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

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SCT171+2 : TPTP v9.3.1. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39

% Computer : n002.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 08:27:28 AM UTC 2026

% Result   : Theorem 31.93s 19.16s
% Output   : Refutation 35.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  884
% Syntax   : Number of formulae    : 1770 ( 504 unt;   0 typ;   0 def)
%            Number of atoms       : 4939 ( 927 equ;   0 cnn)
%            Maximal formula atoms :   28 (   2 avg)
%            Number of connectives : 27225 ( 630   ~;  98   |; 488   &;23426   @)
%                                         ( 179 <=>;2404  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  450 ( 448 usr; 141 con; 0-3 aty)
%            Number of variables   : 3956 (   0   ^;3918   !;  38   ?;3956   :)

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

thf(hAPP_f1733357041l_bool_decl,type,
    hAPP_f1733357041l_bool: $i > $i > $i ).

thf(hAPP_P1151433609l_bool_decl,type,
    hAPP_P1151433609l_bool: $i > $i > $i ).

thf(member720722004le_alt_decl,type,
    member720722004le_alt: $i ).

thf(hAPP_A1561816353le_alt_decl,type,
    hAPP_A1561816353le_alt: $i > $i > $i ).

thf(hAPP_A1171966089le_alt_decl,type,
    hAPP_A1171966089le_alt: $i > $i > $i ).

thf(produc1456060119le_alt_decl,type,
    produc1456060119le_alt: $i ).

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

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

thf(hAPP_f1817389232t_bool_decl,type,
    hAPP_f1817389232t_bool: $i > $i > $i ).

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

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

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

thf(collect_Product_unit_decl,type,
    collect_Product_unit: $i > $i ).

thf(hAPP_b1096750261t_bool_decl,type,
    hAPP_b1096750261t_bool: $i > $i > $i ).

thf(cOMBK_790042732t_unit_decl,type,
    cOMBK_790042732t_unit: $i ).

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

thf(top_to207207712i_bool_decl,type,
    top_to207207712i_bool: $i ).

thf(collec279390863e_indi_decl,type,
    collec279390863e_indi: $i > $i ).

thf(hAPP_b2116075462i_bool_decl,type,
    hAPP_b2116075462i_bool: $i > $i > $i ).

thf(cOMBK_1391252605e_indi_decl,type,
    cOMBK_1391252605e_indi: $i ).

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

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

thf(hAPP_A1906804694t_bool_decl,type,
    hAPP_A1906804694t_bool: $i > $i > $i ).

thf(cOMBS_995062533t_bool_decl,type,
    cOMBS_995062533t_bool: $i > $i > $i ).

thf(hAPP_f1000663785t_bool_decl,type,
    hAPP_f1000663785t_bool: $i > $i > $i ).

thf(hAPP_A725195434t_bool_decl,type,
    hAPP_A725195434t_bool: $i > $i > $i ).

thf(hAPP_A340536322t_bool_decl,type,
    hAPP_A340536322t_bool: $i > $i > $i ).

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

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

thf(suc_decl,type,
    suc: $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(hAPP_f1138659662l_bool_decl,type,
    hAPP_f1138659662l_bool: $i > $i > $i ).

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

thf(is_fun20916972t_bool_decl,type,
    is_fun20916972t_bool: $i > $o ).

thf(is_fun1420103068l_bool_decl,type,
    is_fun1420103068l_bool: $i > $o ).

thf(hAPP_f1344932147l_bool_decl,type,
    hAPP_f1344932147l_bool: $i > $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(cOMBI_nat_decl,type,
    cOMBI_nat: $i ).

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

thf(hAPP_n454528608t_bool_decl,type,
    hAPP_n454528608t_bool: $i > $i > $i ).

thf(hAPP_f590186314t_bool_decl,type,
    hAPP_f590186314t_bool: $i > $i > $i ).

thf(cOMBK_776703103e_indi_decl,type,
    cOMBK_776703103e_indi: $i ).

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

thf(hAPP_f560517119l_bool_decl,type,
    hAPP_f560517119l_bool: $i > $i > $i ).

thf(collec612883262t_bool_decl,type,
    collec612883262t_bool: $i > $i ).

thf(top_to846262053l_bool_decl,type,
    top_to846262053l_bool: $i ).

thf(hAPP_b805997823l_bool_decl,type,
    hAPP_b805997823l_bool: $i > $i > $i ).

thf(cOMBK_715978704t_bool_decl,type,
    cOMBK_715978704t_bool: $i ).

thf(top_to1849101472l_bool_decl,type,
    top_to1849101472l_bool: $i ).

thf(collec1517527055t_bool_decl,type,
    collec1517527055t_bool: $i > $i ).

thf(hAPP_b651754310l_bool_decl,type,
    hAPP_b651754310l_bool: $i > $i > $i ).

thf(cOMBK_577652221t_bool_decl,type,
    cOMBK_577652221t_bool: $i ).

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

thf(is_Arr859726945e_indi_decl,type,
    is_Arr859726945e_indi: $i > $o ).

thf(finite1949902593t_unit_decl,type,
    finite1949902593t_unit: $i > $i ).

thf(is_fun701126715l_bool_decl,type,
    is_fun701126715l_bool: $i > $o ).

thf(hAPP_f1378099862l_bool_decl,type,
    hAPP_f1378099862l_bool: $i > $i > $i ).

thf(hAPP_f966397426l_bool_decl,type,
    hAPP_f966397426l_bool: $i > $i > $i ).

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

thf(hAPP_f103356543l_bool_decl,type,
    hAPP_f103356543l_bool: $i > $i > $i ).

thf(ord_le1568362934t_bool_decl,type,
    ord_le1568362934t_bool: $i ).

thf(hAPP_A1781286015t_bool_decl,type,
    hAPP_A1781286015t_bool: $i > $i > $i ).

thf(hAPP_f1840820673t_bool_decl,type,
    hAPP_f1840820673t_bool: $i > $i > $i ).

thf(hAPP_f775987425t_bool_decl,type,
    hAPP_f775987425t_bool: $i > $i > $i ).

thf(cOMBC_441619036t_bool_decl,type,
    cOMBC_441619036t_bool: $i ).

thf(hAPP_f1068593625t_bool_decl,type,
    hAPP_f1068593625t_bool: $i > $i > $i ).

thf(hAPP_A64811457t_bool_decl,type,
    hAPP_A64811457t_bool: $i > $i > $i ).

thf(hAPP_f189058133l_bool_decl,type,
    hAPP_f189058133l_bool: $i > $i > $i ).

thf(is_fun292781289l_bool_decl,type,
    is_fun292781289l_bool: $i > $o ).

thf(hAPP_P1305865168l_bool_decl,type,
    hAPP_P1305865168l_bool: $i > $i > $i ).

thf(is_Arr723427730le_alt_decl,type,
    is_Arr723427730le_alt: $i > $o ).

thf(arrow_207701375_below_decl,type,
    arrow_207701375_below: $i > $i > $i > $i ).

thf(hAPP_f137597973t_bool_decl,type,
    hAPP_f137597973t_bool: $i > $i > $i ).

thf(hAPP_b910261233t_bool_decl,type,
    hAPP_b910261233t_bool: $i > $i > $i ).

thf(if_fun1158274329t_bool_decl,type,
    if_fun1158274329t_bool: $i ).

thf(top_to1773227171t_bool_decl,type,
    top_to1773227171t_bool: $i ).

thf(hAPP_P288224245l_bool_decl,type,
    hAPP_P288224245l_bool: $i > $i > $i ).

thf(cOMBS_nat_bool_bool_decl,type,
    cOMBS_nat_bool_bool: $i > $i > $i ).

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

thf(hAPP_n1006566506l_bool_decl,type,
    hAPP_n1006566506l_bool: $i > $i > $i ).

thf(hAPP_b1461182872l_bool_decl,type,
    hAPP_b1461182872l_bool: $i > $i > $i ).

thf(cOMBK_776847951t_bool_decl,type,
    cOMBK_776847951t_bool: $i ).

thf(hAPP_f800510211t_bool_decl,type,
    hAPP_f800510211t_bool: $i > $i > $i ).

thf(hAPP_f1722879237t_bool_decl,type,
    hAPP_f1722879237t_bool: $i > $i > $i ).

thf(cOMBC_226598744l_bool_decl,type,
    cOMBC_226598744l_bool: $i ).

thf(hAPP_n215258509l_bool_decl,type,
    hAPP_n215258509l_bool: $i > $i > $i ).

thf(hAPP_A1014090479t_bool_decl,type,
    hAPP_A1014090479t_bool: $i > $i > $i ).

thf(hAPP_f1384787615l_bool_decl,type,
    hAPP_f1384787615l_bool: $i > $i > $i ).

thf(hAPP_f350403485e_indi_decl,type,
    hAPP_f350403485e_indi: $i > $i > $i ).

thf(hAPP_f1975142533t_bool_decl,type,
    hAPP_f1975142533t_bool: $i > $i > $i ).

thf(cOMBC_1894996001t_bool_decl,type,
    cOMBC_1894996001t_bool: $i ).

thf(finite955821396le_alt_decl,type,
    finite955821396le_alt: $i ).

thf(member_nat_decl,type,
    member_nat: $i ).

thf(hAPP_f817344902l_bool_decl,type,
    hAPP_f817344902l_bool: $i > $i > $i ).

thf(hAPP_f1597773170l_bool_decl,type,
    hAPP_f1597773170l_bool: $i > $i > $i ).

thf(hAPP_f740740988l_bool_decl,type,
    hAPP_f740740988l_bool: $i > $i > $i ).

thf(collec1376511890le_alt_decl,type,
    collec1376511890le_alt: $i > $i ).

thf(hAPP_b763490121t_bool_decl,type,
    hAPP_b763490121t_bool: $i > $i > $i ).

thf(cOMBK_1733734784le_alt_decl,type,
    cOMBK_1733734784le_alt: $i ).

thf(hAPP_A416869060i_bool_decl,type,
    hAPP_A416869060i_bool: $i > $i > $i ).

thf(hAPP_f1282033109i_bool_decl,type,
    hAPP_f1282033109i_bool: $i > $i > $i ).

thf(hAPP_f651290349i_bool_decl,type,
    hAPP_f651290349i_bool: $i > $i > $i ).

thf(cOMBC_264525026l_bool_decl,type,
    cOMBC_264525026l_bool: $i ).

thf(hAPP_f160177134l_bool_decl,type,
    hAPP_f160177134l_bool: $i > $i > $i ).

thf(hAPP_A45661955l_bool_decl,type,
    hAPP_A45661955l_bool: $i > $i > $i ).

thf(top_to935749874l_bool_decl,type,
    top_to935749874l_bool: $i ).

thf(hAPP_A701636433l_bool_decl,type,
    hAPP_A701636433l_bool: $i > $i > $i ).

thf(hAPP_f1841347694t_bool_decl,type,
    hAPP_f1841347694t_bool: $i > $i > $i ).

thf(finite_card_nat_decl,type,
    finite_card_nat: $i > $i ).

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

thf(hAPP_f229349961t_bool_decl,type,
    hAPP_f229349961t_bool: $i > $i > $i ).

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

thf(hAPP_f1426445843l_bool_decl,type,
    hAPP_f1426445843l_bool: $i > $i > $i ).

thf(hAPP_P1813625415t_bool_decl,type,
    hAPP_P1813625415t_bool: $i > $i > $i ).

thf(hAPP_A85603248t_bool_decl,type,
    hAPP_A85603248t_bool: $i > $i > $i ).

thf(hAPP_f2027600413t_bool_decl,type,
    hAPP_f2027600413t_bool: $i > $i > $i ).

thf(cOMBB_640263118e_indi_decl,type,
    cOMBB_640263118e_indi: $i > $i ).

thf(hAPP_f102394819t_bool_decl,type,
    hAPP_f102394819t_bool: $i > $i > $i ).

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

thf(arrow_912654623le_Lin_decl,type,
    arrow_912654623le_Lin: $i ).

thf(hAPP_f416620757at_nat_decl,type,
    hAPP_f416620757at_nat: $i > $i > $i ).

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

thf(is_fun1084921220e_indi_decl,type,
    is_fun1084921220e_indi: $i > $o ).

thf(hAPP_n619554777e_indi_decl,type,
    hAPP_n619554777e_indi: $i > $i > $i ).

thf(hAPP_f1146629647l_bool_decl,type,
    hAPP_f1146629647l_bool: $i > $i > $i ).

thf(cOMBB_1015721476ol_nat_decl,type,
    cOMBB_1015721476ol_nat: $i > $i ).

thf(hAPP_b589554111l_bool_decl,type,
    hAPP_b589554111l_bool: $i > $i > $i ).

thf(ord_less_eq_bool_decl,type,
    ord_less_eq_bool: $i ).

thf(hAPP_f1965705105l_bool_decl,type,
    hAPP_f1965705105l_bool: $i > $i > $i ).

thf(hAPP_f2016919811l_bool_decl,type,
    hAPP_f2016919811l_bool: $i > $i > $i ).

thf(arrow_1550141362nimity_decl,type,
    arrow_1550141362nimity: $i ).

thf(hAPP_f1898540574t_bool_decl,type,
    hAPP_f1898540574t_bool: $i > $i > $i ).

thf(hAPP_f1283354413t_bool_decl,type,
    hAPP_f1283354413t_bool: $i > $i > $i ).

thf(cOMBC_1373788917t_bool_decl,type,
    cOMBC_1373788917t_bool: $i ).

thf(hAPP_f446648900l_bool_decl,type,
    hAPP_f446648900l_bool: $i > $i > $i ).

thf(is_fun2015243113i_bool_decl,type,
    is_fun2015243113i_bool: $i > $o ).

thf(pi_Arr1801471756t_bool_decl,type,
    pi_Arr1801471756t_bool: $i > $i > $i ).

thf(hAPP_f1637334154l_bool_decl,type,
    hAPP_f1637334154l_bool: $i > $i > $i ).

thf(pi_Pro1873779901t_bool_decl,type,
    pi_Pro1873779901t_bool: $i > $i > $i ).

thf(hAPP_f1021828400l_bool_decl,type,
    hAPP_f1021828400l_bool: $i > $i > $i ).

thf(hAPP_f2053170815l_bool_decl,type,
    hAPP_f2053170815l_bool: $i > $i > $i ).

thf(arrow_583275979e_Prof_decl,type,
    arrow_583275979e_Prof: $i ).

thf(hilber951314860di_nat_decl,type,
    hilber951314860di_nat: $i > $i > $i ).

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

thf(hAPP_b1013836512t_bool_decl,type,
    hAPP_b1013836512t_bool: $i > $i > $i ).

thf(cOMBK_bool_nat_decl,type,
    cOMBK_bool_nat: $i ).

thf(hAPP_P957402556i_bool_decl,type,
    hAPP_P957402556i_bool: $i > $i > $i ).

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

thf(member161528657e_indi_decl,type,
    member161528657e_indi: $i ).

thf(hAPP_f1700034367l_bool_decl,type,
    hAPP_f1700034367l_bool: $i > $i > $i ).

thf(ord_le1079191765l_bool_decl,type,
    ord_le1079191765l_bool: $i ).

thf(hAPP_A659996934l_bool_decl,type,
    hAPP_A659996934l_bool: $i > $i > $i ).

thf(hAPP_f147218624l_bool_decl,type,
    hAPP_f147218624l_bool: $i > $i > $i ).

thf(hAPP_f1547458257l_bool_decl,type,
    hAPP_f1547458257l_bool: $i > $i > $i ).

thf(ord_le1482529602l_bool_decl,type,
    ord_le1482529602l_bool: $i ).

thf(hAPP_f1895971544l_bool_decl,type,
    hAPP_f1895971544l_bool: $i > $i > $i ).

thf(hAPP_f1570138413i_bool_decl,type,
    hAPP_f1570138413i_bool: $i > $i > $i ).

thf(hAPP_f1428735377l_bool_decl,type,
    hAPP_f1428735377l_bool: $i > $i > $i ).

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

thf(undefi1471133025le_alt_decl,type,
    undefi1471133025le_alt: $i > $i ).

thf(arrow_1486210539le_alt_decl,type,
    arrow_1486210539le_alt: $i ).

thf(hAPP_f2043811403e_indi_decl,type,
    hAPP_f2043811403e_indi: $i > $i > $i ).

thf(hAPP_f431432850i_bool_decl,type,
    hAPP_f431432850i_bool: $i > $i > $i ).

thf(hAPP_f719005683l_bool_decl,type,
    hAPP_f719005683l_bool: $i > $i > $i ).

thf(cOMBK_1673635960le_alt_decl,type,
    cOMBK_1673635960le_alt: $i ).

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

thf(hAPP_f1028172757l_bool_decl,type,
    hAPP_f1028172757l_bool: $i > $i > $i ).

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

thf(hAPP_f427533077t_bool_decl,type,
    hAPP_f427533077t_bool: $i > $i > $i ).

thf(hAPP_f1458726223t_bool_decl,type,
    hAPP_f1458726223t_bool: $i > $i > $i ).

thf(cOMBC_2133163426l_bool_decl,type,
    cOMBC_2133163426l_bool: $i ).

