Leo-III---1.8.0.THM-Ref.s

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%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SCT171+3 : TPTP v9.3.1. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39

% Computer : n006.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 : Sun Sep 27 08:27:29 AM UTC 2026

% Result   : Theorem 26.95s 10.27s
% Output   : Refutation 29.04s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  645
% Syntax   : Number of formulae    : 1292 ( 362 unt;   0 typ;   0 def)
%            Number of atoms       : 3914 ( 853 equ;   0 cnn)
%            Maximal formula atoms :   28 (   3 avg)
%            Number of connectives : 22849 ( 396   ~;  90   |; 483   &;19831   @)
%                                         ( 138 <=>;1911  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  249 ( 247 usr;  89 con; 0-3 aty)
%            Number of variables   : 3091 (   0   ^;3057   !;  34   ?;3091   :)

% Comments : 
%------------------------------------------------------------------------------
thf(hBOOL_decl,type,
    hBOOL: $i > $o ).

thf(hAPP_f592646513l_bool_decl,type,
    hAPP_f592646513l_bool: $i > $i > $i ).

thf(hAPP_P229966473l_bool_decl,type,
    hAPP_P229966473l_bool: $i > $i > $i ).

thf(member1441201108le_alt_decl,type,
    member1441201108le_alt: $i ).

thf(hAPP_A702847159le_alt_decl,type,
    hAPP_A702847159le_alt: $i > $i > $i ).

thf(hAPP_A1505516597le_alt_decl,type,
    hAPP_A1505516597le_alt: $i > $i > $i ).

thf(produc1400112471le_alt_decl,type,
    produc1400112471le_alt: $i ).

thf(c_decl,type,
    c: $i ).

thf(d_decl,type,
    d: $i ).

thf(hAPP_f412050202t_bool_decl,type,
    hAPP_f412050202t_bool: $i > $i > $i ).

thf(f_decl,type,
    f: $i ).

thf(p_decl,type,
    p: $i ).

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

thf(times_times_nat_decl,type,
    times_times_nat: $i > $i ).

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

thf(plus_plus_nat_decl,type,
    plus_plus_nat: $i ).

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

thf(hAPP_n1699378549t_bool_decl,type,
    hAPP_n1699378549t_bool: $i > $i > $i ).

thf(ord_less_eq_nat_decl,type,
    ord_less_eq_nat: $i ).

thf(suc_decl,type,
    suc: $i ).

thf(zero_zero_nat_decl,type,
    zero_zero_nat: $i ).

thf(size_size_nat_decl,type,
    size_size_nat: $i ).

thf(hAPP_f210572555l_bool_decl,type,
    hAPP_f210572555l_bool: $i > $i > $i ).

thf(hAPP_f1460506473l_bool_decl,type,
    hAPP_f1460506473l_bool: $i > $i > $i ).

thf(cOMBK_1693871704t_bool_decl,type,
    cOMBK_1693871704t_bool: $i ).

thf(is_fun279392540l_bool_decl,type,
    is_fun279392540l_bool: $i > $o ).

thf(hAPP_b1812770943l_bool_decl,type,
    hAPP_b1812770943l_bool: $i > $i > $i ).

thf(hAPP_f256804927l_bool_decl,type,
    hAPP_f256804927l_bool: $i > $i > $i ).

thf(cOMBK_69806648l_bool_decl,type,
    cOMBK_69806648l_bool: $i ).

thf(one_one_nat_decl,type,
    one_one_nat: $i ).

thf(nat_size_decl,type,
    nat_size: $i ).

thf(hAPP_f1749234559l_bool_decl,type,
    hAPP_f1749234559l_bool: $i > $i > $i ).

thf(hAPP_f1581553471l_bool_decl,type,
    hAPP_f1581553471l_bool: $i > $i > $i ).

thf(ord_le2085964885l_bool_decl,type,
    ord_le2085964885l_bool: $i ).

thf(hAPP_f54304608l_bool_decl,type,
    hAPP_f54304608l_bool: $i > $i > $i ).

thf(inj_on_nat_nat_decl,type,
    inj_on_nat_nat: $i > $i ).

thf(top_top_fun_nat_bool_decl,type,
    top_top_fun_nat_bool: $i ).

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

thf(is_fun1568535512t_bool_decl,type,
    is_fun1568535512t_bool: $i > $o ).

thf(hAPP_P332578347t_bool_decl,type,
    hAPP_P332578347t_bool: $i > $i > $i ).

thf(ord_less_nat_decl,type,
    ord_less_nat: $i ).

thf(hAPP_f1313392232ol_nat_decl,type,
    hAPP_f1313392232ol_nat: $i > $i > $i ).

thf(hAPP_f566237389l_bool_decl,type,
    hAPP_f566237389l_bool: $i > $i > $i ).

thf(member496995196t_bool_decl,type,
    member496995196t_bool: $i ).

thf(is_fun2093718614t_bool_decl,type,
    is_fun2093718614t_bool: $i > $o ).

thf(hAPP_n539120590t_bool_decl,type,
    hAPP_n539120590t_bool: $i > $i > $i ).

thf(is_bool_decl,type,
    is_bool: $i > $o ).

thf(hAPP_f817604743l_bool_decl,type,
    hAPP_f817604743l_bool: $i > $i > $i ).

thf(hAPP_f167218729l_bool_decl,type,
    hAPP_f167218729l_bool: $i > $i > $i ).

thf(hAPP_f1277514478l_bool_decl,type,
    hAPP_f1277514478l_bool: $i > $i > $i ).

thf(top_to1853035173l_bool_decl,type,
    top_to1853035173l_bool: $i ).

thf(hAPP_A1677245848t_bool_decl,type,
    hAPP_A1677245848t_bool: $i > $i > $i ).

thf(hAPP_f329301088t_bool_decl,type,
    hAPP_f329301088t_bool: $i > $i > $i ).

thf(hAPP_f573120177t_bool_decl,type,
    hAPP_f573120177t_bool: $i > $i > $i ).

thf(cOMBC_633721483t_bool_decl,type,
    cOMBC_633721483t_bool: $i ).

thf(hAPP_f515126293t_bool_decl,type,
    hAPP_f515126293t_bool: $i > $i > $i ).

thf(hAPP_A1102281708t_bool_decl,type,
    hAPP_A1102281708t_bool: $i > $i > $i ).

thf(arrow_1721807329e_Prof_decl,type,
    arrow_1721807329e_Prof: $i ).

thf(pi_Arr990697634t_bool_decl,type,
    pi_Arr990697634t_bool: $i > $i > $i ).

thf(top_to1576102282i_bool_decl,type,
    top_to1576102282i_bool: $i ).

thf(hAPP_f1659309744l_bool_decl,type,
    hAPP_f1659309744l_bool: $i > $i > $i ).

thf(cOMBK_657557929e_indi_decl,type,
    cOMBK_657557929e_indi: $i ).

thf(arrow_1681063817le_Lin_decl,type,
    arrow_1681063817le_Lin: $i ).

thf(hAPP_A60074736l_bool_decl,type,
    hAPP_A60074736l_bool: $i > $i > $i ).

thf(hAPP_P324742453l_bool_decl,type,
    hAPP_P324742453l_bool: $i > $i > $i ).

thf(hAPP_f2068374643l_bool_decl,type,
    hAPP_f2068374643l_bool: $i > $i > $i ).

thf(cOMBK_246631416le_alt_decl,type,
    cOMBK_246631416le_alt: $i ).

thf(hilber195283148at_nat_decl,type,
    hilber195283148at_nat: $i > $i > $i ).

thf(is_fun1236654035i_bool_decl,type,
    is_fun1236654035i_bool: $i > $o ).

thf(hAPP_f1552576127i_bool_decl,type,
    hAPP_f1552576127i_bool: $i > $i > $i ).

thf(hAPP_f324780729l_bool_decl,type,
    hAPP_f324780729l_bool: $i > $i > $i ).

thf(hAPP_f1377535679l_bool_decl,type,
    hAPP_f1377535679l_bool: $i > $i > $i ).

thf(ord_le1546299023t_bool_decl,type,
    ord_le1546299023t_bool: $i ).

thf(ord_le1393483395t_bool_decl,type,
    ord_le1393483395t_bool: $i ).

thf(top_to1257323279t_bool_decl,type,
    top_to1257323279t_bool: $i ).

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

thf(hAPP_f2028818269l_bool_decl,type,
    hAPP_f2028818269l_bool: $i > $i > $i ).

thf(hAPP_f1666015481l_bool_decl,type,
    hAPP_f1666015481l_bool: $i > $i > $i ).

thf(member880664588l_bool_decl,type,
    member880664588l_bool: $i ).

thf(pi_fun1575168891l_bool_decl,type,
    pi_fun1575168891l_bool: $i > $i > $i ).

thf(hAPP_f387058535l_bool_decl,type,
    hAPP_f387058535l_bool: $i > $i > $i ).

thf(hAPP_b1787118453l_bool_decl,type,
    hAPP_b1787118453l_bool: $i > $i > $i ).

thf(member_bool_decl,type,
    member_bool: $i ).

thf(pi_Pro666468413t_bool_decl,type,
    pi_Pro666468413t_bool: $i > $i > $i ).

thf(top_to1647826457l_bool_decl,type,
    top_to1647826457l_bool: $i ).

thf(hAPP_f1842612975t_bool_decl,type,
    hAPP_f1842612975t_bool: $i > $i > $i ).

thf(cOMBS_131695599t_bool_decl,type,
    cOMBS_131695599t_bool: $i > $i ).

thf(hAPP_f427493225t_bool_decl,type,
    hAPP_f427493225t_bool: $i > $i > $i ).

thf(hAPP_A1455239488t_bool_decl,type,
    hAPP_A1455239488t_bool: $i > $i > $i ).

thf(is_fun1217980910e_indi_decl,type,
    is_fun1217980910e_indi: $i > $o ).

thf(hilber693666498di_nat_decl,type,
    hilber693666498di_nat: $i > $i > $i ).

thf(is_fun961089132t_bool_decl,type,
    is_fun961089132t_bool: $i > $o ).

thf(hAPP_n588788980t_bool_decl,type,
    hAPP_n588788980t_bool: $i > $i > $i ).

thf(top_to178429151t_bool_decl,type,
    top_to178429151t_bool: $i ).

thf(hAPP_f1345320373l_bool_decl,type,
    hAPP_f1345320373l_bool: $i > $i > $i ).

thf(member357566570t_bool_decl,type,
    member357566570t_bool: $i ).

thf(pi_boo538701011t_bool_decl,type,
    pi_boo538701011t_bool: $i > $i > $i ).

thf(hAPP_b1703662281t_bool_decl,type,
    hAPP_b1703662281t_bool: $i > $i > $i ).

thf(hAPP_f1599966040l_bool_decl,type,
    hAPP_f1599966040l_bool: $i > $i > $i ).

thf(top_to522745736l_bool_decl,type,
    top_to522745736l_bool: $i ).

thf(hAPP_n821919323i_bool_decl,type,
    hAPP_n821919323i_bool: $i > $i > $i ).

thf(hAPP_P1875867302i_bool_decl,type,
    hAPP_P1875867302i_bool: $i > $i > $i ).

thf(hAPP_f1909278132t_bool_decl,type,
    hAPP_f1909278132t_bool: $i > $i > $i ).

thf(hAPP_f1297018969t_bool_decl,type,
    hAPP_f1297018969t_bool: $i > $i > $i ).

thf(cOMBC_510421983t_bool_decl,type,
    cOMBC_510421983t_bool: $i ).

thf(hAPP_f863359027l_bool_decl,type,
    hAPP_f863359027l_bool: $i > $i > $i ).

thf(ord_le1004900979t_bool_decl,type,
    ord_le1004900979t_bool: $i ).

thf(hAPP_f250445784l_bool_decl,type,
    hAPP_f250445784l_bool: $i > $i > $i ).

thf(hAPP_f1253375959l_bool_decl,type,
    hAPP_f1253375959l_bool: $i > $i > $i ).

thf(member520425275t_bool_decl,type,
    member520425275t_bool: $i ).

thf(pi_fun150026276t_bool_decl,type,
    pi_fun150026276t_bool: $i > $i > $i ).

thf(hAPP_f1924755118l_bool_decl,type,
    hAPP_f1924755118l_bool: $i > $i > $i ).

thf(cOMBK_2038534567t_bool_decl,type,
    cOMBK_2038534567t_bool: $i ).

thf(hAPP_f777333846l_bool_decl,type,
    hAPP_f777333846l_bool: $i > $i > $i ).

thf(hAPP_f461621971l_bool_decl,type,
    hAPP_f461621971l_bool: $i > $i > $i ).

thf(member760917689t_bool_decl,type,
    member760917689t_bool: $i ).

thf(hAPP_f312250286l_bool_decl,type,
    hAPP_f312250286l_bool: $i > $i > $i ).

thf(top_to1714702858l_bool_decl,type,
    top_to1714702858l_bool: $i ).

thf(top_top_bool_decl,type,
    top_top_bool: $i ).

thf(e_decl,type,
    e: $i ).

thf(hAPP_f1740414619t_bool_decl,type,
    hAPP_f1740414619t_bool: $i > $i > $i ).

thf(cOMBS_1064524443t_bool_decl,type,
    cOMBS_1064524443t_bool: $i > $i ).

thf(hAPP_f586238575t_bool_decl,type,
    hAPP_f586238575t_bool: $i > $i > $i ).

thf(cOMBB_2107911302e_indi_decl,type,
    cOMBB_2107911302e_indi: $i > $i ).

thf(if_fun2098446489t_bool_decl,type,
    if_fun2098446489t_bool: $i ).

thf(hAPP_f446868133i_bool_decl,type,
    hAPP_f446868133i_bool: $i > $i > $i ).

thf(cOMBC_1996607964t_bool_decl,type,
    cOMBC_1996607964t_bool: $i ).

thf(hAPP_f224734595t_bool_decl,type,
    hAPP_f224734595t_bool: $i > $i > $i ).

thf(cOMBB_1883918730e_indi_decl,type,
    cOMBB_1883918730e_indi: $i > $i ).

thf(h_decl,type,
    h: $i ).

thf(n_decl,type,
    n: $i ).

thf(hAPP_A1805174428t_bool_decl,type,
    hAPP_A1805174428t_bool: $i > $i > $i ).

thf(hAPP_f1808153265t_bool_decl,type,
    hAPP_f1808153265t_bool: $i > $i > $i ).

thf(cOMBC_1353880399t_bool_decl,type,
    cOMBC_1353880399t_bool: $i ).

thf(hAPP_f721938099t_bool_decl,type,
    hAPP_f721938099t_bool: $i > $i > $i ).

thf(cOMBB_2032668066e_indi_decl,type,
    cOMBB_2032668066e_indi: $i > $i ).

thf(arrow_1644373103_mktop_decl,type,
    arrow_1644373103_mktop: $i ).

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

thf(hAPP_A1906441908t_bool_decl,type,
    hAPP_A1906441908t_bool: $i > $i > $i ).

thf(hAPP_f248867553t_bool_decl,type,
    hAPP_f248867553t_bool: $i > $i > $i ).

thf(cOMBC_898791271t_bool_decl,type,
    cOMBC_898791271t_bool: $i ).

thf(hAPP_f210227915t_bool_decl,type,
    hAPP_f210227915t_bool: $i > $i > $i ).

thf(cOMBB_1769989562e_indi_decl,type,
    cOMBB_1769989562e_indi: $i > $i ).

thf(arrow_230821333_above_decl,type,
    arrow_230821333_above: $i ).

thf(arrow_1495666017_mkbot_decl,type,
    arrow_1495666017_mkbot: $i ).

thf(b_decl,type,
    b: $i ).

thf(a_decl,type,
    a: $i ).

thf(lab_decl,type,
    lab: $i ).

thf(lba_decl,type,
    lba: $i ).

thf(hAPP_P606313927t_bool_decl,type,
    hAPP_P606313927t_bool: $i > $i > $i ).

thf(inj_on1073981917di_nat_decl,type,
    inj_on1073981917di_nat: $i > $i ).

thf(hAPP_A1637648121di_nat_decl,type,
    hAPP_A1637648121di_nat: $i > $i > $i ).

thf(hAPP_n1951273283e_indi_decl,type,
    hAPP_n1951273283e_indi: $i > $i > $i ).

thf(hAPP_A1625428400t_bool_decl,type,
    hAPP_A1625428400t_bool: $i > $i > $i ).

thf(hAPP_f393984045t_bool_decl,type,
    hAPP_f393984045t_bool: $i > $i > $i ).

thf(hAPP_f965095724l_bool_decl,type,
    hAPP_f965095724l_bool: $i > $i > $i ).

thf(hAPP_A621939144t_bool_decl,type,
    hAPP_A621939144t_bool: $i > $i > $i ).

thf(hAPP_f344580165t_bool_decl,type,
    hAPP_f344580165t_bool: $i > $i > $i ).

thf(ord_le906188671t_bool_decl,type,
    ord_le906188671t_bool: $i ).

thf(hAPP_P607165281l_bool_decl,type,
    hAPP_P607165281l_bool: $i > $i > $i ).

thf(member_Product_unit_decl,type,
    member_Product_unit: $i ).

thf(hAPP_f2120083535ol_nat_decl,type,
    hAPP_f2120083535ol_nat: $i > $i > $i ).

thf(finite1686180860e_indi_decl,type,
    finite1686180860e_indi: $i ).

thf(hAPP_f1837019376l_bool_decl,type,
    hAPP_f1837019376l_bool: $i > $i > $i ).

thf(hAPP_f1358350510ol_nat_decl,type,
    hAPP_f1358350510ol_nat: $i > $i > $i ).

thf(hAPP_A1941004017t_bool_decl,type,
    hAPP_A1941004017t_bool: $i > $i > $i ).

thf(hAPP_f1306865520l_bool_decl,type,
    hAPP_f1306865520l_bool: $i > $i > $i ).

thf(hAPP_f816335862ol_nat_decl,type,
    hAPP_f816335862ol_nat: $i > $i > $i ).

thf(is_Arr43961803e_indi_decl,type,
    is_Arr43961803e_indi: $i > $o ).

thf(hAPP_b1588041841t_bool_decl,type,
    hAPP_b1588041841t_bool: $i > $i > $i ).

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

thf(hAPP_A1785763630i_bool_decl,type,
    hAPP_A1785763630i_bool: $i > $i > $i ).

thf(hAPP_A2046586321t_bool_decl,type,
    hAPP_A2046586321t_bool: $i > $i > $i ).

thf(hAPP_f22590837l_bool_decl,type,
    hAPP_f22590837l_bool: $i > $i > $i ).

thf(top_to565915683t_bool_decl,type,
    top_to565915683t_bool: $i ).

thf(hAPP_f1582908258e_indi_decl,type,
    hAPP_f1582908258e_indi: $i > $i > $i ).

thf(cOMBK_306730240le_alt_decl,type,
    cOMBK_306730240le_alt: $i ).

thf(cOMBK_1076156777e_indi_decl,type,
    cOMBK_1076156777e_indi: $i ).

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

thf(hAPP_f340261009t_bool_decl,type,
    hAPP_f340261009t_bool: $i > $i > $i ).

thf(cOMBK_545135096l_bool_decl,type,
    cOMBK_545135096l_bool: $i ).

thf(is_Arr1861959080le_alt_decl,type,
    is_Arr1861959080le_alt: $i > $o ).

thf(hAPP_f111185985l_bool_decl,type,
    hAPP_f111185985l_bool: $i > $i > $i ).

thf(hAPP_f2018922499l_bool_decl,type,
    hAPP_f2018922499l_bool: $i > $i > $i ).

thf(cOMBC_62805014l_bool_decl,type,
    cOMBC_62805014l_bool: $i ).

thf(hAPP_A1602262231l_bool_decl,type,
    hAPP_A1602262231l_bool: $i > $i > $i ).

thf(member1493247163e_indi_decl,type,
    member1493247163e_indi: $i ).

thf(collec2096990994le_alt_decl,type,
    collec2096990994le_alt: $i ).

thf(hAPP_f1165814111t_bool_decl,type,
    hAPP_f1165814111t_bool: $i > $i > $i ).

thf(cOMBK_859929070le_alt_decl,type,
    cOMBK_859929070le_alt: $i ).

thf(hAPP_f1617919085t_bool_decl,type,
    hAPP_f1617919085t_bool: $i > $i > $i ).

thf(hAPP_f1351174655l_bool_decl,type,
    hAPP_f1351174655l_bool: $i > $i > $i ).

thf(hAPP_f1348208725i_bool_decl,type,
    hAPP_f1348208725i_bool: $i > $i > $i ).

thf(cOMBK_1915602921le_alt_decl,type,
    cOMBK_1915602921le_alt: $i ).

thf(arrow_610963188ctator_decl,type,
    arrow_610963188ctator: $i ).

thf(collec1553055422t_bool_decl,type,
    collec1553055422t_bool: $i ).

thf(cOMBK_1656150864t_bool_decl,type,
    cOMBK_1656150864t_bool: $i ).

thf(hAPP_P1676879539t_bool_decl,type,
    hAPP_P1676879539t_bool: $i > $i > $i ).

thf(hAPP_P1341894483t_bool_decl,type,
    hAPP_P1341894483t_bool: $i > $i > $i ).

thf(hAPP_A568203993t_bool_decl,type,
    hAPP_A568203993t_bool: $i > $i > $i ).

thf(hAPP_A572596845t_bool_decl,type,
    hAPP_A572596845t_bool: $i > $i > $i ).

thf(hAPP_f1324249913t_bool_decl,type,
    hAPP_f1324249913t_bool: $i > $i > $i ).

thf(cOMBB_747702273le_alt_decl,type,
    cOMBB_747702273le_alt: $i > $i ).

thf(hAPP_f653880381t_bool_decl,type,
    hAPP_f653880381t_bool: $i > $i > $i ).

thf(hAPP_A1553574765l_bool_decl,type,
    hAPP_A1553574765l_bool: $i > $i > $i ).

thf(hAPP_f415146997l_bool_decl,type,
    hAPP_f415146997l_bool: $i > $i > $i ).

thf(hAPP_f1066247963t_bool_decl,type,
    hAPP_f1066247963t_bool: $i > $i > $i ).

thf(cOMBK_812212462t_unit_decl,type,
    cOMBK_812212462t_unit: $i ).

thf(hAPP_A1664620203t_bool_decl,type,
    hAPP_A1664620203t_bool: $i > $i > $i ).

thf(hAPP_f2058969401t_bool_decl,type,
    hAPP_f2058969401t_bool: $i > $i > $i ).

thf(cOMBC_364043868t_bool_decl,type,
    cOMBC_364043868t_bool: $i ).

thf(hAPP_f1663053423t_bool_decl,type,
    hAPP_f1663053423t_bool: $i > $i > $i ).

thf(hAPP_P710098616e_indi_decl,type,
    hAPP_P710098616e_indi: $i > $i > $i ).

thf(arrow_1539419881_below_decl,type,
    arrow_1539419881_below: $i > $i > $i > $i ).

thf(hAPP_A862370221t_bool_decl,type,
    hAPP_A862370221t_bool: $i > $i > $i ).

thf(hAPP_A187815023l_bool_decl,type,
    hAPP_A187815023l_bool: $i > $i > $i ).

thf(hAPP_P504138941le_alt_decl,type,
    hAPP_P504138941le_alt: $i > $i > $i ).

thf(hAPP_f1868437069l_bool_decl,type,
    hAPP_f1868437069l_bool: $i > $i > $i ).

thf(member1648671474le_alt_decl,type,
    member1648671474le_alt: $i ).

thf(pi_Pro1928973619le_alt_decl,type,
    pi_Pro1928973619le_alt: $i > $i > $i ).

thf(hAPP_f407092109l_bool_decl,type,
    hAPP_f407092109l_bool: $i > $i > $i ).

thf(member234128621e_indi_decl,type,
    member234128621e_indi: $i ).

thf(pi_Pro1270767662e_indi_decl,type,
    pi_Pro1270767662e_indi: $i > $i > $i ).

thf(hAPP_f1847883341l_bool_decl,type,
    hAPP_f1847883341l_bool: $i > $i > $i ).

thf(member2079083634t_unit_decl,type,
    member2079083634t_unit: $i ).

thf(pi_Pro1122146355t_unit_decl,type,
    pi_Pro1122146355t_unit: $i > $i > $i ).

thf(hAPP_P1844795325t_unit_decl,type,
    hAPP_P1844795325t_unit: $i > $i > $i ).

thf(arrow_1587283740nimity_decl,type,
    arrow_1587283740nimity: $i ).

thf(hAPP_f49469479t_bool_decl,type,
    hAPP_f49469479t_bool: $i > $i > $i ).

thf(cOMBC_864945570l_bool_decl,type,
    cOMBC_864945570l_bool: $i ).

thf(hAPP_f721935245l_bool_decl,type,
    hAPP_f721935245l_bool: $i > $i > $i ).

thf(member797673069le_alt_decl,type,
    member797673069le_alt: $i ).

thf(pi_Arr1199386158le_alt_decl,type,
    pi_Arr1199386158le_alt: $i > $i > $i ).

thf(hAPP_A638717112le_alt_decl,type,
    hAPP_A638717112le_alt: $i > $i > $i ).

thf(arrow_1654180089le_IIA_decl,type,
    arrow_1654180089le_IIA: $i ).

thf(finite106199483e_indi_decl,type,
    finite106199483e_indi: $i ).

thf(hAPP_f2127575245l_bool_decl,type,
    hAPP_f2127575245l_bool: $i > $i > $i ).

thf(member1463820796le_alt_decl,type,
    member1463820796le_alt: $i ).

thf(pi_boo115158845le_alt_decl,type,
    pi_boo115158845le_alt: $i > $i > $i ).

thf(hAPP_b55004359le_alt_decl,type,
    hAPP_b55004359le_alt: $i > $i > $i ).

thf(hAPP_f1539445765l_bool_decl,type,
    hAPP_f1539445765l_bool: $i > $i > $i ).

thf(cOMBB_84213429le_alt_decl,type,
    cOMBB_84213429le_alt: $i > $i ).

thf(cOMBC_1635684702l_bool_decl,type,
    cOMBC_1635684702l_bool: $i ).

thf(hAPP_f156764033l_bool_decl,type,
    hAPP_f156764033l_bool: $i > $i > $i ).

thf(cOMBB_2112722489le_alt_decl,type,
    cOMBB_2112722489le_alt: $i > $i ).

thf(hAPP_f612708895l_bool_decl,type,
    hAPP_f612708895l_bool: $i > $i > $i ).

thf(ord_le742797417l_bool_decl,type,
    ord_le742797417l_bool: $i ).

thf(393,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_xt1_I10_J) ).

thf(2163,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(257,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_491_xt1_I7_J) ).

thf(1665,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(219,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1001_nat__add__left__cancel__less) ).

thf(1501,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(196,axiom,
    top_to178429151t_bool @ is_fun2093718614t_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Arrow____Order____Mirabelle____) ).

thf(1411,plain,
    top_to178429151t_bool @ is_fun2093718614t_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(210,axiom,
    ! [A: $i] :
      ( ( top_to1853035173l_bool @ ( cOMBK_657557929e_indi @ hAPP_f1659309744l_bool ) @ ( A @ pi_Arr990697634t_bool ) )
      = top_to522745736l_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_Pi__UNIV) ).

thf(1469,plain,
    ! [A: $i] :
      ( ( top_to1853035173l_bool @ ( cOMBK_657557929e_indi @ hAPP_f1659309744l_bool ) @ ( A @ pi_Arr990697634t_bool ) )
      = top_to522745736l_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(384,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ is_Arr43961803e_indi )
     => ( ( top_to1576102282i_bool @ ( C @ inj_on1073981917di_nat @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ( ( ( A @ ( C @ hAPP_A1637648121di_nat ) )
            = B )
         => ( ( B @ ( C @ ( top_to1576102282i_bool @ hilber693666498di_nat ) @ hAPP_n1951273283e_indi ) )
            = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_inv__f__eq) ).

thf(2131,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ is_Arr43961803e_indi )
     => ( ( top_to1576102282i_bool @ ( C @ inj_on1073981917di_nat @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ( ( ( A @ ( C @ hAPP_A1637648121di_nat ) )
            = B )
         => ( ( B @ ( C @ ( top_to1576102282i_bool @ hilber693666498di_nat ) @ hAPP_n1951273283e_indi ) )
            = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(368,axiom,
    ! [A: $i] : ( top_to1576102282i_bool @ ( A @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_iso__tuple__UNIV__I) ).

thf(2072,plain,
    ! [A: $i] : ( top_to1576102282i_bool @ ( A @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(276,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1837019376l_bool ) @ is_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_027) ).

thf(1729,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1837019376l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(459,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( D @ is_fun961089132t_bool )
         => ( ( C @ ( D @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
           => ( D @ ( B @ hAPP_f210572555l_bool ) @ ( D @ ( A @ hAPP_f592646513l_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) )
     => ( B @ ( C @ pi_fun1575168891l_bool ) @ ( A @ ( member880664588l_bool @ hAPP_f1666015481l_bool ) @ hAPP_f167218729l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_629_Pi__I) ).

thf(2412,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( D @ is_fun961089132t_bool )
         => ( ( C @ ( D @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
           => ( D @ ( B @ hAPP_f210572555l_bool ) @ ( D @ ( A @ hAPP_f592646513l_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) )
     => ( B @ ( C @ pi_fun1575168891l_bool ) @ ( A @ ( member880664588l_bool @ hAPP_f1666015481l_bool ) @ hAPP_f167218729l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(66,axiom,
    ! [A: $i] : ( A @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1059_lessI) ).

thf(909,plain,
    ! [A: $i] : ( A @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(308,axiom,
    ! [A: $i] :
      ( ( A @ is_fun2093718614t_bool )
     => ( ( A @ ( top_to178429151t_bool @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( A = top_to178429151t_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_535_top__le) ).

thf(1840,plain,
    ! [A: $i] :
      ( ( A @ is_fun2093718614t_bool )
     => ( ( A @ ( top_to178429151t_bool @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( A = top_to178429151t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(438,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( C @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_xt1_I3_J) ).

thf(2331,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( C @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(426,axiom,
    ! [A: $i] :
      ( ( top_to1853035173l_bool @ ( cOMBK_2038534567t_bool @ hAPP_f1924755118l_bool ) @ ( A @ pi_fun150026276t_bool ) )
      = top_to1714702858l_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_Pi__UNIV) ).

thf(2280,plain,
    ! [A: $i] :
      ( ( top_to1853035173l_bool @ ( cOMBK_2038534567t_bool @ hAPP_f1924755118l_bool ) @ ( A @ pi_fun150026276t_bool ) )
      = top_to1714702858l_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(416,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_bool )
     => ( B @ ( A @ hAPP_b1812770943l_bool ) @ is_fun279392540l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order__) ).

thf(2250,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_bool )
     => ( B @ ( A @ hAPP_b1812770943l_bool ) @ is_fun279392540l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(318,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
    <=> ( ~ ( A @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
        & ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_394_less__le__not__le) ).

thf(1879,plain,
    ! [A: $i,B: $i] :
      ( ( ( ~ ( A @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( ~ ( A @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(176,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( A @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [D: $i] :
              ( ( C @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( ( D @ ( suc @ hAPP_nat_nat ) @ ( A @ hAPP_nat_bool ) @ hBOOL )
               => ( D @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) )
         => ( B @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1115_inc__induct) ).

thf(1337,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( A @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [D: $i] :
              ( ( C @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( ( D @ ( suc @ hAPP_nat_nat ) @ ( A @ hAPP_nat_bool ) @ hBOOL )
               => ( D @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) )
         => ( B @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(273,axiom,
    ! [A: $i] : ( top_to1257323279t_bool @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_iso__tuple__UNIV__I) ).

thf(1718,plain,
    ! [A: $i] : ( top_to1257323279t_bool @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(610,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_1915602921le_alt @ hAPP_f1348208725i_bool ) @ ( C @ pi_Pro1270767662e_indi ) @ ( B @ ( member234128621e_indi @ hAPP_f407092109l_bool ) @ hAPP_f1306865520l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_P710098616e_indi ) @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_582_funcset__mem) ).

thf(3053,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_1915602921le_alt @ hAPP_f1348208725i_bool ) @ ( C @ pi_Pro1270767662e_indi ) @ ( B @ ( member234128621e_indi @ hAPP_f407092109l_bool ) @ hAPP_f1306865520l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_P710098616e_indi ) @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(440,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ hAPP_A1455239488t_bool ) )
      = ( C @ ( B @ hAPP_A1785763630i_bool ) @ ( A @ hAPP_b1588041841t_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow_) ).

thf(2341,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ hAPP_A1455239488t_bool ) )
      = ( C @ ( B @ hAPP_A1785763630i_bool ) @ ( A @ hAPP_b1588041841t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(476,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      <=> ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_409_linorder__antisym__conv1) ).

thf(2480,plain,
    ! [A: $i,B: $i] :
      ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( ( A = B )
         => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
        & ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(112,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2093718614t_bool )
        & ( A @ is_fun2093718614t_bool ) )
     => ( ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( ( A = B )
          | ( B @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_449_order__le__imp__less__or__eq) ).

thf(1083,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2093718614t_bool )
        & ( A @ is_fun2093718614t_bool ) )
     => ( ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( ( A = B )
          | ( B @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(301,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_xt1_I9_J) ).

thf(1818,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(164,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( D @ ( A @ hAPP_n539120590t_bool ) @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( F @ ( E @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( A @ hAPP_n539120590t_bool ) @ ( E @ ( A @ hAPP_n539120590t_bool ) @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) )
         => ( B @ ( C @ ( A @ hAPP_n539120590t_bool ) @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_863_order__le__less__subst2) ).

