284 = SV605 )
        = $false )
      | ( ( SV284 = SV605 )
        = $true )
      | ( ( SV844 = SV931 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14620]) ).

thf(14652,plain,
    ! [SV605: nat,SV284: nat,SV931: nat,SV844: nat] :
      ( ( ( SV844 = SV931 )
        = $false )
      | ( ( SV284 = SV605 )
        = $true )
      | ( ( SV844 = SV931 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[14621]) ).

thf(14653,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
          | ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_equal_neg,[status(thm)],[14623]) ).

thf(14654,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_equal_neg,[status(thm)],[14623]) ).

thf(14655,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
          | ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_equal_neg,[status(thm)],[14625]) ).

thf(14656,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_equal_neg,[status(thm)],[14625]) ).

thf(14657,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
          | ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_equal_neg,[status(thm)],[14627]) ).

thf(14658,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_equal_neg,[status(thm)],[14627]) ).

thf(14659,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
          | ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_equal_neg,[status(thm)],[14629]) ).

thf(14660,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
          = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_equal_neg,[status(thm)],[14629]) ).

thf(14661,plain,
    ! [SV956: nat,SV937: nat,SV857: nat,SV632: nat,SV312: nat] :
      ( ( ( ~ ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
              | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) ) )
        = $true )
      | ( ( ( times_times_nat @ SV632 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV857 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14631]) ).

thf(14662,plain,
    ! [SV312: nat,SV857: nat,SV937: nat,SV956: nat,SV632: nat] :
      ( ( ( ( ( times_times_nat @ SV632 @ ( sK33_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
            = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ ( sK43_SY1942 @ SV937 @ SV956 @ SV857 @ SV632 @ SV312 ) ) @ SV312 ) )
          | ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ ( sK33_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
            = ( plus_plus_nat @ ( times_times_nat @ SV632 @ ( sK43_SY1942 @ SV937 @ SV956 @ SV857 @ SV632 @ SV312 ) ) @ SV312 ) ) )
        = $true )
      | ( ( ( times_times_nat @ SV632 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV857 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14632]) ).

thf(14663,plain,
    ! [SV956: nat,SV937: nat,SV857: nat,SV632: nat,SV312: nat] :
      ( ( ( ~ ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
              | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) ) )
        = $true )
      | ( ( ( times_times_nat @ SV857 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14633]) ).

thf(14664,plain,
    ! [SV312: nat,SV857: nat,SV937: nat,SV956: nat,SV632: nat] :
      ( ( ( ( ( times_times_nat @ SV632 @ ( sK34_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
            = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ ( sK44_SY1943 @ SV937 @ SV956 @ SV857 @ SV632 @ SV312 ) ) @ SV312 ) )
          | ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ ( sK34_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
            = ( plus_plus_nat @ ( times_times_nat @ SV632 @ ( sK44_SY1943 @ SV937 @ SV956 @ SV857 @ SV632 @ SV312 ) ) @ SV312 ) ) )
        = $true )
      | ( ( ( times_times_nat @ SV857 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14634]) ).

thf(14665,plain,
    ! [SV639: nat,SV860: nat,SV319: nat > nat > $o] :
      ( ( ( ~ ( SV319 @ ( sK48_SY1422 @ SV860 @ SV639 @ SV319 ) @ ( sK49_SY1947 @ SV639 @ SV860 @ SV319 ) ) )
        = $false )
      | ( ( SV319 @ SV639 @ SV860 )
        = $true )
      | ( ( SV319 @ ( sK40_SY1421 @ SV860 @ SV639 @ SV319 ) @ zero_zero_nat )
        = $false )
      | ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
        = $false )
      | ( ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14636]) ).

thf(14666,plain,
    ! [SV639: nat,SV860: nat,SV319: nat > nat > $o] :
      ( ( ( SV319 @ ( sK48_SY1422 @ SV860 @ SV639 @ SV319 ) @ ( plus_plus_nat @ ( sK48_SY1422 @ SV860 @ SV639 @ SV319 ) @ ( sK49_SY1947 @ SV639 @ SV860 @ SV319 ) ) )
        = $false )
      | ( ( SV319 @ SV639 @ SV860 )
        = $true )
      | ( ( SV319 @ ( sK40_SY1421 @ SV860 @ SV639 @ SV319 ) @ zero_zero_nat )
        = $false )
      | ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
        = $false )
      | ( ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14636]) ).