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

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

thf(hAPP_f1639180358l_bool_decl,type,
    hAPP_f1639180358l_bool: $i > $i > $i ).

thf(cOMBK_350223551e_indi_decl,type,
    cOMBK_350223551e_indi: $i ).

thf(collec1567922785t_bool_decl,type,
    collec1567922785t_bool: $i > $i ).

thf(hAPP_f783549695i_bool_decl,type,
    hAPP_f783549695i_bool: $i > $i > $i ).

thf(hAPP_A711952286t_bool_decl,type,
    hAPP_A711952286t_bool: $i > $i > $i ).

thf(hAPP_f114580065t_bool_decl,type,
    hAPP_f114580065t_bool: $i > $i > $i ).

thf(cOMBC_1377016489t_bool_decl,type,
    cOMBC_1377016489t_bool: $i ).

thf(hAPP_A28770973t_bool_decl,type,
    hAPP_A28770973t_bool: $i > $i > $i ).

thf(hAPP_A1202525278t_bool_decl,type,
    hAPP_A1202525278t_bool: $i > $i > $i ).

thf(hAPP_f882250837l_bool_decl,type,
    hAPP_f882250837l_bool: $i > $i > $i ).

thf(hAPP_f1082951236l_bool_decl,type,
    hAPP_f1082951236l_bool: $i > $i > $i ).

thf(hAPP_f563440173l_bool_decl,type,
    hAPP_f563440173l_bool: $i > $i > $i ).

thf(ord_le1028202352i_bool_decl,type,
    ord_le1028202352i_bool: $i ).

thf(hAPP_f649586561t_bool_decl,type,
    hAPP_f649586561t_bool: $i > $i > $i ).

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

thf(hAPP_f618557131t_bool_decl,type,
    hAPP_f618557131t_bool: $i > $i > $i ).

thf(cOMBB_800536526ol_nat_decl,type,
    cOMBB_800536526ol_nat: $i > $i ).

thf(hAPP_f750478076l_bool_decl,type,
    hAPP_f750478076l_bool: $i > $i > $i ).

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

thf(finite354462354e_indi_decl,type,
    finite354462354e_indi: $i > $i ).

thf(hAPP_A955165183l_bool_decl,type,
    hAPP_A955165183l_bool: $i > $i > $i ).

thf(hAPP_A1948275303t_bool_decl,type,
    hAPP_A1948275303t_bool: $i > $i > $i ).

thf(hAPP_f1393414918t_bool_decl,type,
    hAPP_f1393414918t_bool: $i > $i > $i ).

thf(cOMBK_1662914336e_indi_decl,type,
    cOMBK_1662914336e_indi: $i ).

thf(hAPP_f866114756l_bool_decl,type,
    hAPP_f866114756l_bool: $i > $i > $i ).

thf(hAPP_f1332130404l_bool_decl,type,
    hAPP_f1332130404l_bool: $i > $i > $i ).

thf(hAPP_f1283454584e_indi_decl,type,
    hAPP_f1283454584e_indi: $i > $i > $i ).

thf(hAPP_f742658307l_bool_decl,type,
    hAPP_f742658307l_bool: $i > $i > $i ).

thf(hAPP_f1332197581l_bool_decl,type,
    hAPP_f1332197581l_bool: $i > $i > $i ).

thf(member1704306684t_bool_decl,type,
    member1704306684t_bool: $i ).

thf(hAPP_f621397159l_bool_decl,type,
    hAPP_f621397159l_bool: $i > $i > $i ).

thf(member1265098019t_bool_decl,type,
    member1265098019t_bool: $i ).

thf(hAPP_f1898839893l_bool_decl,type,
    hAPP_f1898839893l_bool: $i > $i > $i ).

thf(hAPP_f961197973l_bool_decl,type,
    hAPP_f961197973l_bool: $i > $i > $i ).

thf(hAPP_f1996228283l_bool_decl,type,
    hAPP_f1996228283l_bool: $i > $i > $i ).

thf(cOMBC_1455277858l_bool_decl,type,
    cOMBC_1455277858l_bool: $i ).

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

thf(hAPP_f1044120523t_bool_decl,type,
    hAPP_f1044120523t_bool: $i > $i > $i ).

thf(cOMBB_930893948e_indi_decl,type,
    cOMBB_930893948e_indi: $i > $i ).

thf(hAPP_f684072049t_bool_decl,type,
    hAPP_f684072049t_bool: $i > $i > $i ).

thf(hAPP_A630236912t_bool_decl,type,
    hAPP_A630236912t_bool: $i > $i > $i ).

thf(hAPP_f832306437t_bool_decl,type,
    hAPP_f832306437t_bool: $i > $i > $i ).

thf(cOMBC_325526267t_bool_decl,type,
    cOMBC_325526267t_bool: $i ).

thf(hAPP_f1009478556t_bool_decl,type,
    hAPP_f1009478556t_bool: $i > $i > $i ).

thf(hAPP_f1291635206l_bool_decl,type,
    hAPP_f1291635206l_bool: $i > $i > $i ).

thf(hAPP_f322109294l_bool_decl,type,
    hAPP_f322109294l_bool: $i > $i > $i ).

thf(hAPP_P1122857141l_bool_decl,type,
    hAPP_P1122857141l_bool: $i > $i > $i ).

thf(hAPP_f1931036015t_bool_decl,type,
    hAPP_f1931036015t_bool: $i > $i > $i ).

thf(cOMBB_810329756e_indi_decl,type,
    cOMBB_810329756e_indi: $i > $i ).

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

thf(hAPP_f339859954l_bool_decl,type,
    hAPP_f339859954l_bool: $i > $i > $i ).

thf(hAPP_f1882280879t_bool_decl,type,
    hAPP_f1882280879t_bool: $i > $i > $i ).

thf(cOMBB_552200224e_indi_decl,type,
    cOMBB_552200224e_indi: $i > $i ).

thf(hAPP_A1895296483di_nat_decl,type,
    hAPP_A1895296483di_nat: $i > $i > $i ).

thf(undefined_bool_decl,type,
    undefined_bool: $i > $i ).

thf(bool_decl,type,
    bool: $i ).

thf(hAPP_f67777128l_bool_decl,type,
    hAPP_f67777128l_bool: $i > $i > $i ).

thf(hAPP_f620747982l_bool_decl,type,
    hAPP_f620747982l_bool: $i > $i > $i ).

thf(cOMBS_178315313t_bool_decl,type,
    cOMBS_178315313t_bool: $i > $i > $i ).

thf(hAPP_f599997089l_bool_decl,type,
    hAPP_f599997089l_bool: $i > $i > $i ).

thf(hAPP_P401722323t_bool_decl,type,
    hAPP_P401722323t_bool: $i > $i > $i ).

thf(hAPP_f66927821l_bool_decl,type,
    hAPP_f66927821l_bool: $i > $i > $i ).

thf(cOMBB_1146692694ol_nat_decl,type,
    cOMBB_1146692694ol_nat: $i > $i ).

thf(hAPP_f937100551l_bool_decl,type,
    hAPP_f937100551l_bool: $i > $i > $i ).

thf(hAPP_f1363425282l_bool_decl,type,
    hAPP_f1363425282l_bool: $i > $i > $i ).

thf(hAPP_f1570313510t_bool_decl,type,
    hAPP_f1570313510t_bool: $i > $i > $i ).

thf(cOMBK_583454926ol_nat_decl,type,
    cOMBK_583454926ol_nat: $i ).

thf(pi_fun1555365306t_bool_decl,type,
    pi_fun1555365306t_bool: $i > $i > $i ).

thf(hAPP_f633903640l_bool_decl,type,
    hAPP_f633903640l_bool: $i > $i > $i ).

thf(cOMBK_1918246033t_bool_decl,type,
    cOMBK_1918246033t_bool: $i ).

thf(hAPP_f537623936l_bool_decl,type,
    hAPP_f537623936l_bool: $i > $i > $i ).

thf(hAPP_A433435097l_bool_decl,type,
    hAPP_A433435097l_bool: $i > $i > $i ).

thf(hAPP_f1092358369t_bool_decl,type,
    hAPP_f1092358369t_bool: $i > $i > $i ).

thf(cOMBB_333235735le_alt_decl,type,
    cOMBB_333235735le_alt: $i > $i ).

thf(hAPP_f372913425t_bool_decl,type,
    hAPP_f372913425t_bool: $i > $i > $i ).

thf(hAPP_A643475905l_bool_decl,type,
    hAPP_A643475905l_bool: $i > $i > $i ).

thf(hAPP_f212509069l_bool_decl,type,
    hAPP_f212509069l_bool: $i > $i > $i ).

thf(hAPP_f863441901l_bool_decl,type,
    hAPP_f863441901l_bool: $i > $i > $i ).

thf(cOMBC_1528317666l_bool_decl,type,
    cOMBC_1528317666l_bool: $i ).

thf(hAPP_f881677315l_bool_decl,type,
    hAPP_f881677315l_bool: $i > $i > $i ).

thf(hAPP_P667392034l_bool_decl,type,
    hAPP_P667392034l_bool: $i > $i > $i ).

thf(hAPP_f1117143157l_bool_decl,type,
    hAPP_f1117143157l_bool: $i > $i > $i ).

thf(hAPP_A1120018583t_bool_decl,type,
    hAPP_A1120018583t_bool: $i > $i > $i ).

thf(hAPP_f581841297t_bool_decl,type,
    hAPP_f581841297t_bool: $i > $i > $i ).

thf(cOMBK_1685845624l_bool_decl,type,
    cOMBK_1685845624l_bool: $i ).

thf(hAPP_f23348649l_bool_decl,type,
    hAPP_f23348649l_bool: $i > $i > $i ).

thf(cOMBK_761999167t_bool_decl,type,
    cOMBK_761999167t_bool: $i ).

thf(hAPP_f574392641l_bool_decl,type,
    hAPP_f574392641l_bool: $i > $i > $i ).

thf(ord_at4362885an_nat_decl,type,
    ord_at4362885an_nat: $i > $i ).

thf(hAPP_f1216491309l_bool_decl,type,
    hAPP_f1216491309l_bool: $i > $i > $i ).

thf(ord_le2143686384l_bool_decl,type,
    ord_le2143686384l_bool: $i ).

thf(hAPP_f557371893l_bool_decl,type,
    hAPP_f557371893l_bool: $i > $i > $i ).

thf(hAPP_f1500902601l_bool_decl,type,
    hAPP_f1500902601l_bool: $i > $i > $i ).

thf(cOMBC_1722249314l_bool_decl,type,
    cOMBC_1722249314l_bool: $i ).

thf(hAPP_P1645359566e_indi_decl,type,
    hAPP_P1645359566e_indi: $i > $i > $i ).

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

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

thf(undefi1052853330e_indi_decl,type,
    undefi1052853330e_indi: $i > $i ).

thf(arrow_132732488e_indi_decl,type,
    arrow_132732488e_indi: $i ).

thf(hAPP_P822772139t_bool_decl,type,
    hAPP_P822772139t_bool: $i > $i > $i ).

thf(arrow_885770895le_IIA_decl,type,
    arrow_885770895le_IIA: $i ).

thf(image_837079859di_nat_decl,type,
    image_837079859di_nat: $i > $i > $i ).

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

thf(hAPP_n1600508401i_bool_decl,type,
    hAPP_n1600508401i_bool: $i > $i > $i ).

thf(hAPP_f595617317i_bool_decl,type,
    hAPP_f595617317i_bool: $i > $i > $i ).

thf(cOMBC_70761414t_bool_decl,type,
    cOMBC_70761414t_bool: $i ).

thf(inj_on398823523t_bool_decl,type,
    inj_on398823523t_bool: $i > $i ).

thf(hAPP_f560261801l_bool_decl,type,
    hAPP_f560261801l_bool: $i > $i > $i ).

thf(hAPP_f1077635369i_bool_decl,type,
    hAPP_f1077635369i_bool: $i > $i > $i ).

thf(cOMBK_1399131793t_bool_decl,type,
    cOMBK_1399131793t_bool: $i ).

thf(in_rel1361124802le_alt_decl,type,
    in_rel1361124802le_alt: $i > $i > $i > $i ).

thf(hAPP_f1234917389l_bool_decl,type,
    hAPP_f1234917389l_bool: $i > $i > $i ).

thf(member219620739le_alt_decl,type,
    member219620739le_alt: $i ).

thf(pi_Arr1064242500le_alt_decl,type,
    pi_Arr1064242500le_alt: $i > $i > $i ).

thf(hAPP_A503573454le_alt_decl,type,
    hAPP_A503573454le_alt: $i > $i > $i ).

thf(hAPP_f272527115l_bool_decl,type,
    hAPP_f272527115l_bool: $i > $i > $i ).

thf(ord_le1976645739t_bool_decl,type,
    ord_le1976645739t_bool: $i ).

thf(ord_le1874503007t_bool_decl,type,
    ord_le1874503007t_bool: $i ).

thf(hAPP_f177302985l_bool_decl,type,
    hAPP_f177302985l_bool: $i > $i > $i ).

thf(member928589940t_bool_decl,type,
    member928589940t_bool: $i ).

thf(pi_Pro1925515229t_bool_decl,type,
    pi_Pro1925515229t_bool: $i > $i > $i ).

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

thf(ord_le1260664009l_bool_decl,type,
    ord_le1260664009l_bool: $i ).

thf(cOMBC_943734388l_bool_decl,type,
    cOMBC_943734388l_bool: $i ).

thf(hAPP_f452450509l_bool_decl,type,
    hAPP_f452450509l_bool: $i > $i > $i ).

thf(member300433020le_alt_decl,type,
    member300433020le_alt: $i ).

thf(pi_boo1542163389le_alt_decl,type,
    pi_boo1542163389le_alt: $i > $i > $i ).

thf(hAPP_b1482008903le_alt_decl,type,
    hAPP_b1482008903le_alt: $i > $i > $i ).

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

thf(member1619170513t_bool_decl,type,
    member1619170513t_bool: $i ).

thf(ord_le382113706t_bool_decl,type,
    ord_le382113706t_bool: $i ).

thf(ord_less_bool_decl,type,
    ord_less_bool: $i ).

thf(hAPP_f758593513l_bool_decl,type,
    hAPP_f758593513l_bool: $i > $i > $i ).

thf(member873781636di_nat_decl,type,
    member873781636di_nat: $i ).

thf(pi_Arr604548589di_nat_decl,type,
    pi_Arr604548589di_nat: $i > $i > $i ).

thf(inj_on1331630279di_nat_decl,type,
    inj_on1331630279di_nat: $i > $i ).

thf(ord_le1791992956i_bool_decl,type,
    ord_le1791992956i_bool: $i ).

thf(hAPP_f2011903565l_bool_decl,type,
    hAPP_f2011903565l_bool: $i > $i > $i ).

thf(member485283698le_alt_decl,type,
    member485283698le_alt: $i ).

thf(pi_Pro1208494515le_alt_decl,type,
    pi_Pro1208494515le_alt: $i > $i > $i ).

thf(hAPP_P1931143485le_alt_decl,type,
    hAPP_P1931143485le_alt: $i > $i > $i ).

thf(hAPP_f1692576003l_bool_decl,type,
    hAPP_f1692576003l_bool: $i > $i > $i ).

thf(cOMBC_344067350l_bool_decl,type,
    cOMBC_344067350l_bool: $i ).

thf(hAPP_f1171266041l_bool_decl,type,
    hAPP_f1171266041l_bool: $i > $i > $i ).

thf(member2021375116l_bool_decl,type,
    member2021375116l_bool: $i ).

thf(pi_fun568395771l_bool_decl,type,
    pi_fun568395771l_bool: $i > $i > $i ).

thf(hAPP_f812095627l_bool_decl,type,
    hAPP_f812095627l_bool: $i > $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(ord_le194694222l_bool_decl,type,
    ord_le194694222l_bool: $i ).

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

thf(hAPP_f1656652505l_bool_decl,type,
    hAPP_f1656652505l_bool: $i > $i > $i ).

thf(cOMBB_711698847le_alt_decl,type,
    cOMBB_711698847le_alt: $i > $i ).

thf(hAPP_f749156301l_bool_decl,type,
    hAPP_f749156301l_bool: $i > $i > $i ).

thf(member234310528e_indi_decl,type,
    member234310528e_indi: $i ).

thf(pi_fun1353458625e_indi_decl,type,
    pi_fun1353458625e_indi: $i > $i > $i ).

thf(ord_le1141238780l_bool_decl,type,
    ord_le1141238780l_bool: $i ).

thf(arrow_312654597_mktop_decl,type,
    arrow_312654597_mktop: $i ).

thf(arrow_1046586475_above_decl,type,
    arrow_1046586475_above: $i ).

thf(arrow_163947511_mkbot_decl,type,
    arrow_163947511_mkbot: $i ).

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

thf(ord_le2113500159t_bool_decl,type,
    ord_le2113500159t_bool: $i ).

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

thf(hAPP_f2134766349l_bool_decl,type,
    hAPP_f2134766349l_bool: $i > $i > $i ).

thf(member930088569t_bool_decl,type,
    member930088569t_bool: $i ).

thf(pi_boo68262458t_bool_decl,type,
    pi_boo68262458t_bool: $i > $i > $i ).

thf(hAPP_b327863236t_bool_decl,type,
    hAPP_b327863236t_bool: $i > $i > $i ).

thf(hAPP_f1836999501l_bool_decl,type,
    hAPP_f1836999501l_bool: $i > $i > $i ).

thf(member104322770t_bool_decl,type,
    member104322770t_bool: $i ).

thf(pi_Arr656802323t_bool_decl,type,
    pi_Arr656802323t_bool: $i > $i > $i ).

thf(hAPP_A739031709t_bool_decl,type,
    hAPP_A739031709t_bool: $i > $i > $i ).