thf(1295,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( D @ ( A @ hAPP_n539120590t_bool ) @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( F @ ( E @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( A @ hAPP_n539120590t_bool ) @ ( E @ ( A @ hAPP_n539120590t_bool ) @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) )
         => ( B @ ( C @ ( A @ hAPP_n539120590t_bool ) @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(448,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f415146997l_bool ) @ is_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__prod_Itc__Arrow_) ).

thf(2363,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f415146997l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(136,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_fun1575168891l_bool ) @ ( B @ ( member880664588l_bool @ hAPP_f1666015481l_bool ) @ hAPP_f167218729l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_f210572555l_bool ) @ ( A @ ( B @ hAPP_f592646513l_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_557_Pi__mem) ).

thf(1211,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_fun1575168891l_bool ) @ ( B @ ( member880664588l_bool @ hAPP_f1666015481l_bool ) @ hAPP_f167218729l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_f210572555l_bool ) @ ( A @ ( B @ hAPP_f592646513l_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(643,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_436_order__less__imp__le) ).

thf(3317,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(162,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1002_trans__less__add1) ).

thf(1290,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(248,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1106_Suc__leI) ).

thf(1618,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(607,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( member1441201108le_alt @ ( cOMBC_864945570l_bool @ hAPP_f49469479t_bool ) @ hAPP_f515126293t_bool ) @ ( A @ ( member1441201108le_alt @ ( cOMBC_864945570l_bool @ hAPP_f49469479t_bool ) @ hAPP_f515126293t_bool ) @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
    <=> ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_980_pred__subset__eq) ).

thf(3040,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( B @ ( member1441201108le_alt @ ( cOMBC_864945570l_bool @ hAPP_f49469479t_bool ) @ hAPP_f515126293t_bool ) @ ( A @ ( member1441201108le_alt @ ( cOMBC_864945570l_bool @ hAPP_f49469479t_bool ) @ hAPP_f515126293t_bool ) @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
      & ( ( B @ ( member1441201108le_alt @ ( cOMBC_864945570l_bool @ hAPP_f49469479t_bool ) @ hAPP_f515126293t_bool ) @ ( A @ ( member1441201108le_alt @ ( cOMBC_864945570l_bool @ hAPP_f49469479t_bool ) @ hAPP_f515126293t_bool ) @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(522,axiom,
    ! [A: $i] :
      ~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_981_less__not__refl) ).

thf(2671,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(376,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ is_Arr43961803e_indi )
        & ( A @ is_Arr43961803e_indi ) )
     => ( ( top_to1576102282i_bool @ ( C @ inj_on1073981917di_nat @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ( ( ( A @ ( C @ hAPP_A1637648121di_nat ) )
            = ( B @ ( C @ hAPP_A1637648121di_nat ) ) )
         => ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_614_injD) ).

thf(2099,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ is_Arr43961803e_indi )
        & ( A @ is_Arr43961803e_indi ) )
     => ( ( top_to1576102282i_bool @ ( C @ inj_on1073981917di_nat @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ( ( ( A @ ( C @ hAPP_A1637648121di_nat ) )
            = ( B @ ( C @ hAPP_A1637648121di_nat ) ) )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(568,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_84213429le_alt @ hAPP_f1539445765l_bool ) @ hAPP_A187815023l_bool ) )
      = ( C @ ( B @ hAPP_A702847159le_alt ) @ ( A @ hAPP_P229966473l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu_) ).

thf(2837,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_84213429le_alt @ hAPP_f1539445765l_bool ) @ hAPP_A187815023l_bool ) )
      = ( C @ ( B @ hAPP_A702847159le_alt ) @ ( A @ hAPP_P229966473l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(57,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f817604743l_bool ) @ is_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__prod_Itc__Arrow____) ).

thf(878,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f817604743l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(9,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
        = ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) ) )
    <=> ( ( B = C )
        | ( A = zero_zero_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1179_nat__mult__eq__cancel__disj) ).

thf(677,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( B = C )
          | ( A = zero_zero_nat ) )
       => ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
          = ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) ) ) )
      & ( ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
          = ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) ) )
       => ( ( B = C )
          | ( A = zero_zero_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(485,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      | ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_365_linorder__linear) ).

thf(2512,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      | ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(599,axiom,
    ! [A: $i,B: $i] :
      ( ( arrow_1681063817le_Lin @ ( cOMBK_2038534567t_bool @ hAPP_f1924755118l_bool ) @ ( arrow_1721807329e_Prof @ pi_fun150026276t_bool ) @ ( B @ ( member520425275t_bool @ hAPP_f1253375959l_bool ) @ hAPP_f250445784l_bool ) @ hBOOL )
     => ( ! [C: $i] :
            ( ( arrow_1721807329e_Prof @ ( C @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
           => ! [D: $i,E: $i] :
                ( ( ( E @ is_Arr1861959080le_alt )
                  & ( D @ is_Arr1861959080le_alt ) )
               => ( ( D != E )
                 => ( ( A @ ( C @ hAPP_A1677245848t_bool ) @ ( E @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                   => ( C @ ( B @ hAPP_f412050202t_bool ) @ ( E @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ) )
       => ( A @ ( B @ ( arrow_610963188ctator @ hAPP_f1552576127i_bool ) @ hAPP_A1785763630i_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_dictatorI) ).

thf(2976,plain,
    ! [A: $i,B: $i] :
      ( ( arrow_1681063817le_Lin @ ( cOMBK_2038534567t_bool @ hAPP_f1924755118l_bool ) @ ( arrow_1721807329e_Prof @ pi_fun150026276t_bool ) @ ( B @ ( member520425275t_bool @ hAPP_f1253375959l_bool ) @ hAPP_f250445784l_bool ) @ hBOOL )
     => ( ! [C: $i] :
            ( ( arrow_1721807329e_Prof @ ( C @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
           => ! [D: $i,E: $i] :
                ( ( ( E @ is_Arr1861959080le_alt )
                  & ( D @ is_Arr1861959080le_alt ) )
               => ( ( D != E )
                 => ( ( A @ ( C @ hAPP_A1677245848t_bool ) @ ( E @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                   => ( C @ ( B @ hAPP_f412050202t_bool ) @ ( E @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ) )
       => ( A @ ( B @ ( arrow_610963188ctator @ hAPP_f1552576127i_bool ) @ hAPP_A1785763630i_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(380,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
    <=> ( A @ ( B @ hAPP_bool_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_mem__def) ).

thf(2117,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ hAPP_bool_bool ) @ hBOOL )
       => ( B @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ( A @ ( B @ hAPP_bool_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(194,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2093718614t_bool )
        & ( A @ is_fun2093718614t_bool ) )
     => ( ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( ( B != A )
         => ( B @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_469_xt1_I11_J) ).

thf(1406,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2093718614t_bool )
        & ( A @ is_fun2093718614t_bool ) )
     => ( ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( ( B != A )
         => ( B @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(410,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_501_order__le__less__trans) ).

thf(2231,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(107,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1158_mult__less__mono2) ).

thf(1068,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(203,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_1693871704t_bool @ hAPP_f1460506473l_bool ) @ ( C @ pi_fun1575168891l_bool ) @ ( B @ ( member880664588l_bool @ hAPP_f1666015481l_bool ) @ hAPP_f167218729l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_f592646513l_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_591_funcset__mem) ).

thf(1443,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_1693871704t_bool @ hAPP_f1460506473l_bool ) @ ( C @ pi_fun1575168891l_bool ) @ ( B @ ( member880664588l_bool @ hAPP_f1666015481l_bool ) @ hAPP_f167218729l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_f592646513l_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(298,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2093718614t_bool )
        & ( A @ is_fun2093718614t_bool ) )
     => ( ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
         => ( B = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_xt1_I5_J) ).

thf(1808,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2093718614t_bool )
        & ( A @ is_fun2093718614t_bool ) )
     => ( ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(517,axiom,
    arrow_1721807329e_Prof @ ( e @ ( p @ ( arrow_1495666017_mkbot @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( e @ ( c @ ( p @ ( arrow_230821333_above @ cOMBB_1769989562e_indi @ hAPP_f210227915t_bool ) @ ( cOMBC_898791271t_bool @ hAPP_f248867553t_bool ) @ hAPP_A1906441908t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( e @ ( p @ ( arrow_1644373103_mktop @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai) ).

thf(2659,plain,
    arrow_1721807329e_Prof @ ( e @ ( p @ ( arrow_1495666017_mkbot @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( e @ ( c @ ( p @ ( arrow_230821333_above @ cOMBB_1769989562e_indi @ hAPP_f210227915t_bool ) @ ( cOMBC_898791271t_bool @ hAPP_f248867553t_bool ) @ hAPP_A1906441908t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( e @ ( p @ ( arrow_1644373103_mktop @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(234,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ( B @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
        & ( A @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1171_one__le__mult__iff) ).

thf(1569,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( B @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          & ( A @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ( B @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          & ( A @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(415,axiom,
    ! [A: $i] : ( top_to522745736l_bool @ ( A @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_UNIV__I) ).

thf(2248,plain,
    ! [A: $i] : ( top_to522745736l_bool @ ( A @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(218,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ( ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ~ ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_904_add__leE) ).

thf(1497,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ( ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ~ ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(292,axiom,
    ! [A: $i] :
      ( ! [B: $i,C: $i] :
          ( ( ( C @ is_Arr43961803e_indi )
            & ( B @ is_Arr43961803e_indi ) )
         => ( ( ( B @ ( A @ hAPP_A1637648121di_nat ) )
              = ( C @ ( A @ hAPP_A1637648121di_nat ) ) )
           => ( B = C ) ) )
     => ( top_to1576102282i_bool @ ( A @ inj_on1073981917di_nat @ hAPP_f1599966040l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_656_injI) ).

thf(1788,plain,
    ! [A: $i] :
      ( ! [B: $i,C: $i] :
          ( ( ( C @ is_Arr43961803e_indi )
            & ( B @ is_Arr43961803e_indi ) )
         => ( ( ( B @ ( A @ hAPP_A1637648121di_nat ) )
              = ( C @ ( A @ hAPP_A1637648121di_nat ) ) )
           => ( B = C ) ) )
     => ( top_to1576102282i_bool @ ( A @ inj_on1073981917di_nat @ hAPP_f1599966040l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(259,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_xt1_I1_J) ).

thf(1671,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(123,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_bool )
     => ( B @ ( A @ hAPP_bool_bool ) @ is_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) ).

thf(1137,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_bool )
     => ( B @ ( A @ hAPP_bool_bool ) @ is_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(606,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( E @ is_Arr1861959080le_alt )
        & ( D @ is_Arr1861959080le_alt )
        & ( B @ is_Arr1861959080le_alt )
        & ( A @ is_Arr1861959080le_alt ) )
     => ( ( D != E )
       => ( ( arrow_1681063817le_Lin @ ( C @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
         => ( ( E @ ( D @ ( C @ arrow_1539419881_below ) ) @ ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
          <=> ( ( ( B != D )
               => ( ( ( A != D )
                   => ( C @ ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
                  & ( ( A = D )
                   => ( ( C @ ( B @ ( E @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                      | ( B = E ) ) ) ) )
              & ( ( B = D )
               => ( C @ ( E @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
              & ( A != B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_in__below) ).

thf(3004,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( E @ is_Arr1861959080le_alt )
        & ( D @ is_Arr1861959080le_alt )
        & ( B @ is_Arr1861959080le_alt )
        & ( A @ is_Arr1861959080le_alt ) )
     => ( ( D != E )
       => ( ( arrow_1681063817le_Lin @ ( C @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
         => ( ( ( ( ( B != D )
                 => ( ( ( A != D )
                     => ( C @ ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
                    & ( ( A = D )
                     => ( ( C @ ( B @ ( E @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                        | ( B = E ) ) ) ) )
                & ( ( B = D )
                 => ( C @ ( E @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
                & ( A != B ) )
             => ( E @ ( D @ ( C @ arrow_1539419881_below ) ) @ ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
            & ( ( E @ ( D @ ( C @ arrow_1539419881_below ) ) @ ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
             => ( ( ( B != D )
                 => ( ( ( A != D )
                     => ( C @ ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
                    & ( ( A = D )
                     => ( ( C @ ( B @ ( E @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                        | ( B = E ) ) ) ) )
                & ( ( B = D )
                 => ( C @ ( E @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
                & ( A != B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(544,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_xt1_I6_J) ).

thf(2740,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(624,axiom,
    ! [A: $i] : ( top_to565915683t_bool @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_iso__tuple__UNIV__I) ).

thf(3175,plain,
    ! [A: $i] : ( top_to565915683t_bool @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(20,axiom,
    ! [A: $i,B: $i] :
      ( ( A
        = ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) ) )
     => ( ( A = zero_zero_nat )
        | ( B = one_one_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1167_mult__eq__self__implies__10) ).

thf(715,plain,
    ! [A: $i,B: $i] :
      ( ( A
        = ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) ) )
     => ( ( A = zero_zero_nat )
        | ( B = one_one_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(388,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( D @ is_bool )
         => ( ( C @ ( D @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
           => ( D @ ( B @ hAPP_b1812770943l_bool ) @ ( D @ ( A @ hAPP_b1703662281t_bool ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) )
     => ( B @ ( C @ pi_boo538701011t_bool ) @ ( A @ ( member357566570t_bool @ hAPP_f1345320373l_bool ) @ hAPP_f817604743l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_643_Pi__I) ).

thf(2141,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( D @ is_bool )
         => ( ( C @ ( D @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
           => ( D @ ( B @ hAPP_b1812770943l_bool ) @ ( D @ ( A @ hAPP_b1703662281t_bool ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) )
     => ( B @ ( C @ pi_boo538701011t_bool ) @ ( A @ ( member357566570t_bool @ hAPP_f1345320373l_bool ) @ hAPP_f817604743l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(535,axiom,
    ~ ( fFalse @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).

thf(2712,plain,
    ~ ( fFalse @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(172,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_736_add__le__imp__le__right) ).

thf(1327,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(14,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun279392540l_bool )
     => ( ( B @ ( A @ ( cOMBK_69806648l_bool @ hAPP_f256804927l_bool ) @ hAPP_b1812770943l_bool ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe) ).

thf(698,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun279392540l_bool )
     => ( ( B @ ( A @ ( cOMBK_69806648l_bool @ hAPP_f256804927l_bool ) @ hAPP_b1812770943l_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(471,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P710098616e_indi ) @ is_Arr43961803e_indi ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc_) ).

thf(2459,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P710098616e_indi ) @ is_Arr43961803e_indi ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(357,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_order__trans) ).

thf(2042,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(220,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_xt1_I6_J) ).

thf(1507,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(512,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_Arr43961803e_indi )
     => ( ( top_to1576102282i_bool @ ( B @ inj_on1073981917di_nat @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ( ( A @ ( B @ hAPP_A1637648121di_nat ) @ ( B @ ( top_to1576102282i_bool @ hilber693666498di_nat ) @ hAPP_n1951273283e_indi ) )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_inv__f__f) ).

thf(2607,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_Arr43961803e_indi )
     => ( ( top_to1576102282i_bool @ ( B @ inj_on1073981917di_nat @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ( ( A @ ( B @ hAPP_A1637648121di_nat ) @ ( B @ ( top_to1576102282i_bool @ hilber693666498di_nat ) @ hAPP_n1951273283e_indi ) )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(526,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Arr990697634t_bool ) @ ( B @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_A60074736l_bool ) @ ( A @ ( B @ hAPP_A1677245848t_bool ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_577_Pi__mem) ).

thf(2686,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Arr990697634t_bool ) @ ( B @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_A60074736l_bool ) @ ( A @ ( B @ hAPP_A1677245848t_bool ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(34,axiom,
    ! [A: $i] :
      ( ! [B: $i,C: $i] :
          ( ( ( B @ ( A @ hAPP_nat_nat ) )
            = ( C @ ( A @ hAPP_nat_nat ) ) )
         => ( B = C ) )
     => ( top_top_fun_nat_bool @ ( A @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_657_injI) ).

thf(797,plain,
    ! [A: $i] :
      ( ! [B: $i,C: $i] :
          ( ( ( B @ ( A @ hAPP_nat_nat ) )
            = ( C @ ( A @ hAPP_nat_nat ) ) )
         => ( B = C ) )
     => ( top_top_fun_nat_bool @ ( A @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(433,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( B @ ( D @ ( A @ hAPP_f816335862ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( ( F @ is_fun961089132t_bool )
                & ( E @ is_fun961089132t_bool ) )
             => ( ( F @ ( E @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
               => ( F @ ( A @ hAPP_f816335862ol_nat ) @ ( E @ ( A @ hAPP_f816335862ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) )
         => ( B @ ( C @ ( A @ hAPP_f816335862ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_884_order__le__less__subst2) ).

thf(2316,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( B @ ( D @ ( A @ hAPP_f816335862ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( ( F @ is_fun961089132t_bool )
                & ( E @ is_fun961089132t_bool ) )
             => ( ( F @ ( E @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
               => ( F @ ( A @ hAPP_f816335862ol_nat ) @ ( E @ ( A @ hAPP_f816335862ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) )
         => ( B @ ( C @ ( A @ hAPP_f816335862ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(286,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B = A )
       => ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_xt1_I2_J) ).

thf(1761,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B = A )
       => ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(177,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1014_le__add1) ).

thf(1342,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(180,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_n588788980t_bool ) @ is_fun961089132t_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabell) ).

thf(1354,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_n588788980t_bool ) @ is_fun961089132t_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(389,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( B @ hAPP_n588788980t_bool ) @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( E @ ( F @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n588788980t_bool ) @ ( F @ ( B @ hAPP_n588788980t_bool ) @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
         => ( D @ ( B @ hAPP_n588788980t_bool ) @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_679_xt7) ).

thf(2146,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( B @ hAPP_n588788980t_bool ) @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( E @ ( F @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n588788980t_bool ) @ ( F @ ( B @ hAPP_n588788980t_bool ) @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
         => ( D @ ( B @ hAPP_n588788980t_bool ) @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(597,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_970_in__mono) ).

thf(2972,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(182,axiom,
    ! [A: $i] :
      ( zero_zero_nat
     != ( A @ ( suc @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1071_Zero__not__Suc) ).

thf(1359,plain,
    ! [A: $i] :
      ( zero_zero_nat
     != ( A @ ( suc @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(184,axiom,
    ! [A: $i] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
     != zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1068_nat_Osimps_I3_J) ).

thf(1366,plain,
    ! [A: $i] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
     != zero_zero_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(487,axiom,
    e @ is_Arr1861959080le_alt,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_e____) ).

thf(2516,plain,
    e @ is_Arr1861959080le_alt,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(4,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) )
      = ( C @ ( B @ times_times_nat @ hAPP_nat_nat ) @ ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1149_add__mult__distrib) ).

thf(651,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) )
      = ( C @ ( B @ times_times_nat @ hAPP_nat_nat ) @ ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(404,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P1341894483t_bool ) @ is_fun961089132t_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__prod_Itc__Arrow____Orde) ).

thf(2216,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P1341894483t_bool ) @ is_fun961089132t_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(635,axiom,
    e @ ( p @ ( arrow_1495666017_mkbot @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( e @ ( c @ ( p @ ( arrow_230821333_above @ cOMBB_1769989562e_indi @ hAPP_f210227915t_bool ) @ ( cOMBC_898791271t_bool @ hAPP_f248867553t_bool ) @ hAPP_A1906441908t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( e @ ( p @ ( arrow_1644373103_mktop @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( d @ ( e @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).

thf(3236,plain,
    e @ ( p @ ( arrow_1495666017_mkbot @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( e @ ( c @ ( p @ ( arrow_230821333_above @ cOMBB_1769989562e_indi @ hAPP_f210227915t_bool ) @ ( cOMBC_898791271t_bool @ hAPP_f248867553t_bool ) @ hAPP_A1906441908t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( e @ ( p @ ( arrow_1644373103_mktop @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( d @ ( e @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(478,axiom,
    b @ is_Arr1861959080le_alt,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_b____) ).

thf(2491,plain,
    b @ is_Arr1861959080le_alt,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(122,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ( A = B )
        | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1081_less__Suc__eq) ).

thf(1127,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A = B )
          | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ( A = B )
          | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(600,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_946_psubset__subset__trans) ).

thf(2985,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(191,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
        & ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1160_mult__less__cancel2) ).

thf(1391,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          & ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          & ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(235,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( C @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_733_ab__semigroup__add__class_Oadd__ac_I1_J) ).

thf(1576,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( C @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(455,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B != A )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_471_xt1_I11_J) ).

thf(2400,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B != A )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(564,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
    <=> ( ~ ( A @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
        & ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_712_less__fun__def) ).

thf(2825,plain,
    ! [A: $i,B: $i] :
      ( ( ( ~ ( A @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( ~ ( A @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(224,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
        = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
     => ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_729_add__imp__eq) ).

thf(1529,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
        = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(340,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ hAPP_A2046586321t_bool ) )
      = ( C @ ( B @ hAPP_A1637648121di_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__049) ).

thf(1967,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ hAPP_A2046586321t_bool ) )
      = ( C @ ( B @ hAPP_A1637648121di_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(385,axiom,
    top_to1576102282i_bool @ ( h @ inj_on1073981917di_nat @ hAPP_f1599966040l_bool ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_injh) ).

thf(2136,plain,
    top_to1576102282i_bool @ ( h @ inj_on1073981917di_nat @ hAPP_f1599966040l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(268,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_1769989562e_indi @ hAPP_f210227915t_bool ) @ hAPP_A621939144t_bool ) )
      = ( C @ ( B @ hAPP_A1677245848t_bool ) @ ( A @ hAPP_f344580165t_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp_073) ).

thf(1703,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_1769989562e_indi @ hAPP_f210227915t_bool ) @ hAPP_A621939144t_bool ) )
      = ( C @ ( B @ hAPP_A1677245848t_bool ) @ ( A @ hAPP_f344580165t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(214,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( suc @ hAPP_nat_nat ) )
        = ( B @ ( suc @ hAPP_nat_nat ) ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1063_nat_Oinject) ).

thf(1482,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
       => ( ( A @ ( suc @ hAPP_nat_nat ) )
          = ( B @ ( suc @ hAPP_nat_nat ) ) ) )
      & ( ( ( A @ ( suc @ hAPP_nat_nat ) )
          = ( B @ ( suc @ hAPP_nat_nat ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(150,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
        = zero_zero_nat )
    <=> ( ( B = zero_zero_nat )
        & ( A = zero_zero_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1051_add__is__0) ).

thf(1254,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( B = zero_zero_nat )
          & ( A = zero_zero_nat ) )
       => ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
          = zero_zero_nat ) )
      & ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
          = zero_zero_nat )
       => ( ( B = zero_zero_nat )
          & ( A = zero_zero_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(628,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_1635684702l_bool @ hAPP_f653880381t_bool ) @ hAPP_f1663053423t_bool ) @ hAPP_A862370221t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A187815023l_bool ) @ hAPP_f592646513l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000t) ).

thf(3195,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_1635684702l_bool @ hAPP_f653880381t_bool ) @ hAPP_f1663053423t_bool ) @ hAPP_A862370221t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A187815023l_bool ) @ hAPP_f592646513l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

thf(608,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_order__eq__refl) ).

thf(3046,plain,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(151,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1060_Suc__mono) ).

thf(1264,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(304,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_375_linorder__not__le) ).

thf(1826,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(345,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_408_not__leE) ).

thf(1992,plain,
    ! [A: $i,B: $i] :
      ( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(382,axiom,
    ! [A: $i] :
      ~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_order__less__irrefl) ).

thf(2126,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(195,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1105_le__imp__less__Suc) ).

thf(1409,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(630,axiom,
    ! [A: $i] :
      ( ( A @ ( top_to1853035173l_bool @ hAPP_f592646513l_bool ) @ hBOOL )
    <=> ( top_top_bool @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_top__apply) ).

thf(3204,plain,
    ! [A: $i] :
      ( ( ( top_top_bool @ hBOOL )
       => ( A @ ( top_to1853035173l_bool @ hAPP_f592646513l_bool ) @ hBOOL ) )
      & ( ( A @ ( top_to1853035173l_bool @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( top_top_bool @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(68,axiom,
    ! [A: $i] :
      ( ( zero_zero_nat @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1050_Nat_Oadd__0__right) ).

thf(917,plain,
    ! [A: $i] :
      ( ( zero_zero_nat @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(15,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( D @ ( B @ ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1180_left__add__mult__distrib) ).

thf(702,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( D @ ( B @ ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(305,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f22590837l_bool ) @ is_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn_038) ).

thf(1832,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f22590837l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(73,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( A @ ( B @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1091_not__less__eq__eq) ).

thf(934,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(39,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( ( A @ ( suc @ hAPP_nat_nat ) )
         != B )
       => ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1076_Suc__lessI) ).

thf(817,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( ( A @ ( suc @ hAPP_nat_nat ) )
         != B )
       => ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(49,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_967_in__mono) ).

thf(853,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(320,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro666468413t_bool ) @ ( B @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_P324742453l_bool ) @ ( A @ ( B @ hAPP_P606313927t_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_547_Pi__mem) ).

thf(1892,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro666468413t_bool ) @ ( B @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_P324742453l_bool ) @ ( A @ ( B @ hAPP_P606313927t_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(496,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_Arr1861959080le_alt )
     => ( B @ ( A @ hAPP_A862370221t_bool ) @ is_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__HOL__Ob) ).

thf(2552,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_Arr1861959080le_alt )
     => ( B @ ( A @ hAPP_A862370221t_bool ) @ is_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(55,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_n539120590t_bool ) @ is_fun2093718614t_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfn) ).

thf(870,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_n539120590t_bool ) @ is_fun2093718614t_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(552,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_864945570l_bool @ hAPP_f49469479t_bool ) @ hAPP_f515126293t_bool ) @ hAPP_P606313927t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu_) ).

thf(2767,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_864945570l_bool @ hAPP_f49469479t_bool ) @ hAPP_f515126293t_bool ) @ hAPP_P606313927t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(245,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ? [C: $i] :
          ( B
          = ( C @ ( suc @ hAPP_nat_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1120_Suc__le__D) ).

thf(1609,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ? [C: $i] :
          ( B
          = ( C @ ( suc @ hAPP_nat_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(92,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_746_add__strict__right__mono) ).

thf(1013,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(192,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1108_Suc__le__lessD) ).

thf(1398,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(120,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ hAPP_n539120590t_bool ) @ ( B @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
     => ( ( A @ ( D @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( F @ ( E @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( C @ hAPP_n539120590t_bool ) @ ( E @ ( C @ hAPP_n539120590t_bool ) @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) )
         => ( A @ ( C @ hAPP_n539120590t_bool ) @ ( B @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_829_order__less__le__subst1) ).

thf(1115,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ hAPP_n539120590t_bool ) @ ( B @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
     => ( ( A @ ( D @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( F @ ( E @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( C @ hAPP_n539120590t_bool ) @ ( E @ ( C @ hAPP_n539120590t_bool ) @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) )
         => ( A @ ( C @ hAPP_n539120590t_bool ) @ ( B @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(641,axiom,
    ! [A: $i] : ( top_to565915683t_bool @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_516_top__greatest) ).

thf(3312,plain,
    ! [A: $i] : ( top_to565915683t_bool @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

thf(541,axiom,
    ~ ! [A: $i] :
        ( ( A @ is_fun961089132t_bool )
       => ( ( A @ ( a @ ( b @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
         => ~ ( arrow_1681063817le_Lin @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_) ).

thf(2730,plain,
    ~ ! [A: $i] :
        ( ( A @ is_fun961089132t_bool )
       => ( ( A @ ( a @ ( b @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
         => ~ ( arrow_1681063817le_Lin @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(290,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ hAPP_f816335862ol_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( D @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( ( F @ is_fun961089132t_bool )
                & ( E @ is_fun961089132t_bool ) )
             => ( ( F @ ( E @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
               => ( F @ ( C @ hAPP_f816335862ol_nat ) @ ( E @ ( C @ hAPP_f816335862ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) )
         => ( A @ ( C @ hAPP_f816335862ol_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_850_order__less__le__subst1) ).

thf(1778,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ hAPP_f816335862ol_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( D @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( ( F @ is_fun961089132t_bool )
                & ( E @ is_fun961089132t_bool ) )
             => ( ( F @ ( E @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
               => ( F @ ( C @ hAPP_f816335862ol_nat ) @ ( E @ ( C @ hAPP_f816335862ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) )
         => ( A @ ( C @ hAPP_f816335862ol_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(451,axiom,
    ! [A: $i] : ( top_to1853035173l_bool @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_iso__tuple__UNIV__I) ).

thf(2388,plain,
    ! [A: $i] : ( top_to1853035173l_bool @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(143,axiom,
    ! [A: $i,B: $i] :
      ( ( top_top_fun_nat_bool @ ( B @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ! [C: $i] :
            ( ( C @ ( A @ hAPP_nat_nat ) @ ( B @ hAPP_nat_nat ) )
            = C )
       => ( ( B @ ( top_top_fun_nat_bool @ hilber195283148at_nat ) )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_652_inj__imp__inv__eq) ).

thf(1232,plain,
    ! [A: $i,B: $i] :
      ( ( top_top_fun_nat_bool @ ( B @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ! [C: $i] :
            ( ( C @ ( A @ hAPP_nat_nat ) @ ( B @ hAPP_nat_nat ) )
            = C )
       => ( ( B @ ( top_top_fun_nat_bool @ hilber195283148at_nat ) )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(311,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_246631416le_alt @ hAPP_f2068374643l_bool ) @ ( C @ pi_Pro666468413t_bool ) @ ( B @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_P606313927t_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_581_funcset__mem) ).

thf(1847,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_246631416le_alt @ hAPP_f2068374643l_bool ) @ ( C @ pi_Pro666468413t_bool ) @ ( B @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_P606313927t_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(615,axiom,
    ! [A: $i] : ( A @ ( top_to1714702858l_bool @ hAPP_f312250286l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_top1I) ).

thf(3099,plain,
    ! [A: $i] : ( A @ ( top_to1714702858l_bool @ hAPP_f312250286l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

thf(294,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_Arr43961803e_indi )
     => ( B @ ( A @ hAPP_A60074736l_bool ) @ is_fun279392540l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It_005) ).

thf(1800,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_Arr43961803e_indi )
     => ( B @ ( A @ hAPP_A60074736l_bool ) @ is_fun279392540l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(395,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( arrow_610963188ctator @ hAPP_f1552576127i_bool ) @ hAPP_A1785763630i_bool ) @ hBOOL )
    <=> ! [C: $i] :
          ( ( arrow_1721807329e_Prof @ ( C @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
         => ( ( C @ ( A @ hAPP_f412050202t_bool ) )
            = ( B @ ( C @ hAPP_A1677245848t_bool ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_dictator__def) ).

thf(2169,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i] :
            ( ( arrow_1721807329e_Prof @ ( C @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
           => ( ( C @ ( A @ hAPP_f412050202t_bool ) )
              = ( B @ ( C @ hAPP_A1677245848t_bool ) ) ) )
       => ( B @ ( A @ ( arrow_610963188ctator @ hAPP_f1552576127i_bool ) @ hAPP_A1785763630i_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( arrow_610963188ctator @ hAPP_f1552576127i_bool ) @ hAPP_A1785763630i_bool ) @ hBOOL )
       => ! [C: $i] :
            ( ( arrow_1721807329e_Prof @ ( C @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
           => ( ( C @ ( A @ hAPP_f412050202t_bool ) )
              = ( B @ ( C @ hAPP_A1677245848t_bool ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(456,axiom,
    ! [A: $i,B: $i] :
      ( ( A != B )
     => ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_429_xt1_I12_J) ).

thf(2403,plain,
    ! [A: $i,B: $i] :
      ( ( A != B )
     => ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(300,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ hAPP_A1785763630i_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A2046586321t_bool ) @ hAPP_nat_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000) ).

thf(1815,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ hAPP_A1785763630i_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A2046586321t_bool ) @ hAPP_nat_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(217,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
        = ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
     => ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_728_add__right__imp__eq) ).

thf(1494,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
        = ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
     => ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(406,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun279392540l_bool )
     => ( B @ ( A @ hAPP_f111185985l_bool ) @ is_fun279392540l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn_037) ).

thf(2222,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun279392540l_bool )
     => ( B @ ( A @ hAPP_f111185985l_bool ) @ is_fun279392540l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(198,axiom,
    ! [A: $i] :
      ( ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( A = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1053_le__0__eq) ).

thf(1415,plain,
    ! [A: $i] :
      ( ( ( A = zero_zero_nat )
       => ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A = zero_zero_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(208,axiom,
    ! [A: $i] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1054_less__eq__nat_Osimps_I1_J) ).

thf(1465,plain,
    ! [A: $i] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(272,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( D @ ( A @ hAPP_n539120590t_bool ) @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( F @ ( E @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( A @ hAPP_n539120590t_bool ) @ ( E @ ( A @ hAPP_n539120590t_bool ) @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) )
         => ( B @ ( C @ ( A @ hAPP_n539120590t_bool ) @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_900_order__less__le__subst2) ).

thf(1714,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( D @ ( A @ hAPP_n539120590t_bool ) @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( F @ ( E @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( A @ hAPP_n539120590t_bool ) @ ( E @ ( A @ hAPP_n539120590t_bool ) @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) )
         => ( B @ ( C @ ( A @ hAPP_n539120590t_bool ) @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(571,axiom,
    ~ ( lba @ ( b @ ( a @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79__096_Ia_M_Ab_J_A_126_058_ALba_096) ).

thf(2880,plain,
    ~ ( lba @ ( b @ ( a @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(314,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( A @ ( C @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_ord__eq__le__trans) ).

thf(1858,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( A @ ( C @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(261,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun961089132t_bool )
     => ( B @ ( A @ hAPP_P606313927t_bool ) @ is_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__045) ).

thf(1677,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun961089132t_bool )
     => ( B @ ( A @ hAPP_P606313927t_bool ) @ is_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(556,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_951_subset__psubset__trans) ).