thf(14667,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14637]) ).

thf(14668,plain,
    ! [SV206: nat,SV540: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14638]) ).

thf(14669,plain,
    ! [SV540: nat,SV206: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14639]) ).

thf(14670,plain,
    ! [SV206: nat,SV540: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV206 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV540 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14640]) ).

thf(14671,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14645]) ).

thf(14672,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14646]) ).

thf(14673,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
           != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
          | ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
           != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14648]) ).

thf(14674,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) ) )
        = $true )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14649]) ).

thf(14675,plain,
    ! [SV837: nat,SV962: nat,SV966: nat,SV597: nat,SV273: nat] :
      ( ( ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ ( sK46_SY1874 @ SV966 @ SV962 @ SV837 @ SV597 @ SV273 ) ) )
          = ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ ( sK50_SY1946 @ SV837 @ SV962 @ SV966 @ SV597 @ SV273 ) ) ) )
        = $true )
      | ( ( ( plus_plus_nat @ SV273 @ ( times_times_nat @ SV597 @ SV962 ) )
          = ( plus_plus_nat @ SV837 @ ( times_times_nat @ SV597 @ SV966 ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14650]) ).

thf(14676,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14653]) ).

thf(14677,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14653]) ).

thf(14678,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14655]) ).

thf(14679,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14655]) ).

thf(14680,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14657]) ).

thf(14681,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14657]) ).

thf(14682,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14659]) ).

thf(14683,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
              | ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14659]) ).

thf(14684,plain,
    ! [SV956: nat,SV937: nat,SV857: nat,SV632: nat,SV312: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
          | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV632 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV857 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14661]) ).

thf(14685,plain,
    ! [SV312: nat,SV857: nat,SV937: nat,SV956: nat,SV632: nat] :
      ( ( ( ( times_times_nat @ SV632 @ ( sK33_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
          = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ ( sK43_SY1942 @ SV937 @ SV956 @ SV857 @ SV632 @ SV312 ) ) @ SV312 ) )
        = $true )
      | ( ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ ( sK33_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV632 @ ( sK43_SY1942 @ SV937 @ SV956 @ SV857 @ SV632 @ SV312 ) ) @ SV312 ) )
        = $true )
      | ( ( ( times_times_nat @ SV632 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV857 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[14662]) ).

thf(14686,plain,
    ! [SV956: nat,SV937: nat,SV857: nat,SV632: nat,SV312: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV312 @ SV632 )
          | ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV857 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14663]) ).

thf(14687,plain,
    ! [SV312: nat,SV857: nat,SV937: nat,SV956: nat,SV632: nat] :
      ( ( ( ( times_times_nat @ SV632 @ ( sK34_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
          = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ ( sK44_SY1943 @ SV937 @ SV956 @ SV857 @ SV632 @ SV312 ) ) @ SV312 ) )
        = $true )
      | ( ( ( times_times_nat @ ( plus_plus_nat @ SV632 @ SV857 ) @ ( sK34_SY1887 @ SV956 @ SV937 @ SV857 @ SV632 @ SV312 ) )
          = ( plus_plus_nat @ ( times_times_nat @ SV632 @ ( sK44_SY1943 @ SV937 @ SV956 @ SV857 @ SV632 @ SV312 ) ) @ SV312 ) )
        = $true )
      | ( ( ( times_times_nat @ SV857 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[14664]) ).

thf(14688,plain,
    ! [SV639: nat,SV860: nat,SV319: nat > nat > $o] :
      ( ( ( SV319 @ ( sK48_SY1422 @ SV860 @ SV639 @ SV319 ) @ ( sK49_SY1947 @ SV639 @ SV860 @ SV319 ) )
        = $true )
      | ( ( SV319 @ SV639 @ SV860 )
        = $true )
      | ( ( SV319 @ ( sK40_SY1421 @ SV860 @ SV639 @ SV319 ) @ zero_zero_nat )
        = $false )
      | ( ( SV319 @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) )
        = $false )
      | ( ( SV319 @ ( sK16_SY1934 @ SV639 @ SV860 @ SV319 ) @ ( sK11_SY1419 @ SV860 @ SV639 @ SV319 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14665]) ).