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

thf(ord_le64728819t_bool_decl,type,
    ord_le64728819t_bool: $i ).

thf(hAPP_f1598887207l_bool_decl,type,
    hAPP_f1598887207l_bool: $i > $i > $i ).

thf(member1024687843t_unit_decl,type,
    member1024687843t_unit: $i ).

thf(pi_nat_Product_unit_decl,type,
    pi_nat_Product_unit: $i > $i > $i ).

thf(hAPP_n633340360t_unit_decl,type,
    hAPP_n633340360t_unit: $i > $i > $i ).

thf(inj_on1507564774t_bool_decl,type,
    inj_on1507564774t_bool: $i > $i ).

thf(hAPP_f2022872455l_bool_decl,type,
    hAPP_f2022872455l_bool: $i > $i > $i ).

thf(member1935624595e_indi_decl,type,
    member1935624595e_indi: $i ).

thf(pi_fun596906370e_indi_decl,type,
    pi_fun596906370e_indi: $i > $i > $i ).

thf(inj_on302999388e_indi_decl,type,
    inj_on302999388e_indi: $i > $i ).

thf(finite921964625e_indi_decl,type,
    finite921964625e_indi: $i ).

thf(finite274731772t_bool_decl,type,
    finite274731772t_bool: $i ).

thf(finite945540987t_bool_decl,type,
    finite945540987t_bool: $i > $i ).

thf(hAPP_f1338606733l_bool_decl,type,
    hAPP_f1338606733l_bool: $i > $i > $i ).

thf(member1402889547l_bool_decl,type,
    member1402889547l_bool: $i ).

thf(pi_fun1236347660l_bool_decl,type,
    pi_fun1236347660l_bool: $i > $i > $i ).

thf(hAPP_f591334822l_bool_decl,type,
    hAPP_f591334822l_bool: $i > $i > $i ).

thf(hAPP_f840347317l_bool_decl,type,
    hAPP_f840347317l_bool: $i > $i > $i ).

thf(member1258284266t_bool_decl,type,
    member1258284266t_bool: $i ).

thf(pi_boo1746012499t_bool_decl,type,
    pi_boo1746012499t_bool: $i > $i > $i ).

thf(hAPP_f785487437l_bool_decl,type,
    hAPP_f785487437l_bool: $i > $i > $i ).

thf(member1226631410t_unit_decl,type,
    member1226631410t_unit: $i ).

thf(pi_Pro269694131t_unit_decl,type,
    pi_Pro269694131t_unit: $i > $i > $i ).

thf(hAPP_P992343101t_unit_decl,type,
    hAPP_P992343101t_unit: $i > $i > $i ).

thf(hAPP_f2040535501l_bool_decl,type,
    hAPP_f2040535501l_bool: $i > $i > $i ).

thf(member_fun_nat_nat_decl,type,
    member_fun_nat_nat: $i ).

thf(pi_nat_nat_decl,type,
    pi_nat_nat: $i > $i > $i ).

thf(inj_on67207011le_alt_decl,type,
    inj_on67207011le_alt: $i > $i ).

thf(finite_finite_bool_decl,type,
    finite_finite_bool: $i ).

thf(finite1044330389le_alt_decl,type,
    finite1044330389le_alt: $i > $i ).

thf(finite_card_bool_decl,type,
    finite_card_bool: $i > $i ).

thf(hAPP_f2078760383l_bool_decl,type,
    hAPP_f2078760383l_bool: $i > $i > $i ).

thf(ord_le319160163t_bool_decl,type,
    ord_le319160163t_bool: $i ).

thf(hAPP_f1747206697l_bool_decl,type,
    hAPP_f1747206697l_bool: $i > $i > $i ).

thf(cOMBB_885534287le_alt_decl,type,
    cOMBB_885534287le_alt: $i > $i ).

thf(hAPP_f1980578603l_bool_decl,type,
    hAPP_f1980578603l_bool: $i > $i > $i ).

thf(member363954533t_bool_decl,type,
    member363954533t_bool: $i ).

thf(pi_fun328162388t_bool_decl,type,
    pi_fun328162388t_bool: $i > $i > $i ).

thf(inj_on735362094t_bool_decl,type,
    inj_on735362094t_bool: $i > $i ).

thf(inj_on1962565012t_bool_decl,type,
    inj_on1962565012t_bool: $i > $i ).

thf(finite1323840035t_bool_decl,type,
    finite1323840035t_bool: $i ).

thf(finite1524925796t_bool_decl,type,
    finite1524925796t_bool: $i > $i ).

thf(hAPP_f715600357l_bool_decl,type,
    hAPP_f715600357l_bool: $i > $i > $i ).

thf(member416763266t_unit_decl,type,
    member416763266t_unit: $i ).

thf(pi_fun1012573681t_unit_decl,type,
    pi_fun1012573681t_unit: $i > $i > $i ).

thf(hAPP_f1636264423t_unit_decl,type,
    hAPP_f1636264423t_unit: $i > $i > $i ).

thf(hAPP_f1957108621l_bool_decl,type,
    hAPP_f1957108621l_bool: $i > $i > $i ).

thf(member1941767151t_unit_decl,type,
    member1941767151t_unit: $i ).

thf(pi_fun1390764464t_unit_decl,type,
    pi_fun1390764464t_unit: $i > $i > $i ).

thf(hAPP_f1716204858t_unit_decl,type,
    hAPP_f1716204858t_unit: $i > $i > $i ).

thf(ord_le197158773l_bool_decl,type,
    ord_le197158773l_bool: $i ).

thf(hAPP_f1518101645l_bool_decl,type,
    hAPP_f1518101645l_bool: $i > $i > $i ).

thf(member1024929995t_bool_decl,type,
    member1024929995t_bool: $i ).

thf(pi_boo679625100t_bool_decl,type,
    pi_boo679625100t_bool: $i > $i > $i ).

thf(hAPP_b821377302t_bool_decl,type,
    hAPP_b821377302t_bool: $i > $i > $i ).

thf(arrow_1549387998ctator_decl,type,
    arrow_1549387998ctator: $i ).

thf(hAPP_f1160956173l_bool_decl,type,
    hAPP_f1160956173l_bool: $i > $i > $i ).

thf(member982489409t_unit_decl,type,
    member982489409t_unit: $i ).

thf(pi_fun623621634t_unit_decl,type,
    pi_fun623621634t_unit: $i > $i > $i ).

thf(hAPP_f754536332t_unit_decl,type,
    hAPP_f754536332t_unit: $i > $i > $i ).

thf(hAPP_f1951378235l_bool_decl,type,
    hAPP_f1951378235l_bool: $i > $i > $i ).

thf(member_fun_nat_bool_decl,type,
    member_fun_nat_bool: $i ).

thf(pi_nat_bool_decl,type,
    pi_nat_bool: $i > $i > $i ).

thf(hAPP_f1140532045l_bool_decl,type,
    hAPP_f1140532045l_bool: $i > $i > $i ).

thf(member1618799570e_indi_decl,type,
    member1618799570e_indi: $i ).

thf(pi_fun268174099e_indi_decl,type,
    pi_fun268174099e_indi: $i > $i > $i ).

thf(hAPP_f1152614183t_bool_decl,type,
    hAPP_f1152614183t_bool: $i > $i > $i ).

thf(cOMBC_420816290l_bool_decl,type,
    cOMBC_420816290l_bool: $i ).

thf(hAPP_f144393719l_bool_decl,type,
    hAPP_f144393719l_bool: $i > $i > $i ).

thf(member_fun_bool_nat_decl,type,
    member_fun_bool_nat: $i ).

thf(pi_bool_nat_decl,type,
    pi_bool_nat: $i > $i > $i ).

thf(hAPP_bool_nat_decl,type,
    hAPP_bool_nat: $i > $i > $i ).

thf(hAPP_f544923081l_bool_decl,type,
    hAPP_f544923081l_bool: $i > $i > $i ).

thf(member1801639028e_indi_decl,type,
    member1801639028e_indi: $i ).

thf(pi_nat1476290531e_indi_decl,type,
    pi_nat1476290531e_indi: $i > $i > $i ).

thf(hAPP_f813426957l_bool_decl,type,
    hAPP_f813426957l_bool: $i > $i > $i ).

thf(member1044213697t_bool_decl,type,
    member1044213697t_bool: $i ).

thf(pi_Pro1114473858t_bool_decl,type,
    pi_Pro1114473858t_bool: $i > $i > $i ).

thf(hAPP_P1245388556t_bool_decl,type,
    hAPP_P1245388556t_bool: $i > $i > $i ).

thf(hAPP_f2087408397l_bool_decl,type,
    hAPP_f2087408397l_bool: $i > $i > $i ).

thf(member48503289l_bool_decl,type,
    member48503289l_bool: $i ).

thf(pi_fun187048122l_bool_decl,type,
    pi_fun187048122l_bool: $i > $i > $i ).

thf(hAPP_f721327224l_bool_decl,type,
    hAPP_f721327224l_bool: $i > $i > $i ).

thf(hAPP_f1950626059l_bool_decl,type,
    hAPP_f1950626059l_bool: $i > $i > $i ).

thf(member87760213it_nat_decl,type,
    member87760213it_nat: $i ).

thf(pi_Product_unit_nat_decl,type,
    pi_Product_unit_nat: $i > $i > $i ).

thf(hAPP_P426034740it_nat_decl,type,
    hAPP_P426034740it_nat: $i > $i > $i ).

thf(hAPP_P32877782t_bool_decl,type,
    hAPP_P32877782t_bool: $i > $i > $i ).

thf(hAPP_f1387788301l_bool_decl,type,
    hAPP_f1387788301l_bool: $i > $i > $i ).

thf(member220564739e_indi_decl,type,
    member220564739e_indi: $i ).

thf(pi_Pro58544964e_indi_decl,type,
    pi_Pro58544964e_indi: $i > $i > $i ).

thf(hAPP_f1063991245l_bool_decl,type,
    hAPP_f1063991245l_bool: $i > $i > $i ).

thf(member689634176t_bool_decl,type,
    member689634176t_bool: $i ).

thf(pi_Arr742795713t_bool_decl,type,
    pi_Arr742795713t_bool: $i > $i > $i ).

thf(hAPP_A1433148491t_bool_decl,type,
    hAPP_A1433148491t_bool: $i > $i > $i ).

thf(hAPP_f627309453l_bool_decl,type,
    hAPP_f627309453l_bool: $i > $i > $i ).

thf(member1775405935t_bool_decl,type,
    member1775405935t_bool: $i ).

thf(pi_Pro831923248t_bool_decl,type,
    pi_Pro831923248t_bool: $i > $i > $i ).

thf(hAPP_P1157363642t_bool_decl,type,
    hAPP_P1157363642t_bool: $i > $i > $i ).

thf(6,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBS_995062533t_bool ) @ hAPP_A1906804694t_bool ) )
      = ( C @ ( B @ hAPP_A340536322t_bool ) @ ( C @ ( A @ hAPP_A725195434t_bool ) @ hAPP_f1000663785t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_053) ).

thf(892,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBS_995062533t_bool ) @ hAPP_A1906804694t_bool ) )
      = ( C @ ( B @ hAPP_A340536322t_bool ) @ ( C @ ( A @ hAPP_A725195434t_bool ) @ hAPP_f1000663785t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(143,axiom,
    ! [A: $i] :
      ( ( top_to1647826457l_bool @ ( cOMBK_1673635960le_alt @ hAPP_f719005683l_bool ) @ ( A @ pi_Pro1873779901t_bool ) )
      = top_to846262053l_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_Pi__UNIV) ).

thf(1322,plain,
    ! [A: $i] :
      ( ( top_to1647826457l_bool @ ( cOMBK_1673635960le_alt @ hAPP_f719005683l_bool ) @ ( A @ pi_Pro1873779901t_bool ) )
      = top_to846262053l_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(261,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f620747982l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__Arrow____Order____M) ).

thf(1718,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f620747982l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(378,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ hBOOL )
      <=> ( B @ hBOOL ) )
     => ( ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
       => ( A @ ( C @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_ord__eq__le__trans) ).

thf(2094,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( B @ hBOOL )
         => ( C @ hBOOL ) )
        & ( ( C @ hBOOL )
         => ( B @ hBOOL ) ) )
     => ( ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
       => ( A @ ( C @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(194,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( D @ is_Arr859726945e_indi )
         => ( ( C @ ( D @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
           => ( D @ ( B @ hAPP_A659996934l_bool ) @ ( D @ ( A @ hAPP_A340536322t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) )
     => ( B @ ( C @ pi_Arr1801471756t_bool ) @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_390_Pi__I) ).

thf(1469,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( D @ is_Arr859726945e_indi )
         => ( ( C @ ( D @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
           => ( D @ ( B @ hAPP_A659996934l_bool ) @ ( D @ ( A @ hAPP_A340536322t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) )
     => ( B @ ( C @ pi_Arr1801471756t_bool ) @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(868,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro58544964e_indi ) @ ( B @ ( member220564739e_indi @ hAPP_f1387788301l_bool ) @ hAPP_f817344902l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P957402556i_bool ) @ ( A @ ( B @ hAPP_P1645359566e_indi ) @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_PiE) ).

thf(4169,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro58544964e_indi ) @ ( B @ ( member220564739e_indi @ hAPP_f1387788301l_bool ) @ hAPP_f817344902l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P957402556i_bool ) @ ( A @ ( B @ hAPP_P1645359566e_indi ) @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).

thf(76,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/sandbox2/benchmark/theBenchmark.p',fact_652_less__trans__Suc) ).

thf(1105,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)],[76]) ).

thf(294,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_Arr723427730le_alt )
     => ( B @ ( A @ hAPP_A433435097l_bool ) @ is_fun1420103068l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__fun_Itc) ).

thf(1840,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_Arr723427730le_alt )
     => ( B @ ( A @ hAPP_A433435097l_bool ) @ is_fun1420103068l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(297,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/sandbox2/benchmark/theBenchmark.p',fact_654_Suc__lessD) ).

thf(1850,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)],[297]) ).

thf(343,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/sandbox2/benchmark/theBenchmark.p',fact_538_nat__add__right__cancel) ).

thf(1982,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)],[343]) ).

thf(483,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_456_psubset__subset__trans) ).

thf(2559,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(479,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ is_Arr859726945e_indi )
     => ( ( top_to207207712i_bool @ ( C @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( ( A @ ( C @ hAPP_A1895296483di_nat ) )
            = B )
         => ( ( B @ ( C @ ( top_to207207712i_bool @ hilber951314860di_nat ) @ hAPP_n619554777e_indi ) )
            = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_inv__f__eq) ).

thf(2544,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ is_Arr859726945e_indi )
     => ( ( top_to207207712i_bool @ ( C @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( ( A @ ( C @ hAPP_A1895296483di_nat ) )
            = B )
         => ( ( B @ ( C @ ( top_to207207712i_bool @ hilber951314860di_nat ) @ hAPP_n619554777e_indi ) )
            = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(102,axiom,
    arrow_1550141362nimity @ is_fun292781289l_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Arrow__Order__Mirabelle__wylsunqmtb_Ounanimity) ).

thf(1179,plain,
    arrow_1550141362nimity @ is_fun292781289l_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(713,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_xt1_I9_J) ).

thf(3566,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).

thf(132,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1895971544l_bool ) @ is_fun1420103068l_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__010) ).

thf(1295,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1895971544l_bool ) @ is_fun1420103068l_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(52,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/sandbox2/benchmark/theBenchmark.p',fact_535_nat__add__left__commute) ).

thf(1036,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)],[52]) ).

thf(529,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun20916972t_bool )
        & ( A @ is_fun20916972t_bool ) )
     => ( ! [C: $i,D: $i] :
            ( ( ( D @ is_Arr723427730le_alt )
              & ( C @ is_Arr723427730le_alt ) )
           => ( ( B @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
            <=> ( A @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_pred__equals__eq2) ).

thf(2822,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun20916972t_bool )
        & ( A @ is_fun20916972t_bool ) )
     => ( ( ( B = A )
         => ! [C: $i,D: $i] :
              ( ( ( D @ is_Arr723427730le_alt )
                & ( C @ is_Arr723427730le_alt ) )
             => ( ( ( A @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                 => ( B @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
                & ( ( B @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                 => ( A @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) ) )
        & ( ! [C: $i,D: $i] :
              ( ( ( D @ is_Arr723427730le_alt )
                & ( C @ is_Arr723427730le_alt ) )
             => ( ( ( A @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                 => ( B @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
                & ( ( B @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                 => ( A @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(228,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( cOMBK_1673635960le_alt @ hAPP_f719005683l_bool ) @ hAPP_P1122857141l_bool ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__prod_It) ).

thf(1586,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( cOMBK_1673635960le_alt @ hAPP_f719005683l_bool ) @ hAPP_P1122857141l_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(202,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun1568535512t_bool )
     => ( B @ ( A @ hAPP_f2028818269l_bool ) @ is_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_000tc__HOL__) ).

thf(1501,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun1568535512t_bool )
     => ( B @ ( A @ hAPP_f2028818269l_bool ) @ is_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(516,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/sandbox2/benchmark/theBenchmark.p',fact_235_xt1_I5_J) ).

thf(2744,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)],[516]) ).

thf(107,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/sandbox2/benchmark/theBenchmark.p',fact_671_less__Suc__eq__0__disj) ).

thf(1190,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)],[107]) ).

thf(585,axiom,
    f @ ( arrow_885770895le_IIA @ hAPP_f446648900l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_assms_I3_J) ).

thf(3053,plain,
    f @ ( arrow_885770895le_IIA @ hAPP_f446648900l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(847,axiom,
    ~ ( lab @ ( a @ ( b @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79__096_Ib_M_Aa_J_A_126_058_ALab_096) ).

thf(4101,plain,
    ~ ( lab @ ( a @ ( b @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).

thf(433,axiom,
    ! [A: $i] :
      ( ( A @ ( top_to846262053l_bool @ hAPP_f1733357041l_bool ) @ hBOOL )
    <=> ( top_top_bool @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_top__apply) ).

thf(2336,plain,
    ! [A: $i] :
      ( ( ( top_top_bool @ hBOOL )
       => ( A @ ( top_to846262053l_bool @ hAPP_f1733357041l_bool ) @ hBOOL ) )
      & ( ( A @ ( top_to846262053l_bool @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ( top_top_bool @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(360,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f560261801l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_027) ).

thf(2031,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f560261801l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(838,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_xt1_I9_J) ).

thf(4062,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).

thf(275,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/sandbox2/benchmark/theBenchmark.p',fact_569_less__mono__imp__le__mono) ).

thf(1767,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)],[275]) ).

thf(825,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le2143686384l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
       => ( A @ ( B @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_476_set__rev__mp) ).

thf(4022,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le2143686384l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
       => ( A @ ( B @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).