thf(2777,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(131,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun1568535512t_bool )
     => ( B @ ( A @ hAPP_f2028818269l_bool ) @ is_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_000tc__HOL__) ).

thf(1183,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun1568535512t_bool )
     => ( B @ ( A @ hAPP_f2028818269l_bool ) @ is_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(102,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1004_add__less__mono1) ).

thf(1051,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(64,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f167218729l_bool ) @ is_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_034) ).

thf(905,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f167218729l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(613,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( C @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_xt1_I3_J) ).

thf(3075,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( C @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(299,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun961089132t_bool )
     => ( ( B @ ( A @ ( fTrue @ ( if_fun2098446489t_bool @ hAPP_b1588041841t_bool ) @ hAPP_f427493225t_bool ) @ hAPP_f515126293t_bool ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbp) ).

thf(1811,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun961089132t_bool )
     => ( ( B @ ( A @ ( fTrue @ ( if_fun2098446489t_bool @ hAPP_b1588041841t_bool ) @ hAPP_f427493225t_bool ) @ hAPP_f515126293t_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(498,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun961089132t_bool ) )
     => ( ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
      <=> ( ( A = B )
          | ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_932_subset__iff__psubset__eq) ).

thf(2555,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun961089132t_bool ) )
     => ( ( ( ( A = B )
            | ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
         => ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
        & ( ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
         => ( ( A = B )
            | ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(36,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P332578347t_bool ) @ is_fun1568535512t_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__047) ).

thf(806,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P332578347t_bool ) @ is_fun1568535512t_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(237,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun2093718614t_bool )
     => ( B @ ( A @ hAPP_f324780729l_bool ) @ is_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc___008) ).

thf(1581,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun2093718614t_bool )
     => ( B @ ( A @ hAPP_f324780729l_bool ) @ is_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(439,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( C @ ( B @ hAPP_f816335862ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( ( F @ is_fun961089132t_bool )
                & ( E @ is_fun961089132t_bool ) )
             => ( ( E @ ( F @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
               => ( E @ ( B @ hAPP_f816335862ol_nat ) @ ( F @ ( B @ hAPP_f816335862ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) )
         => ( D @ ( B @ hAPP_f816335862ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_702_xt7) ).

thf(2335,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( C @ ( B @ hAPP_f816335862ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( ( F @ is_fun961089132t_bool )
                & ( E @ is_fun961089132t_bool ) )
             => ( ( E @ ( F @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
               => ( E @ ( B @ hAPP_f816335862ol_nat ) @ ( F @ ( B @ hAPP_f816335862ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) )
         => ( D @ ( B @ hAPP_f816335862ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(81,axiom,
    ( arrow_1721807329e_Prof
    = ( arrow_1681063817le_Lin @ ( cOMBK_657557929e_indi @ hAPP_f1659309744l_bool ) @ ( top_to1576102282i_bool @ pi_Arr990697634t_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_579_Prof__def) ).

thf(966,plain,
    ( arrow_1721807329e_Prof
    = ( arrow_1681063817le_Lin @ ( cOMBK_657557929e_indi @ hAPP_f1659309744l_bool ) @ ( top_to1576102282i_bool @ pi_Arr990697634t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(592,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_477_order__less__le__trans) ).

thf(2964,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(309,axiom,
    ! [A: $i] :
      ( ( n @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( lba @ ( lab @ ( A @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ ( cOMBC_510421983t_bool @ hAPP_f1297018969t_bool ) @ hAPP_f1909278132t_bool ) @ ( cOMBC_633721483t_bool @ hAPP_f573120177t_bool ) @ hAPP_f329301088t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( a @ ( b @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_n_I2_J) ).

thf(1843,plain,
    ! [A: $i] :
      ( ( n @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( lba @ ( lab @ ( A @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ ( cOMBC_510421983t_bool @ hAPP_f1297018969t_bool ) @ hAPP_f1909278132t_bool ) @ ( cOMBC_633721483t_bool @ hAPP_f573120177t_bool ) @ hAPP_f329301088t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( a @ ( b @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(24,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
        = ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) ) )
    <=> ( ( A = zero_zero_nat )
        | ( B = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1153_mult__cancel1) ).

thf(734,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( A = zero_zero_nat )
          | ( B = C ) )
       => ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
          = ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) ) ) )
      & ( ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
          = ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) ) )
       => ( ( A = zero_zero_nat )
          | ( B = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(319,axiom,
    ! [A: $i] :
      ( ( A @ ( top_to1576102282i_bool @ hAPP_A1785763630i_bool ) @ hBOOL )
    <=> ( top_top_bool @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_top__apply) ).

thf(1886,plain,
    ! [A: $i] :
      ( ( ( top_top_bool @ hBOOL )
       => ( A @ ( top_to1576102282i_bool @ hAPP_A1785763630i_bool ) @ hBOOL ) )
      & ( ( A @ ( top_to1576102282i_bool @ hAPP_A1785763630i_bool ) @ hBOOL )
       => ( top_top_bool @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(201,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1075_less__trans__Suc) ).

thf(1433,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(538,axiom,
    c @ is_Arr1861959080le_alt,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_c____) ).

thf(2718,plain,
    c @ is_Arr1861959080le_alt,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(232,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1074_less__SucE) ).

thf(1564,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(322,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_430_leD) ).

thf(1896,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(399,axiom,
    ! [A: $i] :
      ( ( A @ is_fun961089132t_bool )
     => ( ( A != top_to565915683t_bool )
      <=> ( top_to565915683t_bool @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_less__top) ).

thf(2190,plain,
    ! [A: $i] :
      ( ( A @ is_fun961089132t_bool )
     => ( ( ( top_to565915683t_bool @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
         => ( A != top_to565915683t_bool ) )
        & ( ( A != top_to565915683t_bool )
         => ( top_to565915683t_bool @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(493,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_ord__eq__less__trans) ).

thf(2530,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(491,axiom,
    arrow_1681063817le_Lin @ is_fun279392540l_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_OLin) ).

thf(2523,plain,
    arrow_1681063817le_Lin @ is_fun279392540l_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(293,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_order__less__imp__not__eq) ).

thf(1796,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(121,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
        = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
    <=> ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_991_nat__add__left__cancel) ).

thf(1119,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B = C )
       => ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
          = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) )
      & ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
          = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
       => ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(30,axiom,
    ! [A: $i,B: $i] :
      ( ( one_one_nat
        = ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) ) )
    <=> ( ( B = one_one_nat )
        & ( A = one_one_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1147_nat__1__eq__mult__iff) ).

thf(774,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( B = one_one_nat )
          & ( A = one_one_nat ) )
       => ( one_one_nat
          = ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) ) ) )
      & ( ( one_one_nat
          = ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) ) )
       => ( ( B = one_one_nat )
          & ( A = one_one_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(223,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_510421983t_bool @ hAPP_f1297018969t_bool ) @ hAPP_f1909278132t_bool ) @ hAPP_A1102281708t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A1455239488t_bool ) @ hAPP_f427493225t_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_074) ).

thf(1526,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_510421983t_bool @ hAPP_f1297018969t_bool ) @ hAPP_f1909278132t_bool ) @ hAPP_A1102281708t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A1455239488t_bool ) @ hAPP_f427493225t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(386,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1010_less__imp__le__nat) ).

thf(2137,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(414,axiom,
    ~ ! [A: $i] :
        ( ( top_to1576102282i_bool @ ( finite1686180860e_indi @ hAPP_f2120083535ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [B: $i] :
              ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( lba @ ( lab @ ( B @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ ( cOMBC_510421983t_bool @ hAPP_f1297018969t_bool ) @ hAPP_f1909278132t_bool ) @ ( cOMBC_633721483t_bool @ hAPP_f573120177t_bool ) @ hAPP_f329301088t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( a @ ( b @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
         => ~ ( lba @ ( lab @ ( one_one_nat @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ ( cOMBC_510421983t_bool @ hAPP_f1297018969t_bool ) @ hAPP_f1909278132t_bool ) @ ( cOMBC_633721483t_bool @ hAPP_f573120177t_bool ) @ hAPP_f329301088t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( b @ ( a @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_) ).

thf(2242,plain,
    ~ ! [A: $i] :
        ( ( top_to1576102282i_bool @ ( finite1686180860e_indi @ hAPP_f2120083535ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [B: $i] :
              ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( lba @ ( lab @ ( B @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ ( cOMBC_510421983t_bool @ hAPP_f1297018969t_bool ) @ hAPP_f1909278132t_bool ) @ ( cOMBC_633721483t_bool @ hAPP_f573120177t_bool ) @ hAPP_f329301088t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( a @ ( b @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
         => ~ ( lba @ ( lab @ ( one_one_nat @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ ( cOMBC_510421983t_bool @ hAPP_f1297018969t_bool ) @ hAPP_f1909278132t_bool ) @ ( cOMBC_633721483t_bool @ hAPP_f573120177t_bool ) @ hAPP_f329301088t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( b @ ( a @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(428,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun961089132t_bool ) )
     => ( ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
      <=> ( ( A != B )
          & ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_925_psubset__eq) ).

thf(2286,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun961089132t_bool ) )
     => ( ( ( ( A != B )
            & ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
         => ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
        & ( ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
         => ( ( A != B )
            & ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(377,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ is_Arr43961803e_indi )
        & ( A @ is_Arr43961803e_indi ) )
     => ( ( D @ ( C @ inj_on1073981917di_nat @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ( ( D @ ( B @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
         => ( ( D @ ( A @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
           => ( ( ( B @ ( C @ hAPP_A1637648121di_nat ) )
                = ( A @ ( C @ hAPP_A1637648121di_nat ) ) )
            <=> ( B = A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_543_inj__on__iff) ).

thf(2103,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ is_Arr43961803e_indi )
        & ( A @ is_Arr43961803e_indi ) )
     => ( ( D @ ( C @ inj_on1073981917di_nat @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ( ( D @ ( B @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
         => ( ( D @ ( A @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
           => ( ( ( B = A )
               => ( ( B @ ( C @ hAPP_A1637648121di_nat ) )
                  = ( A @ ( C @ hAPP_A1637648121di_nat ) ) ) )
              & ( ( ( B @ ( C @ hAPP_A1637648121di_nat ) )
                  = ( A @ ( C @ hAPP_A1637648121di_nat ) ) )
               => ( B = A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(547,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro1122146355t_unit ) @ ( B @ ( member2079083634t_unit @ hAPP_f1847883341l_bool ) @ hAPP_f22590837l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P332578347t_bool ) @ ( A @ ( B @ hAPP_P1844795325t_unit ) @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_PiE) ).

thf(2750,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro1122146355t_unit ) @ ( B @ ( member2079083634t_unit @ hAPP_f1847883341l_bool ) @ hAPP_f22590837l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P332578347t_bool ) @ ( A @ ( B @ hAPP_P1844795325t_unit ) @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(118,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_739_add__right__mono) ).

thf(1104,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(267,axiom,
    ! [A: $i] :
      ( ( A @ ( top_to522745736l_bool @ hAPP_f965095724l_bool ) @ hBOOL )
    <=> ( top_top_bool @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_top__apply) ).

thf(1697,plain,
    ! [A: $i] :
      ( ( ( top_top_bool @ hBOOL )
       => ( A @ ( top_to522745736l_bool @ hAPP_f965095724l_bool ) @ hBOOL ) )
      & ( ( A @ ( top_to522745736l_bool @ hAPP_f965095724l_bool ) @ hBOOL )
       => ( top_top_bool @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(146,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( C @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_990_nat__add__assoc) ).

thf(1242,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( C @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(243,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_742_add__less__imp__less__left) ).

thf(1604,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(351,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ( A != B )
        & ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1008_nat__less__le) ).

thf(2011,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A != B )
          & ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ( A != B )
          & ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(69,axiom,
    ! [A: $i,B: $i] :
      ~ ( B @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1000_not__add__less2) ).

thf(920,plain,
    ! [A: $i,B: $i] :
      ~ ( B @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(639,axiom,
    ~ ! [A: $i] :
        ( ( A @ is_fun961089132t_bool )
       => ( ( A @ ( b @ ( a @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
         => ~ ( arrow_1681063817le_Lin @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_) ).

thf(3301,plain,
    ~ ! [A: $i] :
        ( ( A @ is_fun961089132t_bool )
       => ( ( A @ ( b @ ( a @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
         => ~ ( arrow_1681063817le_Lin @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(265,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
     => ( ( B = A )
       => ( C @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_xt1_I4_J) ).

thf(1691,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
     => ( ( B = A )
       => ( C @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(28,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
        = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
    <=> ( ( B
          = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
        & ( A
          = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1157_mult__eq__1__iff) ).

thf(761,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( B
            = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
          & ( A
            = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) )
       => ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
          = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) )
      & ( ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
          = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
       => ( ( B
            = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
          & ( A
            = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(38,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
        & ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1162_nat__0__less__mult__iff) ).

thf(810,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          & ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          & ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(587,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P229966473l_bool ) @ is_fun279392540l_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__048) ).

thf(2954,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P229966473l_bool ) @ is_fun279392540l_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(254,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( ( B @ ( D @ ( A @ hAPP_f1313392232ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( ( F @ is_fun279392540l_bool )
                & ( E @ is_fun279392540l_bool ) )
             => ( ( F @ ( E @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
               => ( F @ ( A @ hAPP_f1313392232ol_nat ) @ ( E @ ( A @ hAPP_f1313392232ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) )
         => ( B @ ( C @ ( A @ hAPP_f1313392232ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_881_order__le__less__subst2) ).

thf(1651,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( ( B @ ( D @ ( A @ hAPP_f1313392232ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( ( F @ is_fun279392540l_bool )
                & ( E @ is_fun279392540l_bool ) )
             => ( ( F @ ( E @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
               => ( F @ ( A @ hAPP_f1313392232ol_nat ) @ ( E @ ( A @ hAPP_f1313392232ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) )
         => ( B @ ( C @ ( A @ hAPP_f1313392232ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(638,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( E @ is_Arr1861959080le_alt )
        & ( D @ is_Arr1861959080le_alt )
        & ( B @ is_Arr1861959080le_alt )
        & ( A @ is_Arr1861959080le_alt ) )
     => ( ( D != E )
       => ( ( arrow_1681063817le_Lin @ ( C @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
         => ( ( E @ ( D @ ( C @ ( arrow_230821333_above @ hAPP_f344580165t_bool ) @ hAPP_A1941004017t_bool ) @ hAPP_A568203993t_bool ) @ ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
          <=> ( ( ( A != E )
               => ( ( ( B != E )
                   => ( C @ ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
                  & ( ( B = E )
                   => ( ( C @ ( D @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                      | ( A = D ) ) ) ) )
              & ( ( A = E )
               => ( C @ ( B @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
              & ( A != B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_in__above) ).

thf(3265,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( E @ is_Arr1861959080le_alt )
        & ( D @ is_Arr1861959080le_alt )
        & ( B @ is_Arr1861959080le_alt )
        & ( A @ is_Arr1861959080le_alt ) )
     => ( ( D != E )
       => ( ( arrow_1681063817le_Lin @ ( C @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
         => ( ( ( ( ( A != E )
                 => ( ( ( B != E )
                     => ( C @ ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
                    & ( ( B = E )
                     => ( ( C @ ( D @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                        | ( A = D ) ) ) ) )
                & ( ( A = E )
                 => ( C @ ( B @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
                & ( A != B ) )
             => ( E @ ( D @ ( C @ ( arrow_230821333_above @ hAPP_f344580165t_bool ) @ hAPP_A1941004017t_bool ) @ hAPP_A568203993t_bool ) @ ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
            & ( ( E @ ( D @ ( C @ ( arrow_230821333_above @ hAPP_f344580165t_bool ) @ hAPP_A1941004017t_bool ) @ hAPP_A568203993t_bool ) @ ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
             => ( ( ( A != E )
                 => ( ( ( B != E )
                     => ( C @ ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
                    & ( ( B = E )
                     => ( ( C @ ( D @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                        | ( A = D ) ) ) ) )
                & ( ( A = E )
                 => ( C @ ( B @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
                & ( A != B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(71,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( ( A @ ( C @ times_times_nat @ hAPP_nat_nat ) )
          = ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) ) )
      <=> ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1178_nat__mult__eq__cancel1) ).

thf(925,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( ( A = B )
         => ( ( A @ ( C @ times_times_nat @ hAPP_nat_nat ) )
            = ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) ) ) )
        & ( ( ( A @ ( C @ times_times_nat @ hAPP_nat_nat ) )
            = ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) ) )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(327,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun961089132t_bool ) )
     => ( ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
      <=> ( ( A = B )
          | ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_402_order__le__less) ).

thf(1915,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun961089132t_bool ) )
     => ( ( ( ( A = B )
            | ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
         => ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
        & ( ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
         => ( ( A = B )
            | ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(270,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ hAPP_n588788980t_bool ) @ ( B @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( A @ ( D @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( F @ ( E @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( C @ hAPP_n588788980t_bool ) @ ( E @ ( C @ hAPP_n588788980t_bool ) @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
         => ( A @ ( C @ hAPP_n588788980t_bool ) @ ( B @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_827_order__less__le__subst1) ).

thf(1708,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ hAPP_n588788980t_bool ) @ ( B @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( A @ ( D @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( F @ ( E @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( C @ hAPP_n588788980t_bool ) @ ( E @ ( C @ hAPP_n588788980t_bool ) @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
         => ( A @ ( C @ hAPP_n588788980t_bool ) @ ( B @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(373,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A != B )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_linorder__cases) ).

thf(2093,plain,
    ! [A: $i,B: $i] :
      ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A != B )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(481,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_374_linorder__not__less) ).

thf(2496,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(560,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_959_set__mp) ).

thf(2790,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(518,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_bool )
     => ( B @ ( A @ hAPP_b1703662281t_bool ) @ is_fun961089132t_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabel) ).

thf(2660,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_bool )
     => ( B @ ( A @ hAPP_b1703662281t_bool ) @ is_fun961089132t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(317,axiom,
    ! [A: $i,B: $i] :
      ( ( A != B )
    <=> ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
        | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_linorder__neq__iff) ).

thf(1868,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( A != B ) )
      & ( ( A != B )
       => ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(364,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun279392540l_bool )
     => ( B @ ( A @ hAPP_f1749234559l_bool ) @ is_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn_036) ).

thf(2061,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun279392540l_bool )
     => ( B @ ( A @ hAPP_f1749234559l_bool ) @ is_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(554,axiom,
    ~ ( lab @ ( a @ ( b @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80__096_Ib_M_Aa_J_A_126_058_ALab_096) ).

thf(2773,plain,
    ~ ( lab @ ( a @ ( b @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(506,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ is_Arr1861959080le_alt )
        & ( B @ is_Arr1861959080le_alt ) )
     => ( ( B != C )
       => ( ( arrow_1681063817le_Lin @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
         => ( arrow_1681063817le_Lin @ ( C @ ( B @ ( A @ arrow_1539419881_below ) ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_578_below__Lin) ).

thf(2589,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ is_Arr1861959080le_alt )
        & ( B @ is_Arr1861959080le_alt ) )
     => ( ( B != C )
       => ( ( arrow_1681063817le_Lin @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
         => ( arrow_1681063817le_Lin @ ( C @ ( B @ ( A @ arrow_1539419881_below ) ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(420,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_Arr43961803e_indi )
     => ( B @ ( A @ hAPP_A1677245848t_bool ) @ is_fun961089132t_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__fun_It_006) ).

thf(2264,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_Arr43961803e_indi )
     => ( B @ ( A @ hAPP_A1677245848t_bool ) @ is_fun961089132t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(61,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( ( C @ ( B @ hAPP_f1313392232ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( ( F @ is_fun279392540l_bool )
                & ( E @ is_fun279392540l_bool ) )
             => ( ( E @ ( F @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
               => ( E @ ( B @ hAPP_f1313392232ol_nat ) @ ( F @ ( B @ hAPP_f1313392232ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) )
         => ( D @ ( B @ hAPP_f1313392232ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_699_xt7) ).

thf(894,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( ( C @ ( B @ hAPP_f1313392232ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( ( F @ is_fun279392540l_bool )
                & ( E @ is_fun279392540l_bool ) )
             => ( ( E @ ( F @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
               => ( E @ ( B @ hAPP_f1313392232ol_nat ) @ ( F @ ( B @ hAPP_f1313392232ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) )
         => ( D @ ( B @ hAPP_f1313392232ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(511,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ hAPP_f1358350510ol_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( D @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( ( F @ is_fun2093718614t_bool )
                & ( E @ is_fun2093718614t_bool ) )
             => ( ( F @ ( E @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
               => ( F @ ( C @ hAPP_f1358350510ol_nat ) @ ( E @ ( C @ hAPP_f1358350510ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) )
         => ( A @ ( C @ hAPP_f1358350510ol_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_854_order__less__le__subst1) ).

thf(2601,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ hAPP_f1358350510ol_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( D @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( ( F @ is_fun2093718614t_bool )
                & ( E @ is_fun2093718614t_bool ) )
             => ( ( F @ ( E @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
               => ( F @ ( C @ hAPP_f1358350510ol_nat ) @ ( E @ ( C @ hAPP_f1358350510ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) )
         => ( A @ ( C @ hAPP_f1358350510ol_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(95,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1552576127i_bool ) @ is_fun1236654035i_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_025) ).

thf(1021,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1552576127i_bool ) @ is_fun1236654035i_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(509,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ is_Arr1861959080le_alt )
        & ( B @ is_Arr1861959080le_alt ) )
     => ( ( B != C )
       => ( ( arrow_1681063817le_Lin @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
         => ( arrow_1681063817le_Lin @ ( C @ ( B @ ( A @ ( arrow_230821333_above @ hAPP_f344580165t_bool ) @ hAPP_A1941004017t_bool ) @ hAPP_A568203993t_bool ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_above__Lin) ).

thf(2596,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ is_Arr1861959080le_alt )
        & ( B @ is_Arr1861959080le_alt ) )
     => ( ( B != C )
       => ( ( arrow_1681063817le_Lin @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
         => ( arrow_1681063817le_Lin @ ( C @ ( B @ ( A @ ( arrow_230821333_above @ hAPP_f344580165t_bool ) @ hAPP_A1941004017t_bool ) @ hAPP_A568203993t_bool ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(425,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun961089132t_bool ) )
     => ( ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( ( A != B )
         => ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_457_order__le__neq__trans) ).

thf(2277,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun961089132t_bool ) )
     => ( ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( ( A != B )
         => ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(40,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_747_add__less__cancel__left) ).

thf(820,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(595,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro1270767662e_indi ) @ ( B @ ( member234128621e_indi @ hAPP_f407092109l_bool ) @ hAPP_f1306865520l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_P1875867302i_bool ) @ ( A @ ( B @ hAPP_P710098616e_indi ) @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_548_Pi__mem) ).

thf(2969,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro1270767662e_indi ) @ ( B @ ( member234128621e_indi @ hAPP_f407092109l_bool ) @ hAPP_f1306865520l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_P1875867302i_bool ) @ ( A @ ( B @ hAPP_P710098616e_indi ) @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(12,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( cOMBK_1693871704t_bool @ hAPP_f1460506473l_bool ) @ hAPP_f210572555l_bool ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc) ).

thf(693,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( cOMBK_1693871704t_bool @ hAPP_f1460506473l_bool ) @ hAPP_f210572555l_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(356,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ( A = B )
        | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_406_order__le__less) ).

thf(2032,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A = B )
          | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ( A = B )
          | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(575,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( A @ ( C @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_ord__eq__le__trans) ).

thf(2890,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( A @ ( C @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(145,axiom,
    ! [A: $i,B: $i] :
      ( ( zero_zero_nat @ ( B @ hAPP_nat_bool ) @ hBOOL )
     => ( ! [C: $i] :
            ( ( C @ ( B @ hAPP_nat_bool ) @ hBOOL )
           => ( C @ ( suc @ hAPP_nat_nat ) @ ( B @ hAPP_nat_bool ) @ hBOOL ) )
       => ( A @ ( B @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1126_nat__induct) ).

thf(1238,plain,
    ! [A: $i,B: $i] :
      ( ( zero_zero_nat @ ( B @ hAPP_nat_bool ) @ hBOOL )
     => ( ! [C: $i] :
            ( ( C @ ( B @ hAPP_nat_bool ) @ hBOOL )
           => ( C @ ( suc @ hAPP_nat_nat ) @ ( B @ hAPP_nat_bool ) @ hBOOL ) )
       => ( A @ ( B @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(303,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f54304608l_bool ) @ is_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).

thf(1824,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f54304608l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(390,axiom,
    ! [A: $i] :
      ( ( A @ ( top_top_fun_nat_bool @ hAPP_nat_bool ) @ hBOOL )
    <=> ( top_top_bool @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_top__apply) ).

thf(2150,plain,
    ! [A: $i] :
      ( ( ( top_top_bool @ hBOOL )
       => ( A @ ( top_top_fun_nat_bool @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( A @ ( top_top_fun_nat_bool @ hAPP_nat_bool ) @ hBOOL )
       => ( top_top_bool @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(185,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1019_add__le__mono1) ).

thf(1370,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(307,axiom,
    ! [A: $i] :
      ( ( A @ is_fun961089132t_bool )
     => ( ( A @ ( top_to565915683t_bool @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( A = top_to565915683t_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_534_top__le) ).

thf(1837,plain,
    ! [A: $i] :
      ( ( A @ is_fun961089132t_bool )
     => ( ( A @ ( top_to565915683t_bool @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( A = top_to565915683t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(516,axiom,
    ! [A: $i] :
      ( ( ( ~ ( n @ ( A @ ( h @ hAPP_A1637648121di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( ( ( ( A @ ( h @ hAPP_A1637648121di_nat ) )
               != n )
             => ( e @ ( A @ ( p @ hAPP_A1677245848t_bool ) @ ( arrow_1495666017_mkbot @ hAPP_f393984045t_bool ) @ hAPP_A568203993t_bool ) @ ( e @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
            & ( ( ( A @ ( h @ hAPP_A1637648121di_nat ) )
                = n )
             => ( e @ ( c @ ( A @ ( p @ hAPP_A1677245848t_bool ) @ ( arrow_230821333_above @ hAPP_f344580165t_bool ) @ hAPP_A1941004017t_bool ) @ hAPP_A568203993t_bool ) @ ( e @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) )
        & ( ( n @ ( A @ ( h @ hAPP_A1637648121di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( e @ ( A @ ( p @ hAPP_A1677245848t_bool ) @ ( arrow_1644373103_mktop @ hAPP_f393984045t_bool ) @ hAPP_A568203993t_bool ) @ ( e @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) )
    <=> ( ( ~ ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( h @ hAPP_A1637648121di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( lba @ ( b @ ( a @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
        & ( ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( h @ hAPP_A1637648121di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( lab @ ( b @ ( a @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am) ).

thf(2628,plain,
    ! [A: $i] :
      ( ( ( ( ~ ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( h @ hAPP_A1637648121di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( lba @ ( b @ ( a @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
          & ( ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( h @ hAPP_A1637648121di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( lab @ ( b @ ( a @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) )
       => ( ( ~ ( n @ ( A @ ( h @ hAPP_A1637648121di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( ( ( ( A @ ( h @ hAPP_A1637648121di_nat ) )
                 != n )
               => ( e @ ( A @ ( p @ hAPP_A1677245848t_bool ) @ ( arrow_1495666017_mkbot @ hAPP_f393984045t_bool ) @ hAPP_A568203993t_bool ) @ ( e @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
              & ( ( ( A @ ( h @ hAPP_A1637648121di_nat ) )
                  = n )
               => ( e @ ( c @ ( A @ ( p @ hAPP_A1677245848t_bool ) @ ( arrow_230821333_above @ hAPP_f344580165t_bool ) @ hAPP_A1941004017t_bool ) @ hAPP_A568203993t_bool ) @ ( e @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) )
          & ( ( n @ ( A @ ( h @ hAPP_A1637648121di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( e @ ( A @ ( p @ hAPP_A1677245848t_bool ) @ ( arrow_1644373103_mktop @ hAPP_f393984045t_bool ) @ hAPP_A568203993t_bool ) @ ( e @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) )
      & ( ( ( ~ ( n @ ( A @ ( h @ hAPP_A1637648121di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( ( ( ( A @ ( h @ hAPP_A1637648121di_nat ) )
                 != n )
               => ( e @ ( A @ ( p @ hAPP_A1677245848t_bool ) @ ( arrow_1495666017_mkbot @ hAPP_f393984045t_bool ) @ hAPP_A568203993t_bool ) @ ( e @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
              & ( ( ( A @ ( h @ hAPP_A1637648121di_nat ) )
                  = n )
               => ( e @ ( c @ ( A @ ( p @ hAPP_A1677245848t_bool ) @ ( arrow_230821333_above @ hAPP_f344580165t_bool ) @ hAPP_A1941004017t_bool ) @ hAPP_A568203993t_bool ) @ ( e @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) )
          & ( ( n @ ( A @ ( h @ hAPP_A1637648121di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( e @ ( A @ ( p @ hAPP_A1677245848t_bool ) @ ( arrow_1644373103_mktop @ hAPP_f393984045t_bool ) @ hAPP_A568203993t_bool ) @ ( e @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) )
       => ( ( ~ ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( h @ hAPP_A1637648121di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( lba @ ( b @ ( a @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
          & ( ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( h @ hAPP_A1637648121di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( lab @ ( b @ ( a @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(629,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ is_Arr1861959080le_alt )
        & ( C @ is_Arr1861959080le_alt )
        & ( B @ is_Arr1861959080le_alt )
        & ( A @ is_Arr1861959080le_alt ) )
     => ( ( ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) )
          = ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) ) )
       => ~ ( ( A = C )
           => ( B != D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_Pair__inject) ).

thf(3198,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ is_Arr1861959080le_alt )
        & ( C @ is_Arr1861959080le_alt )
        & ( B @ is_Arr1861959080le_alt )
        & ( A @ is_Arr1861959080le_alt ) )
     => ( ( ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) )
          = ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) ) )
       => ~ ( ( A = C )
           => ( B != D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(642,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun961089132t_bool ) )
     => ( ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
         => ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_908_equalityI) ).

thf(3314,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun961089132t_bool ) )
     => ( ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).

thf(42,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1084_add__Suc) ).

thf(830,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(396,axiom,
    ( top_to1853035173l_bool
    = ( fTrue @ ( cOMBK_1656150864t_bool @ hAPP_b1812770943l_bool ) @ ( collec1553055422t_bool @ hAPP_f111185985l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_UNIV__def) ).

thf(2179,plain,
    ( top_to1853035173l_bool
    = ( fTrue @ ( cOMBK_1656150864t_bool @ hAPP_b1812770943l_bool ) @ ( collec1553055422t_bool @ hAPP_f111185985l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(397,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
     => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1012_less__or__eq__imp__le) ).

thf(2181,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
        | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
     => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(609,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_2112722489le_alt @ hAPP_f156764033l_bool ) @ hAPP_A1553574765l_bool ) )
      = ( C @ ( B @ hAPP_A1505516597le_alt ) @ ( A @ hAPP_f1539445765l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__) ).

thf(3050,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_2112722489le_alt @ hAPP_f156764033l_bool ) @ hAPP_A1553574765l_bool ) )
      = ( C @ ( B @ hAPP_A1505516597le_alt ) @ ( A @ hAPP_f1539445765l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(409,axiom,
    ! [A: $i,B: $i] :
      ( ( A != B )
     => ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_linorder__neqE) ).

thf(2228,plain,
    ! [A: $i,B: $i] :
      ( ( A != B )
     => ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(18,axiom,
    ! [A: $i] :
      ( ( A @ ( one_one_nat @ times_times_nat @ hAPP_nat_nat ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1148_nat__mult__1) ).

thf(710,plain,
    ! [A: $i] :
      ( ( A @ ( one_one_nat @ times_times_nat @ hAPP_nat_nat ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(46,axiom,
    ! [A: $i] :
      ~ ( A @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1092_Suc__n__not__le__n) ).

thf(842,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(84,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1103_less__Suc__eq__le) ).

thf(974,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(119,axiom,
    ! [A: $i] :
      ( ( one_one_nat = A )
    <=> ( A = one_one_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_734_one__reorient) ).

thf(1106,plain,
    ! [A: $i] :
      ( ( ( A = one_one_nat )
       => ( one_one_nat = A ) )
      & ( ( one_one_nat = A )
       => ( A = one_one_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(589,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_915_subsetD) ).

thf(2958,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(199,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_748_add__less__cancel__right) ).

thf(1423,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(640,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( D @ is_Arr43961803e_indi )
         => ( ( C @ ( D @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
           => ( D @ ( B @ hAPP_A1677245848t_bool ) @ ( D @ ( A @ hAPP_A638717112le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) )
     => ( B @ ( C @ pi_Arr1199386158le_alt ) @ ( A @ ( member797673069le_alt @ hAPP_f721935245l_bool ) @ hAPP_f1837019376l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_634_Pi__I) ).

thf(3307,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( D @ is_Arr43961803e_indi )
         => ( ( C @ ( D @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
           => ( D @ ( B @ hAPP_A1677245848t_bool ) @ ( D @ ( A @ hAPP_A638717112le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) )
     => ( B @ ( C @ pi_Arr1199386158le_alt ) @ ( A @ ( member797673069le_alt @ hAPP_f721935245l_bool ) @ hAPP_f1837019376l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(331,axiom,
    ! [A: $i] :
      ( ( A @ is_bool )
     => ( ( A = fFalse )
        | ( A = fTrue ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).

thf(1938,plain,
    ! [A: $i] :
      ( ( A @ is_bool )
     => ( ( A = fFalse )
        | ( A = fTrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(48,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ hAPP_f1313392232ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( ( F @ is_fun279392540l_bool )
                & ( E @ is_fun279392540l_bool ) )
             => ( ( E @ ( F @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
               => ( E @ ( B @ hAPP_f1313392232ol_nat ) @ ( F @ ( B @ hAPP_f1313392232ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) )
         => ( D @ ( A @ ( B @ hAPP_f1313392232ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_798_xt4) ).