thf(14689,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
          | ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[14671]) ).

thf(14690,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[14671]) ).

thf(14691,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
         != ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14673]) ).

thf(14692,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
         != ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14673]) ).

thf(14693,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) ) )
        = $true )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14674]) ).

thf(14694,plain,
    ! [SV595: nat,SV928: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) ) )
        = $true )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14674]) ).

thf(14695,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
          | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14676]) ).

thf(14696,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
          | ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14677]) ).

thf(14697,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
          | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14678]) ).

thf(14698,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
          | ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14679]) ).

thf(14699,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
          | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14680]) ).

thf(14700,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
          | ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14681]) ).

thf(14701,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
          | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14682]) ).

thf(14702,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
          | ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14683]) ).

thf(14703,plain,
    ! [SV956: nat,SV857: nat,SV937: nat,SV632: nat,SV312: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV312 @ SV632 ) )
        = $false )
      | ( ( ( times_times_nat @ SV632 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV857 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14684]) ).

thf(14704,plain,
    ! [SV956: nat,SV937: nat,SV857: nat,SV632: nat,SV312: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV632 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV857 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14684]) ).

thf(14705,plain,
    ! [SV956: nat,SV937: nat,SV857: nat,SV632: nat,SV312: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV312 @ SV632 ) )
        = $false )
      | ( ( ( times_times_nat @ SV857 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14686]) ).

thf(14706,plain,
    ! [SV956: nat,SV937: nat,SV857: nat,SV632: nat,SV312: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) ) )
        = $false )
      | ( ( ( times_times_nat @ SV857 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14686]) ).

thf(14707,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) ) )
        = $true )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[14689]) ).

thf(14708,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14691]) ).

thf(14709,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14692]) ).

thf(14710,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14693]) ).

thf(14711,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14694]) ).

thf(14712,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
        = $true )
      | ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[14695]) ).

thf(14713,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
        = $true )
      | ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[14696]) ).

thf(14714,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
        = $true )
      | ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[14697]) ).

thf(14715,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
        = $true )
      | ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[14698]) ).

thf(14716,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
        = $true )
      | ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[14699]) ).

thf(14717,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
        = $true )
      | ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[14700]) ).

thf(14718,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
        = $true )
      | ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[14701]) ).

thf(14719,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
        = $true )
      | ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[14702]) ).

thf(14720,plain,
    ! [SV956: nat,SV857: nat,SV937: nat,SV632: nat,SV312: nat] :
      ( ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $true )
      | ( ( ( times_times_nat @ SV632 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV857 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14703]) ).

thf(14721,plain,
    ! [SV956: nat,SV937: nat,SV857: nat,SV632: nat,SV312: nat] :
      ( ( ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) )
        = $true )
      | ( ( ( times_times_nat @ SV632 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV857 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14704]) ).

thf(14722,plain,
    ! [SV956: nat,SV937: nat,SV857: nat,SV632: nat,SV312: nat] :
      ( ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $true )
      | ( ( ( times_times_nat @ SV857 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14705]) ).

thf(14723,plain,
    ! [SV956: nat,SV937: nat,SV857: nat,SV632: nat,SV312: nat] :
      ( ( ( dvd_dvd_nat @ SV312 @ ( plus_plus_nat @ SV632 @ SV857 ) )
        = $true )
      | ( ( ( times_times_nat @ SV857 @ SV937 )
          = ( plus_plus_nat @ ( times_times_nat @ SV632 @ SV956 ) @ SV312 ) )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV857 )
        = $false )
      | ( ( dvd_dvd_nat @ SV312 @ SV632 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14706]) ).

thf(14724,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14707]) ).

thf(14725,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
          | ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[14708]) ).

thf(14726,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_equal_pos,[status(thm)],[14708]) ).

thf(14727,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14710]) ).

thf(14728,plain,
    ! [SV595: nat,SV928: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14710]) ).

thf(14729,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14711]) ).

thf(14730,plain,
    ! [SV595: nat,SV928: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14711]) ).