thf(264,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBS_178315313t_bool ) @ hAPP_A340536322t_bool ) )
      = ( C @ ( B @ hAPP_A340536322t_bool ) @ ( C @ ( A @ hAPP_A1906804694t_bool ) @ hAPP_f137597973t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000) ).

thf(1729,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBS_178315313t_bool ) @ hAPP_A340536322t_bool ) )
      = ( C @ ( B @ hAPP_A340536322t_bool ) @ ( C @ ( A @ hAPP_A1906804694t_bool ) @ hAPP_f137597973t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(468,axiom,
    ! [A: $i] :
      ( ( ( ~ ( n @ ( A @ ( h @ hAPP_A1895296483di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( ( ( ( A @ ( h @ hAPP_A1895296483di_nat ) )
               != n )
             => ( e @ ( A @ ( p @ hAPP_A340536322t_bool ) @ ( arrow_163947511_mkbot @ hAPP_f102394819t_bool ) @ hAPP_A1014090479t_bool ) @ ( e @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
            & ( ( ( A @ ( h @ hAPP_A1895296483di_nat ) )
                = n )
             => ( e @ ( c @ ( A @ ( p @ hAPP_A340536322t_bool ) @ ( arrow_1046586475_above @ hAPP_f684072049t_bool ) @ hAPP_A28770973t_bool ) @ hAPP_A1014090479t_bool ) @ ( e @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) )
        & ( ( n @ ( A @ ( h @ hAPP_A1895296483di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( e @ ( A @ ( p @ hAPP_A340536322t_bool ) @ ( arrow_312654597_mktop @ hAPP_f102394819t_bool ) @ hAPP_A1014090479t_bool ) @ ( e @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) )
    <=> ( ( ~ ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( h @ hAPP_A1895296483di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( lba @ ( b @ ( a @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
        & ( ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( h @ hAPP_A1895296483di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( lab @ ( b @ ( a @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Am) ).

thf(2463,plain,
    ! [A: $i] :
      ( ( ( ( ~ ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( h @ hAPP_A1895296483di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( lba @ ( b @ ( a @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
          & ( ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( h @ hAPP_A1895296483di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( lab @ ( b @ ( a @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) )
       => ( ( ~ ( n @ ( A @ ( h @ hAPP_A1895296483di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( ( ( ( A @ ( h @ hAPP_A1895296483di_nat ) )
                 != n )
               => ( e @ ( A @ ( p @ hAPP_A340536322t_bool ) @ ( arrow_163947511_mkbot @ hAPP_f102394819t_bool ) @ hAPP_A1014090479t_bool ) @ ( e @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
              & ( ( ( A @ ( h @ hAPP_A1895296483di_nat ) )
                  = n )
               => ( e @ ( c @ ( A @ ( p @ hAPP_A340536322t_bool ) @ ( arrow_1046586475_above @ hAPP_f684072049t_bool ) @ hAPP_A28770973t_bool ) @ hAPP_A1014090479t_bool ) @ ( e @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) )
          & ( ( n @ ( A @ ( h @ hAPP_A1895296483di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( e @ ( A @ ( p @ hAPP_A340536322t_bool ) @ ( arrow_312654597_mktop @ hAPP_f102394819t_bool ) @ hAPP_A1014090479t_bool ) @ ( e @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) )
      & ( ( ( ~ ( n @ ( A @ ( h @ hAPP_A1895296483di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( ( ( ( A @ ( h @ hAPP_A1895296483di_nat ) )
                 != n )
               => ( e @ ( A @ ( p @ hAPP_A340536322t_bool ) @ ( arrow_163947511_mkbot @ hAPP_f102394819t_bool ) @ hAPP_A1014090479t_bool ) @ ( e @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
              & ( ( ( A @ ( h @ hAPP_A1895296483di_nat ) )
                  = n )
               => ( e @ ( c @ ( A @ ( p @ hAPP_A340536322t_bool ) @ ( arrow_1046586475_above @ hAPP_f684072049t_bool ) @ hAPP_A28770973t_bool ) @ hAPP_A1014090479t_bool ) @ ( e @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) )
          & ( ( n @ ( A @ ( h @ hAPP_A1895296483di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( e @ ( A @ ( p @ hAPP_A340536322t_bool ) @ ( arrow_312654597_mktop @ hAPP_f102394819t_bool ) @ hAPP_A1014090479t_bool ) @ ( e @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) )
       => ( ( ~ ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( h @ hAPP_A1895296483di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( lba @ ( b @ ( a @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
          & ( ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( h @ hAPP_A1895296483di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( lab @ ( b @ ( a @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(316,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1117143157l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__prod_Itc__Arrow_) ).

thf(1899,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1117143157l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(422,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_order__less__le__trans) ).

thf(2280,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(614,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ is_Arr859726945e_indi )
        & ( A @ is_Arr859726945e_indi ) )
     => ( ( top_to207207712i_bool @ ( C @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( ( A @ ( C @ hAPP_A1895296483di_nat ) )
            = ( B @ ( C @ hAPP_A1895296483di_nat ) ) )
        <=> ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_382_inj__eq) ).

thf(3172,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ is_Arr859726945e_indi )
        & ( A @ is_Arr859726945e_indi ) )
     => ( ( top_to207207712i_bool @ ( C @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( ( A = B )
           => ( ( A @ ( C @ hAPP_A1895296483di_nat ) )
              = ( B @ ( C @ hAPP_A1895296483di_nat ) ) ) )
          & ( ( ( A @ ( C @ hAPP_A1895296483di_nat ) )
              = ( B @ ( C @ hAPP_A1895296483di_nat ) ) )
           => ( A = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(250,axiom,
    ! [A: $i] :
      ( A
     != ( A @ ( suc @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_641_n__not__Suc__n) ).

thf(1686,plain,
    ! [A: $i] :
      ( A
     != ( A @ ( suc @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(416,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_541_eq__imp__le) ).

thf(2250,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)],[416]) ).

thf(300,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Arr1801471756t_bool ) @ ( B @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_A659996934l_bool ) @ ( A @ ( B @ hAPP_A340536322t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_PiE) ).

thf(1855,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Arr1801471756t_bool ) @ ( B @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_A659996934l_bool ) @ ( A @ ( B @ hAPP_A340536322t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(270,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P401722323t_bool ) @ is_fun20916972t_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__prod_Itc__Arrow____Orde) ).

thf(1750,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P401722323t_bool ) @ is_fun20916972t_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(41,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ is_Arr723427730le_alt )
        & ( B @ is_Arr723427730le_alt )
        & ( A @ is_fun20916972t_bool ) )
     => ( C @ ( B @ ( A @ arrow_207701375_below ) ) @ is_fun20916972t_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Arrow__Order__Mirabelle__wylsunqmtb_Obelow) ).

thf(1005,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ is_Arr723427730le_alt )
        & ( B @ is_Arr723427730le_alt )
        & ( A @ is_fun20916972t_bool ) )
     => ( C @ ( B @ ( A @ arrow_207701375_below ) ) @ is_fun20916972t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(581,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_order__less__trans) ).

thf(3040,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(797,axiom,
    ? [A: $i] :
      ( ( arrow_912654623le_Lin @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
      & ( A @ is_fun20916972t_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_579_linear__alt) ).

thf(3910,plain,
    ? [A: $i] :
      ( ( arrow_912654623le_Lin @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
      & ( A @ is_fun20916972t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).

thf(603,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/sandbox2/benchmark/theBenchmark.p',fact_543_le__antisym) ).

thf(3108,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)],[603]) ).

thf(577,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ is_Arr859726945e_indi )
        & ( A @ is_Arr859726945e_indi ) )
     => ( ( D @ ( C @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( D @ ( B @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
         => ( ( D @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
           => ( ( ( B @ ( C @ hAPP_A1895296483di_nat ) )
                = ( A @ ( C @ hAPP_A1895296483di_nat ) ) )
            <=> ( B = A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_369_inj__on__iff) ).

thf(3012,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ is_Arr859726945e_indi )
        & ( A @ is_Arr859726945e_indi ) )
     => ( ( D @ ( C @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( D @ ( B @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
         => ( ( D @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
           => ( ( ( B = A )
               => ( ( B @ ( C @ hAPP_A1895296483di_nat ) )
                  = ( A @ ( C @ hAPP_A1895296483di_nat ) ) ) )
              & ( ( ( B @ ( C @ hAPP_A1895296483di_nat ) )
                  = ( A @ ( C @ hAPP_A1895296483di_nat ) ) )
               => ( B = A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(423,axiom,
    ! [A: $i] : ( top_top_bool @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_top__greatest) ).

thf(2282,plain,
    ! [A: $i] : ( top_top_bool @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(694,axiom,
    ! [A: $i] :
      ~ ( A @ ( top_to935749874l_bool @ ( ord_le194694222l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_not__top__less) ).

thf(3498,plain,
    ! [A: $i] :
      ~ ( A @ ( top_to935749874l_bool @ ( ord_le194694222l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).

thf(252,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/sandbox2/benchmark/theBenchmark.p',fact_649_less__antisym) ).

thf(1692,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)],[252]) ).

thf(135,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1428735377l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Arrow____Order____Mirabelle__) ).

thf(1305,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1428735377l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(180,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_466_set__mp) ).

thf(1437,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(109,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_bool )
     => ( ( B @ ( A @ ( cOMBK_577652221t_bool @ hAPP_b651754310l_bool ) @ hAPP_f446648900l_bool ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order__) ).

thf(1211,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_bool )
     => ( ( B @ ( A @ ( cOMBK_577652221t_bool @ hAPP_b651754310l_bool ) @ hAPP_f446648900l_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(817,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B @ is_Arr859726945e_indi )
     => ( ( D @ ( C @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( D @ ( B @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
         => ( ( ( B @ ( C @ hAPP_A1895296483di_nat ) )
              = A )
           => ( ( A @ ( C @ ( D @ hilber951314860di_nat ) @ hAPP_n619554777e_indi ) )
              = B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_388_inv__into__f__eq) ).

thf(3990,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B @ is_Arr859726945e_indi )
     => ( ( D @ ( C @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( D @ ( B @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
         => ( ( ( B @ ( C @ hAPP_A1895296483di_nat ) )
              = A )
           => ( ( A @ ( C @ ( D @ hilber951314860di_nat ) @ hAPP_n619554777e_indi ) )
              = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).

thf(832,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_1673635960le_alt @ hAPP_f719005683l_bool ) @ ( C @ pi_Pro1873779901t_bool ) @ ( B @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_P1813625415t_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_377_funcset__mem) ).

thf(4037,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_1673635960le_alt @ hAPP_f719005683l_bool ) @ ( C @ pi_Pro1873779901t_bool ) @ ( B @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_P1813625415t_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).

thf(429,axiom,
    ! [A: $i] :
      ( ( A @ is_fun1568535512t_bool )
     => ( ( A @ ( top_to1257323279t_bool @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
      <=> ( A = top_to1257323279t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_354_top__unique) ).

thf(2309,plain,
    ! [A: $i] :
      ( ( A @ is_fun1568535512t_bool )
     => ( ( ( A = top_to1257323279t_bool )
         => ( A @ ( top_to1257323279t_bool @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) )
        & ( ( A @ ( top_to1257323279t_bool @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
         => ( A = top_to1257323279t_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(552,axiom,
    ! [A: $i] : ( top_top_fun_nat_bool @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_410_subset__UNIV) ).

thf(2940,plain,
    ! [A: $i] : ( top_top_fun_nat_bool @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(172,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/sandbox2/benchmark/theBenchmark.p',fact_663_less__eq__Suc__le) ).

thf(1406,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)],[172]) ).

thf(495,axiom,
    ! [A: $i] :
      ( ( A @ ( arrow_1550141362nimity @ hAPP_f446648900l_bool ) @ hBOOL )
    <=> ! [B: $i] :
          ( ( arrow_583275979e_Prof @ ( B @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
         => ! [C: $i,D: $i] :
              ( ( ( D @ is_Arr723427730le_alt )
                & ( C @ is_Arr723427730le_alt ) )
             => ( ! [E: $i] :
                    ( ( E @ is_Arr859726945e_indi )
                   => ( E @ ( B @ hAPP_A340536322t_bool ) @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
               => ( B @ ( A @ hAPP_f1817389232t_bool ) @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_unanimity__def) ).

thf(2622,plain,
    ! [A: $i] :
      ( ( ! [B: $i] :
            ( ( arrow_583275979e_Prof @ ( B @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
           => ! [C: $i,D: $i] :
                ( ( ( D @ is_Arr723427730le_alt )
                  & ( C @ is_Arr723427730le_alt ) )
               => ( ! [E: $i] :
                      ( ( E @ is_Arr859726945e_indi )
                     => ( E @ ( B @ hAPP_A340536322t_bool ) @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
                 => ( B @ ( A @ hAPP_f1817389232t_bool ) @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) )
       => ( A @ ( arrow_1550141362nimity @ hAPP_f446648900l_bool ) @ hBOOL ) )
      & ( ( A @ ( arrow_1550141362nimity @ hAPP_f446648900l_bool ) @ hBOOL )
       => ! [B: $i] :
            ( ( arrow_583275979e_Prof @ ( B @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
           => ! [C: $i,D: $i] :
                ( ( ( D @ is_Arr723427730le_alt )
                  & ( C @ is_Arr723427730le_alt ) )
               => ( ! [E: $i] :
                      ( ( E @ is_Arr859726945e_indi )
                     => ( E @ ( B @ hAPP_A340536322t_bool ) @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
                 => ( B @ ( A @ hAPP_f1817389232t_bool ) @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(781,axiom,
    ! [A: $i] : ( top_to1773227171t_bool @ ( A @ ( ord_le64728819t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_top__greatest) ).

thf(3858,plain,
    ! [A: $i] : ( top_to1773227171t_bool @ ( A @ ( ord_le64728819t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).

thf(524,axiom,
    ! [A: $i] :
      ~ ( A @ ( top_top_bool @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_not__top__less) ).

thf(2808,plain,
    ! [A: $i] :
      ~ ( A @ ( top_top_bool @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(208,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_930893948e_indi @ hAPP_f1044120523t_bool ) @ hAPP_A1202525278t_bool ) )
      = ( C @ ( B @ hAPP_A340536322t_bool ) @ ( A @ hAPP_f684072049t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy_051) ).

thf(1522,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_930893948e_indi @ hAPP_f1044120523t_bool ) @ hAPP_A1202525278t_bool ) )
      = ( C @ ( B @ hAPP_A340536322t_bool ) @ ( A @ hAPP_f684072049t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(751,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_fun268174099e_indi ) @ ( B @ ( member1618799570e_indi @ hAPP_f1140532045l_bool ) @ hAPP_f882250837l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_f1570138413i_bool ) @ ( A @ ( B @ hAPP_f350403485e_indi ) @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_PiE) ).

thf(3762,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_fun268174099e_indi ) @ ( B @ ( member1618799570e_indi @ hAPP_f1140532045l_bool ) @ hAPP_f882250837l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_f1570138413i_bool ) @ ( A @ ( B @ hAPP_f350403485e_indi ) @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).

thf(287,axiom,
    ! [A: $i] :
      ( ( A @ is_fun1568535512t_bool )
     => ( ( A @ collect_Product_unit )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_Collect__def) ).

thf(1808,plain,
    ! [A: $i] :
      ( ( A @ is_fun1568535512t_bool )
     => ( ( A @ collect_Product_unit )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(671,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( zero_zero_nat @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ ( cOMBC_nat_nat_bool @ hAPP_f229349961t_bool ) @ hAPP_n1699378549t_bool ) @ ( B @ ( member_nat @ ( cOMBC_226598744l_bool @ hAPP_f1722879237t_bool ) @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat @ hAPP_f1146629647l_bool ) @ cOMBS_nat_bool_bool ) @ collect_nat @ finite_card_nat )
       != zero_zero_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_682_card__less) ).

thf(3417,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( zero_zero_nat @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ ( cOMBC_nat_nat_bool @ hAPP_f229349961t_bool ) @ hAPP_n1699378549t_bool ) @ ( B @ ( member_nat @ ( cOMBC_226598744l_bool @ hAPP_f1722879237t_bool ) @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat @ hAPP_f1146629647l_bool ) @ cOMBS_nat_bool_bool ) @ collect_nat @ finite_card_nat )
       != zero_zero_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).

thf(683,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le197158773l_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/sandbox2/benchmark/theBenchmark.p',fact_512_psubsetD) ).

thf(3460,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le197158773l_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)],[683]) ).

thf(555,axiom,
    ! [A: $i] : ( top_to846262053l_bool @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_iso__tuple__UNIV__I) ).

thf(2947,plain,
    ! [A: $i] : ( top_to846262053l_bool @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(329,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( C @ ( D @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_f1895971544l_bool ) @ ( D @ ( A @ hAPP_f1895971544l_bool ) @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_fun1555365306t_bool ) @ ( A @ ( C @ pi_fun1555365306t_bool ) @ ( ord_le2143686384l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_503_Pi__mono) ).

thf(1939,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( C @ ( D @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_f1895971544l_bool ) @ ( D @ ( A @ hAPP_f1895971544l_bool ) @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_fun1555365306t_bool ) @ ( A @ ( C @ pi_fun1555365306t_bool ) @ ( ord_le2143686384l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(806,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/sandbox2/benchmark/theBenchmark.p',fact_99_xt1_I10_J) ).

thf(3959,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)],[806]) ).

thf(599,axiom,
    ! [A: $i] :
      ( ( A @ is_fun701126715l_bool )
     => ( ( A @ ( top_to935749874l_bool @ ( ord_le1482529602l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
       => ( A = top_to935749874l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_359_top__le) ).

thf(3098,plain,
    ! [A: $i] :
      ( ( A @ is_fun701126715l_bool )
     => ( ( A @ ( top_to935749874l_bool @ ( ord_le1482529602l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
       => ( A = top_to935749874l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(65,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/sandbox2/benchmark/theBenchmark.p',fact_434_add__less__cancel__left) ).