thf(847,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ hAPP_f1313392232ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( ( F @ is_fun279392540l_bool )
                & ( E @ is_fun279392540l_bool ) )
             => ( ( E @ ( F @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
               => ( E @ ( B @ hAPP_f1313392232ol_nat ) @ ( F @ ( B @ hAPP_f1313392232ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) )
         => ( D @ ( A @ ( B @ hAPP_f1313392232ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(464,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_489_xt1_I7_J) ).

thf(2433,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(475,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ hAPP_A1677245848t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A1625428400t_bool ) @ hAPP_A568203993t_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_059) ).

thf(2477,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ hAPP_A1677245848t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A1625428400t_bool ) @ hAPP_A568203993t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(264,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_less__imp__neq) ).

thf(1687,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(207,axiom,
    ! [A: $i] :
      ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ? [B: $i] :
          ( A
          = ( B @ ( suc @ hAPP_nat_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1094_gr0__conv__Suc) ).

thf(1457,plain,
    ! [A: $i] :
      ( ( ? [B: $i] :
            ( A
            = ( B @ ( suc @ hAPP_nat_nat ) ) )
       => ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ? [B: $i] :
            ( A
            = ( B @ ( suc @ hAPP_nat_nat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(367,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_995_eq__imp__le) ).

thf(2068,plain,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(250,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B
         != ( A @ ( suc @ hAPP_nat_nat ) ) )
       => ~ ! [C: $i] :
              ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( B
               != ( C @ ( suc @ hAPP_nat_nat ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1121_lessE) ).

thf(1624,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B
         != ( A @ ( suc @ hAPP_nat_nat ) ) )
       => ~ ! [C: $i] :
              ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( B
               != ( C @ ( suc @ hAPP_nat_nat ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(110,axiom,
    ! [A: $i] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
      = ( A @ ( one_one_nat @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1119_Suc__eq__plus1__left) ).

thf(1079,plain,
    ! [A: $i] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
      = ( A @ ( one_one_nat @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(403,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun1568535512t_bool )
     => ( B @ ( A @ hAPP_P1676879539t_bool ) @ is_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__HOL__Obool) ).

thf(2213,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun1568535512t_bool )
     => ( B @ ( A @ hAPP_P1676879539t_bool ) @ is_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(441,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_438_order__less__imp__le) ).

thf(2344,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(479,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_xt1_I6_J) ).

thf(2492,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(343,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun961089132t_bool ) )
     => ( ( A != B )
       => ( ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
         => ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_415_order__neq__le__trans) ).

thf(1983,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun961089132t_bool ) )
     => ( ( A != B )
       => ( ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
         => ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(501,axiom,
    arrow_1681063817le_Lin @ ( cOMBK_2038534567t_bool @ hAPP_f1924755118l_bool ) @ ( arrow_1721807329e_Prof @ pi_fun150026276t_bool ) @ ( f @ ( member520425275t_bool @ hAPP_f1253375959l_bool ) @ hAPP_f250445784l_bool ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_assms_I1_J) ).

thf(2577,plain,
    arrow_1681063817le_Lin @ ( cOMBK_2038534567t_bool @ hAPP_f1924755118l_bool ) @ ( arrow_1721807329e_Prof @ pi_fun150026276t_bool ) @ ( f @ ( member520425275t_bool @ hAPP_f1253375959l_bool ) @ hAPP_f250445784l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(540,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( B = A )
       => ( C @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_xt1_I4_J) ).

thf(2726,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( B = A )
       => ( C @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(605,axiom,
    c != d,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096c_A_126_061_Ad_096) ).

thf(3001,plain,
    c != d,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(569,axiom,
    ! [A: $i] :
      ( ( ( ~ ( n @ ( A @ ( h @ hAPP_A1637648121di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( ( ( ( A @ ( h @ hAPP_A1637648121di_nat ) )
               != n )
             => ( e @ ( A @ ( p @ hAPP_A1677245848t_bool ) @ ( arrow_1495666017_mkbot @ hAPP_f393984045t_bool ) @ hAPP_A568203993t_bool ) @ ( d @ ( e @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
            & ( ( ( A @ ( h @ hAPP_A1637648121di_nat ) )
                = n )
             => ( e @ ( c @ ( A @ ( p @ hAPP_A1677245848t_bool ) @ ( arrow_230821333_above @ hAPP_f344580165t_bool ) @ hAPP_A1941004017t_bool ) @ hAPP_A568203993t_bool ) @ ( d @ ( e @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) )
        & ( ( n @ ( A @ ( h @ hAPP_A1637648121di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( e @ ( A @ ( p @ hAPP_A1677245848t_bool ) @ ( arrow_1644373103_mktop @ hAPP_f393984045t_bool ) @ hAPP_A568203993t_bool ) @ ( d @ ( e @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) )
    <=> ( ( ~ ( n @ ( A @ ( h @ hAPP_A1637648121di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( lba @ ( a @ ( b @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
        & ( ( n @ ( A @ ( h @ hAPP_A1637648121di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( lab @ ( a @ ( b @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk) ).

thf(2840,plain,
    ! [A: $i] :
      ( ( ( ( ~ ( n @ ( A @ ( h @ hAPP_A1637648121di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( lba @ ( a @ ( b @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
          & ( ( n @ ( A @ ( h @ hAPP_A1637648121di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( lab @ ( a @ ( b @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) )
       => ( ( ~ ( n @ ( A @ ( h @ hAPP_A1637648121di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( ( ( ( A @ ( h @ hAPP_A1637648121di_nat ) )
                 != n )
               => ( e @ ( A @ ( p @ hAPP_A1677245848t_bool ) @ ( arrow_1495666017_mkbot @ hAPP_f393984045t_bool ) @ hAPP_A568203993t_bool ) @ ( d @ ( e @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
              & ( ( ( A @ ( h @ hAPP_A1637648121di_nat ) )
                  = n )
               => ( e @ ( c @ ( A @ ( p @ hAPP_A1677245848t_bool ) @ ( arrow_230821333_above @ hAPP_f344580165t_bool ) @ hAPP_A1941004017t_bool ) @ hAPP_A568203993t_bool ) @ ( d @ ( e @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) )
          & ( ( n @ ( A @ ( h @ hAPP_A1637648121di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( e @ ( A @ ( p @ hAPP_A1677245848t_bool ) @ ( arrow_1644373103_mktop @ hAPP_f393984045t_bool ) @ hAPP_A568203993t_bool ) @ ( d @ ( e @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) )
      & ( ( ( ~ ( n @ ( A @ ( h @ hAPP_A1637648121di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( ( ( ( A @ ( h @ hAPP_A1637648121di_nat ) )
                 != n )
               => ( e @ ( A @ ( p @ hAPP_A1677245848t_bool ) @ ( arrow_1495666017_mkbot @ hAPP_f393984045t_bool ) @ hAPP_A568203993t_bool ) @ ( d @ ( e @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
              & ( ( ( A @ ( h @ hAPP_A1637648121di_nat ) )
                  = n )
               => ( e @ ( c @ ( A @ ( p @ hAPP_A1677245848t_bool ) @ ( arrow_230821333_above @ hAPP_f344580165t_bool ) @ hAPP_A1941004017t_bool ) @ hAPP_A568203993t_bool ) @ ( d @ ( e @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) )
          & ( ( n @ ( A @ ( h @ hAPP_A1637648121di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( e @ ( A @ ( p @ hAPP_A1677245848t_bool ) @ ( arrow_1644373103_mktop @ hAPP_f393984045t_bool ) @ hAPP_A568203993t_bool ) @ ( d @ ( e @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) )
       => ( ( ~ ( n @ ( A @ ( h @ hAPP_A1637648121di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( lba @ ( a @ ( b @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
          & ( ( n @ ( A @ ( h @ hAPP_A1637648121di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( lab @ ( a @ ( b @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(125,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( D @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_737_add__mono) ).

thf(1143,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( D @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(379,axiom,
    ! [A: $i] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_993_le__refl) ).

thf(2115,plain,
    ! [A: $i] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(313,axiom,
    ! [A: $i] :
      ( ( A @ is_fun2093718614t_bool )
     => ( ( A @ ( top_to178429151t_bool @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
      <=> ( A = top_to178429151t_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_526_top__unique) ).

thf(1851,plain,
    ! [A: $i] :
      ( ( A @ is_fun2093718614t_bool )
     => ( ( ( A = top_to178429151t_bool )
         => ( A @ ( top_to178429151t_bool @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) )
        & ( ( A @ ( top_to178429151t_bool @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
         => ( A = top_to178429151t_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(584,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_545135096l_bool @ hAPP_f340261009t_bool ) @ ( C @ pi_boo115158845le_alt ) @ ( B @ ( member1463820796le_alt @ hAPP_f2127575245l_bool ) @ hAPP_f1351174655l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_b55004359le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_597_funcset__mem) ).

thf(2946,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_545135096l_bool @ hAPP_f340261009t_bool ) @ ( C @ pi_boo115158845le_alt ) @ ( B @ ( member1463820796le_alt @ hAPP_f2127575245l_bool ) @ hAPP_f1351174655l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_b55004359le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(533,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_Arr1861959080le_alt )
     => ( B @ ( A @ hAPP_A187815023l_bool ) @ is_fun279392540l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__fun_Itc) ).

thf(2709,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_Arr1861959080le_alt )
     => ( B @ ( A @ hAPP_A187815023l_bool ) @ is_fun279392540l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(341,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
     => ( ( ( B = C )
         => ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( ( ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
         => ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_987_nat__less__cases) ).

thf(1970,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
     => ( ( ( B = C )
         => ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( ( ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
         => ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(141,axiom,
    ! [A: $i] :
      ( ( top_to1647826457l_bool @ ( cOMBK_246631416le_alt @ hAPP_f2068374643l_bool ) @ ( A @ pi_Pro666468413t_bool ) )
      = top_to1853035173l_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_Pi__UNIV) ).

thf(1227,plain,
    ! [A: $i] :
      ( ( top_to1647826457l_bool @ ( cOMBK_246631416le_alt @ hAPP_f2068374643l_bool ) @ ( A @ pi_Pro666468413t_bool ) )
      = top_to1853035173l_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(85,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
        = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
    <=> ( ( ( B
            = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
          & ( A = zero_zero_nat ) )
        | ( ( B = zero_zero_nat )
          & ( A
            = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1097_add__is__1) ).

thf(980,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( ( B
              = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
            & ( A = zero_zero_nat ) )
          | ( ( B = zero_zero_nat )
            & ( A
              = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) )
       => ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
          = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) )
      & ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
          = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
       => ( ( ( B
              = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
            & ( A = zero_zero_nat ) )
          | ( ( B = zero_zero_nat )
            & ( A
              = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(529,axiom,
    ! [A: $i] :
      ~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1046_less__nat__zero__code) ).

thf(2692,plain,
    ! [A: $i] :
      ~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(226,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( D @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1020_add__le__mono) ).

thf(1540,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( D @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(90,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun279392540l_bool )
     => ( ( B @ ( A @ ( cOMBK_657557929e_indi @ hAPP_f1659309744l_bool ) @ hAPP_A60074736l_bool ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_057) ).

thf(1006,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun279392540l_bool )
     => ( ( B @ ( A @ ( cOMBK_657557929e_indi @ hAPP_f1659309744l_bool ) @ hAPP_A60074736l_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(636,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_Arr1861959080le_alt )
        & ( A @ is_Arr1861959080le_alt ) )
     => ( ( A != B )
       => ? [C: $i] :
            ( ( C @ ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
            & ( arrow_1681063817le_Lin @ ( C @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
            & ( C @ is_fun961089132t_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_complete__Lin) ).

thf(3237,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_Arr1861959080le_alt )
        & ( A @ is_Arr1861959080le_alt ) )
     => ( ( A != B )
       => ? [C: $i] :
            ( ( C @ ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
            & ( arrow_1681063817le_Lin @ ( C @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
            & ( C @ is_fun961089132t_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(284,axiom,
    ! [A: $i] :
      ~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1044_not__less0) ).

thf(1755,plain,
    ! [A: $i] :
      ~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(233,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( A @ ( B @ pi_Pro666468413t_bool ) @ ( A @ ( C @ pi_Pro666468413t_bool ) @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_715_Pi__anti__mono) ).

thf(1567,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( A @ ( B @ pi_Pro666468413t_bool ) @ ( A @ ( C @ pi_Pro666468413t_bool ) @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(173,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      <=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1176_nat__mult__le__cancel1) ).

thf(1329,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
        & ( ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(129,axiom,
    ! [A: $i,B: $i] :
      ( ( ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) )
        = ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
    <=> ( ( ( B
            = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
          & ( A = zero_zero_nat ) )
        | ( ( B = zero_zero_nat )
          & ( A
            = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1098_one__is__add) ).

thf(1160,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( ( B
              = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
            & ( A = zero_zero_nat ) )
          | ( ( B = zero_zero_nat )
            & ( A
              = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) )
       => ( ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) )
          = ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) )
      & ( ( ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) )
          = ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
       => ( ( ( B
              = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
            & ( A = zero_zero_nat ) )
          | ( ( B = zero_zero_nat )
            & ( A
              = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(435,axiom,
    ! [A: $i,B: $i] :
      ( ( arrow_1681063817le_Lin @ ( B @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( arrow_1681063817le_Lin @ ( A @ ( B @ ( arrow_1495666017_mkbot @ hAPP_f393984045t_bool ) @ hAPP_A568203993t_bool ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_mkbot__Lin) ).

thf(2323,plain,
    ! [A: $i,B: $i] :
      ( ( arrow_1681063817le_Lin @ ( B @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( arrow_1681063817le_Lin @ ( A @ ( B @ ( arrow_1495666017_mkbot @ hAPP_f393984045t_bool ) @ hAPP_A568203993t_bool ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(163,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( suc @ hAPP_nat_nat ) )
        = ( B @ ( suc @ hAPP_nat_nat ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1062_Suc__inject) ).

thf(1292,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( suc @ hAPP_nat_nat ) )
        = ( B @ ( suc @ hAPP_nat_nat ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(631,axiom,
    ! [A: $i] : ( top_to565915683t_bool @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_UNIV__I) ).

thf(3210,plain,
    ! [A: $i] : ( top_to565915683t_bool @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(461,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ hAPP_f816335862ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( ( F @ is_fun961089132t_bool )
                & ( E @ is_fun961089132t_bool ) )
             => ( ( E @ ( F @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
               => ( E @ ( B @ hAPP_f816335862ol_nat ) @ ( F @ ( B @ hAPP_f816335862ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) )
         => ( D @ ( A @ ( B @ hAPP_f816335862ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_801_xt4) ).

thf(2419,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ hAPP_f816335862ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( ( F @ is_fun961089132t_bool )
                & ( E @ is_fun961089132t_bool ) )
             => ( ( E @ ( F @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
               => ( E @ ( B @ hAPP_f816335862ol_nat ) @ ( F @ ( B @ hAPP_f816335862ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) )
         => ( D @ ( A @ ( B @ hAPP_f816335862ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(469,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_order__less__imp__triv) ).

thf(2455,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(253,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( top_top_fun_nat_bool @ ( C @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( ( A @ ( C @ hAPP_nat_nat ) )
          = ( B @ ( C @ hAPP_nat_nat ) ) )
      <=> ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_613_inj__eq) ).

thf(1644,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( top_top_fun_nat_bool @ ( C @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( ( A = B )
         => ( ( A @ ( C @ hAPP_nat_nat ) )
            = ( B @ ( C @ hAPP_nat_nat ) ) ) )
        & ( ( ( A @ ( C @ hAPP_nat_nat ) )
            = ( B @ ( C @ hAPP_nat_nat ) ) )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(246,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2093718614t_bool )
        & ( A @ is_fun2093718614t_bool ) )
     => ( ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( ( A != B )
         => ( B @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_459_order__le__neq__trans) ).

thf(1612,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2093718614t_bool )
        & ( A @ is_fun2093718614t_bool ) )
     => ( ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( ( A != B )
         => ( B @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(128,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( zero_zero_nat @ ( B @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( B @ hAPP_nat_bool ) @ hBOOL )
       => ? [C: $i] :
            ( ( C @ ( B @ hAPP_nat_bool ) @ hBOOL )
            & ! [D: $i] :
                ( ( C @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
               => ~ ( D @ ( B @ hAPP_nat_bool ) @ hBOOL ) )
            & ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1057_ex__least__nat__le) ).

thf(1155,plain,
    ! [A: $i,B: $i] :
      ( ~ ( zero_zero_nat @ ( B @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( B @ hAPP_nat_bool ) @ hBOOL )
       => ? [C: $i] :
            ( ( C @ ( B @ hAPP_nat_bool ) @ hBOOL )
            & ! [D: $i] :
                ( ( C @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
               => ~ ( D @ ( B @ hAPP_nat_bool ) @ hBOOL ) )
            & ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(111,axiom,
    top_to1257323279t_bool @ is_fun1568535512t_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL) ).

thf(1082,plain,
    top_to1257323279t_bool @ is_fun1568535512t_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(353,axiom,
    ! [A: $i] : ( top_to1576102282i_bool @ ( A @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_UNIV__I) ).

thf(2023,plain,
    ! [A: $i] : ( top_to1576102282i_bool @ ( A @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(338,axiom,
    arrow_1681063817le_Lin @ ( lab @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74__096Lab_A_058_ALin_096) ).

thf(1964,plain,
    arrow_1681063817le_Lin @ ( lab @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(256,axiom,
    ! [A: $i] :
      ( ( A @ ( top_to1714702858l_bool @ hAPP_f312250286l_bool ) @ hBOOL )
    <=> ( top_top_bool @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_top__apply) ).

thf(1659,plain,
    ! [A: $i] :
      ( ( ( top_top_bool @ hBOOL )
       => ( A @ ( top_to1714702858l_bool @ hAPP_f312250286l_bool ) @ hBOOL ) )
      & ( ( A @ ( top_to1714702858l_bool @ hAPP_f312250286l_bool ) @ hBOOL )
       => ( top_top_bool @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(483,axiom,
    ! [A: $i] : ( top_to1714702858l_bool @ ( A @ ( member520425275t_bool @ hAPP_f1253375959l_bool ) @ hAPP_f250445784l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_UNIV__I) ).

thf(2504,plain,
    ! [A: $i] : ( top_to1714702858l_bool @ ( A @ ( member520425275t_bool @ hAPP_f1253375959l_bool ) @ hAPP_f250445784l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(206,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1163_Suc__mult__less__cancel1) ).

thf(1451,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( C @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(477,axiom,
    ( ( e @ ( p @ ( arrow_1495666017_mkbot @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( e @ ( c @ ( p @ ( arrow_230821333_above @ cOMBB_1769989562e_indi @ hAPP_f210227915t_bool ) @ ( cOMBC_898791271t_bool @ hAPP_f248867553t_bool ) @ hAPP_A1906441908t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( e @ ( p @ ( arrow_1644373103_mktop @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( e @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
  <=> ( lba @ ( lab @ ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ ( cOMBC_510421983t_bool @ hAPP_f1297018969t_bool ) @ hAPP_f1909278132t_bool ) @ ( cOMBC_633721483t_bool @ hAPP_f573120177t_bool ) @ hAPP_f329301088t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( b @ ( a @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am) ).

thf(2487,plain,
    ( ( ( lba @ ( lab @ ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ ( cOMBC_510421983t_bool @ hAPP_f1297018969t_bool ) @ hAPP_f1909278132t_bool ) @ ( cOMBC_633721483t_bool @ hAPP_f573120177t_bool ) @ hAPP_f329301088t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( b @ ( a @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( e @ ( p @ ( arrow_1495666017_mkbot @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( e @ ( c @ ( p @ ( arrow_230821333_above @ cOMBB_1769989562e_indi @ hAPP_f210227915t_bool ) @ ( cOMBC_898791271t_bool @ hAPP_f248867553t_bool ) @ hAPP_A1906441908t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( e @ ( p @ ( arrow_1644373103_mktop @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( e @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
    & ( ( e @ ( p @ ( arrow_1495666017_mkbot @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( e @ ( c @ ( p @ ( arrow_230821333_above @ cOMBB_1769989562e_indi @ hAPP_f210227915t_bool ) @ ( cOMBC_898791271t_bool @ hAPP_f248867553t_bool ) @ hAPP_A1906441908t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( e @ ( p @ ( arrow_1644373103_mktop @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( e @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( lba @ ( lab @ ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ ( cOMBC_510421983t_bool @ hAPP_f1297018969t_bool ) @ hAPP_f1909278132t_bool ) @ ( cOMBC_633721483t_bool @ hAPP_f573120177t_bool ) @ hAPP_f329301088t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( b @ ( a @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(152,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1021_add__leD2) ).

thf(1266,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(5,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( D @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1144_mult__le__mono) ).

thf(654,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( D @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(445,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_747702273le_alt @ hAPP_f1324249913t_bool ) @ hAPP_A572596845t_bool ) )
      = ( C @ ( B @ hAPP_A1553574765l_bool ) @ ( A @ hAPP_f653880381t_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___076) ).

thf(2355,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_747702273le_alt @ hAPP_f1324249913t_bool ) @ hAPP_A572596845t_bool ) )
      = ( C @ ( B @ hAPP_A1553574765l_bool ) @ ( A @ hAPP_f653880381t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(67,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1080_Suc__less__eq) ).

thf(911,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(334,axiom,
    a @ is_Arr1861959080le_alt,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_a____) ).

thf(1947,plain,
    a @ is_Arr1861959080le_alt,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(88,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1168_n__less__m__mult__n) ).

thf(1002,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(200,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( C @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_xt1_I3_J) ).

thf(1429,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( C @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(360,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_511_xt1_I8_J) ).

thf(2052,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(274,axiom,
    ? [A: $i] :
      ( ( lba @ ( lab @ ( one_one_nat @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ ( cOMBC_510421983t_bool @ hAPP_f1297018969t_bool ) @ hAPP_f1909278132t_bool ) @ ( cOMBC_633721483t_bool @ hAPP_f573120177t_bool ) @ hAPP_f329301088t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( b @ ( a @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
      & ! [B: $i] :
          ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( lba @ ( lab @ ( B @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ ( cOMBC_510421983t_bool @ hAPP_f1297018969t_bool ) @ hAPP_f1909278132t_bool ) @ ( cOMBC_633721483t_bool @ hAPP_f573120177t_bool ) @ hAPP_f329301088t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( a @ ( b @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
      & ( top_to1576102282i_bool @ ( finite1686180860e_indi @ hAPP_f2120083535ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I) ).

thf(1720,plain,
    ? [A: $i] :
      ( ( lba @ ( lab @ ( one_one_nat @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ ( cOMBC_510421983t_bool @ hAPP_f1297018969t_bool ) @ hAPP_f1909278132t_bool ) @ ( cOMBC_633721483t_bool @ hAPP_f573120177t_bool ) @ hAPP_f329301088t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( b @ ( a @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
      & ! [B: $i] :
          ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( lba @ ( lab @ ( B @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ ( cOMBC_510421983t_bool @ hAPP_f1297018969t_bool ) @ hAPP_f1909278132t_bool ) @ ( cOMBC_633721483t_bool @ hAPP_f573120177t_bool ) @ hAPP_f329301088t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( a @ ( b @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
      & ( top_to1576102282i_bool @ ( finite1686180860e_indi @ hAPP_f2120083535ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(1,conjecture,
    p @ ( f @ hAPP_f412050202t_bool ) @ ( d @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ( p @ ( f @ hAPP_f412050202t_bool ) @ ( d @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(647,plain,
    ~ ( p @ ( f @ hAPP_f412050202t_bool ) @ ( d @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(86,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1078_less__antisym) ).

thf(997,plain,
    ! [A: $i,B: $i] :
      ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(467,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2093718614t_bool )
        & ( A @ is_fun2093718614t_bool ) )
     => ( ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
         => ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_order__antisym) ).

thf(2450,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2093718614t_bool )
        & ( A @ is_fun2093718614t_bool ) )
     => ( ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(239,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( A @ ( B @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_961_set__rev__mp) ).

thf(1588,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( A @ ( B @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(127,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( zero_zero_nat @ ( B @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( B @ hAPP_nat_bool ) @ hBOOL )
       => ? [C: $i] :
            ( ( one_one_nat @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ hAPP_nat_bool ) @ hBOOL )
            & ! [D: $i] :
                ( ( C @ ( D @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
               => ~ ( D @ ( B @ hAPP_nat_bool ) @ hBOOL ) )
            & ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1056_ex__least__nat__less) ).

thf(1150,plain,
    ! [A: $i,B: $i] :
      ( ~ ( zero_zero_nat @ ( B @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( B @ hAPP_nat_bool ) @ hBOOL )
       => ? [C: $i] :
            ( ( one_one_nat @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ hAPP_nat_bool ) @ hBOOL )
            & ! [D: $i] :
                ( ( C @ ( D @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
               => ~ ( D @ ( B @ hAPP_nat_bool ) @ hBOOL ) )
            & ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(148,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1085_add__Suc__right) ).

thf(1249,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(489,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_xt1_I5_J) ).

thf(2519,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(106,axiom,
    ! [A: $i] :
      ( ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( A = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1095_less__Suc0) ).

thf(1060,plain,
    ! [A: $i] :
      ( ( ( A = zero_zero_nat )
       => ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A = zero_zero_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(503,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_order__less__asym_H) ).

thf(2581,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(473,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_linorder__le__cases) ).

thf(2465,plain,
    ! [A: $i,B: $i] :
      ( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(174,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_956_set__mp) ).

thf(1333,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(559,axiom,
    ! [A: $i] : ( A @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_order__refl) ).

thf(2788,plain,
    ! [A: $i] : ( A @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(113,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_740_add__le__cancel__left) ).

thf(1086,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(266,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_order__less__not__sym) ).

thf(1695,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(623,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro1270767662e_indi ) @ ( B @ ( member234128621e_indi @ hAPP_f407092109l_bool ) @ hAPP_f1306865520l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P1875867302i_bool ) @ ( A @ ( B @ hAPP_P710098616e_indi ) @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_PiE) ).

thf(3173,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro1270767662e_indi ) @ ( B @ ( member234128621e_indi @ hAPP_f407092109l_bool ) @ hAPP_f1306865520l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P1875867302i_bool ) @ ( A @ ( B @ hAPP_P710098616e_indi ) @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

thf(562,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_1076156777e_indi @ hAPP_f329301088t_bool ) @ ( C @ pi_Arr1199386158le_alt ) @ ( B @ ( member797673069le_alt @ hAPP_f721935245l_bool ) @ hAPP_f1837019376l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_A638717112le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_596_funcset__mem) ).

thf(2793,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_1076156777e_indi @ hAPP_f329301088t_bool ) @ ( C @ pi_Arr1199386158le_alt ) @ ( B @ ( member797673069le_alt @ hAPP_f721935245l_bool ) @ hAPP_f1837019376l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_A638717112le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(604,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
    <=> ( A @ ( B @ hAPP_f592646513l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_mem__def) ).

thf(2995,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( B @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( A @ ( B @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(514,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      <=> ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_441_linorder__antisym__conv2) ).

thf(2617,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( ( A = B )
         => ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
        & ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(580,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( D @ is_bool )
         => ( ( C @ ( D @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
           => ( D @ ( B @ hAPP_b1703662281t_bool ) @ ( D @ ( A @ hAPP_b55004359le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) )
     => ( B @ ( C @ pi_boo115158845le_alt ) @ ( A @ ( member1463820796le_alt @ hAPP_f2127575245l_bool ) @ hAPP_f1351174655l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_635_Pi__I) ).

thf(2909,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( D @ is_bool )
         => ( ( C @ ( D @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
           => ( D @ ( B @ hAPP_b1703662281t_bool ) @ ( D @ ( A @ hAPP_b55004359le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) )
     => ( B @ ( C @ pi_boo115158845le_alt ) @ ( A @ ( member1463820796le_alt @ hAPP_f2127575245l_bool ) @ hAPP_f1351174655l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(134,axiom,
    ! [A: $i] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1043_le0) ).

thf(1202,plain,
    ! [A: $i] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(401,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ hAPP_n539120590t_bool ) @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( E @ ( F @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n539120590t_bool ) @ ( F @ ( B @ hAPP_n539120590t_bool ) @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) )
         => ( D @ ( A @ ( B @ hAPP_n539120590t_bool ) @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_768_xt6) ).

thf(2203,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ hAPP_n539120590t_bool ) @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( E @ ( F @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n539120590t_bool ) @ ( F @ ( B @ hAPP_n539120590t_bool ) @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) )
         => ( D @ ( A @ ( B @ hAPP_n539120590t_bool ) @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(532,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_linorder__antisym__conv3) ).

thf(2702,plain,
    ! [A: $i,B: $i] :
      ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( ( B = A )
         => ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
        & ( ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(551,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
    <=> ( A @ ( B @ hAPP_P606313927t_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_mem__def) ).

thf(2761,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ hAPP_P606313927t_bool ) @ hBOOL )
       => ( B @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( A @ ( B @ hAPP_P606313927t_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(362,axiom,
    ! [A: $i] : ( A @ ( top_to1576102282i_bool @ hAPP_A1785763630i_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_top1I) ).

thf(2057,plain,
    ! [A: $i] : ( A @ ( top_to1576102282i_bool @ hAPP_A1785763630i_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(271,axiom,
    ! [A: $i] : ( top_to1853035173l_bool @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_UNIV__I) ).

thf(1712,plain,
    ! [A: $i] : ( top_to1853035173l_bool @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(160,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_738_add__left__mono) ).

thf(1286,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(645,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_497_order__le__less__trans) ).

thf(3321,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(519,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_fun150026276t_bool ) @ ( B @ ( member520425275t_bool @ hAPP_f1253375959l_bool ) @ hAPP_f250445784l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_f1277514478l_bool ) @ ( A @ ( B @ hAPP_f412050202t_bool ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_576_Pi__mem) ).

thf(2662,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_fun150026276t_bool ) @ ( B @ ( member520425275t_bool @ hAPP_f1253375959l_bool ) @ hAPP_f250445784l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_f1277514478l_bool ) @ ( A @ ( B @ hAPP_f412050202t_bool ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(132,axiom,
    ! [A: $i] :
      ( A
     != ( A @ ( suc @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1065_n__not__Suc__n) ).

thf(1185,plain,
    ! [A: $i] :
      ( A
     != ( A @ ( suc @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(21,axiom,
    ( ( zero_zero_nat @ ( nat_size @ hAPP_nat_nat ) )
    = zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1182_nat_Osize_I1_J) ).

thf(718,plain,
    ( ( zero_zero_nat @ ( nat_size @ hAPP_nat_nat ) )
    = zero_zero_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(60,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1016_nat__add__left__cancel__le) ).

thf(888,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(412,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B = A )
       => ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_xt1_I4_J) ).

thf(2235,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B = A )
       => ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(157,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_735_add__le__imp__le__left) ).

thf(1278,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(348,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f387058535l_bool ) @ is_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).

thf(2001,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f387058535l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(524,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
    <=> ( ~ ( A @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
        & ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_713_less__fun__def) ).

thf(2677,plain,
    ! [A: $i,B: $i] :
      ( ( ( ~ ( A @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( ~ ( A @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(336,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
      | ~ ( B @ ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Nat__Onat_T) ).

thf(1959,plain,
    ! [A: $i,B: $i] :
      ( ( A = B )
      | ~ ( B @ ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(424,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_order__less__asym) ).

thf(2275,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(155,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
        = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
     => ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_730_add__left__imp__eq) ).

thf(1273,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
        = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
     => ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(25,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
        = one_one_nat )
    <=> ( ( B = one_one_nat )
        & ( A = one_one_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1145_nat__mult__eq__1__iff) ).

thf(745,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( B = one_one_nat )
          & ( A = one_one_nat ) )
       => ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
          = one_one_nat ) )
      & ( ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
          = one_one_nat )
       => ( ( B = one_one_nat )
          & ( A = one_one_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(166,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun1236654035i_bool )
     => ( B @ ( A @ hilber693666498di_nat ) @ is_fun1217980910e_indi ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Hilbert__Choice_Oinv__into_000tc__Arrow____Order____Mirabelle____tpnfnnbpu) ).

thf(1301,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun1236654035i_bool )
     => ( B @ ( A @ hilber693666498di_nat ) @ is_fun1217980910e_indi ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(576,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( B @ ( A @ hAPP_P606313927t_bool ) @ hBOOL )
    <=> ! [B: $i,C: $i] :
          ( ( ( C @ is_Arr1861959080le_alt )
            & ( B @ is_Arr1861959080le_alt ) )
         => ( C @ ( B @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( A @ hAPP_P606313927t_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_split__paired__All) ).

thf(2894,plain,
    ! [A: $i] :
      ( ( ! [B: $i,C: $i] :
            ( ( ( C @ is_Arr1861959080le_alt )
              & ( B @ is_Arr1861959080le_alt ) )
           => ( C @ ( B @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( A @ hAPP_P606313927t_bool ) @ hBOOL ) )
       => ! [B: $i] : ( B @ ( A @ hAPP_P606313927t_bool ) @ hBOOL ) )
      & ( ! [B: $i] : ( B @ ( A @ hAPP_P606313927t_bool ) @ hBOOL )
       => ! [B: $i,C: $i] :
            ( ( ( C @ is_Arr1861959080le_alt )
              & ( B @ is_Arr1861959080le_alt ) )
           => ( C @ ( B @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( A @ hAPP_P606313927t_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(492,axiom,
    ! [A: $i] :
      ( ( A @ ( top_to1257323279t_bool @ hAPP_P1676879539t_bool ) @ hBOOL )
    <=> ( top_top_bool @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_top__apply) ).