thf(14731,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false )
      | ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14712]) ).

thf(14732,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
        = $false )
      | ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14713]) ).

thf(14733,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false )
      | ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14714]) ).

thf(14734,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
        = $false )
      | ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14715]) ).

thf(14735,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false )
      | ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14716]) ).

thf(14736,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
        = $false )
      | ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14717]) ).

thf(14737,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false )
      | ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14718]) ).

thf(14738,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 ) )
        = $false )
      | ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14719]) ).

thf(14739,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14724]) ).

thf(14740,plain,
    ! [SV595: nat,SV928: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14724]) ).

thf(14741,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) ) )
        = $true )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[14725]) ).

thf(14742,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14727]) ).

thf(14743,plain,
    ! [SV595: nat,SV928: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14728]) ).

thf(14744,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14729]) ).

thf(14745,plain,
    ! [SV595: nat,SV928: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14730]) ).

thf(14746,plain,
    ! [SV303: nat,SV624: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14731]) ).

thf(14747,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14732]) ).

thf(14748,plain,
    ! [SV303: nat,SV624: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14733]) ).

thf(14749,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14734]) ).

thf(14750,plain,
    ! [SV303: nat,SV624: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14735]) ).

thf(14751,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14736]) ).

thf(14752,plain,
    ! [SV303: nat,SV624: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14737]) ).

thf(14753,plain,
    ! [SV624: nat,SV303: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( ~ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14738]) ).

thf(14754,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14739]) ).

thf(14755,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14740]) ).

thf(14756,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14741]) ).

thf(14757,plain,
    ! [SV303: nat,SV624: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14747]) ).

thf(14758,plain,
    ! [SV303: nat,SV624: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14749]) ).

thf(14759,plain,
    ! [SV303: nat,SV624: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14751]) ).

thf(14760,plain,
    ! [SV303: nat,SV624: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14753]) ).

thf(14761,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14754]) ).

thf(14762,plain,
    ! [SV595: nat,SV928: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14754]) ).

thf(14763,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14755]) ).

thf(14764,plain,
    ! [SV595: nat,SV928: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14755]) ).

thf(14765,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14756]) ).

thf(14766,plain,
    ! [SV595: nat,SV928: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
              | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) ) )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14756]) ).

thf(14767,plain,
    ! [SV303: nat,SV624: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14757]) ).

thf(14768,plain,
    ! [SV303: nat,SV624: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14758]) ).

thf(14769,plain,
    ! [SV303: nat,SV624: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14759]) ).

thf(14770,plain,
    ! [SV303: nat,SV624: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV303 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV624 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14760]) ).

thf(14771,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14761]) ).

thf(14772,plain,
    ! [SV595: nat,SV928: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14762]) ).

thf(14773,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14763]) ).

thf(14774,plain,
    ! [SV595: nat,SV928: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14764]) ).

thf(14775,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14765]) ).

thf(14776,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
          | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[14766]) ).

thf(14777,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14775]) ).

thf(14778,plain,
    ! [SV595: nat,SV928: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14775]) ).

thf(14779,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14776]) ).

thf(14780,plain,
    ! [SV595: nat,SV928: nat] :
      ( ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 ) )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[14776]) ).

thf(14781,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14777]) ).

thf(14782,plain,
    ! [SV595: nat,SV928: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14778]) ).

thf(14783,plain,
    ! [SV928: nat,SV595: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14779]) ).

thf(14784,plain,
    ! [SV595: nat,SV928: nat] :
      ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $true )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV928 )
        = $false )
      | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ SV595 )
        = $false )
      | ( ( ( divide_divide_nat @ SV595 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
          = ( divide_divide_nat @ SV928 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[14780]) ).