thf(1073,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)],[65]) ).

thf(100,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/sandbox2/benchmark/theBenchmark.p',fact_552_add__less__mono) ).

thf(1173,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)],[100]) ).

thf(849,axiom,
    ! [A: $i] : ( A @ ( top_to1773227171t_bool @ hAPP_P1813625415t_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_top1I) ).

thf(4105,plain,
    ! [A: $i] : ( A @ ( top_to1773227171t_bool @ hAPP_P1813625415t_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).

thf(628,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_488_equalityD2) ).

thf(3217,plain,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

thf(247,axiom,
    bool @ undefined_bool @ is_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__HOL__Obool) ).

thf(1671,plain,
    bool @ undefined_bool @ is_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(606,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le64728819t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_487_in__mono) ).

thf(3120,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le64728819t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(137,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f387058535l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).

thf(1310,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f387058535l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(846,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( B @ ( C @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
         => ( A @ ( C @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) )
     => ( A @ ( B @ ( ord_le2143686384l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_509_subsetI) ).

thf(4097,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( B @ ( C @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
         => ( A @ ( C @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) )
     => ( A @ ( B @ ( ord_le2143686384l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).

thf(548,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_Arr859726945e_indi )
     => ( ( top_to207207712i_bool @ ( B @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( A @ ( B @ hAPP_A1895296483di_nat ) @ ( B @ ( top_to207207712i_bool @ hilber951314860di_nat ) @ hAPP_n619554777e_indi ) )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_inv__f__f) ).

thf(2918,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_Arr859726945e_indi )
     => ( ( top_to207207712i_bool @ ( B @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( A @ ( B @ hAPP_A1895296483di_nat ) @ ( B @ ( top_to207207712i_bool @ hilber951314860di_nat ) @ hAPP_n619554777e_indi ) )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(465,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1482529602l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_469_set__mp) ).

thf(2448,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1482529602l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(514,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_boo68262458t_bool ) @ ( B @ ( member930088569t_bool @ hAPP_f2134766349l_bool ) @ hAPP_f740740988l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_b651754310l_bool ) @ ( A @ ( B @ hAPP_b327863236t_bool ) @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_PiE) ).

thf(2712,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_boo68262458t_bool ) @ ( B @ ( member930088569t_bool @ hAPP_f2134766349l_bool ) @ hAPP_f740740988l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_b651754310l_bool ) @ ( A @ ( B @ hAPP_b327863236t_bool ) @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(116,axiom,
    ! [A: $i] :
      ~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_617_not__less0) ).

thf(1233,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)],[116]) ).

thf(363,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_n1600508401i_bool ) @ is_fun2015243113i_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsu) ).

thf(2042,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_n1600508401i_bool ) @ is_fun2015243113i_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(390,axiom,
    ! [A: $i] : ( A @ ( ord_less_eq_nat @ ( cOMBC_nat_nat_bool @ hAPP_f229349961t_bool ) @ hAPP_n1699378549t_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_602_finite__Collect__le__nat) ).

thf(2146,plain,
    ! [A: $i] : ( A @ ( ord_less_eq_nat @ ( cOMBC_nat_nat_bool @ hAPP_f229349961t_bool ) @ hAPP_n1699378549t_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(189,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun20916972t_bool )
     => ( B @ ( A @ hAPP_f1332130404l_bool ) @ is_fun701126715l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___036) ).

thf(1458,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun20916972t_bool )
     => ( B @ ( A @ hAPP_f1332130404l_bool ) @ is_fun701126715l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(827,axiom,
    f @ ( arrow_1550141362nimity @ hAPP_f446648900l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_u) ).

thf(4026,plain,
    f @ ( arrow_1550141362nimity @ hAPP_f446648900l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).

thf(583,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_467_set__mp) ).

thf(3044,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(96,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/sandbox2/benchmark/theBenchmark.p',fact_546_not__add__less1) ).

thf(1164,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)],[96]) ).

thf(430,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( F @ is_Arr723427730le_alt )
        & ( E @ is_Arr723427730le_alt )
        & ( D @ is_Arr723427730le_alt )
        & ( C @ is_Arr723427730le_alt ) )
     => ( ( E != F )
       => ( ( C != D )
         => ( ( E != D )
           => ( ( F != C )
             => ( ( arrow_583275979e_Prof @ ( B @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
               => ( ( arrow_583275979e_Prof @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
                 => ( ! [G: $i] :
                        ( ( G @ is_Arr859726945e_indi )
                       => ( ( G @ ( B @ hAPP_A340536322t_bool ) @ ( F @ ( E @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                        <=> ( G @ ( A @ hAPP_A340536322t_bool ) @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) )
                   => ( ( B @ ( f @ hAPP_f1817389232t_bool ) @ ( F @ ( E @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                    <=> ( A @ ( f @ hAPP_f1817389232t_bool ) @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6__C2_C) ).

thf(2316,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( F @ is_Arr723427730le_alt )
        & ( E @ is_Arr723427730le_alt )
        & ( D @ is_Arr723427730le_alt )
        & ( C @ is_Arr723427730le_alt ) )
     => ( ( E != F )
       => ( ( C != D )
         => ( ( E != D )
           => ( ( F != C )
             => ( ( arrow_583275979e_Prof @ ( B @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
               => ( ( arrow_583275979e_Prof @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
                 => ( ! [G: $i] :
                        ( ( G @ is_Arr859726945e_indi )
                       => ( ( ( G @ ( A @ hAPP_A340536322t_bool ) @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                           => ( G @ ( B @ hAPP_A340536322t_bool ) @ ( F @ ( E @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
                          & ( ( G @ ( B @ hAPP_A340536322t_bool ) @ ( F @ ( E @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                           => ( G @ ( A @ hAPP_A340536322t_bool ) @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) )
                   => ( ( ( A @ ( f @ hAPP_f1817389232t_bool ) @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                       => ( B @ ( f @ hAPP_f1817389232t_bool ) @ ( F @ ( E @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
                      & ( ( B @ ( f @ hAPP_f1817389232t_bool ) @ ( F @ ( E @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                       => ( A @ ( f @ hAPP_f1817389232t_bool ) @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(679,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( A != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_order__less__imp__not__eq) ).

thf(3446,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).

thf(670,axiom,
    ! [A: $i] :
      ~ ( A @ ( top_to1773227171t_bool @ ( ord_le2113500159t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_not__top__less) ).

thf(3414,plain,
    ! [A: $i] :
      ~ ( A @ ( top_to1773227171t_bool @ ( ord_le2113500159t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).

thf(688,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1141238780l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_517_psubsetD) ).

thf(3481,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1141238780l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).

thf(60,axiom,
    finite955821396le_alt @ is_fun1420103068l_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Finite__Set_Ofinite_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsun) ).

thf(1063,plain,
    finite955821396le_alt @ is_fun1420103068l_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(531,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/sandbox2/benchmark/theBenchmark.p',fact_533_nat__less__cases) ).

thf(2844,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)],[531]) ).

thf(205,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_1455277858l_bool @ hAPP_f1996228283l_bool ) @ hAPP_f961197973l_bool ) @ hAPP_bool_bool ) )
      = ( B @ ( C @ ( A @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).

thf(1507,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_1455277858l_bool @ hAPP_f1996228283l_bool ) @ hAPP_f961197973l_bool ) @ hAPP_bool_bool ) )
      = ( B @ ( C @ ( A @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(113,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1637334154l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__HOL__Obool_) ).

thf(1222,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1637334154l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(439,axiom,
    ! [A: $i] : ( A @ ( top_to846262053l_bool @ hAPP_f1733357041l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_top1I) ).

thf(2360,plain,
    ! [A: $i] : ( A @ ( top_to846262053l_bool @ hAPP_f1733357041l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(71,axiom,
    top_to935749874l_bool @ is_fun701126715l_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__Arrow____Order____Mira) ).

thf(1095,plain,
    top_to935749874l_bool @ is_fun701126715l_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(731,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2015243113i_bool )
        & ( A @ is_fun2015243113i_bool ) )
     => ( ( A != B )
       => ( ( A @ ( B @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
         => ( A @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_xt1_I12_J) ).

thf(3634,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2015243113i_bool )
        & ( A @ is_fun2015243113i_bool ) )
     => ( ( A != B )
       => ( ( A @ ( B @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
         => ( A @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).

thf(460,axiom,
    ! [A: $i] :
      ( ( A @ ( top_to1257323279t_bool @ hAPP_P1676879539t_bool ) @ hBOOL )
    <=> ( top_top_bool @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_top__apply) ).

thf(2432,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)],[460]) ).

thf(844,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ is_Arr723427730le_alt )
        & ( C @ is_Arr723427730le_alt ) )
     => ( ( C != D )
       => ( ( arrow_583275979e_Prof @ ( B @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
         => ( ( arrow_583275979e_Prof @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
           => ( ! [E: $i] :
                  ( ( E @ is_Arr859726945e_indi )
                 => ( ( E @ ( B @ hAPP_A340536322t_bool ) @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                  <=> ( E @ ( A @ hAPP_A340536322t_bool ) @ ( C @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) )
             => ( ( B @ ( f @ hAPP_f1817389232t_bool ) @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
              <=> ( A @ ( f @ hAPP_f1817389232t_bool ) @ ( C @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10__C3_C) ).

thf(4079,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ is_Arr723427730le_alt )
        & ( C @ is_Arr723427730le_alt ) )
     => ( ( C != D )
       => ( ( arrow_583275979e_Prof @ ( B @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
         => ( ( arrow_583275979e_Prof @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
           => ( ! [E: $i] :
                  ( ( E @ is_Arr859726945e_indi )
                 => ( ( ( E @ ( A @ hAPP_A340536322t_bool ) @ ( C @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                     => ( E @ ( B @ hAPP_A340536322t_bool ) @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
                    & ( ( E @ ( B @ hAPP_A340536322t_bool ) @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                     => ( E @ ( A @ hAPP_A340536322t_bool ) @ ( C @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) )
             => ( ( ( A @ ( f @ hAPP_f1817389232t_bool ) @ ( C @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                 => ( B @ ( f @ hAPP_f1817389232t_bool ) @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
                & ( ( B @ ( f @ hAPP_f1817389232t_bool ) @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                 => ( A @ ( f @ hAPP_f1817389232t_bool ) @ ( C @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).

thf(356,axiom,
    ! [A: $i] :
      ( ( A @ is_fun20916972t_bool )
     => ( A @ collec1376511890le_alt @ is_fun20916972t_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O) ).

thf(2020,plain,
    ! [A: $i] :
      ( ( A @ is_fun20916972t_bool )
     => ( A @ collec1376511890le_alt @ is_fun20916972t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(31,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun701126715l_bool )
     => ( B @ ( A @ hAPP_f1378099862l_bool ) @ is_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__007) ).

thf(973,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun701126715l_bool )
     => ( B @ ( A @ hAPP_f1378099862l_bool ) @ is_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(767,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
      | ~ ( A @ hBOOL )
      | ~ ( B @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).

thf(3809,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
      | ~ ( A @ hBOOL )
      | ~ ( B @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).

thf(449,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_437_equalityI) ).

thf(2400,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(451,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_order__less__asym_H) ).

thf(2405,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(537,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A != B )
       => ( ( D @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
         => ( ( D @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
           => ( ( A @ ( C @ hAPP_nat_nat ) )
             != ( B @ ( C @ hAPP_nat_nat ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_366_inj__on__contraD) ).

thf(2869,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A != B )
       => ( ( D @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
         => ( ( D @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
           => ( ( A @ ( C @ hAPP_nat_nat ) )
             != ( B @ ( C @ hAPP_nat_nat ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(777,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_1399131793t_bool @ hAPP_f1077635369i_bool ) @ ( C @ pi_fun596906370e_indi ) @ ( B @ ( member1935624595e_indi @ hAPP_f2022872455l_bool ) @ hAPP_f1021828400l_bool ) @ hBOOL )
     => ( ( C @ ( B @ inj_on302999388e_indi @ hAPP_f560517119l_bool ) @ hBOOL )
       => ( ( C @ ( cOMBK_350223551e_indi @ hAPP_f1639180358l_bool ) @ ( D @ pi_Arr1801471756t_bool ) @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
         => ( ( D @ ( A @ inj_on1507564774t_bool @ hAPP_f160177134l_bool ) @ hBOOL )
           => ( ( C @ ( finite274731772t_bool @ hAPP_f560517119l_bool ) @ hBOOL )
             => ( ( D @ ( finite921964625e_indi @ hAPP_f160177134l_bool ) @ hBOOL )
               => ( ( C @ finite945540987t_bool )
                  = ( D @ finite354462354e_indi ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_596_card__bij) ).

thf(3836,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_1399131793t_bool @ hAPP_f1077635369i_bool ) @ ( C @ pi_fun596906370e_indi ) @ ( B @ ( member1935624595e_indi @ hAPP_f2022872455l_bool ) @ hAPP_f1021828400l_bool ) @ hBOOL )
     => ( ( C @ ( B @ inj_on302999388e_indi @ hAPP_f560517119l_bool ) @ hBOOL )
       => ( ( C @ ( cOMBK_350223551e_indi @ hAPP_f1639180358l_bool ) @ ( D @ pi_Arr1801471756t_bool ) @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
         => ( ( D @ ( A @ inj_on1507564774t_bool @ hAPP_f160177134l_bool ) @ hBOOL )
           => ( ( C @ ( finite274731772t_bool @ hAPP_f560517119l_bool ) @ hBOOL )
             => ( ( D @ ( finite921964625e_indi @ hAPP_f160177134l_bool ) @ hBOOL )
               => ( ( C @ finite945540987t_bool )
                  = ( D @ finite354462354e_indi ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).

thf(406,axiom,
    ! [A: $i] : ( top_to1257323279t_bool @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_iso__tuple__UNIV__I) ).

thf(2216,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)],[406]) ).

thf(120,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_bool )
     => ( B @ ( A @ hAPP_b1461182872l_bool ) @ is_fun701126715l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabell) ).

thf(1243,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_bool )
     => ( B @ ( A @ hAPP_b1461182872l_bool ) @ is_fun701126715l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(86,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_nat_nat_nat @ hAPP_f416620757at_nat ) @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( B @ ( C @ ( A @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Nat__Onat_U) ).

thf(1127,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_nat_nat_nat @ hAPP_f416620757at_nat ) @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = ( B @ ( C @ ( A @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(411,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
    <=> ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
        & ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_order__eq__iff) ).

thf(2227,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(224,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun1568535512t_bool )
     => ( B @ ( A @ hAPP_P1676879539t_bool ) @ is_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__HOL__Obool) ).

thf(1576,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun1568535512t_bool )
     => ( B @ ( A @ hAPP_P1676879539t_bool ) @ is_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(646,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( produc1456060119le_alt @ ( member720722004le_alt @ cOMBB_711698847le_alt @ cOMBB_885534287le_alt @ hAPP_f1747206697l_bool ) @ ( cOMBC_943734388l_bool @ cOMBB_333235735le_alt @ hAPP_f1092358369t_bool ) @ ( cOMBC_441619036t_bool @ hAPP_f775987425t_bool ) @ hAPP_f1840820673t_bool ) @ ( A @ ( produc1456060119le_alt @ ( member720722004le_alt @ cOMBB_711698847le_alt @ cOMBB_885534287le_alt @ hAPP_f1747206697l_bool ) @ ( cOMBC_943734388l_bool @ cOMBB_333235735le_alt @ hAPP_f1092358369t_bool ) @ ( cOMBC_441619036t_bool @ hAPP_f775987425t_bool ) @ hAPP_f1840820673t_bool ) @ ( ord_le319160163t_bool @ hAPP_f2078760383l_bool ) @ hAPP_f212509069l_bool ) @ hBOOL )
    <=> ( B @ ( A @ ( ord_le64728819t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_405_pred__subset__eq2) ).

thf(3308,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ ( ord_le64728819t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ( B @ ( produc1456060119le_alt @ ( member720722004le_alt @ cOMBB_711698847le_alt @ cOMBB_885534287le_alt @ hAPP_f1747206697l_bool ) @ ( cOMBC_943734388l_bool @ cOMBB_333235735le_alt @ hAPP_f1092358369t_bool ) @ ( cOMBC_441619036t_bool @ hAPP_f775987425t_bool ) @ hAPP_f1840820673t_bool ) @ ( A @ ( produc1456060119le_alt @ ( member720722004le_alt @ cOMBB_711698847le_alt @ cOMBB_885534287le_alt @ hAPP_f1747206697l_bool ) @ ( cOMBC_943734388l_bool @ cOMBB_333235735le_alt @ hAPP_f1092358369t_bool ) @ ( cOMBC_441619036t_bool @ hAPP_f775987425t_bool ) @ hAPP_f1840820673t_bool ) @ ( ord_le319160163t_bool @ hAPP_f2078760383l_bool ) @ hAPP_f212509069l_bool ) @ hBOOL ) )
      & ( ( B @ ( produc1456060119le_alt @ ( member720722004le_alt @ cOMBB_711698847le_alt @ cOMBB_885534287le_alt @ hAPP_f1747206697l_bool ) @ ( cOMBC_943734388l_bool @ cOMBB_333235735le_alt @ hAPP_f1092358369t_bool ) @ ( cOMBC_441619036t_bool @ hAPP_f775987425t_bool ) @ hAPP_f1840820673t_bool ) @ ( A @ ( produc1456060119le_alt @ ( member720722004le_alt @ cOMBB_711698847le_alt @ cOMBB_885534287le_alt @ hAPP_f1747206697l_bool ) @ ( cOMBC_943734388l_bool @ cOMBB_333235735le_alt @ hAPP_f1092358369t_bool ) @ ( cOMBC_441619036t_bool @ hAPP_f775987425t_bool ) @ hAPP_f1840820673t_bool ) @ ( ord_le319160163t_bool @ hAPP_f2078760383l_bool ) @ hAPP_f212509069l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le64728819t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).