thf(2524,plain,
    ! [A: $i] :
      ( ( ( top_top_bool @ hBOOL )
       => ( A @ ( top_to1257323279t_bool @ hAPP_P1676879539t_bool ) @ hBOOL ) )
      & ( ( A @ ( top_to1257323279t_bool @ hAPP_P1676879539t_bool ) @ hBOOL )
       => ( top_top_bool @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(577,axiom,
    ! [A: $i] : ( A @ ( cOMBI_nat @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_580_inj__on__id2) ).

thf(2904,plain,
    ! [A: $i] : ( A @ ( cOMBI_nat @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(262,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun1217980910e_indi )
     => ( ( top_to1576102282i_bool @ ( B @ inj_on1073981917di_nat @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ( ! [C: $i] :
              ( ( C @ ( A @ hAPP_n1951273283e_indi ) @ ( B @ hAPP_A1637648121di_nat ) )
              = C )
         => ( ( B @ ( top_to1576102282i_bool @ hilber693666498di_nat ) )
            = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_651_inj__imp__inv__eq) ).

thf(1680,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun1217980910e_indi )
     => ( ( top_to1576102282i_bool @ ( B @ inj_on1073981917di_nat @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ( ! [C: $i] :
              ( ( C @ ( A @ hAPP_n1951273283e_indi ) @ ( B @ hAPP_A1637648121di_nat ) )
              = C )
         => ( ( B @ ( top_to1576102282i_bool @ hilber693666498di_nat ) )
            = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(614,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ is_Arr1861959080le_alt )
        & ( B @ is_Arr1861959080le_alt )
        & ( A @ is_Arr1861959080le_alt ) )
     => ( ( D @ ( C @ ( arrow_1495666017_mkbot @ hAPP_f393984045t_bool ) @ hAPP_A568203993t_bool ) @ ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
      <=> ( ( ( A != D )
           => ( C @ ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
          & ( ( A = D )
           => ( A != B ) )
          & ( B != D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_in__mkbot) ).

thf(3079,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ is_Arr1861959080le_alt )
        & ( B @ is_Arr1861959080le_alt )
        & ( A @ is_Arr1861959080le_alt ) )
     => ( ( ( ( ( A != D )
             => ( C @ ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
            & ( ( A = D )
             => ( A != B ) )
            & ( B != D ) )
         => ( D @ ( C @ ( arrow_1495666017_mkbot @ hAPP_f393984045t_bool ) @ hAPP_A568203993t_bool ) @ ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
        & ( ( D @ ( C @ ( arrow_1495666017_mkbot @ hAPP_f393984045t_bool ) @ hAPP_A568203993t_bool ) @ ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
         => ( ( ( A != D )
             => ( C @ ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
            & ( ( A = D )
             => ( A != B ) )
            & ( B != D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(282,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
     => ( ( C @ ( B @ hAPP_f1358350510ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( ( F @ is_fun2093718614t_bool )
                & ( E @ is_fun2093718614t_bool ) )
             => ( ( E @ ( F @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
               => ( E @ ( B @ hAPP_f1358350510ol_nat ) @ ( F @ ( B @ hAPP_f1358350510ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) )
         => ( D @ ( B @ hAPP_f1358350510ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_706_xt7) ).

thf(1747,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
     => ( ( C @ ( B @ hAPP_f1358350510ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( ( F @ is_fun2093718614t_bool )
                & ( E @ is_fun2093718614t_bool ) )
             => ( ( E @ ( F @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
               => ( E @ ( B @ hAPP_f1358350510ol_nat ) @ ( F @ ( B @ hAPP_f1358350510ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) )
         => ( D @ ( B @ hAPP_f1358350510ol_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(644,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_487_xt1_I7_J) ).

thf(3319,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).

thf(249,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( ( C = A )
       => ( A @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_ord__le__eq__trans) ).

thf(1620,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( ( C = A )
       => ( A @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(190,axiom,
    ! [A: $i] :
      ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ? [B: $i] :
          ( A
          = ( B @ ( suc @ hAPP_nat_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1117_gr0__implies__Suc) ).

thf(1388,plain,
    ! [A: $i] :
      ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ? [B: $i] :
          ( A
          = ( B @ ( suc @ hAPP_nat_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(41,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( ( B = A )
       => ( C @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_xt1_I4_J) ).

thf(826,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( ( B = A )
       => ( C @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(78,axiom,
    ! [A: $i] : ( top_to1853035173l_bool @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_719_subset__UNIV) ).

thf(958,plain,
    ! [A: $i] : ( top_to1853035173l_bool @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(454,axiom,
    ! [A: $i] : ( top_to1647826457l_bool @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_UNIV__I) ).

thf(2398,plain,
    ! [A: $i] : ( top_to1647826457l_bool @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(537,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f412050202t_bool ) @ is_fun961089132t_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__015) ).

thf(2716,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f412050202t_bool ) @ is_fun961089132t_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(339,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_fun150026276t_bool ) @ ( B @ ( member520425275t_bool @ hAPP_f1253375959l_bool ) @ hAPP_f250445784l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_f1277514478l_bool ) @ ( A @ ( B @ hAPP_f412050202t_bool ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_PiE) ).

thf(1965,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_fun150026276t_bool ) @ ( B @ ( member520425275t_bool @ hAPP_f1253375959l_bool ) @ hAPP_f250445784l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_f1277514478l_bool ) @ ( A @ ( B @ hAPP_f412050202t_bool ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(530,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B @ is_Arr43961803e_indi )
     => ( ( D @ ( C @ inj_on1073981917di_nat @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ( ( D @ ( B @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
         => ( ( ( B @ ( C @ hAPP_A1637648121di_nat ) )
              = A )
           => ( ( A @ ( C @ ( D @ hilber693666498di_nat ) @ hAPP_n1951273283e_indi ) )
              = B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_618_inv__into__f__eq) ).

thf(2695,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B @ is_Arr43961803e_indi )
     => ( ( D @ ( C @ inj_on1073981917di_nat @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ( ( D @ ( B @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
         => ( ( ( B @ ( C @ hAPP_A1637648121di_nat ) )
              = A )
           => ( ( A @ ( C @ ( D @ hilber693666498di_nat ) @ hAPP_n1951273283e_indi ) )
              = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(634,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro1928973619le_alt ) @ ( B @ ( member1648671474le_alt @ hAPP_f1868437069l_bool ) @ hAPP_f415146997l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P1341894483t_bool ) @ ( A @ ( B @ hAPP_P504138941le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_PiE) ).

thf(3234,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro1928973619le_alt ) @ ( B @ ( member1648671474le_alt @ hAPP_f1868437069l_bool ) @ hAPP_f415146997l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P1341894483t_bool ) @ ( A @ ( B @ hAPP_P504138941le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(359,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( B @ hAPP_n588788980t_bool ) @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( E @ ( F @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n588788980t_bool ) @ ( F @ ( B @ hAPP_n588788980t_bool ) @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
         => ( D @ ( B @ hAPP_n588788980t_bool ) @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_667_xt5) ).

thf(2048,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( B @ hAPP_n588788980t_bool ) @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( E @ ( F @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n588788980t_bool ) @ ( F @ ( B @ hAPP_n588788980t_bool ) @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
         => ( D @ ( B @ hAPP_n588788980t_bool ) @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(247,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun279392540l_bool )
        & ( A @ is_fun279392540l_bool ) )
     => ( ( B @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
         => ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_905_equalityI) ).

thf(1615,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun279392540l_bool )
        & ( A @ is_fun279392540l_bool ) )
     => ( ( B @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(291,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( D @ ( A @ hAPP_n588788980t_bool ) @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( F @ ( E @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( A @ hAPP_n588788980t_bool ) @ ( E @ ( A @ hAPP_n588788980t_bool ) @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
         => ( B @ ( C @ ( A @ hAPP_n588788980t_bool ) @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_861_order__le__less__subst2) ).

thf(1784,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( D @ ( A @ hAPP_n588788980t_bool ) @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( F @ ( E @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( A @ hAPP_n588788980t_bool ) @ ( E @ ( A @ hAPP_n588788980t_bool ) @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
         => ( B @ ( C @ ( A @ hAPP_n588788980t_bool ) @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(523,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun961089132t_bool ) )
     => ( ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( ( A = B )
          | ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_447_order__le__imp__less__or__eq) ).

thf(2674,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun961089132t_bool ) )
     => ( ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( ( A = B )
          | ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(486,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_657557929e_indi @ hAPP_f1659309744l_bool ) @ ( C @ pi_Arr990697634t_bool ) @ ( B @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_A1677245848t_bool ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_611_funcset__mem) ).

thf(2514,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_657557929e_indi @ hAPP_f1659309744l_bool ) @ ( C @ pi_Arr990697634t_bool ) @ ( B @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_A1677245848t_bool ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(124,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i,E: $i] :
          ( ( E @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( E @ ( C @ hAPP_nat_nat ) @ ( D @ ( C @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( C @ hAPP_nat_nat ) @ ( A @ ( C @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1024_less__mono__imp__le__mono) ).

thf(1139,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i,E: $i] :
          ( ( E @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( E @ ( C @ hAPP_nat_nat ) @ ( D @ ( C @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( C @ hAPP_nat_nat ) @ ( A @ ( C @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(355,axiom,
    ! [A: $i,B: $i] :
      ( ( A != B )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_419_order__neq__le__trans) ).

thf(2029,plain,
    ! [A: $i,B: $i] :
      ( ( A != B )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(168,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1017_trans__le__add1) ).

thf(1312,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(32,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) )
      = ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1165_mult__Suc) ).

thf(787,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) )
      = ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(543,axiom,
    ! [A: $i] : ( A @ ( top_to565915683t_bool @ hAPP_P606313927t_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_top1I) ).

thf(2738,plain,
    ! [A: $i] : ( A @ ( top_to565915683t_bool @ hAPP_P606313927t_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(19,axiom,
    ! [A: $i] : ( A @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1141_le__cube) ).

thf(713,plain,
    ! [A: $i] : ( A @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(278,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_ord__eq__le__trans) ).

thf(1733,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(105,axiom,
    ! [A: $i] : ( top_to1853035173l_bool @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_512_top__greatest) ).

thf(1058,plain,
    ! [A: $i] : ( top_to1853035173l_bool @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(549,axiom,
    n @ ( h @ ( top_to1576102282i_bool @ hilber693666498di_nat ) @ hAPP_n1951273283e_indi ) @ ( p @ hAPP_A1677245848t_bool ) @ ( d @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0) ).

thf(2753,plain,
    n @ ( h @ ( top_to1576102282i_bool @ hilber693666498di_nat ) @ hAPP_n1951273283e_indi ) @ ( p @ hAPP_A1677245848t_bool ) @ ( d @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(114,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1026_termination__basic__simps_I4_J) ).

thf(1092,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(287,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( B @ hAPP_n539120590t_bool ) @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( E @ ( F @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n539120590t_bool ) @ ( F @ ( B @ hAPP_n539120590t_bool ) @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) )
         => ( D @ ( B @ hAPP_n539120590t_bool ) @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_669_xt5) ).

thf(1765,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( B @ hAPP_n539120590t_bool ) @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( E @ ( F @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n539120590t_bool ) @ ( F @ ( B @ hAPP_n539120590t_bool ) @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) )
         => ( D @ ( B @ hAPP_n539120590t_bool ) @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(470,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      | ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_994_nat__le__linear) ).

thf(2457,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      | ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(462,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( C @ ( D @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_f1277514478l_bool ) @ ( D @ ( A @ hAPP_f412050202t_bool ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_fun150026276t_bool ) @ ( A @ ( member520425275t_bool @ hAPP_f1253375959l_bool ) @ hAPP_f250445784l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_649_Pi__I) ).

thf(2425,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( C @ ( D @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_f1277514478l_bool ) @ ( D @ ( A @ hAPP_f412050202t_bool ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_fun150026276t_bool ) @ ( A @ ( member520425275t_bool @ hAPP_f1253375959l_bool ) @ hAPP_f250445784l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(260,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_boo538701011t_bool ) @ ( B @ ( member357566570t_bool @ hAPP_f1345320373l_bool ) @ hAPP_f817604743l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_b1812770943l_bool ) @ ( A @ ( B @ hAPP_b1703662281t_bool ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_PiE) ).

thf(1675,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_boo538701011t_bool ) @ ( B @ ( member357566570t_bool @ hAPP_f1345320373l_bool ) @ hAPP_f817604743l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_b1812770943l_bool ) @ ( A @ ( B @ hAPP_b1703662281t_bool ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(154,axiom,
    ! [A: $i,B: $i] : ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1013_le__add2) ).

thf(1271,plain,
    ! [A: $i,B: $i] : ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(432,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun961089132t_bool ) )
     => ( ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
      <=> ( ( A != B )
          & ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_382_order__less__le) ).

thf(2308,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun961089132t_bool ) )
     => ( ( ( ( A != B )
            & ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
         => ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
        & ( ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
         => ( ( A != B )
            & ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(252,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1104_Suc__le__eq) ).

thf(1638,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(139,axiom,
    top_to1576102282i_bool @ is_fun1236654035i_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Arrow____Order____Mirabelle_____002) ).

thf(1224,plain,
    top_to1576102282i_bool @ is_fun1236654035i_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(446,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ hAPP_n588788980t_bool ) @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( E @ ( F @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n588788980t_bool ) @ ( F @ ( B @ hAPP_n588788980t_bool ) @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
         => ( D @ ( A @ ( B @ hAPP_n588788980t_bool ) @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_778_xt4) ).

thf(2358,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ hAPP_n588788980t_bool ) @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( E @ ( F @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n588788980t_bool ) @ ( F @ ( B @ hAPP_n588788980t_bool ) @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
         => ( D @ ( A @ ( B @ hAPP_n588788980t_bool ) @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(181,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2093718614t_bool )
        & ( A @ is_fun2093718614t_bool ) )
     => ( ( A != B )
       => ( ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
         => ( B @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_417_order__neq__le__trans) ).

thf(1356,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2093718614t_bool )
        & ( A @ is_fun2093718614t_bool ) )
     => ( ( A != B )
       => ( ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
         => ( B @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(442,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( D @ is_Arr43961803e_indi )
         => ( ( C @ ( D @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
           => ( D @ ( B @ hAPP_A60074736l_bool ) @ ( D @ ( A @ hAPP_A1677245848t_bool ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) )
     => ( B @ ( C @ pi_Arr990697634t_bool ) @ ( A @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_650_Pi__I) ).

thf(2346,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( D @ is_Arr43961803e_indi )
         => ( ( C @ ( D @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
           => ( D @ ( B @ hAPP_A60074736l_bool ) @ ( D @ ( A @ hAPP_A1677245848t_bool ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) )
     => ( B @ ( C @ pi_Arr990697634t_bool ) @ ( A @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(616,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( F @ is_Arr1861959080le_alt )
        & ( E @ is_Arr1861959080le_alt )
        & ( D @ is_Arr1861959080le_alt )
        & ( C @ is_Arr1861959080le_alt ) )
     => ( ( E != F )
       => ( ( C != D )
         => ( ( E != D )
           => ( ( F != C )
             => ( ( arrow_1721807329e_Prof @ ( B @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
               => ( ( arrow_1721807329e_Prof @ ( A @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
                 => ( ! [G: $i] :
                        ( ( G @ is_Arr43961803e_indi )
                       => ( ( G @ ( B @ hAPP_A1677245848t_bool ) @ ( F @ ( E @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                        <=> ( G @ ( A @ hAPP_A1677245848t_bool ) @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) )
                   => ( ( B @ ( f @ hAPP_f412050202t_bool ) @ ( F @ ( E @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                     => ( A @ ( f @ hAPP_f412050202t_bool ) @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7__C1_C) ).

thf(3101,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( F @ is_Arr1861959080le_alt )
        & ( E @ is_Arr1861959080le_alt )
        & ( D @ is_Arr1861959080le_alt )
        & ( C @ is_Arr1861959080le_alt ) )
     => ( ( E != F )
       => ( ( C != D )
         => ( ( E != D )
           => ( ( F != C )
             => ( ( arrow_1721807329e_Prof @ ( B @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
               => ( ( arrow_1721807329e_Prof @ ( A @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
                 => ( ! [G: $i] :
                        ( ( G @ is_Arr43961803e_indi )
                       => ( ( ( G @ ( A @ hAPP_A1677245848t_bool ) @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                           => ( G @ ( B @ hAPP_A1677245848t_bool ) @ ( F @ ( E @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
                          & ( ( G @ ( B @ hAPP_A1677245848t_bool ) @ ( F @ ( E @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                           => ( G @ ( A @ hAPP_A1677245848t_bool ) @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) )
                   => ( ( B @ ( f @ hAPP_f412050202t_bool ) @ ( F @ ( E @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                     => ( A @ ( f @ hAPP_f412050202t_bool ) @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(62,axiom,
    ! [A: $i] :
      ( ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) )
      = ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1110_less__eq__Suc__le__raw) ).

thf(900,plain,
    ! [A: $i] :
      ( ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) )
      = ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(159,axiom,
    ! [A: $i] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
     != zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1069_Suc__not__Zero) ).

thf(1282,plain,
    ! [A: $i] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
     != zero_zero_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(31,axiom,
    ! [A: $i] :
      ( ( one_one_nat @ ( A @ times_times_nat @ hAPP_nat_nat ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1146_nat__mult__1__right) ).

thf(784,plain,
    ! [A: $i] :
      ( ( one_one_nat @ ( A @ times_times_nat @ hAPP_nat_nat ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(297,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_499_order__le__less__trans) ).

thf(1806,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(578,axiom,
    f @ ( arrow_1654180089le_IIA @ hAPP_f312250286l_bool ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms_I3_J) ).

thf(2906,plain,
    f @ ( arrow_1654180089le_IIA @ hAPP_f312250286l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(216,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_745_add__strict__left__mono) ).

thf(1492,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(227,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
        = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
    <=> ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_732_add__left__cancel) ).

thf(1542,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B = C )
       => ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
          = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) )
      & ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
          = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
       => ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(400,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
    <=> ( A @ ( B @ hAPP_f965095724l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_mem__def) ).

thf(2197,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ hAPP_f965095724l_bool ) @ hBOOL )
       => ( B @ ( A @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
       => ( A @ ( B @ hAPP_f965095724l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(53,axiom,
    ! [A: $i] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
     != A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1064_Suc__n__not__n) ).

thf(863,plain,
    ! [A: $i] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
     != A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(370,axiom,
    ? [A: $i] :
      ( ( arrow_1681063817le_Lin @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
      & ( A @ is_fun961089132t_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1030_linear__alt) ).

thf(2084,plain,
    ? [A: $i] :
      ( ( arrow_1681063817le_Lin @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
      & ( A @ is_fun961089132t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(515,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ hAPP_n588788980t_bool ) @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( E @ ( F @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n588788980t_bool ) @ ( F @ ( B @ hAPP_n588788980t_bool ) @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
         => ( D @ ( A @ ( B @ hAPP_n588788980t_bool ) @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_766_xt6) ).

thf(2624,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ hAPP_n588788980t_bool ) @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( E @ ( F @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n588788980t_bool ) @ ( F @ ( B @ hAPP_n588788980t_bool ) @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
         => ( D @ ( A @ ( B @ hAPP_n588788980t_bool ) @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(321,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun961089132t_bool )
     => ( B @ ( A @ hAPP_f863359027l_bool ) @ is_fun279392540l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___043) ).

thf(1894,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun961089132t_bool )
     => ( B @ ( A @ hAPP_f863359027l_bool ) @ is_fun279392540l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(601,axiom,
    e @ ( p @ ( arrow_1495666017_mkbot @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( e @ ( c @ ( p @ ( arrow_230821333_above @ cOMBB_1769989562e_indi @ hAPP_f210227915t_bool ) @ ( cOMBC_898791271t_bool @ hAPP_f248867553t_bool ) @ hAPP_A1906441908t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( e @ ( p @ ( arrow_1644373103_mktop @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( e @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).

thf(2987,plain,
    e @ ( p @ ( arrow_1495666017_mkbot @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( e @ ( c @ ( p @ ( arrow_230821333_above @ cOMBB_1769989562e_indi @ hAPP_f210227915t_bool ) @ ( cOMBC_898791271t_bool @ hAPP_f248867553t_bool ) @ hAPP_A1906441908t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( e @ ( p @ ( arrow_1644373103_mktop @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( e @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(289,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2093718614t_bool )
        & ( A @ is_fun2093718614t_bool ) )
     => ( ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
        <=> ( B = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_order__antisym__conv) ).

thf(1771,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2093718614t_bool )
        & ( A @ is_fun2093718614t_bool ) )
     => ( ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( ( ( B = A )
           => ( A @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) )
          & ( ( A @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
           => ( B = A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(583,axiom,
    lab @ ( b @ ( a @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).

thf(2945,plain,
    lab @ ( b @ ( a @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(58,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1169_n__less__n__mult__m) ).

thf(880,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(99,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1007_add__lessD1) ).

thf(1043,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(570,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ is_Arr1861959080le_alt )
        & ( C @ is_Arr1861959080le_alt )
        & ( B @ is_Arr1861959080le_alt )
        & ( A @ is_Arr1861959080le_alt ) )
     => ( ( ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) )
          = ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) ) )
      <=> ( ( B = D )
          & ( A = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_Pair__eq) ).

thf(2871,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ is_Arr1861959080le_alt )
        & ( C @ is_Arr1861959080le_alt )
        & ( B @ is_Arr1861959080le_alt )
        & ( A @ is_Arr1861959080le_alt ) )
     => ( ( ( ( B = D )
            & ( A = C ) )
         => ( ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) )
            = ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) ) ) )
        & ( ( ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) )
            = ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) ) )
         => ( ( B = D )
            & ( A = C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(187,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1077_less__SucI) ).

thf(1376,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(258,axiom,
    ( ( e @ ( p @ ( arrow_1495666017_mkbot @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( e @ ( c @ ( p @ ( arrow_230821333_above @ cOMBB_1769989562e_indi @ hAPP_f210227915t_bool ) @ ( cOMBC_898791271t_bool @ hAPP_f248867553t_bool ) @ hAPP_A1906441908t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( e @ ( p @ ( arrow_1644373103_mktop @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( d @ ( e @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
  <=> ( lba @ ( lab @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ ( cOMBC_510421983t_bool @ hAPP_f1297018969t_bool ) @ hAPP_f1909278132t_bool ) @ ( cOMBC_633721483t_bool @ hAPP_f573120177t_bool ) @ hAPP_f329301088t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( a @ ( b @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk) ).

thf(1667,plain,
    ( ( ( lba @ ( lab @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ ( cOMBC_510421983t_bool @ hAPP_f1297018969t_bool ) @ hAPP_f1909278132t_bool ) @ ( cOMBC_633721483t_bool @ hAPP_f573120177t_bool ) @ hAPP_f329301088t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( a @ ( b @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( e @ ( p @ ( arrow_1495666017_mkbot @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( e @ ( c @ ( p @ ( arrow_230821333_above @ cOMBB_1769989562e_indi @ hAPP_f210227915t_bool ) @ ( cOMBC_898791271t_bool @ hAPP_f248867553t_bool ) @ hAPP_A1906441908t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( e @ ( p @ ( arrow_1644373103_mktop @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( d @ ( e @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
    & ( ( e @ ( p @ ( arrow_1495666017_mkbot @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( e @ ( c @ ( p @ ( arrow_230821333_above @ cOMBB_1769989562e_indi @ hAPP_f210227915t_bool ) @ ( cOMBC_898791271t_bool @ hAPP_f248867553t_bool ) @ hAPP_A1906441908t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( e @ ( p @ ( arrow_1644373103_mktop @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( d @ ( e @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( lba @ ( lab @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ ( cOMBC_510421983t_bool @ hAPP_f1297018969t_bool ) @ hAPP_f1909278132t_bool ) @ ( cOMBC_633721483t_bool @ hAPP_f573120177t_bool ) @ hAPP_f329301088t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( a @ ( b @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(354,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ is_Arr43961803e_indi )
     => ( ( C @ ( B @ inj_on1073981917di_nat @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ( ( C @ ( A @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
         => ( ( A @ ( B @ hAPP_A1637648121di_nat ) @ ( B @ ( C @ hilber693666498di_nat ) @ hAPP_n1951273283e_indi ) )
            = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_616_inv__into__f__f) ).

thf(2025,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ is_Arr43961803e_indi )
     => ( ( C @ ( B @ inj_on1073981917di_nat @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ( ( C @ ( A @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
         => ( ( A @ ( B @ hAPP_A1637648121di_nat ) @ ( B @ ( C @ hilber693666498di_nat ) @ hAPP_n1951273283e_indi ) )
            = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(545,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( C @ ( D @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_P1341894483t_bool ) @ ( D @ ( A @ hAPP_P504138941le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_Pro1928973619le_alt ) @ ( A @ ( member1648671474le_alt @ hAPP_f1868437069l_bool ) @ hAPP_f415146997l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_636_Pi__I) ).

thf(2742,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( C @ ( D @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_P1341894483t_bool ) @ ( D @ ( A @ hAPP_P504138941le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_Pro1928973619le_alt ) @ ( A @ ( member1648671474le_alt @ hAPP_f1868437069l_bool ) @ hAPP_f415146997l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(27,axiom,
    ! [A: $i] :
      ( ( A @ ( zero_zero_nat @ times_times_nat @ hAPP_nat_nat ) )
      = zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1156_mult__0) ).

thf(758,plain,
    ! [A: $i] :
      ( ( A @ ( zero_zero_nat @ times_times_nat @ hAPP_nat_nat ) )
      = zero_zero_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(383,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1351174655l_bool ) @ is_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__prod_Itc__Arrow____Order____) ).

thf(2129,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1351174655l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(378,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
     => ( ( C = A )
       => ( A @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_ord__le__eq__trans) ).

thf(2111,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
     => ( ( C = A )
       => ( A @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(251,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
        = ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
    <=> ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_731_add__right__cancel) ).

thf(1630,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = C )
       => ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
          = ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) )
      & ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
          = ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
       => ( A = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(277,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      | ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_376_linorder__le__less__linear) ).

thf(1731,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      | ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(315,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_order__eq__refl) ).

thf(1862,plain,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(626,axiom,
    d @ is_Arr1861959080le_alt,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_d____) ).

thf(3192,plain,
    d @ is_Arr1861959080le_alt,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(458,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun279392540l_bool ) )
     => ( B @ ( A @ hAPP_f592646513l_bool ) @ is_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___039) ).

thf(2410,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun279392540l_bool ) )
     => ( B @ ( A @ hAPP_f592646513l_bool ) @ is_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(508,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun961089132t_bool ) )
     => ( ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( ( B != A )
         => ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_467_xt1_I11_J) ).

thf(2593,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun961089132t_bool ) )
     => ( ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( ( B != A )
         => ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(178,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ? [C: $i] :
          ( B
          = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1015_le__iff__add) ).

thf(1344,plain,
    ! [A: $i,B: $i] :
      ( ( ? [C: $i] :
            ( B
            = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
       => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ? [C: $i] :
            ( B
            = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(130,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1166_Suc__mult__le__cancel1) ).

thf(1177,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( C @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(302,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_986_less__not__refl3) ).

thf(1820,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(502,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun1217980910e_indi )
     => ( B @ ( A @ hAPP_n1951273283e_indi ) @ is_Arr43961803e_indi ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oi) ).

thf(2578,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun1217980910e_indi )
     => ( B @ ( A @ hAPP_n1951273283e_indi ) @ is_Arr43961803e_indi ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(619,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ is_Arr1861959080le_alt )
        & ( C @ is_Arr1861959080le_alt ) )
     => ( ( C != D )
       => ( ( arrow_1721807329e_Prof @ ( B @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
         => ( ( arrow_1721807329e_Prof @ ( A @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
           => ( ! [E: $i] :
                  ( ( E @ is_Arr43961803e_indi )
                 => ( ( E @ ( B @ hAPP_A1677245848t_bool ) @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                  <=> ( E @ ( A @ hAPP_A1677245848t_bool ) @ ( C @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) )
             => ( ( B @ ( f @ hAPP_f412050202t_bool ) @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
              <=> ( A @ ( f @ hAPP_f412050202t_bool ) @ ( C @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10__C3_C) ).

thf(3133,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ is_Arr1861959080le_alt )
        & ( C @ is_Arr1861959080le_alt ) )
     => ( ( C != D )
       => ( ( arrow_1721807329e_Prof @ ( B @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
         => ( ( arrow_1721807329e_Prof @ ( A @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
           => ( ! [E: $i] :
                  ( ( E @ is_Arr43961803e_indi )
                 => ( ( ( E @ ( A @ hAPP_A1677245848t_bool ) @ ( C @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                     => ( E @ ( B @ hAPP_A1677245848t_bool ) @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
                    & ( ( E @ ( B @ hAPP_A1677245848t_bool ) @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                     => ( E @ ( A @ hAPP_A1677245848t_bool ) @ ( C @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) )
             => ( ( ( A @ ( f @ hAPP_f412050202t_bool ) @ ( C @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                 => ( B @ ( f @ hAPP_f412050202t_bool ) @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
                & ( ( B @ ( f @ hAPP_f412050202t_bool ) @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                 => ( A @ ( f @ hAPP_f412050202t_bool ) @ ( C @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(51,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1018_trans__le__add2) ).

thf(858,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(611,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( E @ is_Arr1861959080le_alt )
        & ( D @ is_Arr1861959080le_alt )
        & ( C @ is_Arr1861959080le_alt ) )
     => ( ( D != E )
       => ( ( E != C )
         => ( ( D != C )
           => ( ( arrow_1721807329e_Prof @ ( B @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
             => ( ( arrow_1721807329e_Prof @ ( A @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
               => ( ! [F: $i] :
                      ( ( F @ is_Arr43961803e_indi )
                     => ( ( F @ ( B @ hAPP_A1677245848t_bool ) @ ( E @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                      <=> ( F @ ( A @ hAPP_A1677245848t_bool ) @ ( C @ ( E @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) )
                 => ( ( B @ ( f @ hAPP_f412050202t_bool ) @ ( E @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                  <=> ( A @ ( f @ hAPP_f412050202t_bool ) @ ( C @ ( E @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8__C4_C) ).

thf(3055,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( E @ is_Arr1861959080le_alt )
        & ( D @ is_Arr1861959080le_alt )
        & ( C @ is_Arr1861959080le_alt ) )
     => ( ( D != E )
       => ( ( E != C )
         => ( ( D != C )
           => ( ( arrow_1721807329e_Prof @ ( B @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
             => ( ( arrow_1721807329e_Prof @ ( A @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
               => ( ! [F: $i] :
                      ( ( F @ is_Arr43961803e_indi )
                     => ( ( ( F @ ( A @ hAPP_A1677245848t_bool ) @ ( C @ ( E @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                         => ( F @ ( B @ hAPP_A1677245848t_bool ) @ ( E @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
                        & ( ( F @ ( B @ hAPP_A1677245848t_bool ) @ ( E @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                         => ( F @ ( A @ hAPP_A1677245848t_bool ) @ ( C @ ( E @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) )
                 => ( ( ( A @ ( f @ hAPP_f412050202t_bool ) @ ( C @ ( E @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                     => ( B @ ( f @ hAPP_f412050202t_bool ) @ ( E @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
                    & ( ( B @ ( f @ hAPP_f412050202t_bool ) @ ( E @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                     => ( A @ ( f @ hAPP_f412050202t_bool ) @ ( C @ ( E @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(230,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1099_less__add__Suc1) ).

thf(1556,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(495,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ( A != B )
        & ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_386_order__less__le) ).

thf(2542,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A != B )
          & ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ( A != B )
          & ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(75,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
        | ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1055_add__gr__0) ).

thf(943,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          | ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          | ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(417,axiom,
    a != b,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76__096a_A_126_061_Ab_096) ).

thf(2252,plain,
    a != b,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(520,axiom,
    lba @ is_fun961089132t_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_Lba____) ).

thf(2664,plain,
    lba @ is_fun961089132t_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(472,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ hAPP_n539120590t_bool ) @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
     => ( ( A @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( F @ ( E @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( C @ hAPP_n539120590t_bool ) @ ( E @ ( C @ hAPP_n539120590t_bool ) @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) )
         => ( A @ ( C @ hAPP_n539120590t_bool ) @ ( B @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_817_order__le__less__subst1) ).

thf(2461,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ hAPP_n539120590t_bool ) @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
     => ( ( A @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( F @ ( E @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( C @ hAPP_n539120590t_bool ) @ ( E @ ( C @ hAPP_n539120590t_bool ) @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) )
         => ( A @ ( C @ hAPP_n539120590t_bool ) @ ( B @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(598,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro1122146355t_unit ) @ ( B @ ( member2079083634t_unit @ hAPP_f1847883341l_bool ) @ hAPP_f22590837l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_P332578347t_bool ) @ ( A @ ( B @ hAPP_P1844795325t_unit ) @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_549_Pi__mem) ).

thf(2974,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro1122146355t_unit ) @ ( B @ ( member2079083634t_unit @ hAPP_f1847883341l_bool ) @ hAPP_f22590837l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_P332578347t_bool ) @ ( A @ ( B @ hAPP_P1844795325t_unit ) @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(437,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_Arr1861959080le_alt )
     => ( B @ ( A @ hAPP_A568203993t_bool ) @ is_fun961089132t_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000tc__fun_Itc_003) ).

thf(2329,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_Arr1861959080le_alt )
     => ( B @ ( A @ hAPP_A568203993t_bool ) @ is_fun961089132t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(72,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1029_termination__basic__simps_I1_J) ).

thf(932,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(553,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun961089132t_bool ) )
     => ( ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
         => ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_order__antisym) ).