thf(14785,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[10669,14784,14783,14782,14781,14774,14773,14772,14771,14770,14769,14768,14767,14752,14750,14748,14746,14745,14744,14743,14742,14726,14723,14722,14721,14720,14709,14690,14688,14687,14685,14675,14672,14670,14669,14668,14667,14666,14660,14658,14656,14654,14652,14651,14647,14644,14643,14642,14641,14635,14630,14628,14626,14624,14622,14618,14607,14606,14605,14604,14602,14589,14585,14581,14572,14566,14556,14543,14542,14541,14540,14539,14537,14532,14531,14523,14522,14514,14513,14512,14511,14506,14505,14504,14503,14500,14499,14495,14487,14486,14485,14484,14474,14473,14472,14471,14467,14466,14464,14460,14459,14458,14457,14456,14455,14454,14453,14452,14451,14450,14449,14448,14447,14446,14445,14444,14443,14442,14441,14440,14439,14438,14437,14436,14435,14434,14433,14432,14431,14430,14429,14428,14427,14426,14425,14424,14423,14422,14421,14420,14419,14418,14417,14416,14415,14414,14413,14408,14405,14404,14403,14402,14399,14395,14358,14305,14298,14297,14296,14295,14292,14291,14290,14289,14288,14283,14282,14281,14280,14277,14276,14274,14268,14255,14254,14244,14214,14207,14206,14204,14200,14193,14185,14179,14170,14168,14167,14157,14156,14155,14154,14153,14152,14142,14141,14140,14139,14114,14113,14109,14104,14102,14098,14093,14092,14091,14090,14086,14085,14081,14080,14079,14078,14075,14074,14070,14060,14059,14056,14055,14053,14050,14044,14043,14042,14012,14010,14009,14003,14002,14001,14000,13999,13998,13997,13996,13995,13994,13993,13990,13986,13960,13940,13937,13923,13922,13921,13901,13900,13895,13894,13892,13890,13889,13888,13887,13885,13883,13882,13880,13878,13877,13876,13875,13873,13871,13870,13868,13866,13865,13863,13856,13845,13842,13839,13814,13813,13811,13804,13800,13797,13794,13793,13792,13791,13790,13788,13786,13784,13782,13781,13780,13779,13778,13776,13774,13772,13770,13769,13768,13767,13766,13764,13762,13760,13758,13757,13756,13755,13754,13753,13752,13751,13750,13749,13748,13747,13746,13745,13744,13743,13737,13734,13731,13729,13728,13727,13726,13725,13724,13723,13722,13721,13720,13714,13713,13712,13711,13710,13708,13706,13705,13699,13693,13691,13689,13688,13682,13676,13675,13674,13673,13672,13671,13670,13669,13668,13667,13666,13665,13664,13663,13662,13661,13660,13659,13658,13657,13656,13655,13654,13653,13652,13651,13650,13649,13648,13647,13646,13645,13644,13643,13642,13641,13640,13639,13632,13626,13625,13619,13610,13606,13603,13599,13594,13591,13582,13577,13573,13572,13562,13537,13536,13535,13534,13533,13532,13531,13530,13510,13509,13508,13507,13501,13495,13486,13485,13484,13483,13482,13481,13480,13479,13478,13477,13476,13475,13461,13452,13451,13450,13449,13448,13447,13446,13445,13444,13443,13442,13441,13440,13439,13438,13437,13431,13386,13385,13384,13383,13382,13381,13380,13379,13378,13377,13376,13375,13374,13373,13372,13371,13370,13369,13368,13367,13366,13362,13353,13352,13351,13348,13346,13343,13338,13335,13332,13319,13301,13300,13287,13284,13283,13278,13277,13206,13205,13204,13203,13148,13147,13146,13145,13144,13143,13142,13141,13140,13139,13138,13137,13114,13102,13087,13074,13069,13061,13056,13053,13042,13041,13038,12900,12899,12891,12887,12883,12874,12850,12848,12847,12843,12841,12840,12836,12830,12829,12751,12750,12749,12747,12746,12742,12739,12738,12733,12732,12731,12730,12729,12728,12727,12720,12710,12709,12708,12707,12703,12701,12698,12695,12692,12691,12690,12689,12685,12680,12675,12673,12671,12668,12663,12661,12658,12656,12654,12652,12649,12647,12644,12639,12631,12628,12625,12624,12623,12622,12621,12620,12606,12603,12561,12551,12531,12522,12484,12480,12471,12455,12447,12442,12426,12423,12420,12417,12416,12413,12411,12409,12407,12403,12399,12397,12392,12390,12386,12384,12377,12375,12373,12372,12371,12370,12368,12366,12364,12362,12360,12358,12357,12355,12353,12351,12343,12342,12339,12325,12324,12300,12296,12278,12272,12269,12266,12264,12261,12256,12251,12248,12245,12243,12242,12236,12233,12228,12221,12212,12200,12188,12186,12176,12175,12173,12171,12170,12169,12168,12167,12165,12163,12157,12155,12154,12153,12150,12148,12144,12142,12140,12138,12137,12136,12135,12134,12133,12130,12129,12128,12127,12126,12125,12124,12123,12122,12120,12119,12118,12117,12116,12112,12110,12108,12106,12104,12100,12098,12097,12096,12095,12094,12092,12091,12090,12089,12087,12086,12079,12078,12077,12076,12075,12073,12072,12071,12070,12069,12068,12067,12066,12065,12064,12063,12061,12060,12059,12058,12057,12050,12048,12046,12044,12041,12040,12039,12038,12037,12036,12035,12034,12033,12032,12030,12029,12028,12027,12025,12024,12023,12022,12020,12013,11986,11961,11960,11959,11958,11957,11956,11955,11954,11953,11926,11896,11895,11887,11884,11845,11843,11838,11837,11836,11835,11827,11826,11818,11813,11812,11811,11810,11809,11806,11804,11793,11784,11783,11756,11754,11753,11751,11738,11737,11734,11733,11732,11731,11730,11726,11725,11722,11721,11720,11716,11714,11712,11711,11709,11706,11705,11702,11700,11699,11698,11695,11694,11693,11692,11691,11690,11683,11677,11675,11671,11666,11665,11649,11595,11571,11556,11540,11535,11504,11499,11498,11496,11494,11493,11476,11475,11474,11466,11456,11442,11439,11438,11437,11436,11419,11417,11414,11411,11410,11409,11408,11407,11402,11401,11400,11396,11391,11390,11388,11383,11379,11378,11366,11354,11353,11352,11349,11348,11338,11328,11327,11326,11319,11314,11312,11311,11308,11307,11306,11302,11301,11289,11288,11287,11286,11284,11282,11281,11280,11272,11270,11266,11256,11255,11253,11088,11086,11080,11071,10985,10782,10781,10780,10778,10775,10757,10745,10744,10743,10698,10697,10692,10689,10688,10687,10685,10684,10682,10681,10680,10676,10675,10670]) ).