thf(856,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( F @ is_Arr723427730le_alt )
        & ( E @ is_Arr723427730le_alt )
        & ( D @ is_Arr723427730le_alt )
        & ( C @ is_Arr723427730le_alt ) )
     => ( ( E != F )
       => ( ( C != D )
         => ( ( E != D )
           => ( ( F != C )
             => ( ( arrow_583275979e_Prof @ ( B @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
               => ( ( arrow_583275979e_Prof @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
                 => ( ! [G: $i] :
                        ( ( G @ is_Arr859726945e_indi )
                       => ( ( G @ ( B @ hAPP_A340536322t_bool ) @ ( F @ ( E @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                        <=> ( G @ ( A @ hAPP_A340536322t_bool ) @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) )
                   => ( ( B @ ( f @ hAPP_f1817389232t_bool ) @ ( F @ ( E @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                     => ( A @ ( f @ hAPP_f1817389232t_bool ) @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7__C1_C) ).

thf(4124,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( F @ is_Arr723427730le_alt )
        & ( E @ is_Arr723427730le_alt )
        & ( D @ is_Arr723427730le_alt )
        & ( C @ is_Arr723427730le_alt ) )
     => ( ( E != F )
       => ( ( C != D )
         => ( ( E != D )
           => ( ( F != C )
             => ( ( arrow_583275979e_Prof @ ( B @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
               => ( ( arrow_583275979e_Prof @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
                 => ( ! [G: $i] :
                        ( ( G @ is_Arr859726945e_indi )
                       => ( ( ( G @ ( A @ hAPP_A340536322t_bool ) @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                           => ( G @ ( B @ hAPP_A340536322t_bool ) @ ( F @ ( E @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
                          & ( ( G @ ( B @ hAPP_A340536322t_bool ) @ ( F @ ( E @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                           => ( G @ ( A @ hAPP_A340536322t_bool ) @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) )
                   => ( ( B @ ( f @ hAPP_f1817389232t_bool ) @ ( F @ ( E @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                     => ( A @ ( f @ hAPP_f1817389232t_bool ) @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).

thf(285,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/sandbox2/benchmark/theBenchmark.p',fact_636_le__SucE) ).

thf(1803,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)],[285]) ).

thf(788,axiom,
    ~ ! [A: $i] :
        ( ( A @ is_fun20916972t_bool )
       => ( ( A @ ( b @ ( a @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
         => ~ ( arrow_912654623le_Lin @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_) ).

thf(3880,plain,
    ~ ! [A: $i] :
        ( ( A @ is_fun20916972t_bool )
       => ( ( A @ ( b @ ( a @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
         => ~ ( arrow_912654623le_Lin @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).

thf(387,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_boo1542163389le_alt ) @ ( B @ ( member300433020le_alt @ hAPP_f452450509l_bool ) @ hAPP_f2053170815l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_b763490121t_bool ) @ ( A @ ( B @ hAPP_b1482008903le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_PiE) ).

thf(2136,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_boo1542163389le_alt ) @ ( B @ ( member300433020le_alt @ hAPP_f452450509l_bool ) @ hAPP_f2053170815l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_b763490121t_bool ) @ ( A @ ( B @ hAPP_b1482008903le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(257,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/sandbox2/benchmark/theBenchmark.p',fact_427_add__le__cancel__left) ).

thf(1703,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)],[257]) ).

thf(238,axiom,
    ! [A: $i] :
      ( ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
    <=> ? [B: $i] :
        ! [C: $i] :
          ( ( A @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
         => ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_608_finite__nat__set__iff__bounded) ).

thf(1623,plain,
    ! [A: $i] :
      ( ( ? [B: $i] :
          ! [C: $i] :
            ( ( A @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
           => ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) )
      & ( ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
       => ? [B: $i] :
          ! [C: $i] :
            ( ( A @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
           => ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(720,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( ( ( B @ hBOOL )
        <=> ( A @ hBOOL ) )
       => ( C @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_xt1_I4_J) ).

thf(3597,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( ( ( ( A @ hBOOL )
           => ( B @ hBOOL ) )
          & ( ( B @ hBOOL )
           => ( A @ hBOOL ) ) )
       => ( C @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).

thf(500,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/sandbox2/benchmark/theBenchmark.p',fact_244_xt1_I4_J) ).

thf(2654,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)],[500]) ).

thf(258,axiom,
    ( one_one_nat
    = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_656_One__nat__def) ).

thf(1709,plain,
    ( one_one_nat
    = ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(526,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_order__less__le__trans) ).

thf(2814,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(637,axiom,
    ! [A: $i] :
      ( ( A @ is_fun20916972t_bool )
     => ( ( A != top_to1773227171t_bool )
      <=> ( top_to1773227171t_bool @ ( A @ ( ord_le2113500159t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_less__top) ).

thf(3275,plain,
    ! [A: $i] :
      ( ( A @ is_fun20916972t_bool )
     => ( ( ( top_to1773227171t_bool @ ( A @ ( ord_le2113500159t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
         => ( A != top_to1773227171t_bool ) )
        & ( ( A != top_to1773227171t_bool )
         => ( top_to1773227171t_bool @ ( A @ ( ord_le2113500159t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(508,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/sandbox2/benchmark/theBenchmark.p',fact_154_linorder__less__linear) ).

thf(2698,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)],[508]) ).

thf(584,axiom,
    ! [A: $i] :
      ( ( A @ is_fun1420103068l_bool )
     => ( ( A @ ( top_to846262053l_bool @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
      <=> ( A = top_to846262053l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_top__unique) ).

thf(3046,plain,
    ! [A: $i] :
      ( ( A @ is_fun1420103068l_bool )
     => ( ( ( A = top_to846262053l_bool )
         => ( A @ ( top_to846262053l_bool @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) )
        & ( ( A @ ( top_to846262053l_bool @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
         => ( A = top_to846262053l_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(693,axiom,
    c != d,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096c_A_126_061_Ad_096) ).

thf(3495,plain,
    c != d,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).

thf(420,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( B @ ( C @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( A @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_order__less__imp__triv) ).

thf(2274,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( B @ ( C @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( A @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(755,axiom,
    ! [A: $i] : ( A @ ( top_to207207712i_bool @ hAPP_A416869060i_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_top1I) ).

thf(3776,plain,
    ! [A: $i] : ( A @ ( top_to207207712i_bool @ hAPP_A416869060i_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).

thf(780,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ hBOOL )
      <=> ( A @ hBOOL ) )
    <=> ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
        & ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_order__eq__iff) ).

thf(3845,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
          & ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) )
       => ( ( ( A @ hBOOL )
           => ( B @ hBOOL ) )
          & ( ( B @ hBOOL )
           => ( A @ hBOOL ) ) ) )
      & ( ( ( ( A @ hBOOL )
           => ( B @ hBOOL ) )
          & ( ( B @ hBOOL )
           => ( A @ hBOOL ) ) )
       => ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
          & ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).

thf(292,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun2015243113i_bool )
     => ( B @ ( A @ hAPP_f1282033109i_bool ) @ is_fun2015243113i_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__005) ).

thf(1832,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun2015243113i_bool )
     => ( B @ ( A @ hAPP_f1282033109i_bool ) @ is_fun2015243113i_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(345,axiom,
    arrow_132732488e_indi @ undefi1052853330e_indi @ is_Arr859726945e_indi,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi) ).

thf(1992,plain,
    arrow_132732488e_indi @ undefi1052853330e_indi @ is_Arr859726945e_indi,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(386,axiom,
    ! [A: $i] :
      ( ! [B: $i] : ( B @ ( A @ hAPP_P1813625415t_bool ) @ hBOOL )
    <=> ! [B: $i,C: $i] :
          ( ( ( C @ is_Arr723427730le_alt )
            & ( B @ is_Arr723427730le_alt ) )
         => ( C @ ( B @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( A @ hAPP_P1813625415t_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_split__paired__All) ).

thf(2126,plain,
    ! [A: $i] :
      ( ( ! [B: $i,C: $i] :
            ( ( ( C @ is_Arr723427730le_alt )
              & ( B @ is_Arr723427730le_alt ) )
           => ( C @ ( B @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( A @ hAPP_P1813625415t_bool ) @ hBOOL ) )
       => ! [B: $i] : ( B @ ( A @ hAPP_P1813625415t_bool ) @ hBOOL ) )
      & ( ! [B: $i] : ( B @ ( A @ hAPP_P1813625415t_bool ) @ hBOOL )
       => ! [B: $i,C: $i] :
            ( ( ( C @ is_Arr723427730le_alt )
              & ( B @ is_Arr723427730le_alt ) )
           => ( C @ ( B @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( A @ hAPP_P1813625415t_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(131,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( suc @ hAPP_nat_nat ) )
        = ( B @ ( suc @ hAPP_nat_nat ) ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_639_nat_Oinject) ).

thf(1287,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)],[131]) ).

thf(629,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1817389232t_bool ) @ is_fun20916972t_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__011) ).

thf(3221,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1817389232t_bool ) @ is_fun20916972t_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(841,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/sandbox2/benchmark/theBenchmark.p',fact_95_order__less__asym) ).

thf(4070,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)],[841]) ).

thf(863,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
    <=> ( A @ ( B @ hAPP_f446648900l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_mem__def) ).

thf(4151,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ hAPP_f446648900l_bool ) @ hBOOL )
       => ( B @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
       => ( A @ ( B @ hAPP_f446648900l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).

thf(305,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/sandbox2/benchmark/theBenchmark.p',fact_554_add__lessD1) ).

thf(1871,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)],[305]) ).

thf(716,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_xt1_I6_J) ).

thf(3574,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).

thf(512,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_order__trans) ).

thf(2708,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(772,axiom,
    ! [A: $i] :
      ( ( A @ ( top_to1773227171t_bool @ hAPP_P1813625415t_bool ) @ hBOOL )
    <=> ( top_top_bool @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_top__apply) ).

thf(3821,plain,
    ! [A: $i] :
      ( ( ( top_top_bool @ hBOOL )
       => ( A @ ( top_to1773227171t_bool @ hAPP_P1813625415t_bool ) @ hBOOL ) )
      & ( ( A @ ( top_to1773227171t_bool @ hAPP_P1813625415t_bool ) @ hBOOL )
       => ( top_top_bool @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).

thf(145,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/sandbox2/benchmark/theBenchmark.p',fact_655_Suc__less__SucD) ).

thf(1330,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)],[145]) ).

thf(464,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( B != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_order__less__imp__not__eq2) ).

thf(2444,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( B != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(724,axiom,
    ! [A: $i] :
      ( ( A @ is_fun2015243113i_bool )
     => ( ( A @ ( top_to207207712i_bool @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
      <=> ( A = top_to207207712i_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_355_top__unique) ).

thf(3612,plain,
    ! [A: $i] :
      ( ( A @ is_fun2015243113i_bool )
     => ( ( ( A = top_to207207712i_bool )
         => ( A @ ( top_to207207712i_bool @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) )
        & ( ( A @ ( top_to207207712i_bool @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
         => ( A = top_to207207712i_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).

thf(736,axiom,
    ! [A: $i] :
      ( ( A @ is_fun2015243113i_bool )
     => ( ( A != top_to207207712i_bool )
      <=> ( top_to207207712i_bool @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_less__top) ).

thf(3653,plain,
    ! [A: $i] :
      ( ( A @ is_fun2015243113i_bool )
     => ( ( ( top_to207207712i_bool @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
         => ( A != top_to207207712i_bool ) )
        & ( ( A != top_to207207712i_bool )
         => ( top_to207207712i_bool @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).

thf(191,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun292781289l_bool )
     => ( B @ ( A @ hAPP_f446648900l_bool ) @ is_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_017) ).

thf(1462,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun292781289l_bool )
     => ( B @ ( A @ hAPP_f446648900l_bool ) @ is_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(88,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/sandbox2/benchmark/theBenchmark.p',fact_548_nat__add__left__cancel__less) ).

thf(1132,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)],[88]) ).

thf(505,axiom,
    ! [A: $i] :
      ( ( A @ is_fun1568535512t_bool )
     => ( ( A @ ( top_to1257323279t_bool @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( A = top_to1257323279t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_362_top__le) ).

thf(2691,plain,
    ! [A: $i] :
      ( ( A @ is_fun1568535512t_bool )
     => ( ( A @ ( top_to1257323279t_bool @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( A = top_to1257323279t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(284,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( cOMBK_583454926ol_nat @ hAPP_f1570313510t_bool ) @ hAPP_n1699378549t_bool ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Nat__Ona) ).

thf(1800,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( cOMBK_583454926ol_nat @ hAPP_f1570313510t_bool ) @ hAPP_n1699378549t_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(854,axiom,
    ! [A: $i] :
      ( ( A @ ( top_top_fun_nat_bool @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( A = top_top_fun_nat_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_361_top__le) ).

thf(4119,plain,
    ! [A: $i] :
      ( ( A @ ( top_top_fun_nat_bool @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( A = top_top_fun_nat_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).

thf(314,axiom,
    ! [A: $i] :
      ( zero_zero_nat
     != ( A @ ( suc @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_678_Zero__not__Suc) ).

thf(1892,plain,
    ! [A: $i] :
      ( zero_zero_nat
     != ( A @ ( suc @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(313,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_bool )
     => ( B @ ( A @ hAPP_b651754310l_bool ) @ is_fun292781289l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order___) ).

thf(1890,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_bool )
     => ( B @ ( A @ hAPP_b651754310l_bool ) @ is_fun292781289l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(197,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/sandbox2/benchmark/theBenchmark.p',fact_432_add__strict__left__mono) ).

thf(1479,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)],[197]) ).

thf(686,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A != B )
       => ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_order__le__neq__trans) ).

thf(3470,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A != B )
       => ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).

thf(569,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( C = A )
       => ( A @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_ord__less__eq__trans) ).

thf(2989,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( C = A )
       => ( A @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(615,axiom,
    ! [A: $i] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_539_le__refl) ).

thf(3180,plain,
    ! [A: $i] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

thf(632,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( E @ is_Arr723427730le_alt )
        & ( D @ is_Arr723427730le_alt )
        & ( B @ is_Arr723427730le_alt )
        & ( A @ is_Arr723427730le_alt ) )
     => ( ( D != E )
       => ( ( arrow_912654623le_Lin @ ( C @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
         => ( ( E @ ( D @ ( C @ ( arrow_1046586475_above @ hAPP_f684072049t_bool ) @ hAPP_A28770973t_bool ) @ hAPP_A1014090479t_bool ) @ ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
          <=> ( ( ( A != E )
               => ( ( ( B != E )
                   => ( C @ ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
                  & ( ( B = E )
                   => ( ( C @ ( D @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                      | ( A = D ) ) ) ) )
              & ( ( A = E )
               => ( C @ ( B @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
              & ( A != B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_in__above) ).

thf(3231,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( E @ is_Arr723427730le_alt )
        & ( D @ is_Arr723427730le_alt )
        & ( B @ is_Arr723427730le_alt )
        & ( A @ is_Arr723427730le_alt ) )
     => ( ( D != E )
       => ( ( arrow_912654623le_Lin @ ( C @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
         => ( ( ( ( ( A != E )
                 => ( ( ( B != E )
                     => ( C @ ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
                    & ( ( B = E )
                     => ( ( C @ ( D @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                        | ( A = D ) ) ) ) )
                & ( ( A = E )
                 => ( C @ ( B @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
                & ( A != B ) )
             => ( E @ ( D @ ( C @ ( arrow_1046586475_above @ hAPP_f684072049t_bool ) @ hAPP_A28770973t_bool ) @ hAPP_A1014090479t_bool ) @ ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
            & ( ( E @ ( D @ ( C @ ( arrow_1046586475_above @ hAPP_f684072049t_bool ) @ hAPP_A28770973t_bool ) @ hAPP_A1014090479t_bool ) @ ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
             => ( ( ( A != E )
                 => ( ( ( B != E )
                     => ( C @ ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
                    & ( ( B = E )
                     => ( ( C @ ( D @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                        | ( A = D ) ) ) ) )
                & ( ( A = E )
                 => ( C @ ( B @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
                & ( A != B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(74,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1841347694t_bool ) @ is_fun1568535512t_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_019) ).

thf(1100,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1841347694t_bool ) @ is_fun1568535512t_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(821,axiom,
    ! [A: $i] : ( A @ ( cOMBI_nat @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_376_inj__on__id2) ).

thf(4008,plain,
    ! [A: $i] : ( A @ ( cOMBI_nat @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).

thf(394,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_order__less__le__trans) ).

thf(2169,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(450,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_order__less__asym_H) ).

thf(2403,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(68,axiom,
    ( top_to1773227171t_bool
    = ( fTrue @ ( cOMBK_1733734784le_alt @ hAPP_b763490121t_bool ) @ collec1376511890le_alt ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_UNIV__def) ).

thf(1087,plain,
    ( top_to1773227171t_bool
    = ( fTrue @ ( cOMBK_1733734784le_alt @ hAPP_b763490121t_bool ) @ collec1376511890le_alt ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(122,axiom,
    arrow_583275979e_Prof @ is_fun701126715l_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Arrow__Order__Mirabelle__wylsunqmtb_OProf) ).

thf(1247,plain,
    arrow_583275979e_Prof @ is_fun701126715l_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(365,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/sandbox2/benchmark/theBenchmark.p',fact_431_add__strict__mono) ).

thf(2049,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)],[365]) ).

thf(29,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/sandbox2/benchmark/theBenchmark.p',fact_433_add__strict__right__mono) ).

thf(969,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)],[29]) ).

thf(443,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( D @ is_Arr859726945e_indi )
         => ( ( C @ ( D @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
           => ( ( D @ ( A @ hAPP_A1895296483di_nat ) )
              = ( D @ ( B @ hAPP_A1895296483di_nat ) ) ) ) )
     => ( ( C @ ( A @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL )
      <=> ( C @ ( B @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_594_inj__on__cong) ).