thf(2770,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun961089132t_bool ) )
     => ( ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(241,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i,E: $i] :
          ( ( E @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( E @ ( C @ hAPP_nat_nat ) @ ( D @ ( C @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
     => ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( C @ hAPP_nat_nat ) @ ( B @ ( A @ ( C @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1023_mono__nat__linear__lb) ).

thf(1594,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i,E: $i] :
          ( ( E @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( E @ ( C @ hAPP_nat_nat ) @ ( D @ ( C @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
     => ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( C @ hAPP_nat_nat ) @ ( B @ ( A @ ( C @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(147,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      <=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1177_nat__mult__less__cancel1) ).

thf(1245,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
        & ( ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(204,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( A @ ( C @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_ord__eq__le__trans) ).

thf(1445,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( A @ ( C @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(387,axiom,
    ! [A: $i] : ( top_to1647826457l_bool @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_iso__tuple__UNIV__I) ).

thf(2139,plain,
    ! [A: $i] : ( top_to1647826457l_bool @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(391,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ is_Arr43961803e_indi )
        & ( A @ is_Arr43961803e_indi ) )
     => ( ( D @ ( C @ inj_on1073981917di_nat @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ( ( A != B )
         => ( ( D @ ( A @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
           => ( ( D @ ( B @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
             => ( ( A @ ( C @ hAPP_A1637648121di_nat ) )
               != ( B @ ( C @ hAPP_A1637648121di_nat ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_541_inj__on__contraD) ).

thf(2156,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ is_Arr43961803e_indi )
        & ( A @ is_Arr43961803e_indi ) )
     => ( ( D @ ( C @ inj_on1073981917di_nat @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ( ( A != B )
         => ( ( D @ ( A @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
           => ( ( D @ ( B @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
             => ( ( A @ ( C @ hAPP_A1637648121di_nat ) )
               != ( B @ ( C @ hAPP_A1637648121di_nat ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(402,axiom,
    ! [A: $i] :
      ( ( A @ ( top_to565915683t_bool @ hAPP_P606313927t_bool ) @ hBOOL )
    <=> ( top_top_bool @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_top__apply) ).

thf(2207,plain,
    ! [A: $i] :
      ( ( ( top_top_bool @ hBOOL )
       => ( A @ ( top_to565915683t_bool @ hAPP_P606313927t_bool ) @ hBOOL ) )
      & ( ( A @ ( top_to565915683t_bool @ hAPP_P606313927t_bool ) @ hBOOL )
       => ( top_top_bool @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(296,axiom,
    top_to1576102282i_bool @ ( finite1686180860e_indi @ hAPP_f2120083535ol_nat ) @ ( n @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_n_I1_J) ).

thf(1805,plain,
    top_to1576102282i_bool @ ( finite1686180860e_indi @ hAPP_f2120083535ol_nat ) @ ( n @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(484,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
    <=> ( A @ ( B @ hAPP_P1676879539t_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_mem__def) ).

thf(2506,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ hAPP_P1676879539t_bool ) @ hBOOL )
       => ( B @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( A @ ( B @ hAPP_P1676879539t_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(591,axiom,
    ! [A: $i] : ( A @ ( top_to522745736l_bool @ hAPP_f965095724l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_top1I) ).

thf(2962,plain,
    ! [A: $i] : ( A @ ( top_to522745736l_bool @ hAPP_f965095724l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(449,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ inj_on1073981917di_nat @ hAPP_f1599966040l_bool ) @ hBOOL )
    <=> ! [C: $i] :
          ( ( C @ is_Arr43961803e_indi )
         => ( ( B @ ( C @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
           => ! [D: $i] :
                ( ( D @ is_Arr43961803e_indi )
               => ( ( B @ ( D @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
                 => ( ( ( C @ ( A @ hAPP_A1637648121di_nat ) )
                      = ( D @ ( A @ hAPP_A1637648121di_nat ) ) )
                   => ( C = D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_539_inj__on__def) ).

thf(2365,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i] :
            ( ( C @ is_Arr43961803e_indi )
           => ( ( B @ ( C @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
             => ! [D: $i] :
                  ( ( D @ is_Arr43961803e_indi )
                 => ( ( B @ ( D @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
                   => ( ( ( C @ ( A @ hAPP_A1637648121di_nat ) )
                        = ( D @ ( A @ hAPP_A1637648121di_nat ) ) )
                     => ( C = D ) ) ) ) ) )
       => ( B @ ( A @ inj_on1073981917di_nat @ hAPP_f1599966040l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ inj_on1073981917di_nat @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ! [C: $i] :
            ( ( C @ is_Arr43961803e_indi )
           => ( ( B @ ( C @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
             => ! [D: $i] :
                  ( ( D @ is_Arr43961803e_indi )
                 => ( ( B @ ( D @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
                   => ( ( ( C @ ( A @ hAPP_A1637648121di_nat ) )
                        = ( D @ ( A @ hAPP_A1637648121di_nat ) ) )
                     => ( C = D ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(137,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2093718614t_bool )
        & ( A @ is_fun2093718614t_bool ) )
     => ( ( A != B )
       => ( ( A @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
         => ( A @ ( B @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_427_xt1_I12_J) ).

thf(1213,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2093718614t_bool )
        & ( A @ is_fun2093718614t_bool ) )
     => ( ( A != B )
       => ( ( A @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
         => ( A @ ( B @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(567,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_boo115158845le_alt ) @ ( B @ ( member1463820796le_alt @ hAPP_f2127575245l_bool ) @ hAPP_f1351174655l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_b1703662281t_bool ) @ ( A @ ( B @ hAPP_b55004359le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_563_Pi__mem) ).

thf(2835,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_boo115158845le_alt ) @ ( B @ ( member1463820796le_alt @ hAPP_f2127575245l_bool ) @ hAPP_f1351174655l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_b1703662281t_bool ) @ ( A @ ( B @ hAPP_b55004359le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(621,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_859929070le_alt @ hAPP_f1165814111t_bool ) @ ( C @ pi_Pro1122146355t_unit ) @ ( B @ ( member2079083634t_unit @ hAPP_f1847883341l_bool ) @ hAPP_f22590837l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_P1844795325t_unit ) @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_583_funcset__mem) ).

thf(3159,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_859929070le_alt @ hAPP_f1165814111t_bool ) @ ( C @ pi_Pro1122146355t_unit ) @ ( B @ ( member2079083634t_unit @ hAPP_f1847883341l_bool ) @ hAPP_f22590837l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_P1844795325t_unit ) @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(366,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ is_Arr43961803e_indi )
        & ( A @ is_Arr43961803e_indi ) )
     => ( ( D @ ( C @ inj_on1073981917di_nat @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ( ( ( A @ ( C @ hAPP_A1637648121di_nat ) )
            = ( B @ ( C @ hAPP_A1637648121di_nat ) ) )
         => ( ( D @ ( A @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
           => ( ( D @ ( B @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
             => ( A = B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_545_inj__onD) ).

thf(2064,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ is_Arr43961803e_indi )
        & ( A @ is_Arr43961803e_indi ) )
     => ( ( D @ ( C @ inj_on1073981917di_nat @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ( ( ( A @ ( C @ hAPP_A1637648121di_nat ) )
            = ( B @ ( C @ hAPP_A1637648121di_nat ) ) )
         => ( ( D @ ( A @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
           => ( ( D @ ( B @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
             => ( A = B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(93,axiom,
    ! [A: $i,B: $i] :
      ( ( top_top_fun_nat_bool @ ( B @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( B @ hAPP_nat_nat ) @ ( B @ ( top_top_fun_nat_bool @ hilber195283148at_nat ) @ hAPP_nat_nat ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_inv__f__f) ).

thf(1015,plain,
    ! [A: $i,B: $i] :
      ( ( top_top_fun_nat_bool @ ( B @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( B @ hAPP_nat_nat ) @ ( B @ ( top_top_fun_nat_bool @ hilber195283148at_nat ) @ hAPP_nat_nat ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(507,axiom,
    lba @ ( lab @ ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ ( cOMBC_510421983t_bool @ hAPP_f1297018969t_bool ) @ hAPP_f1909278132t_bool ) @ ( cOMBC_633721483t_bool @ hAPP_f573120177t_bool ) @ hAPP_f329301088t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( b @ ( a @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_n_I3_J) ).

thf(2592,plain,
    lba @ ( lab @ ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ ( cOMBC_510421983t_bool @ hAPP_f1297018969t_bool ) @ hAPP_f1909278132t_bool ) @ ( cOMBC_633721483t_bool @ hAPP_f573120177t_bool ) @ hAPP_f329301088t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( b @ ( a @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(87,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_918_subsetD) ).

thf(1000,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(548,axiom,
    f @ ( arrow_1587283740nimity @ hAPP_f312250286l_bool ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_u) ).

thf(2752,plain,
    f @ ( arrow_1587283740nimity @ hAPP_f312250286l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(202,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ? [C: $i] :
          ( B
          = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1101_less__iff__Suc__add) ).

thf(1435,plain,
    ! [A: $i,B: $i] :
      ( ( ? [C: $i] :
            ( B
            = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ? [C: $i] :
            ( B
            = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(594,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Arr1199386158le_alt ) @ ( B @ ( member797673069le_alt @ hAPP_f721935245l_bool ) @ hAPP_f1837019376l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_A1677245848t_bool ) @ ( A @ ( B @ hAPP_A638717112le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_562_Pi__mem) ).

thf(2967,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Arr1199386158le_alt ) @ ( B @ ( member797673069le_alt @ hAPP_f721935245l_bool ) @ hAPP_f1837019376l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_A1677245848t_bool ) @ ( A @ ( B @ hAPP_A638717112le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(452,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C = A )
       => ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_ord__le__eq__trans) ).

thf(2390,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C = A )
       => ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(413,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      | ( A = B )
      | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_linorder__less__linear) ).

thf(2239,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      | ( A = B )
      | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(586,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le742797417l_bool @ hAPP_f612708895l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_913_subsetD) ).

thf(2952,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le742797417l_bool @ hAPP_f612708895l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(374,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_order__less__imp__not__less) ).

thf(2096,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(285,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_898791271t_bool @ hAPP_f248867553t_bool ) @ hAPP_A1906441908t_bool ) @ hAPP_A1625428400t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A621939144t_bool ) @ hAPP_A1941004017t_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_065) ).

thf(1758,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_898791271t_bool @ hAPP_f248867553t_bool ) @ hAPP_A1906441908t_bool ) @ hAPP_A1625428400t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A621939144t_bool ) @ hAPP_A1941004017t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(521,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
     => ( ( B @ ( D @ ( A @ hAPP_f1358350510ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( ( F @ is_fun2093718614t_bool )
                & ( E @ is_fun2093718614t_bool ) )
             => ( ( F @ ( E @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
               => ( F @ ( A @ hAPP_f1358350510ol_nat ) @ ( E @ ( A @ hAPP_f1358350510ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) )
         => ( B @ ( C @ ( A @ hAPP_f1358350510ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_888_order__le__less__subst2) ).

thf(2665,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
     => ( ( B @ ( D @ ( A @ hAPP_f1358350510ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( ( F @ is_fun2093718614t_bool )
                & ( E @ is_fun2093718614t_bool ) )
             => ( ( F @ ( E @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
               => ( F @ ( A @ hAPP_f1358350510ol_nat ) @ ( E @ ( A @ hAPP_f1358350510ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) )
         => ( B @ ( C @ ( A @ hAPP_f1358350510ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(209,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun1236654035i_bool )
     => ( B @ ( A @ hAPP_f1599966040l_bool ) @ is_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc_) ).

thf(1467,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun1236654035i_bool )
     => ( B @ ( A @ hAPP_f1599966040l_bool ) @ is_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(263,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ hAPP_A1625428400t_bool ) )
      = ( C @ ( B @ hAPP_A1677245848t_bool ) @ ( A @ hAPP_f393984045t_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp) ).

thf(1684,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ hAPP_A1625428400t_bool ) )
      = ( C @ ( B @ hAPP_A1677245848t_bool ) @ ( A @ hAPP_f393984045t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(3,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) )
      = ( C @ ( B @ times_times_nat @ hAPP_nat_nat ) @ ( A @ times_times_nat @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1175_nat__mult__assoc) ).

thf(648,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) )
      = ( C @ ( B @ times_times_nat @ hAPP_nat_nat ) @ ( A @ times_times_nat @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(221,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1107_le__less__Suc__eq) ).

thf(1509,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( ( B = A )
         => ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
        & ( ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(525,axiom,
    ! [A: $i] : ( top_to178429151t_bool @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_517_top__greatest) ).

thf(2684,plain,
    ! [A: $i] : ( top_to178429151t_bool @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(211,axiom,
    ! [A: $i] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
     != zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1066_Suc__neq__Zero) ).

thf(1472,plain,
    ! [A: $i] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
     != zero_zero_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(82,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ? [C: $i] :
          ( B
          = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1116_less__imp__Suc__add) ).

thf(968,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ? [C: $i] :
          ( B
          = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(101,axiom,
    ! [A: $i] : ( A @ ( top_top_fun_nat_bool @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_top1I) ).

thf(1049,plain,
    ! [A: $i] : ( A @ ( top_top_fun_nat_bool @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(361,axiom,
    ! [A: $i] :
      ( ( A @ is_bool )
     => ( ( A = fFalse )
        | ( A = fTrue ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).

thf(2054,plain,
    ! [A: $i] :
      ( ( A @ is_bool )
     => ( ( A = fFalse )
        | ( A = fTrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(335,axiom,
    ! [A: $i,B: $i] :
      ( ( A != B )
    <=> ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
        | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_982_nat__neq__iff) ).

thf(1948,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( A != B ) )
      & ( ( A != B )
       => ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(8,axiom,
    ( ( zero_zero_nat @ ( size_size_nat @ hAPP_nat_nat ) )
    = zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1185_nat_Osize_I3_J) ).

thf(675,plain,
    ( ( zero_zero_nat @ ( size_size_nat @ hAPP_nat_nat ) )
    = zero_zero_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(581,axiom,
    ! [A: $i] :
      ( ( A @ ( p @ hAPP_A1677245848t_bool ) @ ( d @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
    <=> ( ( ~ ( n @ ( A @ ( h @ hAPP_A1637648121di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( ( ( ( A @ ( h @ hAPP_A1637648121di_nat ) )
               != n )
             => ( e @ ( A @ ( p @ hAPP_A1677245848t_bool ) @ ( arrow_1495666017_mkbot @ hAPP_f393984045t_bool ) @ hAPP_A568203993t_bool ) @ ( d @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
            & ( ( ( A @ ( h @ hAPP_A1637648121di_nat ) )
                = n )
             => ( e @ ( c @ ( A @ ( p @ hAPP_A1677245848t_bool ) @ ( arrow_230821333_above @ hAPP_f344580165t_bool ) @ hAPP_A1941004017t_bool ) @ hAPP_A568203993t_bool ) @ ( d @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) )
        & ( ( n @ ( A @ ( h @ hAPP_A1637648121di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( e @ ( A @ ( p @ hAPP_A1677245848t_bool ) @ ( arrow_1644373103_mktop @ hAPP_f393984045t_bool ) @ hAPP_A568203993t_bool ) @ ( d @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J) ).

thf(2914,plain,
    ! [A: $i] :
      ( ( ( ( ~ ( n @ ( A @ ( h @ hAPP_A1637648121di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( ( ( ( A @ ( h @ hAPP_A1637648121di_nat ) )
                 != n )
               => ( e @ ( A @ ( p @ hAPP_A1677245848t_bool ) @ ( arrow_1495666017_mkbot @ hAPP_f393984045t_bool ) @ hAPP_A568203993t_bool ) @ ( d @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
              & ( ( ( A @ ( h @ hAPP_A1637648121di_nat ) )
                  = n )
               => ( e @ ( c @ ( A @ ( p @ hAPP_A1677245848t_bool ) @ ( arrow_230821333_above @ hAPP_f344580165t_bool ) @ hAPP_A1941004017t_bool ) @ hAPP_A568203993t_bool ) @ ( d @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) )
          & ( ( n @ ( A @ ( h @ hAPP_A1637648121di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( e @ ( A @ ( p @ hAPP_A1677245848t_bool ) @ ( arrow_1644373103_mktop @ hAPP_f393984045t_bool ) @ hAPP_A568203993t_bool ) @ ( d @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) )
       => ( A @ ( p @ hAPP_A1677245848t_bool ) @ ( d @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
      & ( ( A @ ( p @ hAPP_A1677245848t_bool ) @ ( d @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( ( ~ ( n @ ( A @ ( h @ hAPP_A1637648121di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( ( ( ( A @ ( h @ hAPP_A1637648121di_nat ) )
                 != n )
               => ( e @ ( A @ ( p @ hAPP_A1677245848t_bool ) @ ( arrow_1495666017_mkbot @ hAPP_f393984045t_bool ) @ hAPP_A568203993t_bool ) @ ( d @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
              & ( ( ( A @ ( h @ hAPP_A1637648121di_nat ) )
                  = n )
               => ( e @ ( c @ ( A @ ( p @ hAPP_A1677245848t_bool ) @ ( arrow_230821333_above @ hAPP_f344580165t_bool ) @ hAPP_A1941004017t_bool ) @ hAPP_A568203993t_bool ) @ ( d @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) )
          & ( ( n @ ( A @ ( h @ hAPP_A1637648121di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( e @ ( A @ ( p @ hAPP_A1677245848t_bool ) @ ( arrow_1644373103_mktop @ hAPP_f393984045t_bool ) @ hAPP_A568203993t_bool ) @ ( d @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(238,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ? [C: $i] :
          ( ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
            = B )
          & ( C @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1058_less__imp__add__positive) ).

thf(1583,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ? [C: $i] :
          ( ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
            = B )
          & ( C @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(167,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1172_mult__le__cancel2) ).

thf(1304,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(627,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_boo115158845le_alt ) @ ( B @ ( member1463820796le_alt @ hAPP_f2127575245l_bool ) @ hAPP_f1351174655l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_b1703662281t_bool ) @ ( A @ ( B @ hAPP_b55004359le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_PiE) ).

thf(3193,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_boo115158845le_alt ) @ ( B @ ( member1463820796le_alt @ hAPP_f2127575245l_bool ) @ hAPP_f1351174655l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_b1703662281t_bool ) @ ( A @ ( B @ hAPP_b55004359le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(622,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( F @ is_Arr1861959080le_alt )
        & ( E @ is_Arr1861959080le_alt )
        & ( D @ is_Arr1861959080le_alt )
        & ( C @ is_Arr1861959080le_alt ) )
     => ( ( E != F )
       => ( ( C != D )
         => ( ( E != D )
           => ( ( F != C )
             => ( ( arrow_1721807329e_Prof @ ( B @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
               => ( ( arrow_1721807329e_Prof @ ( A @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
                 => ( ! [G: $i] :
                        ( ( G @ is_Arr43961803e_indi )
                       => ( ( G @ ( B @ hAPP_A1677245848t_bool ) @ ( F @ ( E @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                        <=> ( G @ ( A @ hAPP_A1677245848t_bool ) @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) )
                   => ( ( B @ ( f @ hAPP_f412050202t_bool ) @ ( F @ ( E @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                    <=> ( A @ ( f @ hAPP_f412050202t_bool ) @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__C2_C) ).

thf(3161,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( F @ is_Arr1861959080le_alt )
        & ( E @ is_Arr1861959080le_alt )
        & ( D @ is_Arr1861959080le_alt )
        & ( C @ is_Arr1861959080le_alt ) )
     => ( ( E != F )
       => ( ( C != D )
         => ( ( E != D )
           => ( ( F != C )
             => ( ( arrow_1721807329e_Prof @ ( B @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
               => ( ( arrow_1721807329e_Prof @ ( A @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
                 => ( ! [G: $i] :
                        ( ( G @ is_Arr43961803e_indi )
                       => ( ( ( G @ ( A @ hAPP_A1677245848t_bool ) @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                           => ( G @ ( B @ hAPP_A1677245848t_bool ) @ ( F @ ( E @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
                          & ( ( G @ ( B @ hAPP_A1677245848t_bool ) @ ( F @ ( E @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                           => ( G @ ( A @ hAPP_A1677245848t_bool ) @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) )
                   => ( ( ( A @ ( f @ hAPP_f412050202t_bool ) @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                       => ( B @ ( f @ hAPP_f412050202t_bool ) @ ( F @ ( E @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
                      & ( ( B @ ( f @ hAPP_f412050202t_bool ) @ ( F @ ( E @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                       => ( A @ ( f @ hAPP_f412050202t_bool ) @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(325,axiom,
    ! [A: $i] :
      ~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1042_less__zeroE) ).

thf(1905,plain,
    ! [A: $i] :
      ~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(126,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ! [C: $i] :
            ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( B
             != ( C @ ( suc @ hAPP_nat_nat ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1122_Suc__lessE) ).

thf(1145,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ~ ! [C: $i] :
            ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( B
             != ( C @ ( suc @ hAPP_nat_nat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(94,axiom,
    ! [A: $i] :
      ( ( A @ ( zero_zero_nat @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1049_plus__nat_Oadd__0) ).

thf(1018,plain,
    ! [A: $i] :
      ( ( A @ ( zero_zero_nat @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(50,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
        = A )
     => ( B = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1052_add__eq__self__zero) ).

thf(855,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
        = A )
     => ( B = zero_zero_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(97,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2093718614t_bool )
        & ( A @ is_fun2093718614t_bool ) )
     => ( ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
      <=> ( ( A = B )
          | ( B @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_404_order__le__less) ).

thf(1025,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2093718614t_bool )
        & ( A @ is_fun2093718614t_bool ) )
     => ( ( ( ( A = B )
            | ( B @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) )
         => ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) )
        & ( ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
         => ( ( A = B )
            | ( B @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(16,axiom,
    ! [A: $i] :
      ( ( zero_zero_nat @ ( A @ times_times_nat @ hAPP_nat_nat ) )
      = zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1155_mult__0__right) ).

thf(705,plain,
    ! [A: $i] :
      ( ( zero_zero_nat @ ( A @ times_times_nat @ hAPP_nat_nat ) )
      = zero_zero_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(83,axiom,
    ! [A: $i] :
      ( ( A @ ( suc @ hAPP_nat_nat ) @ ( nat_size @ hAPP_nat_nat ) )
      = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( A @ ( nat_size @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1181_nat_Osize_I2_J) ).

thf(971,plain,
    ! [A: $i] :
      ( ( A @ ( suc @ hAPP_nat_nat ) @ ( nat_size @ hAPP_nat_nat ) )
      = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( A @ ( nat_size @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(283,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_996_le__trans) ).

thf(1753,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(574,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_order__trans) ).

thf(2888,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(572,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_62805014l_bool @ hAPP_f2018922499l_bool ) @ hAPP_f111185985l_bool ) @ hAPP_f592646513l_bool ) )
      = ( B @ ( C @ ( A @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp) ).

thf(2882,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_62805014l_bool @ hAPP_f2018922499l_bool ) @ hAPP_f111185985l_bool ) @ hAPP_f592646513l_bool ) )
      = ( B @ ( C @ ( A @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(500,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ( A = B )
        | ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_not__less__iff__gr__or__eq) ).

thf(2567,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A = B )
          | ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ( A = B )
          | ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(310,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_nat_bool ) @ is_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool) ).

thf(1845,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_nat_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(11,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
      = ( A @ ( B @ times_times_nat @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1174_nat__mult__commute) ).

thf(690,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
      = ( A @ ( B @ times_times_nat @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(222,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ( A
          = ( B @ ( suc @ hAPP_nat_nat ) ) )
        | ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1090_le__Suc__eq) ).

thf(1516,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A
            = ( B @ ( suc @ hAPP_nat_nat ) ) )
          | ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ( A
            = ( B @ ( suc @ hAPP_nat_nat ) ) )
          | ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(242,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ hAPP_f1313392232ol_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( D @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( ( F @ is_fun279392540l_bool )
                & ( E @ is_fun279392540l_bool ) )
             => ( ( F @ ( E @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
               => ( F @ ( C @ hAPP_f1313392232ol_nat ) @ ( E @ ( C @ hAPP_f1313392232ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) )
         => ( A @ ( C @ hAPP_f1313392232ol_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_847_order__less__le__subst1) ).

thf(1598,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ hAPP_f1313392232ol_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( D @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( ( F @ is_fun279392540l_bool )
                & ( E @ is_fun279392540l_bool ) )
             => ( ( F @ ( E @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
               => ( F @ ( C @ hAPP_f1313392232ol_nat ) @ ( E @ ( C @ hAPP_f1313392232ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) )
         => ( A @ ( C @ hAPP_f1313392232ol_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(108,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
        & ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1161_mult__less__cancel1) ).

thf(1070,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          & ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          & ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(56,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1089_Suc__le__mono) ).

thf(872,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(140,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1003_trans__less__add2) ).

thf(1225,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(280,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_479_order__less__le__trans) ).

thf(1743,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(193,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1102_less__eq__Suc__le) ).

thf(1400,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(332,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun961089132t_bool )
     => ( ( B @ ( A @ ( cOMBK_545135096l_bool @ hAPP_f340261009t_bool ) @ hAPP_b1703662281t_bool ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp) ).

thf(1941,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun961089132t_bool )
     => ( ( B @ ( A @ ( cOMBK_545135096l_bool @ hAPP_f340261009t_bool ) @ hAPP_b1703662281t_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(149,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1072_Suc__less__SucD) ).

thf(1252,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(142,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( D @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_744_add__strict__mono) ).

thf(1230,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( D @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(392,axiom,
    ! [A: $i] :
      ( ( A != zero_zero_nat )
     => ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1048_gr0I) ).

thf(2160,plain,
    ! [A: $i] :
      ( ( A != zero_zero_nat )
     => ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(103,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( ( D @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
          = ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1006_less__add__eq__less) ).

thf(1053,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( ( D @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
          = ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(407,axiom,
    ! [A: $i] : ( A @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_order__refl) ).

thf(2224,plain,
    ! [A: $i] : ( A @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(394,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun1236654035i_bool )
     => ( ( B @ ( A @ ( cOMBK_1915602921le_alt @ hAPP_f1348208725i_bool ) @ hAPP_P1875867302i_bool ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___052) ).

thf(2165,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun1236654035i_bool )
     => ( ( B @ ( A @ ( cOMBK_1915602921le_alt @ hAPP_f1348208725i_bool ) @ hAPP_P1875867302i_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(527,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_509_xt1_I8_J) ).

thf(2688,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(531,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro666468413t_bool ) @ ( B @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P324742453l_bool ) @ ( A @ ( B @ hAPP_P606313927t_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_PiE) ).

thf(2700,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro666468413t_bool ) @ ( B @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P324742453l_bool ) @ ( A @ ( B @ hAPP_P606313927t_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(45,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_743_add__less__imp__less__right) ).

thf(840,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(463,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C = A )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_ord__less__eq__trans) ).

thf(2429,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C = A )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(144,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_988_nat__add__commute) ).

thf(1235,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(324,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_bool )
     => ( ( B @ ( A @ ( cOMBK_306730240le_alt @ hAPP_b1703662281t_bool ) @ hAPP_P606313927t_bool ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabe) ).

thf(1901,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_bool )
     => ( ( B @ ( A @ ( cOMBK_306730240le_alt @ hAPP_b1703662281t_bool ) @ hAPP_P606313927t_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(434,axiom,
    arrow_1681063817le_Lin @ ( lba @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75__096Lba_A_058_ALin_096) ).

thf(2322,plain,
    arrow_1681063817le_Lin @ ( lba @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(358,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun1568535512t_bool )
     => ( ( B @ ( A @ ( cOMBK_859929070le_alt @ hAPP_f1165814111t_bool ) @ hAPP_P332578347t_bool ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_00_050) ).

thf(2044,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun1568535512t_bool )
     => ( ( B @ ( A @ ( cOMBK_859929070le_alt @ hAPP_f1165814111t_bool ) @ hAPP_P332578347t_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(236,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( D @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_654_add__less__le__mono) ).

thf(1579,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( D @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(76,axiom,
    ! [A: $i] :
      ( zero_zero_nat
     != ( A @ ( suc @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1070_nat_Osimps_I2_J) ).

thf(951,plain,
    ! [A: $i] :
      ( zero_zero_nat
     != ( A @ ( suc @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(510,axiom,
    ! [A: $i] :
      ( ( arrow_1681063817le_Lin @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( arrow_1721807329e_Prof @ ( A @ ( cOMBK_1076156777e_indi @ hAPP_f329301088t_bool ) @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_const__Lin__Prof) ).

thf(2599,plain,
    ! [A: $i] :
      ( ( arrow_1681063817le_Lin @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( arrow_1721807329e_Prof @ ( A @ ( cOMBK_1076156777e_indi @ hAPP_f329301088t_bool ) @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(37,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1170_one__less__mult) ).

thf(808,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(444,axiom,
    top_to1853035173l_bool @ is_fun279392540l_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Ord) ).

thf(2354,plain,
    top_to1853035173l_bool @ is_fun279392540l_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(65,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( D @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_655_add__le__less__mono) ).

thf(907,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( D @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(534,axiom,
    arrow_1721807329e_Prof @ ( p @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__096P_A_058_AProf_096) ).

thf(2711,plain,
    arrow_1721807329e_Prof @ ( p @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(115,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun279392540l_bool )
        & ( A @ is_fun279392540l_bool ) )
     => ( ( B @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
         => ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_order__antisym) ).

thf(1094,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun279392540l_bool )
        & ( A @ is_fun279392540l_bool ) )
     => ( ( B @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(618,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( F @ is_Arr1861959080le_alt )
        & ( E @ is_Arr1861959080le_alt )
        & ( D @ is_Arr1861959080le_alt )
        & ( C @ is_Arr1861959080le_alt ) )
     => ( ( E != F )
       => ( ( C != D )
         => ( ( arrow_1721807329e_Prof @ ( B @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
           => ( ( arrow_1721807329e_Prof @ ( A @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
             => ( ! [G: $i] :
                    ( ( G @ is_Arr43961803e_indi )
                   => ( ( G @ ( B @ hAPP_A1677245848t_bool ) @ ( F @ ( E @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                    <=> ( G @ ( A @ hAPP_A1677245848t_bool ) @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) )
               => ( ( B @ ( f @ hAPP_f412050202t_bool ) @ ( F @ ( E @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                <=> ( A @ ( f @ hAPP_f412050202t_bool ) @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_pairwise__neutrality) ).

thf(3117,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( F @ is_Arr1861959080le_alt )
        & ( E @ is_Arr1861959080le_alt )
        & ( D @ is_Arr1861959080le_alt )
        & ( C @ is_Arr1861959080le_alt ) )
     => ( ( E != F )
       => ( ( C != D )
         => ( ( arrow_1721807329e_Prof @ ( B @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
           => ( ( arrow_1721807329e_Prof @ ( A @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
             => ( ! [G: $i] :
                    ( ( G @ is_Arr43961803e_indi )
                   => ( ( ( G @ ( A @ hAPP_A1677245848t_bool ) @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                       => ( G @ ( B @ hAPP_A1677245848t_bool ) @ ( F @ ( E @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
                      & ( ( G @ ( B @ hAPP_A1677245848t_bool ) @ ( F @ ( E @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                       => ( G @ ( A @ hAPP_A1677245848t_bool ) @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) )
               => ( ( ( A @ ( f @ hAPP_f412050202t_bool ) @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                   => ( B @ ( f @ hAPP_f412050202t_bool ) @ ( F @ ( E @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
                  & ( ( B @ ( f @ hAPP_f412050202t_bool ) @ ( F @ ( E @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                   => ( A @ ( f @ hAPP_f412050202t_bool ) @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

thf(582,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( produc1400112471le_alt @ ( member1441201108le_alt @ cOMBB_84213429le_alt @ cOMBB_2112722489le_alt @ hAPP_f156764033l_bool ) @ ( cOMBC_1635684702l_bool @ cOMBB_747702273le_alt @ hAPP_f1324249913t_bool ) @ ( cOMBC_364043868t_bool @ hAPP_f2058969401t_bool ) @ hAPP_f1617919085t_bool ) @ ( A @ ( produc1400112471le_alt @ ( member1441201108le_alt @ cOMBB_84213429le_alt @ cOMBB_2112722489le_alt @ hAPP_f156764033l_bool ) @ ( cOMBC_1635684702l_bool @ cOMBB_747702273le_alt @ hAPP_f1324249913t_bool ) @ ( cOMBC_364043868t_bool @ hAPP_f2058969401t_bool ) @ hAPP_f1617919085t_bool ) @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
    <=> ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_718_pred__subset__eq2) ).

thf(2939,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( B @ ( produc1400112471le_alt @ ( member1441201108le_alt @ cOMBB_84213429le_alt @ cOMBB_2112722489le_alt @ hAPP_f156764033l_bool ) @ ( cOMBC_1635684702l_bool @ cOMBB_747702273le_alt @ hAPP_f1324249913t_bool ) @ ( cOMBC_364043868t_bool @ hAPP_f2058969401t_bool ) @ hAPP_f1617919085t_bool ) @ ( A @ ( produc1400112471le_alt @ ( member1441201108le_alt @ cOMBB_84213429le_alt @ cOMBB_2112722489le_alt @ hAPP_f156764033l_bool ) @ ( cOMBC_1635684702l_bool @ cOMBB_747702273le_alt @ hAPP_f1324249913t_bool ) @ ( cOMBC_364043868t_bool @ hAPP_f2058969401t_bool ) @ hAPP_f1617919085t_bool ) @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) )
      & ( ( B @ ( produc1400112471le_alt @ ( member1441201108le_alt @ cOMBB_84213429le_alt @ cOMBB_2112722489le_alt @ hAPP_f156764033l_bool ) @ ( cOMBC_1635684702l_bool @ cOMBB_747702273le_alt @ hAPP_f1324249913t_bool ) @ ( cOMBC_364043868t_bool @ hAPP_f2058969401t_bool ) @ hAPP_f1617919085t_bool ) @ ( A @ ( produc1400112471le_alt @ ( member1441201108le_alt @ cOMBB_84213429le_alt @ cOMBB_2112722489le_alt @ hAPP_f156764033l_bool ) @ ( cOMBC_1635684702l_bool @ cOMBB_747702273le_alt @ hAPP_f1324249913t_bool ) @ ( cOMBC_364043868t_bool @ hAPP_f2058969401t_bool ) @ hAPP_f1617919085t_bool ) @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(612,axiom,
    ( ( p @ ( f @ hAPP_f412050202t_bool ) @ ( d @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
  <=> ( e @ ( p @ ( arrow_1495666017_mkbot @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( e @ ( c @ ( p @ ( arrow_230821333_above @ cOMBB_1769989562e_indi @ hAPP_f210227915t_bool ) @ ( cOMBC_898791271t_bool @ hAPP_f248867553t_bool ) @ hAPP_A1906441908t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( e @ ( p @ ( arrow_1644373103_mktop @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( d @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_PW) ).