thf(14786,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[14785]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : ITP257^3 : TPTP v9.3.1. Bugfixed v9.2.1.
% 0.00/0.06  % Command  : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.30  % Computer : n013.cluster.edu
% 0.17/0.30  % Model    : x86_64 x86_64
% 0.17/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.30  % Memory   : 8046.5625MB
% 0.17/0.30  % OS       : Linux 6.8.0-71-generic
% 0.17/0.30  % CPULimit : 300
% 0.17/0.30  % WCLimit  : 300
% 0.17/0.30  % DateTime : Tue Oct  6 11:24:37 UTC 2026
% 0.17/0.30  % CPUTime  : 
% 0.17/0.30  Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 174.34/35.23  ............................................................................
% 174.34/35.23  
% 174.34/35.23   No.of.Axioms: 426
% 174.34/35.23  
% 174.34/35.23   Length.of.Defs: 0
% 174.34/35.23  
% 174.34/35.23   Contains.Choice.Funs: true
% 174.34/35.23  ............................................................................................................................................................................................................................
% 174.34/35.23  
% 174.34/35.23  ********************************
% 174.34/35.23  *   All subproblems solved!    *
% 174.34/35.23  ********************************
% 174.34/35.23  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:426,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:14785,loop_count:0,foatp_calls:1,translation:fof_full)
% 174.34/35.23  
% 174.34/35.23  %**** Beginning of derivation protocol ****
% 174.34/35.23  % SZS output start CNFRefutation
% See solution above
% 174.34/35.27  
% 174.34/35.27  %**** End of derivation protocol ****
% 174.34/35.27  %**** no. of clauses in derivation: 4974 ****
% 174.34/35.27  %**** clause counter: 14785 ****
% 174.34/35.27  
% 174.34/35.27  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:426,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:14785,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------