thf(2373,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( D @ is_Arr859726945e_indi )
         => ( ( C @ ( D @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
           => ( ( D @ ( A @ hAPP_A1895296483di_nat ) )
              = ( D @ ( B @ hAPP_A1895296483di_nat ) ) ) ) )
     => ( ( ( C @ ( B @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL )
         => ( C @ ( A @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL ) )
        & ( ( C @ ( A @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL )
         => ( C @ ( B @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(169,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1082951236l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_022) ).

thf(1398,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1082951236l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(595,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
      <=> ( ( B @ hBOOL )
        <=> ( A @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_order__antisym__conv) ).

thf(3084,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( ( ( ( ( A @ hBOOL )
             => ( B @ hBOOL ) )
            & ( ( B @ hBOOL )
             => ( A @ hBOOL ) ) )
         => ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) )
        & ( ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
         => ( ( ( A @ hBOOL )
             => ( B @ hBOOL ) )
            & ( ( B @ hBOOL )
             => ( A @ hBOOL ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(795,axiom,
    ! [A: $i] : ( top_to935749874l_bool @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_UNIV__I) ).

thf(3902,plain,
    ! [A: $i] : ( top_to935749874l_bool @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).

thf(221,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1291635206l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_020) ).

thf(1568,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1291635206l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(409,axiom,
    ! [A: $i] :
      ~ ( A @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_order__less__irrefl) ).

thf(2222,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(649,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( member_bool @ ( cOMBC_1455277858l_bool @ hAPP_f1996228283l_bool ) @ hAPP_f961197973l_bool ) @ ( A @ ( member_bool @ ( cOMBC_1455277858l_bool @ hAPP_f1996228283l_bool ) @ hAPP_f961197973l_bool ) @ ( ord_le742797417l_bool @ hAPP_f612708895l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
    <=> ( B @ ( A @ ( ord_le742797417l_bool @ hAPP_f612708895l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_493_pred__subset__eq) ).

thf(3322,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ ( ord_le742797417l_bool @ hAPP_f612708895l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ( B @ ( member_bool @ ( cOMBC_1455277858l_bool @ hAPP_f1996228283l_bool ) @ hAPP_f961197973l_bool ) @ ( A @ ( member_bool @ ( cOMBC_1455277858l_bool @ hAPP_f1996228283l_bool ) @ hAPP_f961197973l_bool ) @ ( ord_le742797417l_bool @ hAPP_f612708895l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) )
      & ( ( B @ ( member_bool @ ( cOMBC_1455277858l_bool @ hAPP_f1996228283l_bool ) @ hAPP_f961197973l_bool ) @ ( A @ ( member_bool @ ( cOMBC_1455277858l_bool @ hAPP_f1996228283l_bool ) @ hAPP_f961197973l_bool ) @ ( ord_le742797417l_bool @ hAPP_f612708895l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le742797417l_bool @ hAPP_f612708895l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(702,axiom,
    ! [A: $i] :
      ~ ( A @ ( top_to207207712i_bool @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_not__top__less) ).

thf(3524,plain,
    ! [A: $i] :
      ~ ( A @ ( top_to207207712i_bool @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).

thf(358,axiom,
    ! [A: $i] :
      ( ( A @ is_fun20916972t_bool )
     => ( A @ inj_on398823523t_bool @ is_fun1420103068l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Fun_Oinj__on_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O) ).

thf(2027,plain,
    ! [A: $i] :
      ( ( A @ is_fun20916972t_bool )
     => ( A @ inj_on398823523t_bool @ is_fun1420103068l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(158,axiom,
    fTrue @ is_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_fTrue) ).

thf(1373,plain,
    fTrue @ is_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(853,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( D @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( ( ( B @ ( C @ hAPP_nat_nat ) )
            = A )
         => ( ( A @ ( C @ ( D @ hilber195283148at_nat ) @ hAPP_nat_nat ) )
            = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_387_inv__into__f__eq) ).

thf(4115,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( D @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( ( ( B @ ( C @ hAPP_nat_nat ) )
            = A )
         => ( ( A @ ( C @ ( D @ hilber195283148at_nat ) @ hAPP_nat_nat ) )
            = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).

thf(493,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
       => ( A @ ( B @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_475_set__rev__mp) ).

thf(2616,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
       => ( A @ ( B @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(192,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun20916972t_bool )
     => ( B @ ( A @ hAPP_f1283454584e_indi ) @ is_Arr859726945e_indi ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__) ).

thf(1465,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun20916972t_bool )
     => ( B @ ( A @ hAPP_f1283454584e_indi ) @ is_Arr859726945e_indi ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(842,axiom,
    ~ ! [A: $i] :
        ( ( top_to207207712i_bool @ ( A @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( top_to207207712i_bool @ ( A @ image_837079859di_nat ) )
         != ( top_to207207712i_bool @ finite354462354e_indi @ ( zero_zero_nat @ ord_at4362885an_nat @ hAPP_n1699378549t_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_698__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_123) ).

thf(4072,plain,
    ~ ! [A: $i] :
        ( ( top_to207207712i_bool @ ( A @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( top_to207207712i_bool @ ( A @ image_837079859di_nat ) )
         != ( top_to207207712i_bool @ finite354462354e_indi @ ( zero_zero_nat @ ord_at4362885an_nat @ hAPP_n1699378549t_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).

thf(288,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/sandbox2/benchmark/theBenchmark.p',fact_418_add__right__cancel) ).

thf(1811,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)],[288]) ).

thf(185,axiom,
    top_to207207712i_bool @ finite354462354e_indi @ ( n @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_n_I1_J) ).

thf(1450,plain,
    top_to207207712i_bool @ finite354462354e_indi @ ( n @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(824,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( C @ ( D @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_P1122857141l_bool ) @ ( D @ ( A @ hAPP_P1122857141l_bool ) @ ( ord_le742797417l_bool @ hAPP_f612708895l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_Pro1873779901t_bool ) @ ( A @ ( C @ pi_Pro1873779901t_bool ) @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_501_Pi__mono) ).

thf(4018,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( C @ ( D @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_P1122857141l_bool ) @ ( D @ ( A @ hAPP_P1122857141l_bool ) @ ( ord_le742797417l_bool @ hAPP_f612708895l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_Pro1873779901t_bool ) @ ( A @ ( C @ pi_Pro1873779901t_bool ) @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).

thf(665,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_fun1390764464t_unit ) @ ( B @ ( member1941767151t_unit @ hAPP_f1957108621l_bool ) @ hAPP_f966397426l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_f1841347694t_bool ) @ ( A @ ( B @ hAPP_f1716204858t_unit ) @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_PiE) ).

thf(3393,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_fun1390764464t_unit ) @ ( B @ ( member1941767151t_unit @ hAPP_f1957108621l_bool ) @ hAPP_f966397426l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_f1841347694t_bool ) @ ( A @ ( B @ hAPP_f1716204858t_unit ) @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).

thf(78,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun20916972t_bool )
     => ( B @ ( A @ hAPP_P1813625415t_bool ) @ is_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__039) ).

thf(1109,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun20916972t_bool )
     => ( B @ ( A @ hAPP_P1813625415t_bool ) @ is_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(542,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun1568535512t_bool )
        & ( A @ is_fun1568535512t_bool ) )
     => ( ( A != B )
       => ( ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
         => ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_order__neq__le__trans) ).

thf(2893,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun1568535512t_bool )
        & ( A @ is_fun1568535512t_bool ) )
     => ( ( A != B )
       => ( ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
         => ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(703,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_order__le__less__trans) ).

thf(3527,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).

thf(687,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ~ ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
         => ~ ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_461_equalityE) ).

thf(3473,plain,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ~ ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
         => ~ ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).

thf(814,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_xt1_I9_J) ).

thf(3983,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).

thf(677,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
    <=> ( A @ ( B @ hAPP_A416869060i_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_mem__def) ).

thf(3438,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ hAPP_A416869060i_bool ) @ hBOOL )
       => ( B @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( A @ ( B @ hAPP_A416869060i_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).

thf(384,axiom,
    ! [A: $i] : ( A @ ( ord_less_nat @ ( cOMBC_nat_nat_bool @ hAPP_f229349961t_bool ) @ hAPP_n1699378549t_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_601_finite__Collect__less__nat) ).

thf(2122,plain,
    ! [A: $i] : ( A @ ( ord_less_nat @ ( cOMBC_nat_nat_bool @ hAPP_f229349961t_bool ) @ hAPP_n1699378549t_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(726,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_459_subset__psubset__trans) ).

thf(3621,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).

thf(550,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/sandbox2/benchmark/theBenchmark.p',fact_528_nat__neq__iff) ).

thf(2925,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)],[550]) ).

thf(810,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_xt1_I10_J) ).

thf(3973,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).

thf(92,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_1015721476ol_nat @ hAPP_f1146629647l_bool ) @ hAPP_n1006566506l_bool ) )
      = ( C @ ( B @ hAPP_nat_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).

thf(1151,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_1015721476ol_nat @ hAPP_f1146629647l_bool ) @ hAPP_n1006566506l_bool ) )
      = ( C @ ( B @ hAPP_nat_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(17,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_n454528608t_bool ) @ is_fun1568535512t_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obo) ).

thf(937,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_n454528608t_bool ) @ is_fun1568535512t_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(427,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( member1265098019t_bool @ ( cOMBC_1722249314l_bool @ hAPP_f1500902601l_bool ) @ hAPP_f189058133l_bool ) @ ( A @ ( member1265098019t_bool @ ( cOMBC_1722249314l_bool @ hAPP_f1500902601l_bool ) @ hAPP_f189058133l_bool ) @ ( ord_le1482529602l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
    <=> ( B @ ( A @ ( ord_le1482529602l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_499_pred__subset__eq) ).

thf(2291,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ ( ord_le1482529602l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
       => ( B @ ( member1265098019t_bool @ ( cOMBC_1722249314l_bool @ hAPP_f1500902601l_bool ) @ hAPP_f189058133l_bool ) @ ( A @ ( member1265098019t_bool @ ( cOMBC_1722249314l_bool @ hAPP_f1500902601l_bool ) @ hAPP_f189058133l_bool ) @ ( ord_le1482529602l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) )
      & ( ( B @ ( member1265098019t_bool @ ( cOMBC_1722249314l_bool @ hAPP_f1500902601l_bool ) @ hAPP_f189058133l_bool ) @ ( A @ ( member1265098019t_bool @ ( cOMBC_1722249314l_bool @ hAPP_f1500902601l_bool ) @ hAPP_f189058133l_bool ) @ ( ord_le1482529602l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le1482529602l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(163,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f783549695i_bool ) @ is_fun2015243113i_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_018) ).

thf(1383,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f783549695i_bool ) @ is_fun2015243113i_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(417,axiom,
    ! [A: $i] : ( A @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_order__refl) ).

thf(2254,plain,
    ! [A: $i] : ( A @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(643,axiom,
    ! [A: $i] :
      ( ( n @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( lba @ ( lab @ ( A @ ( h @ ( ord_less_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ ( cOMBC_1373788917t_bool @ hAPP_f1283354413t_bool ) @ hAPP_f1898540574t_bool ) @ ( cOMBC_1894996001t_bool @ hAPP_f1975142533t_bool ) @ hAPP_f590186314t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( a @ ( b @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_n_I2_J) ).

thf(3300,plain,
    ! [A: $i] :
      ( ( n @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( lba @ ( lab @ ( A @ ( h @ ( ord_less_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ ( cOMBC_1373788917t_bool @ hAPP_f1283354413t_bool ) @ hAPP_f1898540574t_bool ) @ ( cOMBC_1894996001t_bool @ hAPP_f1975142533t_bool ) @ hAPP_f590186314t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( a @ ( b @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(801,axiom,
    arrow_583275979e_Prof @ ( e @ ( p @ ( arrow_163947511_mkbot @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( e @ ( c @ ( p @ ( arrow_1046586475_above @ cOMBB_930893948e_indi @ hAPP_f1044120523t_bool ) @ ( cOMBC_1377016489t_bool @ hAPP_f114580065t_bool ) @ hAPP_A711952286t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( e @ ( p @ ( arrow_312654597_mktop @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/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(3923,plain,
    arrow_583275979e_Prof @ ( e @ ( p @ ( arrow_163947511_mkbot @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( e @ ( c @ ( p @ ( arrow_1046586475_above @ cOMBB_930893948e_indi @ hAPP_f1044120523t_bool ) @ ( cOMBC_1377016489t_bool @ hAPP_f114580065t_bool ) @ hAPP_A711952286t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( e @ ( p @ ( arrow_312654597_mktop @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).

thf(336,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P1645359566e_indi ) @ is_Arr859726945e_indi ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc_) ).

thf(1960,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P1645359566e_indi ) @ is_Arr859726945e_indi ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(482,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/sandbox2/benchmark/theBenchmark.p',fact_253_ord__eq__le__trans) ).

thf(2555,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)],[482]) ).

thf(641,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( cOMBK_583454926ol_nat @ hAPP_f1570313510t_bool ) @ ( B @ pi_nat_nat ) @ ( A @ ( member_fun_nat_nat @ hAPP_f2040535501l_bool ) @ hAPP_f1426445843l_bool ) @ hBOOL )
     => ( ( B @ ( A @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
         => ( C @ finite_card_nat @ ( B @ finite_card_nat @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_586_card__inj) ).

thf(3290,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( cOMBK_583454926ol_nat @ hAPP_f1570313510t_bool ) @ ( B @ pi_nat_nat ) @ ( A @ ( member_fun_nat_nat @ hAPP_f2040535501l_bool ) @ hAPP_f1426445843l_bool ) @ hBOOL )
     => ( ( B @ ( A @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
         => ( C @ finite_card_nat @ ( B @ finite_card_nat @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

thf(104,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/sandbox2/benchmark/theBenchmark.p',fact_323_order__less__le__trans) ).

thf(1183,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)],[104]) ).

thf(372,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ is_Arr723427730le_alt )
        & ( B @ is_Arr723427730le_alt )
        & ( A @ is_fun20916972t_bool ) )
     => ( C @ ( B @ ( A @ in_rel1361124802le_alt ) ) @ is_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_FunDef_Oin__rel_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000) ).

thf(2073,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ is_Arr723427730le_alt )
        & ( B @ is_Arr723427730le_alt )
        & ( A @ is_fun20916972t_bool ) )
     => ( C @ ( B @ ( A @ in_rel1361124802le_alt ) ) @ is_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(355,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ hAPP_A416869060i_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A1948275303t_bool ) @ hAPP_nat_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000) ).

thf(2017,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ hAPP_A416869060i_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A1948275303t_bool ) @ hAPP_nat_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(9,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1138659662l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_021) ).

thf(905,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1138659662l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(472,axiom,
    lba @ ( lab @ ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( h @ ( ord_less_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ ( cOMBC_1373788917t_bool @ hAPP_f1283354413t_bool ) @ hAPP_f1898540574t_bool ) @ ( cOMBC_1894996001t_bool @ hAPP_f1975142533t_bool ) @ hAPP_f590186314t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( b @ ( a @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_n_I3_J) ).

thf(2508,plain,
    lba @ ( lab @ ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( h @ ( ord_less_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ ( cOMBC_1373788917t_bool @ hAPP_f1283354413t_bool ) @ hAPP_f1898540574t_bool ) @ ( cOMBC_1894996001t_bool @ hAPP_f1975142533t_bool ) @ hAPP_f590186314t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( b @ ( a @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(98,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/sandbox2/benchmark/theBenchmark.p',fact_666_less__add__Suc1) ).

thf(1169,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)],[98]) ).

thf(161,axiom,
    ! [A: $i] :
      ( ( A @ ( ord_less_eq_nat @ ( cOMBC_nat_nat_bool @ hAPP_f229349961t_bool ) @ hAPP_n1699378549t_bool ) @ collect_nat @ finite_card_nat )
      = ( A @ ( suc @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_680_card__Collect__le__nat) ).

thf(1377,plain,
    ! [A: $i] :
      ( ( A @ ( ord_less_eq_nat @ ( cOMBC_nat_nat_bool @ hAPP_f229349961t_bool ) @ hAPP_n1699378549t_bool ) @ collect_nat @ finite_card_nat )
      = ( A @ ( suc @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(110,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun2015243113i_bool )
     => ( B @ ( A @ pi_Arr1801471756t_bool ) @ is_fun701126715l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc_) ).

thf(1215,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun2015243113i_bool )
     => ( B @ ( A @ pi_Arr1801471756t_bool ) @ is_fun701126715l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(24,axiom,
    ( top_to1849101472l_bool
    = ( fTrue @ ( cOMBK_577652221t_bool @ hAPP_b651754310l_bool ) @ collec1517527055t_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_UNIV__def) ).

thf(956,plain,
    ( top_to1849101472l_bool
    = ( fTrue @ ( cOMBK_577652221t_bool @ hAPP_b651754310l_bool ) @ collec1517527055t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(311,axiom,
    ! [A: $i] :
      ( ( A @ is_fun2015243113i_bool )
     => ( A @ collec279390863e_indi @ is_fun2015243113i_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi) ).

thf(1886,plain,
    ! [A: $i] :
      ( ( A @ is_fun2015243113i_bool )
     => ( A @ collec279390863e_indi @ is_fun2015243113i_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(766,axiom,
    top_to207207712i_bool @ ( finite921964625e_indi @ hAPP_f160177134l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_595_finite__indi) ).

thf(3808,plain,
    top_to207207712i_bool @ ( finite921964625e_indi @ hAPP_f160177134l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).

thf(330,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f557371893l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl_032) ).

thf(1943,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f557371893l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(562,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/sandbox2/benchmark/theBenchmark.p',fact_529_linorder__neqE__nat) ).

thf(2965,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)],[562]) ).

thf(233,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
         => ( A @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
     => ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_507_subsetI) ).

thf(1600,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
         => ( A @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
     => ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(254,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/sandbox2/benchmark/theBenchmark.p',fact_286_not__leE) ).