thf(3071,plain,
    ( ( ( e @ ( p @ ( arrow_1495666017_mkbot @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( e @ ( c @ ( p @ ( arrow_230821333_above @ cOMBB_1769989562e_indi @ hAPP_f210227915t_bool ) @ ( cOMBC_898791271t_bool @ hAPP_f248867553t_bool ) @ hAPP_A1906441908t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( e @ ( p @ ( arrow_1644373103_mktop @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( d @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( p @ ( f @ hAPP_f412050202t_bool ) @ ( d @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
    & ( ( p @ ( f @ hAPP_f412050202t_bool ) @ ( d @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( e @ ( p @ ( arrow_1495666017_mkbot @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( e @ ( c @ ( p @ ( arrow_230821333_above @ cOMBB_1769989562e_indi @ hAPP_f210227915t_bool ) @ ( cOMBC_898791271t_bool @ hAPP_f248867553t_bool ) @ hAPP_A1906441908t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( e @ ( p @ ( arrow_1644373103_mktop @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( d @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

thf(186,axiom,
    ! [A: $i] :
      ( zero_zero_nat
     != ( A @ ( suc @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1067_Zero__neq__Suc) ).

thf(1372,plain,
    ! [A: $i] :
      ( zero_zero_nat
     != ( A @ ( suc @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(421,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( D @ ( A @ hAPP_n588788980t_bool ) @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( F @ ( E @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( A @ hAPP_n588788980t_bool ) @ ( E @ ( A @ hAPP_n588788980t_bool ) @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
         => ( B @ ( C @ ( A @ hAPP_n588788980t_bool ) @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_898_order__less__le__subst2) ).

thf(2266,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( D @ ( A @ hAPP_n588788980t_bool ) @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( F @ ( E @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( A @ hAPP_n588788980t_bool ) @ ( E @ ( A @ hAPP_n588788980t_bool ) @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
         => ( B @ ( C @ ( A @ hAPP_n588788980t_bool ) @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(330,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun961089132t_bool )
     => ( ( B @ ( A @ ( cOMBK_1076156777e_indi @ hAPP_f329301088t_bool ) @ hAPP_A1677245848t_bool ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp_053) ).

thf(1934,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun961089132t_bool )
     => ( ( B @ ( A @ ( cOMBK_1076156777e_indi @ hAPP_f329301088t_bool ) @ hAPP_A1677245848t_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(585,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( C @ ( D @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_P332578347t_bool ) @ ( D @ ( A @ hAPP_P1844795325t_unit ) @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_Pro1122146355t_unit ) @ ( A @ ( member2079083634t_unit @ hAPP_f1847883341l_bool ) @ hAPP_f22590837l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_621_Pi__I) ).

thf(2948,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( C @ ( D @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_P332578347t_bool ) @ ( D @ ( A @ hAPP_P1844795325t_unit ) @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_Pro1122146355t_unit ) @ ( A @ ( member2079083634t_unit @ hAPP_f1847883341l_bool ) @ hAPP_f22590837l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(323,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_order__antisym) ).

thf(1898,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(312,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun961089132t_bool )
     => ( B @ ( A @ hAPP_f1582908258e_indi ) @ is_Arr43961803e_indi ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__) ).

thf(1849,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun961089132t_bool )
     => ( B @ ( A @ hAPP_f1582908258e_indi ) @ is_Arr43961803e_indi ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(603,axiom,
    ! [A: $i] :
      ~ ( A @ ( top_to565915683t_bool @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_not__top__less) ).

thf(2992,plain,
    ! [A: $i] :
      ~ ( A @ ( top_to565915683t_bool @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).

thf(342,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1027_termination__basic__simps_I5_J) ).

thf(1981,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(6,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) )
        = ( C @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) ) )
    <=> ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1151_Suc__mult__cancel1) ).

thf(656,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B = C )
       => ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) )
          = ( C @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) ) ) )
      & ( ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) )
          = ( C @ ( A @ ( suc @ hAPP_nat_nat ) @ times_times_nat @ hAPP_nat_nat ) ) )
       => ( B = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(295,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A != B )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1011_le__neq__implies__less) ).

thf(1802,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A != B )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(96,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1073_Suc__lessD) ).

thf(1023,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(170,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ hAPP_n539120590t_bool ) @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( E @ ( F @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n539120590t_bool ) @ ( F @ ( B @ hAPP_n539120590t_bool ) @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) )
         => ( D @ ( A @ ( B @ hAPP_n539120590t_bool ) @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_780_xt4) ).

thf(1316,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ hAPP_n539120590t_bool ) @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( E @ ( F @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n539120590t_bool ) @ ( F @ ( B @ hAPP_n539120590t_bool ) @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) )
         => ( D @ ( A @ ( B @ hAPP_n539120590t_bool ) @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(371,axiom,
    ! [A: $i] :
      ( ( A @ is_bool )
     => ( ( A = fFalse )
        | ( A = fTrue ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbp) ).

thf(2088,plain,
    ! [A: $i] :
      ( ( A @ is_bool )
     => ( ( A = fFalse )
        | ( A = fTrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(573,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun961089132t_bool ) )
     => ( ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
         => ( B = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_xt1_I5_J) ).

thf(2885,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun961089132t_bool ) )
     => ( ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(229,axiom,
    ! [A: $i] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
      = ( one_one_nat @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1118_Suc__eq__plus1) ).

thf(1553,plain,
    ! [A: $i] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
      = ( one_one_nat @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(590,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Arr1199386158le_alt ) @ ( B @ ( member797673069le_alt @ hAPP_f721935245l_bool ) @ hAPP_f1837019376l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_A1677245848t_bool ) @ ( A @ ( B @ hAPP_A638717112le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_PiE) ).

thf(2960,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Arr1199386158le_alt ) @ ( B @ ( member797673069le_alt @ hAPP_f721935245l_bool ) @ hAPP_f1837019376l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_A1677245848t_bool ) @ ( A @ ( B @ hAPP_A638717112le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(306,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun961089132t_bool ) )
     => ( ( A != B )
       => ( ( A @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
         => ( A @ ( B @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_425_xt1_I12_J) ).

thf(1834,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun961089132t_bool ) )
     => ( ( A != B )
       => ( ( A @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
         => ( A @ ( B @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(197,axiom,
    ! [A: $i] :
      ( ( A @ ( suc @ hAPP_nat_nat ) @ ( size_size_nat @ hAPP_nat_nat ) )
      = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( A @ ( size_size_nat @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1183_nat_Osize_I4_J) ).

thf(1412,plain,
    ! [A: $i] :
      ( ( A @ ( suc @ hAPP_nat_nat ) @ ( size_size_nat @ hAPP_nat_nat ) )
      = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( A @ ( size_size_nat @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(138,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
        = ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
    <=> ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_992_nat__add__right__cancel) ).

thf(1216,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A = C )
       => ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
          = ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) )
      & ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
          = ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
       => ( A = C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(408,axiom,
    ! [A: $i] : ( top_to1714702858l_bool @ ( A @ ( member520425275t_bool @ hAPP_f1253375959l_bool ) @ hAPP_f250445784l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_iso__tuple__UNIV__I) ).

thf(2226,plain,
    ! [A: $i] : ( top_to1714702858l_bool @ ( A @ ( member520425275t_bool @ hAPP_f1253375959l_bool ) @ hAPP_f250445784l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(347,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_997_le__antisym) ).

thf(1998,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(465,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_364043868t_bool @ hAPP_f2058969401t_bool ) @ hAPP_f1617919085t_bool ) @ hAPP_A1664620203t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A572596845t_bool ) @ hAPP_f1663053423t_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000t_062) ).

thf(2435,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_364043868t_bool @ hAPP_f2058969401t_bool ) @ hAPP_f1617919085t_bool ) @ hAPP_A1664620203t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A572596845t_bool ) @ hAPP_f1663053423t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(47,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( B @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1159_mult__less__mono1) ).

thf(845,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( B @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(10,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( B @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1142_mult__le__mono1) ).

thf(688,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( B @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(63,axiom,
    ! [A: $i] : ( A @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_order__refl) ).

thf(903,plain,
    ! [A: $i] : ( A @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(513,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ hAPP_f1358350510ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( ( F @ is_fun2093718614t_bool )
                & ( E @ is_fun2093718614t_bool ) )
             => ( ( E @ ( F @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
               => ( E @ ( B @ hAPP_f1358350510ol_nat ) @ ( F @ ( B @ hAPP_f1358350510ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) )
         => ( D @ ( A @ ( B @ hAPP_f1358350510ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_805_xt4) ).

thf(2611,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( B @ hAPP_f1358350510ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( ( F @ is_fun2093718614t_bool )
                & ( E @ is_fun2093718614t_bool ) )
             => ( ( E @ ( F @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
               => ( E @ ( B @ hAPP_f1358350510ol_nat ) @ ( F @ ( B @ hAPP_f1358350510ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) )
         => ( D @ ( A @ ( B @ hAPP_f1358350510ol_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(436,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_order__less__imp__not__eq2) ).

thf(2325,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(398,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A = B )
        | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_451_order__le__imp__less__or__eq) ).

thf(2187,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A = B )
        | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(133,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ? [C: $i] :
            ( ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
            & ( A
              = ( C @ ( suc @ hAPP_nat_nat ) ) ) )
        | ( A = zero_zero_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1096_less__Suc__eq__0__disj) ).

thf(1189,plain,
    ! [A: $i,B: $i] :
      ( ( ( ? [C: $i] :
              ( ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
              & ( A
                = ( C @ ( suc @ hAPP_nat_nat ) ) ) )
          | ( A = zero_zero_nat ) )
       => ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ? [C: $i] :
              ( ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
              & ( A
                = ( C @ ( suc @ hAPP_nat_nat ) ) ) )
          | ( A = zero_zero_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(91,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( cOMBK_246631416le_alt @ hAPP_f2068374643l_bool ) @ hAPP_P324742453l_bool ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__prod_It) ).

thf(1010,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( cOMBK_246631416le_alt @ hAPP_f2068374643l_bool ) @ hAPP_P324742453l_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(431,axiom,
    ! [A: $i,B: $i] :
      ( ( A != B )
     => ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_983_linorder__neqE__nat) ).

thf(2305,plain,
    ! [A: $i,B: $i] :
      ( ( A != B )
     => ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(316,axiom,
    ! [A: $i] : ( top_to1257323279t_bool @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_UNIV__I) ).

thf(1866,plain,
    ! [A: $i] : ( top_to1257323279t_bool @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(555,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro1928973619le_alt ) @ ( B @ ( member1648671474le_alt @ hAPP_f1868437069l_bool ) @ hAPP_f415146997l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_P1341894483t_bool ) @ ( A @ ( B @ hAPP_P504138941le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_564_Pi__mem) ).

thf(2775,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro1928973619le_alt ) @ ( B @ ( member1648671474le_alt @ hAPP_f1868437069l_bool ) @ hAPP_f415146997l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_P1341894483t_bool ) @ ( A @ ( B @ hAPP_P504138941le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(561,axiom,
    e @ ( p @ ( arrow_1495666017_mkbot @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( e @ ( c @ ( p @ ( arrow_230821333_above @ cOMBB_1769989562e_indi @ hAPP_f210227915t_bool ) @ ( cOMBC_898791271t_bool @ hAPP_f248867553t_bool ) @ hAPP_A1906441908t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( e @ ( p @ ( arrow_1644373103_mktop @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( d @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).

thf(2792,plain,
    e @ ( p @ ( arrow_1495666017_mkbot @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( e @ ( c @ ( p @ ( arrow_230821333_above @ cOMBB_1769989562e_indi @ hAPP_f210227915t_bool ) @ ( cOMBC_898791271t_bool @ hAPP_f248867553t_bool ) @ hAPP_A1906441908t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( e @ ( p @ ( arrow_1644373103_mktop @ cOMBB_2032668066e_indi @ hAPP_f721938099t_bool ) @ ( cOMBC_1353880399t_bool @ hAPP_f1808153265t_bool ) @ hAPP_A1805174428t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ ( f @ hAPP_f412050202t_bool ) @ ( d @ ( c @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(29,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ times_times_nat @ hAPP_nat_nat ) )
      = ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1164_mult__Suc__right) ).

thf(771,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ times_times_nat @ hAPP_nat_nat ) )
      = ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(579,axiom,
    ! [A: $i] : ( top_to565915683t_bool @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_722_subset__UNIV) ).

thf(2907,plain,
    ! [A: $i] : ( top_to565915683t_bool @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(602,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_bool )
     => ( ( B @ ( A @ ( cOMBK_1656150864t_bool @ hAPP_b1812770943l_bool ) @ hAPP_f592646513l_bool ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order_) ).

thf(2988,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_bool )
     => ( ( B @ ( A @ ( cOMBK_1656150864t_bool @ hAPP_b1812770943l_bool ) @ hAPP_f592646513l_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(375,axiom,
    top_to565915683t_bool @ is_fun961089132t_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__prod_Itc__Arrow____Order____Mir) ).

thf(2098,plain,
    top_to565915683t_bool @ is_fun961089132t_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(457,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B != zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1047_gr__implies__not0) ).

thf(2406,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B != zero_zero_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(497,axiom,
    lab @ is_fun961089132t_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_Lab____) ).

thf(2554,plain,
    lab @ is_fun961089132t_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(117,axiom,
    ! [A: $i,B: $i] :
      ~ ( A @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_999_not__add__less1) ).

thf(1101,plain,
    ! [A: $i,B: $i] :
      ~ ( A @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(281,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_xt1_I6_J) ).

thf(1745,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(596,axiom,
    fTrue @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).

thf(2971,plain,
    fTrue @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(453,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun961089132t_bool )
     => ( ( B @ ( A @ ( cOMBK_812212462t_unit @ hAPP_f1066247963t_bool ) @ hAPP_P1341894483t_bool ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp_051) ).

thf(2394,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun961089132t_bool )
     => ( ( B @ ( A @ ( cOMBK_812212462t_unit @ hAPP_f1066247963t_bool ) @ hAPP_P1341894483t_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(156,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1022_add__leD1) ).

thf(1276,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(240,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( B @ hAPP_n539120590t_bool ) @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( E @ ( F @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n539120590t_bool ) @ ( F @ ( B @ hAPP_n539120590t_bool ) @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) )
         => ( D @ ( B @ hAPP_n539120590t_bool ) @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_681_xt7) ).

thf(1590,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( C @ ( B @ hAPP_n539120590t_bool ) @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( E @ ( F @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_n539120590t_bool ) @ ( F @ ( B @ hAPP_n539120590t_bool ) @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) )
         => ( D @ ( B @ hAPP_n539120590t_bool ) @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(80,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_989_nat__add__left__commute) ).

thf(963,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(423,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_order__less__trans) ).

thf(2273,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(427,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun961089132t_bool )
     => ( ( B @ ( A @ ( fFalse @ ( if_fun2098446489t_bool @ hAPP_b1588041841t_bool ) @ hAPP_f427493225t_bool ) @ hAPP_f515126293t_bool ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbp) ).

thf(2283,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun961089132t_bool )
     => ( ( B @ ( A @ ( fFalse @ ( if_fun2098446489t_bool @ hAPP_b1588041841t_bool ) @ hAPP_f427493225t_bool ) @ hAPP_f515126293t_bool ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(212,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( B @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_order__eq__refl) ).

thf(1476,plain,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( B @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(231,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1082_not__less__eq) ).

thf(1558,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(419,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Arr990697634t_bool ) @ ( B @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_A60074736l_bool ) @ ( A @ ( B @ hAPP_A1677245848t_bool ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_PiE) ).

thf(2262,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Arr990697634t_bool ) @ ( B @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_A60074736l_bool ) @ ( A @ ( B @ hAPP_A1677245848t_bool ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(350,axiom,
    ( top_to565915683t_bool
    = ( fTrue @ ( cOMBK_306730240le_alt @ hAPP_b1703662281t_bool ) @ ( collec2096990994le_alt @ hAPP_f515126293t_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_UNIV__def) ).

thf(2009,plain,
    ( top_to565915683t_bool
    = ( fTrue @ ( cOMBK_306730240le_alt @ hAPP_b1703662281t_bool ) @ ( collec2096990994le_alt @ hAPP_f515126293t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(588,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_812212462t_unit @ hAPP_f1066247963t_bool ) @ ( C @ pi_Pro1928973619le_alt ) @ ( B @ ( member1648671474le_alt @ hAPP_f1868437069l_bool ) @ hAPP_f415146997l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_P504138941le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_598_funcset__mem) ).

thf(2956,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_812212462t_unit @ hAPP_f1066247963t_bool ) @ ( C @ pi_Pro1928973619le_alt ) @ ( B @ ( member1648671474le_alt @ hAPP_f1868437069l_bool ) @ hAPP_f415146997l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_P504138941le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(620,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun961089132t_bool ) )
     => ( ( A = B )
      <=> ( ( A @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_358_order__eq__iff) ).

thf(3149,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun961089132t_bool ) )
     => ( ( ( ( A @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
            & ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
         => ( A = B ) )
        & ( ( A = B )
         => ( ( A @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
            & ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(269,axiom,
    ! [A: $i] : ( A @ ( suc @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1093_inj__Suc) ).

thf(1706,plain,
    ! [A: $i] : ( A @ ( suc @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(429,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ is_Arr43961803e_indi )
        & ( A @ is_Arr43961803e_indi ) )
     => ( ( top_to1576102282i_bool @ ( C @ inj_on1073981917di_nat @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ( ( ( A @ ( C @ hAPP_A1637648121di_nat ) )
            = ( B @ ( C @ hAPP_A1637648121di_nat ) ) )
        <=> ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_612_inj__eq) ).

thf(2294,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ is_Arr43961803e_indi )
        & ( A @ is_Arr43961803e_indi ) )
     => ( ( top_to1576102282i_bool @ ( C @ inj_on1073981917di_nat @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ( ( ( A = B )
           => ( ( A @ ( C @ hAPP_A1637648121di_nat ) )
              = ( B @ ( C @ hAPP_A1637648121di_nat ) ) ) )
          & ( ( ( A @ ( C @ hAPP_A1637648121di_nat ) )
              = ( B @ ( C @ hAPP_A1637648121di_nat ) ) )
           => ( A = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(480,axiom,
    ! [A: $i] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_order__refl) ).

thf(2494,plain,
    ! [A: $i] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(346,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ hAPP_n588788980t_bool ) @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( A @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( F @ ( E @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( C @ hAPP_n588788980t_bool ) @ ( E @ ( C @ hAPP_n588788980t_bool ) @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
         => ( A @ ( C @ hAPP_n588788980t_bool ) @ ( B @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_815_order__le__less__subst1) ).

thf(1994,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ hAPP_n588788980t_bool ) @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( A @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ! [E: $i,F: $i] :
              ( ( F @ ( E @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
             => ( F @ ( C @ hAPP_n588788980t_bool ) @ ( E @ ( C @ hAPP_n588788980t_bool ) @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
         => ( A @ ( C @ hAPP_n588788980t_bool ) @ ( B @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(557,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun961089132t_bool ) )
     => ( ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
        <=> ( B = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_order__antisym__conv) ).

thf(2779,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun961089132t_bool ) )
     => ( ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( ( ( B = A )
           => ( A @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
          & ( ( A @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
           => ( B = A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(100,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( top_top_fun_nat_bool @ ( C @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( ( A @ ( C @ hAPP_nat_nat ) )
          = B )
       => ( ( B @ ( C @ ( top_top_fun_nat_bool @ hilber195283148at_nat ) @ hAPP_nat_nat ) )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_inv__f__eq) ).

thf(1045,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( top_top_fun_nat_bool @ ( C @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( ( A @ ( C @ hAPP_nat_nat ) )
          = B )
       => ( ( B @ ( C @ ( top_top_fun_nat_bool @ hilber195283148at_nat ) @ hAPP_nat_nat ) )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(450,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_order__eq__refl) ).

thf(2384,plain,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(558,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_507_xt1_I8_J) ).

thf(2786,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(109,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1028_termination__basic__simps_I2_J) ).

thf(1077,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(447,axiom,
    fFalse @ is_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_fFalse) ).

thf(2362,plain,
    fFalse @ is_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(411,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_order__trans) ).

thf(2233,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(490,axiom,
    top_top_bool @ is_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__HOL__Obool) ).

thf(2522,plain,
    top_top_bool @ is_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(189,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2093718614t_bool )
        & ( A @ is_fun2093718614t_bool ) )
     => ( ( B @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
      <=> ( ( A != B )
          & ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_384_order__less__le) ).

thf(1380,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2093718614t_bool )
        & ( A @ is_fun2093718614t_bool ) )
     => ( ( ( ( A != B )
            & ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) )
         => ( B @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) )
        & ( ( B @ ( A @ ( ord_le1393483395t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
         => ( ( A != B )
            & ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(33,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun279392540l_bool )
        & ( A @ is_fun279392540l_bool ) )
     => ( ( B @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
        <=> ( B = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_order__antisym__conv) ).

thf(790,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun279392540l_bool )
        & ( A @ is_fun279392540l_bool ) )
     => ( ( B @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( ( ( B = A )
           => ( A @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) )
          & ( ( A @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
           => ( B = A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(54,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( B @ ( A @ hAPP_nat_nat ) @ ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ? [B: $i] :
        ! [C: $i] :
          ( ( C @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ hAPP_nat_nat ) )
          = ( B @ ( A @ hAPP_nat_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1186_weak__decr__stable) ).

thf(867,plain,
    ! [A: $i] :
      ( ! [B: $i] : ( B @ ( A @ hAPP_nat_nat ) @ ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ? [B: $i] :
        ! [C: $i] :
          ( ( C @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ hAPP_nat_nat ) )
          = ( B @ ( A @ hAPP_nat_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(213,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_n821919323i_bool ) @ is_fun1236654035i_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfn_007) ).

thf(1480,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_n821919323i_bool ) @ is_fun1236654035i_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(326,axiom,
    ! [A: $i] :
      ( ( A @ is_fun961089132t_bool )
     => ( ( A @ ( top_to565915683t_bool @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
      <=> ( A = top_to565915683t_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_525_top__unique) ).

thf(1908,plain,
    ! [A: $i] :
      ( ( A @ is_fun961089132t_bool )
     => ( ( ( A = top_to565915683t_bool )
         => ( A @ ( top_to565915683t_bool @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
        & ( ( A @ ( top_to565915683t_bool @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
         => ( A = top_to565915683t_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(349,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
    <=> ( A @ ( B @ hAPP_A1785763630i_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_mem__def) ).

thf(2003,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ hAPP_A1785763630i_bool ) @ hBOOL )
       => ( B @ ( A @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL )
       => ( A @ ( B @ hAPP_A1785763630i_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(381,axiom,
    ! [A: $i] :
      ~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_984_less__irrefl__nat) ).

thf(2123,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(405,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_xt1_I3_J) ).

thf(2218,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(430,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ hAPP_A1677245848t_bool ) )
      = ( C @ ( B @ hAPP_A1677245848t_bool ) @ ( C @ ( A @ hAPP_A1102281708t_bool ) @ hAPP_f515126293t_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000) ).

thf(2302,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBS_1064524443t_bool @ hAPP_f1740414619t_bool ) @ hAPP_A1677245848t_bool ) )
      = ( C @ ( B @ hAPP_A1677245848t_bool ) @ ( C @ ( A @ hAPP_A1102281708t_bool ) @ hAPP_f515126293t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(488,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ is_Arr1861959080le_alt )
        & ( B @ is_Arr1861959080le_alt )
        & ( A @ is_fun961089132t_bool ) )
     => ( C @ ( B @ ( A @ arrow_1539419881_below ) ) @ is_fun961089132t_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_Obelow) ).

thf(2517,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ is_Arr1861959080le_alt )
        & ( B @ is_Arr1861959080le_alt )
        & ( A @ is_fun961089132t_bool ) )
     => ( C @ ( B @ ( A @ arrow_1539419881_below ) ) @ is_fun961089132t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(275,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_985_less__not__refl2) ).

thf(1725,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(158,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_order__trans) ).

thf(1280,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(633,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_939_psubset__imp__subset) ).

thf(3232,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).

thf(494,axiom,
    ! [A: $i] :
      ( ( A != zero_zero_nat )
    <=> ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1045_neq0__conv) ).

thf(2534,plain,
    ! [A: $i] :
      ( ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A != zero_zero_nat ) )
      & ( ( A != zero_zero_nat )
       => ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(418,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_order__antisym__conv) ).

thf(2255,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( ( B = A )
         => ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
        & ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(43,axiom,
    ! [A: $i] : ( one_one_nat @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_653_less__add__one) ).

thf(833,plain,
    ! [A: $i] : ( one_one_nat @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(539,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
    <=> ( ~ ( A @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
        & ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_392_less__le__not__le) ).

thf(2719,plain,
    ! [A: $i,B: $i] :
      ( ( ( ~ ( A @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_le906188671t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( ~ ( A @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(116,axiom,
    ! [A: $i] :
      ( ( A != zero_zero_nat )
     => ~ ! [B: $i] :
            ( A
           != ( B @ ( suc @ hAPP_nat_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1124_nat_Oexhaust) ).

thf(1097,plain,
    ! [A: $i] :
      ( ( A != zero_zero_nat )
     => ~ ! [B: $i] :
            ( A
           != ( B @ ( suc @ hAPP_nat_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(44,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ hAPP_nat_bool ) @ hBOOL )
     => ( ! [C: $i] :
            ( ( C @ ( suc @ hAPP_nat_nat ) @ ( A @ hAPP_nat_bool ) @ hBOOL )
           => ( C @ ( A @ hAPP_nat_bool ) @ hBOOL ) )
       => ( zero_zero_nat @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1125_zero__induct) ).

thf(835,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ hAPP_nat_bool ) @ hBOOL )
     => ( ! [C: $i] :
            ( ( C @ ( suc @ hAPP_nat_nat ) @ ( A @ hAPP_nat_bool ) @ hBOOL )
           => ( C @ ( A @ hAPP_nat_bool ) @ hBOOL ) )
       => ( zero_zero_nat @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(505,axiom,
    ! [A: $i,B: $i] :
      ( ( arrow_1681063817le_Lin @ ( B @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( arrow_1681063817le_Lin @ ( A @ ( B @ ( arrow_1644373103_mktop @ hAPP_f393984045t_bool ) @ hAPP_A568203993t_bool ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_mktop__Lin) ).

thf(2587,plain,
    ! [A: $i,B: $i] :
      ( ( arrow_1681063817le_Lin @ ( B @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( arrow_1681063817le_Lin @ ( A @ ( B @ ( arrow_1644373103_mktop @ hAPP_f393984045t_bool ) @ hAPP_A568203993t_bool ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(542,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( A @ ( B @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_964_set__rev__mp) ).

thf(2736,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ( A @ ( B @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(344,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( member496995196t_bool @ ( cOMBC_62805014l_bool @ hAPP_f2018922499l_bool ) @ hAPP_f111185985l_bool ) @ ( A @ ( member496995196t_bool @ ( cOMBC_62805014l_bool @ hAPP_f2018922499l_bool ) @ hAPP_f111185985l_bool ) @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
    <=> ( B @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_977_pred__subset__eq) ).

thf(1986,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( B @ ( member496995196t_bool @ ( cOMBC_62805014l_bool @ hAPP_f2018922499l_bool ) @ hAPP_f111185985l_bool ) @ ( A @ ( member496995196t_bool @ ( cOMBC_62805014l_bool @ hAPP_f2018922499l_bool ) @ hAPP_f111185985l_bool ) @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) )
      & ( ( B @ ( member496995196t_bool @ ( cOMBC_62805014l_bool @ hAPP_f2018922499l_bool ) @ hAPP_f111185985l_bool ) @ ( A @ ( member496995196t_bool @ ( cOMBC_62805014l_bool @ hAPP_f2018922499l_bool ) @ hAPP_f111185985l_bool ) @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(255,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_2038534567t_bool @ hAPP_f1924755118l_bool ) @ ( C @ pi_fun150026276t_bool ) @ ( B @ ( member520425275t_bool @ hAPP_f1253375959l_bool ) @ hAPP_f250445784l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_f412050202t_bool ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_610_funcset__mem) ).

thf(1657,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_2038534567t_bool @ hAPP_f1924755118l_bool ) @ ( C @ pi_fun150026276t_bool ) @ ( B @ ( member520425275t_bool @ hAPP_f1253375959l_bool ) @ hAPP_f250445784l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_f412050202t_bool ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(625,axiom,
    ! [A: $i] :
      ( ( A @ ( arrow_1587283740nimity @ hAPP_f312250286l_bool ) @ hBOOL )
    <=> ! [B: $i] :
          ( ( arrow_1721807329e_Prof @ ( B @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
         => ! [C: $i,D: $i] :
              ( ( ( D @ is_Arr1861959080le_alt )
                & ( C @ is_Arr1861959080le_alt ) )
             => ( ! [E: $i] :
                    ( ( E @ is_Arr43961803e_indi )
                   => ( E @ ( B @ hAPP_A1677245848t_bool ) @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
               => ( B @ ( A @ hAPP_f412050202t_bool ) @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_unanimity__def) ).

thf(3177,plain,
    ! [A: $i] :
      ( ( ! [B: $i] :
            ( ( arrow_1721807329e_Prof @ ( B @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
           => ! [C: $i,D: $i] :
                ( ( ( D @ is_Arr1861959080le_alt )
                  & ( C @ is_Arr1861959080le_alt ) )
               => ( ! [E: $i] :
                      ( ( E @ is_Arr43961803e_indi )
                     => ( E @ ( B @ hAPP_A1677245848t_bool ) @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
                 => ( B @ ( A @ hAPP_f412050202t_bool ) @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) )
       => ( A @ ( arrow_1587283740nimity @ hAPP_f312250286l_bool ) @ hBOOL ) )
      & ( ( A @ ( arrow_1587283740nimity @ hAPP_f312250286l_bool ) @ hBOOL )
       => ! [B: $i] :
            ( ( arrow_1721807329e_Prof @ ( B @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
           => ! [C: $i,D: $i] :
                ( ( ( D @ is_Arr1861959080le_alt )
                  & ( C @ is_Arr1861959080le_alt ) )
               => ( ! [E: $i] :
                      ( ( E @ is_Arr43961803e_indi )
                     => ( E @ ( B @ hAPP_A1677245848t_bool ) @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
                 => ( B @ ( A @ hAPP_f412050202t_bool ) @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(546,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( C @ ( D @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_P1875867302i_bool ) @ ( D @ ( A @ hAPP_P710098616e_indi ) @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_Pro1270767662e_indi ) @ ( A @ ( member234128621e_indi @ hAPP_f407092109l_bool ) @ hAPP_f1306865520l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_620_Pi__I) ).

thf(2746,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( C @ ( D @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_P1875867302i_bool ) @ ( D @ ( A @ hAPP_P710098616e_indi ) @ ( member1493247163e_indi @ hAPP_A1602262231l_bool ) @ hAPP_f1599966040l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_Pro1270767662e_indi ) @ ( A @ ( member234128621e_indi @ hAPP_f407092109l_bool ) @ hAPP_f1306865520l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(175,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1025_termination__basic__simps_I3_J) ).

thf(1335,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(460,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_481_order__less__le__trans) ).

thf(2417,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(536,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( arrow_1681063817le_Lin @ ( C @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( ( C @ ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( B @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_Lin__irrefl) ).

thf(2714,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( arrow_1681063817le_Lin @ ( C @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
     => ( ( C @ ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( B @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(13,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1143_mult__le__mono2) ).

thf(696,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(22,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ times_times_nat @ hAPP_nat_nat ) )
      = ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1150_add__mult__distrib2) ).

thf(720,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ times_times_nat @ hAPP_nat_nat ) )
      = ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(77,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_633721483t_bool @ hAPP_f573120177t_bool ) @ hAPP_f329301088t_bool ) @ hAPP_A1677245848t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A1102281708t_bool ) @ hAPP_f515126293t_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_066) ).

thf(955,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_633721483t_bool @ hAPP_f573120177t_bool ) @ hAPP_f329301088t_bool ) @ hAPP_A1677245848t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A1102281708t_bool ) @ hAPP_f515126293t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(183,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A
          = ( B @ ( suc @ hAPP_nat_nat ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1087_le__SucE) ).

thf(1363,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( A
          = ( B @ ( suc @ hAPP_nat_nat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(169,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1086_Suc__leD) ).

thf(1314,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(104,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( D @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1005_add__less__mono) ).

thf(1056,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( D @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(7,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
        = zero_zero_nat )
    <=> ( ( B = zero_zero_nat )
        | ( A = zero_zero_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1154_mult__is__0) ).

thf(664,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( B = zero_zero_nat )
          | ( A = zero_zero_nat ) )
       => ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
          = zero_zero_nat ) )
      & ( ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
          = zero_zero_nat )
       => ( ( B = zero_zero_nat )
          | ( A = zero_zero_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(98,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun279392540l_bool )
        & ( A @ is_fun279392540l_bool ) )
     => ( ( A = B )
      <=> ( ( A @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_355_order__eq__iff) ).

thf(1033,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun279392540l_bool )
        & ( A @ is_fun279392540l_bool ) )
     => ( ( ( ( A @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
            & ( B @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) )
         => ( A = B ) )
        & ( ( A = B )
         => ( ( A @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
            & ( B @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(161,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_fun1575168891l_bool ) @ ( B @ ( member880664588l_bool @ hAPP_f1666015481l_bool ) @ hAPP_f167218729l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_f210572555l_bool ) @ ( A @ ( B @ hAPP_f592646513l_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_PiE) ).

thf(1288,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_fun1575168891l_bool ) @ ( B @ ( member880664588l_bool @ hAPP_f1666015481l_bool ) @ hAPP_f167218729l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_f210572555l_bool ) @ ( A @ ( B @ hAPP_f592646513l_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(372,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_Arr43961803e_indi )
        & ( A @ is_fun1236654035i_bool ) )
     => ( B @ ( A @ hAPP_A1785763630i_bool ) @ is_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__HOL__O) ).

thf(2091,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_Arr43961803e_indi )
        & ( A @ is_fun1236654035i_bool ) )
     => ( B @ ( A @ hAPP_A1785763630i_bool ) @ is_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(646,axiom,
    ! [A: $i] : ( A @ ( top_to1853035173l_bool @ hAPP_f592646513l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_top1I) ).

thf(3323,plain,
    ! [A: $i] : ( A @ ( top_to1853035173l_bool @ hAPP_f592646513l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).

thf(79,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun279392540l_bool )
        & ( A @ is_fun279392540l_bool ) )
     => ( ( B @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
         => ( B = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_xt1_I5_J) ).

thf(960,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun279392540l_bool )
        & ( A @ is_fun279392540l_bool ) )
     => ( ( B @ ( A @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(563,axiom,
    ! [A: $i] :
      ( ( A @ ( arrow_1654180089le_IIA @ hAPP_f312250286l_bool ) @ hBOOL )
    <=> ! [B: $i] :
          ( ( arrow_1721807329e_Prof @ ( B @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
         => ! [C: $i] :
              ( ( arrow_1721807329e_Prof @ ( C @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
             => ! [D: $i,E: $i] :
                  ( ( ( E @ is_Arr1861959080le_alt )
                    & ( D @ is_Arr1861959080le_alt ) )
                 => ( ! [F: $i] :
                        ( ( F @ is_Arr43961803e_indi )
                       => ( ( F @ ( B @ hAPP_A1677245848t_bool ) @ ( E @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                        <=> ( F @ ( C @ hAPP_A1677245848t_bool ) @ ( E @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) )
                   => ( ( B @ ( A @ hAPP_f412050202t_bool ) @ ( E @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                    <=> ( C @ ( A @ hAPP_f412050202t_bool ) @ ( E @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_IIA__def) ).

thf(2795,plain,
    ! [A: $i] :
      ( ( ! [B: $i] :
            ( ( arrow_1721807329e_Prof @ ( B @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
           => ! [C: $i] :
                ( ( arrow_1721807329e_Prof @ ( C @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
               => ! [D: $i,E: $i] :
                    ( ( ( E @ is_Arr1861959080le_alt )
                      & ( D @ is_Arr1861959080le_alt ) )
                   => ( ! [F: $i] :
                          ( ( F @ is_Arr43961803e_indi )
                         => ( ( ( F @ ( C @ hAPP_A1677245848t_bool ) @ ( E @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                             => ( F @ ( B @ hAPP_A1677245848t_bool ) @ ( E @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
                            & ( ( F @ ( B @ hAPP_A1677245848t_bool ) @ ( E @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                             => ( F @ ( C @ hAPP_A1677245848t_bool ) @ ( E @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) )
                     => ( ( ( C @ ( A @ hAPP_f412050202t_bool ) @ ( E @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                         => ( B @ ( A @ hAPP_f412050202t_bool ) @ ( E @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
                        & ( ( B @ ( A @ hAPP_f412050202t_bool ) @ ( E @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                         => ( C @ ( A @ hAPP_f412050202t_bool ) @ ( E @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ) ) ) )
       => ( A @ ( arrow_1654180089le_IIA @ hAPP_f312250286l_bool ) @ hBOOL ) )
      & ( ( A @ ( arrow_1654180089le_IIA @ hAPP_f312250286l_bool ) @ hBOOL )
       => ! [B: $i] :
            ( ( arrow_1721807329e_Prof @ ( B @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
           => ! [C: $i] :
                ( ( arrow_1721807329e_Prof @ ( C @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL )
               => ! [D: $i,E: $i] :
                    ( ( ( E @ is_Arr1861959080le_alt )
                      & ( D @ is_Arr1861959080le_alt ) )
                   => ( ! [F: $i] :
                          ( ( F @ is_Arr43961803e_indi )
                         => ( ( ( F @ ( C @ hAPP_A1677245848t_bool ) @ ( E @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                             => ( F @ ( B @ hAPP_A1677245848t_bool ) @ ( E @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
                            & ( ( F @ ( B @ hAPP_A1677245848t_bool ) @ ( E @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                             => ( F @ ( C @ hAPP_A1677245848t_bool ) @ ( E @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) )
                     => ( ( ( C @ ( A @ hAPP_f412050202t_bool ) @ ( E @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                         => ( B @ ( A @ hAPP_f412050202t_bool ) @ ( E @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
                        & ( ( B @ ( A @ hAPP_f412050202t_bool ) @ ( E @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                         => ( C @ ( A @ hAPP_f412050202t_bool ) @ ( E @ ( D @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(352,axiom,
    ! [A: $i] : ( arrow_1721807329e_Prof @ ( lba @ ( lab @ ( A @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ ( cOMBC_510421983t_bool @ hAPP_f1297018969t_bool ) @ hAPP_f1909278132t_bool ) @ ( cOMBC_633721483t_bool @ hAPP_f573120177t_bool ) @ hAPP_f329301088t_bool ) @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_PiProf) ).

thf(2021,plain,
    ! [A: $i] : ( arrow_1721807329e_Prof @ ( lba @ ( lab @ ( A @ ( h @ ( ord_less_nat @ cOMBB_1883918730e_indi @ hAPP_f224734595t_bool ) @ ( cOMBC_1996607964t_bool @ hAPP_f446868133i_bool ) @ hAPP_n821919323i_bool ) @ ( if_fun2098446489t_bool @ cOMBB_2107911302e_indi @ hAPP_f586238575t_bool ) @ ( cOMBC_510421983t_bool @ hAPP_f1297018969t_bool ) @ hAPP_f1909278132t_bool ) @ ( cOMBC_633721483t_bool @ hAPP_f573120177t_bool ) @ hAPP_f329301088t_bool ) @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(365,axiom,
    fTrue @ is_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_fTrue) ).

thf(2063,plain,
    fTrue @ is_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(329,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      | ( A != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Nat__Onat_T) ).

thf(1930,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      | ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(482,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_440_order__less__imp__le) ).

thf(2502,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(179,axiom,
    ( one_one_nat
    = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1109_One__nat__def) ).

thf(1352,plain,
    ( one_one_nat
    = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(188,axiom,
    ! [A: $i] : ( A @ ( suc @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1061_zero__less__Suc) ).

thf(1378,plain,
    ! [A: $i] : ( A @ ( suc @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(474,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ( A = B )
        | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1009_le__eq__less__or__eq) ).

thf(2467,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A = B )
          | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ( A = B )
          | ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(228,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( top_top_fun_nat_bool @ ( C @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( ( A @ ( C @ hAPP_nat_nat ) )
          = ( B @ ( C @ hAPP_nat_nat ) ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_615_injD) ).

thf(1550,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( top_top_fun_nat_bool @ ( C @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( ( A @ ( C @ hAPP_nat_nat ) )
          = ( B @ ( C @ hAPP_nat_nat ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(504,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun279392540l_bool )
     => ( ( B @ ( A @ ( cOMBK_2038534567t_bool @ hAPP_f1924755118l_bool ) @ hAPP_f1277514478l_bool ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_067) ).

thf(2583,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun279392540l_bool )
     => ( ( B @ ( A @ ( cOMBK_2038534567t_bool @ hAPP_f1924755118l_bool ) @ hAPP_f1277514478l_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(89,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1088_le__SucI) ).

thf(1004,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(165,axiom,
    ! [A: $i,B: $i] : ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1100_less__add__Suc2) ).

thf(1299,plain,
    ! [A: $i,B: $i] : ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(617,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( C = A )
       => ( A @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_ord__le__eq__trans) ).

thf(3113,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
     => ( ( C = A )
       => ( A @ ( B @ ( ord_le1004900979t_bool @ hAPP_f863359027l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(422,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A != B )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_461_order__le__neq__trans) ).

thf(2270,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A != B )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(593,axiom,
    lba @ ( a @ ( b @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).

thf(2966,plain,
    lba @ ( a @ ( b @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(153,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ hAPP_A1102281708t_bool ) )
      = ( C @ ( B @ hAPP_A1677245848t_bool ) @ ( C @ ( A @ hAPP_A1455239488t_bool ) @ hAPP_f427493225t_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_075) ).

thf(1268,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBS_131695599t_bool @ hAPP_f1842612975t_bool ) @ hAPP_A1102281708t_bool ) )
      = ( C @ ( B @ hAPP_A1677245848t_bool ) @ ( C @ ( A @ hAPP_A1455239488t_bool ) @ hAPP_f427493225t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(225,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1173_mult__le__cancel1) ).

thf(1532,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( C @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(52,axiom,
    ! [A: $i] :
      ( ( A != zero_zero_nat )
     => ? [B: $i] :
          ( A
          = ( B @ ( suc @ hAPP_nat_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1123_not0__implies__Suc) ).

thf(860,plain,
    ! [A: $i] :
      ( ( A != zero_zero_nat )
     => ? [B: $i] :
          ( A
          = ( B @ ( suc @ hAPP_nat_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(328,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( ~ ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
        & ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_396_less__le__not__le) ).

thf(1923,plain,
    ! [A: $i,B: $i] :
      ( ( ( ~ ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( ~ ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(637,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun961089132t_bool ) )
     => ( ! [C: $i,D: $i] :
            ( ( ( D @ is_Arr1861959080le_alt )
              & ( C @ is_Arr1861959080le_alt ) )
           => ( ( B @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
            <=> ( A @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_pred__equals__eq2) ).

thf(3245,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun961089132t_bool )
        & ( A @ is_fun961089132t_bool ) )
     => ( ( ( B = A )
         => ! [C: $i,D: $i] :
              ( ( ( D @ is_Arr1861959080le_alt )
                & ( C @ is_Arr1861959080le_alt ) )
             => ( ( ( A @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                 => ( B @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
                & ( ( B @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                 => ( A @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ) )
        & ( ! [C: $i,D: $i] :
              ( ( ( D @ is_Arr1861959080le_alt )
                & ( C @ is_Arr1861959080le_alt ) )
             => ( ( ( A @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                 => ( B @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
                & ( ( B @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
                 => ( A @ ( D @ ( C @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(23,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
        = ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) ) )
    <=> ( ( B = zero_zero_nat )
        | ( A = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1152_mult__cancel2) ).

thf(723,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( B = zero_zero_nat )
          | ( A = C ) )
       => ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
          = ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) ) ) )
      & ( ( ( B @ ( A @ times_times_nat @ hAPP_nat_nat ) )
          = ( B @ ( C @ times_times_nat @ hAPP_nat_nat ) ) )
       => ( ( B = zero_zero_nat )
          | ( A = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(244,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1083_add__Suc__shift) ).

thf(1606,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(550,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ is_Arr1861959080le_alt )
        & ( A @ is_Arr1861959080le_alt ) )
     => ( ( arrow_1681063817le_Lin @ ( C @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( ( A != B )
         => ( ~ ( C @ ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
          <=> ( C @ ( A @ ( B @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_notin__Lin__iff) ).

thf(2754,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ is_Arr1861959080le_alt )
        & ( A @ is_Arr1861959080le_alt ) )
     => ( ( arrow_1681063817le_Lin @ ( C @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( ( A != B )
         => ( ( ( C @ ( A @ ( B @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
             => ~ ( C @ ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
            & ( ~ ( C @ ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
             => ( C @ ( A @ ( B @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(35,axiom,
    ! [A: $i] :
      ( ( A @ ( cOMBI_nat @ hAPP_nat_nat ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_COMBI_000tc__Nat__Onat_U) ).

thf(803,plain,
    ! [A: $i] :
      ( ( A @ ( cOMBI_nat @ hAPP_nat_nat ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(171,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      <=> ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1079_not__less__less__Suc__eq) ).

thf(1320,plain,
    ! [A: $i,B: $i] :
      ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( ( ( A = B )
         => ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
        & ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(74,axiom,
    ! [A: $i] :
      ( ( A @ is_fun279392540l_bool )
     => ( ( A @ ( top_to1853035173l_bool @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( A = top_to1853035173l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_530_top__le) ).

thf(940,plain,
    ! [A: $i] :
      ( ( A @ is_fun279392540l_bool )
     => ( ( A @ ( top_to1853035173l_bool @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
       => ( A = top_to1853035173l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(337,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun961089132t_bool )
     => ( B @ ( A @ hAPP_f515126293t_bool ) @ is_fun961089132t_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___044) ).

thf(1962,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun961089132t_bool )
     => ( B @ ( A @ hAPP_f515126293t_bool ) @ is_fun961089132t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(499,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( C @ ( D @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_P324742453l_bool ) @ ( D @ ( A @ hAPP_P606313927t_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_Pro666468413t_bool ) @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_648_Pi__I) ).

thf(2563,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( C @ ( D @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_P324742453l_bool ) @ ( D @ ( A @ hAPP_P606313927t_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_Pro666468413t_bool ) @ ( A @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(369,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2093718614t_bool )
        & ( A @ is_fun2093718614t_bool ) )
     => ( ( A = B )
      <=> ( ( A @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_362_order__eq__iff) ).

thf(2074,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2093718614t_bool )
        & ( A @ is_fun2093718614t_bool ) )
     => ( ( ( ( A @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
            & ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) )
         => ( A = B ) )
        & ( ( A = B )
         => ( ( A @ ( B @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL )
            & ( B @ ( A @ ( ord_le1546299023t_bool @ hAPP_f1377535679l_bool ) @ hAPP_f324780729l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(528,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_407_leI) ).

thf(2690,plain,
    ! [A: $i,B: $i] :
      ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(565,axiom,
    ! [A: $i] : ( A @ ( top_to1257323279t_bool @ hAPP_P1676879539t_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_top1I) ).

thf(2832,plain,
    ! [A: $i] : ( A @ ( top_to1257323279t_bool @ hAPP_P1676879539t_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(363,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun961089132t_bool )
     => ( B @ ( A @ hAPP_f1617919085t_bool ) @ is_fun2093718614t_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___040) ).

thf(2059,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun961089132t_bool )
     => ( B @ ( A @ hAPP_f1617919085t_bool ) @ is_fun2093718614t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(468,axiom,
    ! [A: $i] : ( top_to522745736l_bool @ ( A @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_iso__tuple__UNIV__I) ).

thf(2453,plain,
    ! [A: $i] : ( top_to522745736l_bool @ ( A @ ( member760917689t_bool @ hAPP_f461621971l_bool ) @ hAPP_f777333846l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(17,axiom,
    ! [A: $i] : ( A @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1140_le__square) ).

thf(708,plain,
    ! [A: $i] : ( A @ ( A @ times_times_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(59,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
    <=> ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_741_add__le__cancel__right) ).

thf(882,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
      & ( ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(333,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_boo538701011t_bool ) @ ( B @ ( member357566570t_bool @ hAPP_f1345320373l_bool ) @ hAPP_f817604743l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_b1812770943l_bool ) @ ( A @ ( B @ hAPP_b1703662281t_bool ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_571_Pi__mem) ).

thf(1945,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_boo538701011t_bool ) @ ( B @ ( member357566570t_bool @ hAPP_f1345320373l_bool ) @ hAPP_f817604743l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_b1812770943l_bool ) @ ( A @ ( B @ hAPP_b1703662281t_bool ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(632,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ is_Arr1861959080le_alt )
        & ( B @ is_Arr1861959080le_alt )
        & ( A @ is_Arr1861959080le_alt ) )
     => ( ( D @ ( C @ ( arrow_1644373103_mktop @ hAPP_f393984045t_bool ) @ hAPP_A568203993t_bool ) @ ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
      <=> ( ( ( B != D )
           => ( C @ ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
          & ( ( B = D )
           => ( A != B ) )
          & ( A != D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_in__mktop) ).

thf(3212,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ is_Arr1861959080le_alt )
        & ( B @ is_Arr1861959080le_alt )
        & ( A @ is_Arr1861959080le_alt ) )
     => ( ( ( ( ( B != D )
             => ( C @ ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
            & ( ( B = D )
             => ( A != B ) )
            & ( A != D ) )
         => ( D @ ( C @ ( arrow_1644373103_mktop @ hAPP_f393984045t_bool ) @ hAPP_A568203993t_bool ) @ ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
        & ( ( D @ ( C @ ( arrow_1644373103_mktop @ hAPP_f393984045t_bool ) @ hAPP_A568203993t_bool ) @ ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL )
         => ( ( ( B != D )
             => ( C @ ( B @ ( A @ ( produc1400112471le_alt @ hAPP_A1505516597le_alt ) @ hAPP_A702847159le_alt ) @ ( member1441201108le_alt @ hAPP_P229966473l_bool ) @ hAPP_f592646513l_bool ) @ hBOOL ) )
            & ( ( B = D )
             => ( A != B ) )
            & ( A != D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(70,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1277514478l_bool ) @ is_fun279392540l_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_Mtc__014) ).

thf(923,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1277514478l_bool ) @ is_fun279392540l_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(279,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( member520425275t_bool @ hAPP_f1253375959l_bool ) @ hAPP_f250445784l_bool ) @ hBOOL )
    <=> ( A @ ( B @ hAPP_f312250286l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_mem__def) ).

thf(1737,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ hAPP_f312250286l_bool ) @ hBOOL )
       => ( B @ ( A @ ( member520425275t_bool @ hAPP_f1253375959l_bool ) @ hAPP_f250445784l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( member520425275t_bool @ hAPP_f1253375959l_bool ) @ hAPP_f250445784l_bool ) @ hBOOL )
       => ( A @ ( B @ hAPP_f312250286l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(466,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
    <=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
        & ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_363_order__eq__iff) ).

thf(2438,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(215,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P1875867302i_bool ) @ is_fun1236654035i_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__046) ).

thf(1490,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P1875867302i_bool ) @ is_fun1236654035i_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(288,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1306865520l_bool ) @ is_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn) ).

thf(1769,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1306865520l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(26,axiom,
    ! [A: $i] :
      ( ( A @ ( size_size_nat @ hAPP_nat_nat ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1184_nat__size) ).

thf(755,plain,
    ! [A: $i] :
      ( ( A @ ( size_size_nat @ hAPP_nat_nat ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(566,axiom,
    top_to1576102282i_bool @ ( finite106199483e_indi @ hAPP_f1599966040l_bool ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1031_finite__indi) ).

thf(2834,plain,
    top_to1576102282i_bool @ ( finite106199483e_indi @ hAPP_f1599966040l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(443,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun961089132t_bool )
     => ( B @ ( A @ pi_Pro666468413t_bool ) @ is_fun279392540l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oa) ).

thf(2351,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun961089132t_bool )
     => ( B @ ( A @ pi_Pro666468413t_bool ) @ is_fun279392540l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(135,axiom,
    ! [A: $i] :
      ( ( A @ is_fun279392540l_bool )
     => ( ( A @ ( top_to1853035173l_bool @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
      <=> ( A = top_to1853035173l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_521_top__unique) ).

thf(1204,plain,
    ! [A: $i] :
      ( ( A @ is_fun279392540l_bool )
     => ( ( ( A = top_to1853035173l_bool )
         => ( A @ ( top_to1853035173l_bool @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) )
        & ( ( A @ ( top_to1853035173l_bool @ ( ord_le2085964885l_bool @ hAPP_f1581553471l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL )
         => ( A = top_to1853035173l_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(205,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_69806648l_bool @ hAPP_f256804927l_bool ) @ ( C @ pi_boo538701011t_bool ) @ ( B @ ( member357566570t_bool @ hAPP_f1345320373l_bool ) @ hAPP_f817604743l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_b1703662281t_bool ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_605_funcset__mem) ).

thf(1449,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_69806648l_bool @ hAPP_f256804927l_bool ) @ ( C @ pi_boo538701011t_bool ) @ ( B @ ( member357566570t_bool @ hAPP_f1345320373l_bool ) @ hAPP_f817604743l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_b1703662281t_bool ) @ ( member496995196t_bool @ hAPP_f566237389l_bool ) @ hAPP_f1749234559l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(3328,plain,
    $false,
    inference(e,[status(thm)],[2163,1665,1501,1411,1469,2131,2072,1729,2412,909,1840,2331,2280,2250,1879,1337,1718,3053,2341,2480,1083,1818,1295,2363,1211,3317,1290,1618,3040,2671,2099,2837,878,677,2512,2976,2117,1406,2231,1068,1443,1808,2659,1569,2248,1497,1788,1671,1137,3004,2740,3175,715,2141,2712,1327,698,2459,2042,1507,2607,2686,797,2316,1761,1342,1354,2146,2972,1359,1366,2516,651,2216,3236,2491,1127,2985,1391,1576,2400,2825,1529,1967,2136,1703,1482,1254,3195,3046,1264,1826,1992,2126,1409,3204,917,702,1832,934,817,853,1892,2552,870,2767,1609,1013,1398,1115,3312,2730,1778,2388,1232,1847,3099,1800,2169,2403,1815,1494,2222,1415,1465,1714,2880,1858,1677,2777,1183,1051,905,3075,1811,2555,806,1581,2335,966,2964,1843,734,1886,1433,2718,1564,1896,2190,2530,2523,1796,1119,774,1526,2137,2242,2286,2103,2750,1104,1697,1242,1604,2011,920,3301,1691,761,810,2954,1651,3265,925,1915,1708,2093,2496,2790,2660,1868,2061,2773,2589,2264,894,2601,1021,2596,2277,820,2969,693,2032,2890,1238,1824,2150,1370,1837,2628,3198,3314,830,2179,2181,3050,2228,710,842,974,1106,2958,1423,3307,1938,847,2433,2477,1687,1457,2068,1624,1079,2213,2344,2492,1983,2577,2726,3001,2840,1143,2115,1851,2946,2709,1970,1227,980,2692,1540,1006,3237,1755,1567,1329,1160,2323,1292,3210,2419,2455,1644,1612,1155,1082,2023,1964,1659,2504,1451,2487,1266,654,2355,911,1947,1002,1429,2052,1720,647,997,2450,1588,1150,1249,2519,1060,2581,2465,1333,2788,1086,1695,3173,2793,2995,2617,2909,1202,2203,2702,2761,2057,1712,1286,3321,2662,1185,718,888,2235,1278,2001,2677,1959,2275,1273,745,1301,2894,2524,2904,1680,3079,1747,3319,1620,1388,826,958,2398,2716,1965,2695,3234,2048,1615,1784,2674,2514,1139,2029,1312,787,2738,713,1733,1058,2753,1092,1765,2457,2425,1675,1271,2308,1638,1224,2358,1356,2346,3101,900,1282,784,1806,2906,1492,1542,2197,863,2084,2624,1894,2987,1771,2945,880,1043,2871,1376,1667,2025,2742,758,2129,2111,1630,1731,1862,3192,2410,2593,1344,1177,1820,2578,3133,858,3055,1556,2542,943,2252,2664,2461,2974,2329,932,2770,1594,1245,1445,2139,2156,2207,1805,2506,2962,2365,1213,2835,3159,2064,1015,2592,1000,2752,1435,2967,2390,2239,2952,2096,1758,2665,1467,1684,648,1509,2684,1472,968,1049,2054,1948,675,2914,1583,1304,3193,3161,1905,1145,1018,855,1025,705,971,1753,2888,2882,2567,1845,690,1516,1598,1070,872,1225,1743,1400,1941,1252,1230,2160,1053,2224,2165,2688,2700,840,2429,1235,1901,2322,2044,1579,951,2599,808,2354,907,2711,1094,3117,2939,3071,1372,2266,1934,2948,1898,1849,2992,1981,656,1802,1023,1316,2088,2885,1553,2960,1834,1412,1216,2226,1998,2435,845,688,903,2611,2325,2187,1189,1010,2305,1866,2775,2792,771,2907,2988,2098,2406,2554,1101,1745,2971,2394,1276,1590,963,2273,2283,1476,1558,2262,2009,2956,3149,1706,2294,2494,1994,2779,1045,2384,2786,1077,2362,2233,2522,1380,790,867,1480,1908,2003,2123,2218,2302,2517,1725,1280,3232,2534,2255,833,2719,1097,835,2587,2736,1986,1657,3177,2746,1335,2417,2714,696,720,955,1363,1314,1056,664,1033,1288,2091,3323,960,2795,2021,2063,1930,2502,1352,1378,2467,1550,2583,1004,1299,3113,2270,2966,1268,1532,860,1923,3245,723,1606,2754,803,1320,940,1962,2563,2074,2690,2832,2059,2453,708,882,1945,3212,923,1737,2438,1490,1769,755,2834,2351,1204,1449]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SCT171+3 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.08  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.40  % Computer : n006.cluster.edu
% 0.12/0.40  % Model    : x86_64 x86_64
% 0.12/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40  % Memory   : 8046.5625MB
% 0.12/0.40  % OS       : Linux 6.8.0-71-generic
% 0.12/0.41  % CPULimit : 300
% 0.12/0.41  % WCLimit  : 300
% 0.12/0.41  % DateTime : Sat Sep 26 06:38:11 UTC 2026
% 0.17/0.41  % CPUTime  : 
% 0.17/0.41  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.94/1.19  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.55/1.95  % [INFO] 	 Parsing done (748ms). 
% 2.55/1.98  % [INFO] 	 Running in sequential loop mode. 
% 3.93/2.60  % [INFO] 	 eprover registered as external prover. 
% 3.93/2.61  % [INFO] 	 Scanning for conjecture ... 
% 5.14/3.20  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1414 axioms. Running axiom selection ... 
% 7.17/4.08  % [INFO] 	 Axiom selection finished. Selected 644 axioms (removed 770 axioms). 
% 8.33/4.68  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 8.62/4.72  % [INFO] 	 Type checking passed. 
% 8.62/4.73  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 26.95/10.26  % External prover 'e' found a proof!
% 26.95/10.26  % [INFO] 	 Killing All external provers ... 
% 26.95/10.26  % Time passed: 9626ms (effective reasoning time: 8274ms)
% 26.95/10.26  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 26.95/10.27  % Axioms used in derivation (644): fact_1001_nat__add__left__cancel__less, fact_78__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096, help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_065, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__prod_Itc__Arrow_, fact_222_Pi__UNIV, fact_983_linorder__neqE__nat, fact_1099_less__add__Suc1, fact_402_order__le__less, fact_815_order__le__less__subst1, fact_706_xt7, fact_730_add__left__imp__eq, fact_1170_one__less__mult, fact_25_top1I, fact_780_xt4, fact_827_order__less__le__subst1, fact_908_equalityI, fact_1177_nat__mult__less__cancel1, fact_459_order__le__neq__trans, fact_614_injD, fact_1073_Suc__lessD, fact_1180_left__add__mult__distrib, fact_850_order__less__le__subst1, fact_1044_not__less0, fact_1115_inc__induct, fact_415_order__neq__le__trans, fact_650_Pi__I, fact_1070_nat_Osimps_I2_J, fact_220_PiE, fact_176_UNIV__def, fact_651_inj__imp__inv__eq, gsy_v_Lab____, fact_1013_le__add2, gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool, fact_578_below__Lin, fact_613_inj__eq, fact_386_order__less__le, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpn_038, fact_1071_Zero__not__Suc, gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc_, fact_67_less__top, gsy_c_Hilbert__Choice_Oinv__into_000tc__Arrow____Order____Mirabelle____tpnfnnbpu, fact_108_xt1_I2_J, fact_970_in__mono, fact_718_pred__subset__eq2, fact_1053_le__0__eq, fact_847_order__less__le__subst1, fact_1083_add__Suc__shift, fact_52_top__apply, fact_1173_mult__le__cancel1, fact_491_xt1_I7_J, fact_153_linorder__neqE, fact_1125_zero__induct, fact_430_leD, fact_140_order__less__imp__not__eq, fact_854_order__less__le__subst1, fact_1072_Suc__less__SucD, fact_406_order__le__less, fact_1108_Suc__le__lessD, fact_985_less__not__refl2, fact_363_order__eq__iff, fact_225_in__below, fact_267_order__trans, fact_1119_Suc__eq__plus1__left, fact_1143_mult__le__mono2, fact_250_xt1_I6_J, fact_1021_add__leD2, fact_1144_mult__le__mono, fact_1051_add__is__0, fact_656_injI, fact_596_funcset__mem, fact_382_order__less__le, fact_547_Pi__mem, help_fequal_2_1_fequal_000tc__Nat__Onat_T, fact_989_nat__add__left__commute, fact_1056_ex__least__nat__less, fact_1060_Suc__mono, gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfn, fact_545_inj__onD, fact_334_order__antisym__conv, fact_409_linorder__antisym__conv1, fact_635_Pi__I, fact_1018_trans__le__add2, fact_1059_lessI, fact_1012_less__or__eq__imp__le, fact_224_Pi__UNIV, fact_582_funcset__mem, fact_1074_less__SucE, gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Arrow____Order____Mirabelle____, fact_925_psubset__eq, fact_564_Pi__mem, fact_1183_nat_Osize_I4_J, fact_128_order__less__asym_H, fact_735_add__le__imp__le__left, fact_307_xt1_I3_J, fact_526_top__unique, fact_1052_add__eq__self__zero, fact_1176_nat__mult__le__cancel1, fact_353_order__eq__refl, fact_1103_less__Suc__eq__le, fact_1179_nat__mult__eq__cancel__disj, fact_188_inv__f__f, help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tp_051, fact_1152_mult__cancel2, fact_1068_nat_Osimps_I3_J, fact_254_xt1_I6_J, fact_214_PiE, help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000_059, fact_1047_gr__implies__not0, help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000t_062, fact_530_top__le, fact_50_top__apply, fact_85_n_I2_J, fact_22_Pair__eq, fact_576_Pi__mem, fact_734_one__reorient, fact_1123_not0__implies__Suc, fact_900_order__less__le__subst2, fact_1141_le__cube, fact_30_top1I, gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Arrow____Order____Mirabelle_____002, fact_535_top__le, fact_6__C2_C, fact_991_nat__add__left__cancel, gsy_c_Arrow__Order__Mirabelle__tpnfnnbpuu_Obelow, fact_648_Pi__I, fact_489_xt1_I7_J, fact_275_order__trans, fact_161_order__less__irrefl, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__, gsy_v_Lba____, fact_615_injD, help_fTrue_1_1_T, fact_0_assms_I3_J, fact_374_linorder__not__less, fact_112_ord__less__eq__trans, fact_257_xt1_I5_J, fact_290_xt1_I4_J, fact_1182_nat_Osize_I1_J, fact_264_xt1_I5_J, fact_1017_trans__le__add1, fact_317_ord__eq__le__trans, help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_057, fact_1094_gr0__conv__Suc, fact_1003_trans__less__add2, fact_888_order__le__less__subst2, fact_655_add__le__less__mono, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__O_025, fact_499_order__le__less__trans, fact_1008_nat__less__le, fact_461_order__le__neq__trans, fact_737_add__mono, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__prod_Itc__Arrow____, fact_86_notin__Lin__iff, fact_79__096_Ia_M_Ab_J_A_126_058_ALba_096, gsy_v_b____, fact_408_not__leE, gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order__, fact_247_xt1_I6_J, fact_191_PiE, fact_1042_less__zeroE, gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabell, gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Arrow____Order____Mirabelle____tpnfn_007, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___039, fact_96_order__less__asym, fact_315_xt1_I3_J, fact_41_iso__tuple__UNIV__I, help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000, fact_1086_Suc__leD, fact_562_Pi__mem, fact_719_subset__UNIV, help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_000t, gsy_v_d____, fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto, fact_994_nat__le__linear, fact_3__096P_A_058_AProf_096, gsy_c_fFalse, fact_297_ord__le__eq__trans, fact_40_iso__tuple__UNIV__I, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu___040, fact_657_injI, fact_1181_nat_Osize_I2_J, fact_1162_nat__0__less__mult__iff, fact_1185_nat_Osize_I3_J, help_fTrue_1_1_U, fact_1031_finite__indi, fact_345_order__eq__refl, gsy_c_fTrue, gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oalt_Mtc__048, fact_407_leI, fact_741_add__le__cancel__right, fact_29_top1I, gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabel, fact_425_xt1_I12_J, fact_304_ord__le__eq__trans, fact_653_less__add__one, gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____tpnfnnbpuu__Oindi_000tc__HOL__O, fact_1142_mult__le__mono1, fact_183_n_I3_J, fact_1007_add__lessD1, fact_999_not__add__less1, fact_605_funcset__mem, fact_539_inj__on__def, fact_1100_less__add__Suc2, fact_438_order__less__imp__le, fact_1030_linear__alt, fact_732_add__left__cancel, fact_1004_add__less__mono1, fact_746_add__strict__right__mono, fact_441_linorder__antisym__conv2, fact_1025_termination__basic__simps_I3_J, fact_1148_nat__mult__1, 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% 26.95/10.27  % No. of inferences in proof: 1292
% 26.95/10.27  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 9626 ms resp. 8274 ms w/o parsing
% 29.04/10.88  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 29.04/10.89  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------