thf(1697,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)],[254]) ).

thf(882,axiom,
    ! [A: $i] :
      ( ( A != top_top_fun_nat_bool )
    <=> ( top_top_fun_nat_bool @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_less__top) ).

thf(4211,plain,
    ! [A: $i] :
      ( ( ( top_top_fun_nat_bool @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A != top_top_fun_nat_bool ) )
      & ( ( A != top_top_fun_nat_bool )
       => ( top_top_fun_nat_bool @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).

thf(219,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1009478556t_bool ) @ is_fun1568535512t_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__009) ).

thf(1564,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1009478556t_bool ) @ is_fun1568535512t_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(520,axiom,
    ! [A: $i,B: $i] :
      ( ( A != B )
     => ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_xt1_I12_J) ).

thf(2762,plain,
    ! [A: $i,B: $i] :
      ( ( A != B )
     => ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(830,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_nat1476290531e_indi ) @ ( B @ ( member1801639028e_indi @ hAPP_f544923081l_bool ) @ hAPP_f1428735377l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_n1600508401i_bool ) @ ( A @ ( B @ hAPP_n619554777e_indi ) @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_PiE) ).

thf(4033,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_nat1476290531e_indi ) @ ( B @ ( member1801639028e_indi @ hAPP_f544923081l_bool ) @ hAPP_f1428735377l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_n1600508401i_bool ) @ ( A @ ( B @ hAPP_n619554777e_indi ) @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).

thf(494,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( C @ ( D @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_f1895971544l_bool ) @ ( D @ ( A @ hAPP_f1817389232t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_fun1555365306t_bool ) @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_391_Pi__I) ).

thf(2618,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( C @ ( D @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_f1895971544l_bool ) @ ( D @ ( A @ hAPP_f1817389232t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_fun1555365306t_bool ) @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(315,axiom,
    ! [A: $i] :
      ( ( top_to846262053l_bool @ ( cOMBK_350223551e_indi @ hAPP_f1639180358l_bool ) @ ( A @ pi_Arr1801471756t_bool ) )
      = top_to935749874l_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_Pi__UNIV) ).

thf(1896,plain,
    ! [A: $i] :
      ( ( top_to846262053l_bool @ ( cOMBK_350223551e_indi @ hAPP_f1639180358l_bool ) @ ( A @ pi_Arr1801471756t_bool ) )
      = top_to935749874l_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(399,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( A @ ( B @ pi_Arr1801471756t_bool ) @ ( A @ ( C @ pi_Arr1801471756t_bool ) @ ( ord_le1482529602l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_403_Pi__anti__mono) ).

thf(2190,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( A @ ( B @ pi_Arr1801471756t_bool ) @ ( A @ ( C @ pi_Arr1801471756t_bool ) @ ( ord_le1482529602l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(457,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_fun1353458625e_indi ) @ ( B @ ( member234310528e_indi @ hAPP_f749156301l_bool ) @ hAPP_f742658307l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_f783549695i_bool ) @ ( A @ ( B @ hAPP_f2043811403e_indi ) @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_PiE) ).

thf(2424,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_fun1353458625e_indi ) @ ( B @ ( member234310528e_indi @ hAPP_f749156301l_bool ) @ hAPP_f742658307l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_f783549695i_bool ) @ ( A @ ( B @ hAPP_f2043811403e_indi ) @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(442,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_481_in__mono) ).

thf(2371,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(167,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun2015243113i_bool )
     => ( B @ ( A @ hAPP_f160177134l_bool ) @ is_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc_) ).

thf(1394,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun2015243113i_bool )
     => ( B @ ( A @ hAPP_f160177134l_bool ) @ is_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(523,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( E @ is_Arr723427730le_alt )
        & ( D @ is_Arr723427730le_alt )
        & ( B @ is_Arr723427730le_alt )
        & ( A @ is_Arr723427730le_alt ) )
     => ( ( D != E )
       => ( ( arrow_912654623le_Lin @ ( C @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
         => ( ( E @ ( D @ ( C @ arrow_207701375_below ) ) @ ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
          <=> ( ( ( B != D )
               => ( ( ( A != D )
                   => ( C @ ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
                  & ( ( A = D )
                   => ( ( C @ ( B @ ( E @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                      | ( B = E ) ) ) ) )
              & ( ( B = D )
               => ( C @ ( E @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
              & ( A != B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_523_in__below) ).

thf(2772,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( E @ is_Arr723427730le_alt )
        & ( D @ is_Arr723427730le_alt )
        & ( B @ is_Arr723427730le_alt )
        & ( A @ is_Arr723427730le_alt ) )
     => ( ( D != E )
       => ( ( arrow_912654623le_Lin @ ( C @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
         => ( ( ( ( ( B != D )
                 => ( ( ( A != D )
                     => ( C @ ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
                    & ( ( A = D )
                     => ( ( C @ ( B @ ( E @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                        | ( B = E ) ) ) ) )
                & ( ( B = D )
                 => ( C @ ( E @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
                & ( A != B ) )
             => ( E @ ( D @ ( C @ arrow_207701375_below ) ) @ ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
            & ( ( E @ ( D @ ( C @ arrow_207701375_below ) ) @ ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
             => ( ( ( B != D )
                 => ( ( ( A != D )
                     => ( C @ ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
                    & ( ( A = D )
                     => ( ( C @ ( B @ ( E @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                        | ( B = E ) ) ) ) )
                & ( ( B = D )
                 => ( C @ ( E @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
                & ( A != B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(612,axiom,
    ! [A: $i] :
      ( ( A @ is_fun1568535512t_bool )
     => ( ( A != top_to1257323279t_bool )
      <=> ( top_to1257323279t_bool @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_less__top) ).

thf(3157,plain,
    ! [A: $i] :
      ( ( A @ is_fun1568535512t_bool )
     => ( ( ( top_to1257323279t_bool @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
         => ( A != top_to1257323279t_bool ) )
        & ( ( A != top_to1257323279t_bool )
         => ( top_to1257323279t_bool @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

thf(655,axiom,
    ! [A: $i] :
      ( ( A @ is_fun1420103068l_bool )
     => ( ( A @ ( top_to846262053l_bool @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
       => ( A = top_to846262053l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_357_top__le) ).

thf(3361,plain,
    ! [A: $i] :
      ( ( A @ is_fun1420103068l_bool )
     => ( ( A @ ( top_to846262053l_bool @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
       => ( A = top_to846262053l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).

thf(350,axiom,
    arrow_885770895le_IIA @ is_fun292781289l_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Arrow__Order__Mirabelle__wylsunqmtb_OIIA) ).

thf(2002,plain,
    arrow_885770895le_IIA @ is_fun292781289l_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(38,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/sandbox2/benchmark/theBenchmark.p',fact_565_trans__le__add2) ).

thf(998,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)],[38]) ).

thf(722,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_xt1_I8_J) ).

thf(3606,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).

thf(626,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( C = A )
       => ( A @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_ord__less__eq__trans) ).

thf(3211,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( C = A )
       => ( A @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(392,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A = B )
        | ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_order__le__imp__less__or__eq) ).

thf(2154,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A = B )
        | ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(303,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_333235735le_alt @ hAPP_f1092358369t_bool ) @ hAPP_A64811457t_bool ) )
      = ( C @ ( B @ hAPP_A643475905l_bool ) @ ( A @ hAPP_f372913425t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb___054) ).

thf(1863,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_333235735le_alt @ hAPP_f1092358369t_bool ) @ hAPP_A64811457t_bool ) )
      = ( C @ ( B @ hAPP_A643475905l_bool ) @ ( A @ hAPP_f372913425t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(245,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/sandbox2/benchmark/theBenchmark.p',fact_668_add__is__1) ).

thf(1651,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)],[245]) ).

thf(352,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/sandbox2/benchmark/theBenchmark.p',fact_430_add__less__imp__less__right) ).

thf(2011,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)],[352]) ).

thf(718,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
    <=> ( ~ ( A @ ( B @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
        & ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_less__le__not__le) ).

thf(3582,plain,
    ! [A: $i,B: $i] :
      ( ( ( ~ ( A @ ( B @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ~ ( A @ ( B @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).

thf(13,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/sandbox2/benchmark/theBenchmark.p',fact_422_add__le__imp__le__left) ).

thf(920,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)],[13]) ).

thf(680,axiom,
    ! [A: $i] : ( top_top_fun_nat_bool @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_UNIV__I) ).

thf(3450,plain,
    ! [A: $i] : ( top_top_fun_nat_bool @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).

thf(15,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/sandbox2/benchmark/theBenchmark.p',fact_658_le__less__Suc__eq) ).

thf(925,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)],[15]) ).

thf(148,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/sandbox2/benchmark/theBenchmark.p',fact_642_add__Suc__shift) ).

thf(1338,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)],[148]) ).

thf(818,axiom,
    ! [A: $i] :
      ( ( A @ is_fun292781289l_bool )
     => ( ( A @ ( top_to1849101472l_bool @ ( ord_le2143686384l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
      <=> ( A = top_to1849101472l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_top__unique) ).

thf(3995,plain,
    ! [A: $i] :
      ( ( A @ is_fun292781289l_bool )
     => ( ( ( A = top_to1849101472l_bool )
         => ( A @ ( top_to1849101472l_bool @ ( ord_le2143686384l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) )
        & ( ( A @ ( top_to1849101472l_bool @ ( ord_le2143686384l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
         => ( A = top_to1849101472l_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).

thf(497,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( A != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_order__less__imp__not__eq) ).

thf(2641,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(502,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
    <=> ( ~ ( ( A @ hBOOL )
          <=> ( B @ hBOOL ) )
        & ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_order__less__le) ).

thf(2660,plain,
    ! [A: $i,B: $i] :
      ( ( ( ~ ( ( ( B @ hBOOL )
               => ( A @ hBOOL ) )
              & ( ( A @ hBOOL )
               => ( B @ hBOOL ) ) )
          & ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
       => ( ~ ( ( ( B @ hBOOL )
               => ( A @ hBOOL ) )
              & ( ( A @ hBOOL )
               => ( B @ hBOOL ) ) )
          & ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(349,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_350223551e_indi @ hAPP_f1639180358l_bool ) @ ( C @ pi_Arr1801471756t_bool ) @ ( B @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_A340536322t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_378_funcset__mem) ).

thf(2000,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_350223551e_indi @ hAPP_f1639180358l_bool ) @ ( C @ pi_Arr1801471756t_bool ) @ ( B @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_A340536322t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(234,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_bool )
     => ( B @ ( A @ hAPP_b763490121t_bool ) @ is_fun20916972t_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabel) ).

thf(1604,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_bool )
     => ( B @ ( A @ hAPP_b763490121t_bool ) @ is_fun20916972t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(549,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/sandbox2/benchmark/theBenchmark.p',fact_241_order__antisym) ).

thf(2922,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)],[549]) ).

thf(753,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( member720722004le_alt @ ( cOMBC_420816290l_bool @ hAPP_f1152614183t_bool ) @ hAPP_f137597973t_bool ) @ ( A @ ( member720722004le_alt @ ( cOMBC_420816290l_bool @ hAPP_f1152614183t_bool ) @ hAPP_f137597973t_bool ) @ ( ord_le64728819t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
    <=> ( B @ ( A @ ( ord_le64728819t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_500_pred__subset__eq) ).

thf(3767,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ ( ord_le64728819t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ( B @ ( member720722004le_alt @ ( cOMBC_420816290l_bool @ hAPP_f1152614183t_bool ) @ hAPP_f137597973t_bool ) @ ( A @ ( member720722004le_alt @ ( cOMBC_420816290l_bool @ hAPP_f1152614183t_bool ) @ hAPP_f137597973t_bool ) @ ( ord_le64728819t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
      & ( ( B @ ( member720722004le_alt @ ( cOMBC_420816290l_bool @ hAPP_f1152614183t_bool ) @ hAPP_f137597973t_bool ) @ ( A @ ( member720722004le_alt @ ( cOMBC_420816290l_bool @ hAPP_f1152614183t_bool ) @ hAPP_f137597973t_bool ) @ ( ord_le64728819t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le64728819t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).

thf(586,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_454_psubset__imp__subset) ).

thf(3054,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(375,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/sandbox2/benchmark/theBenchmark.p',fact_420_ab__semigroup__add__class_Oadd__ac_I1_J) ).

thf(2083,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)],[375]) ).

thf(829,axiom,
    ! [A: $i] : ( A @ ( top_to935749874l_bool @ hAPP_f1378099862l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_top1I) ).

thf(4031,plain,
    ! [A: $i] : ( A @ ( top_to935749874l_bool @ hAPP_f1378099862l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).

thf(267,axiom,
    ! [A: $i] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_612_le0) ).

thf(1736,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)],[267]) ).

thf(128,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/sandbox2/benchmark/theBenchmark.p',fact_648_not__less__less__Suc__eq) ).

thf(1274,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)],[128]) ).

thf(453,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( C @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
         => ( ( D @ ( A @ hAPP_nat_nat ) )
            = ( D @ ( B @ hAPP_nat_nat ) ) ) )
     => ( ( C @ ( A @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
      <=> ( C @ ( B @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_593_inj__on__cong) ).

thf(2409,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( C @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
         => ( ( D @ ( A @ hAPP_nat_nat ) )
            = ( D @ ( B @ hAPP_nat_nat ) ) ) )
     => ( ( ( C @ ( B @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
         => ( C @ ( A @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL ) )
        & ( ( C @ ( A @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
         => ( C @ ( B @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(721,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_885534287le_alt @ hAPP_f1747206697l_bool ) @ hAPP_A643475905l_bool ) )
      = ( C @ ( B @ hAPP_A1171966089le_alt ) @ ( A @ hAPP_f1656652505l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__) ).

thf(3603,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_885534287le_alt @ hAPP_f1747206697l_bool ) @ hAPP_A643475905l_bool ) )
      = ( C @ ( B @ hAPP_A1171966089le_alt ) @ ( A @ hAPP_f1656652505l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).

thf(488,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( ( A @ ( C @ hAPP_nat_nat ) )
          = ( B @ ( C @ hAPP_nat_nat ) ) )
       => ( ( D @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
         => ( ( D @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
           => ( A = B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_370_inj__onD) ).

thf(2596,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( ( A @ ( C @ hAPP_nat_nat ) )
          = ( B @ ( C @ hAPP_nat_nat ) ) )
       => ( ( D @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
         => ( ( D @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
           => ( A = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(155,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/sandbox2/benchmark/theBenchmark.p',fact_556_le__eq__less__or__eq) ).

thf(1355,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)],[155]) ).

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_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/sandbox2/benchmark/theBenchmark.p',fact_428_add__le__cancel__right) ).

thf(1487,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)],[199]) ).

thf(747,axiom,
    ! [A: $i] :
      ( ( A @ ( top_top_bool @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
    <=> ( ( A @ hBOOL )
      <=> ( top_top_bool @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_top__unique) ).

thf(3742,plain,
    ! [A: $i] :
      ( ( ( ( ( top_top_bool @ hBOOL )
           => ( A @ hBOOL ) )
          & ( ( A @ hBOOL )
           => ( top_top_bool @ hBOOL ) ) )
       => ( A @ ( top_top_bool @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) )
      & ( ( A @ ( top_top_bool @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
       => ( ( ( top_top_bool @ hBOOL )
           => ( A @ hBOOL ) )
          & ( ( A @ hBOOL )
           => ( top_top_bool @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).

thf(879,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro831923248t_bool ) @ ( B @ ( member1775405935t_bool @ hAPP_f627309453l_bool ) @ hAPP_f1597773170l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P1305865168l_bool ) @ ( A @ ( B @ hAPP_P1157363642t_bool ) @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_PiE) ).

thf(4204,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro831923248t_bool ) @ ( B @ ( member1775405935t_bool @ hAPP_f627309453l_bool ) @ hAPP_f1597773170l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P1305865168l_bool ) @ ( A @ ( B @ hAPP_P1157363642t_bool ) @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).

thf(609,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_order__less__le__trans) ).

thf(3134,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(477,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/sandbox2/benchmark/theBenchmark.p',fact_155_not__less__iff__gr__or__eq) ).

thf(2528,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)],[477]) ).

thf(487,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
    <=> ( ~ ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
        & ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_less__le__not__le) ).

thf(2589,plain,
    ! [A: $i,B: $i] :
      ( ( ( ~ ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( ~ ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(744,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/sandbox2/benchmark/theBenchmark.p',fact_383_injD) ).

thf(3735,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)],[744]) ).

thf(773,axiom,
    ! [A: $i] : ( top_to1849101472l_bool @ ( A @ ( ord_le2143686384l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_407_subset__UNIV) ).

thf(3827,plain,
    ! [A: $i] : ( top_to1849101472l_bool @ ( A @ ( ord_le2143686384l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).

thf(459,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_ord__eq__le__trans) ).

thf(2428,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(150,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/sandbox2/benchmark/theBenchmark.p',fact_643_add__Suc) ).

thf(1343,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)],[150]) ).

thf(823,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_order__le__less__trans) ).

thf(4016,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).

thf(54,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_Arr723427730le_alt )
     => ( B @ ( A @ hAPP_A1014090479t_bool ) @ is_fun20916972t_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__fun_Itc_001) ).

thf(1042,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_Arr723427730le_alt )
     => ( B @ ( A @ hAPP_A1014090479t_bool ) @ is_fun20916972t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(22,axiom,
    ! [A: $i] :
      ( ( A @ is_fun1420103068l_bool )
     => ( A @ collec612883262t_bool @ is_fun1420103068l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyls) ).

thf(952,plain,
    ! [A: $i] :
      ( ( A @ is_fun1420103068l_bool )
     => ( A @ collec612883262t_bool @ is_fun1420103068l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(222,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/sandbox2/benchmark/theBenchmark.p',fact_309_order__le__imp__less__or__eq) ).

thf(1570,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)],[222]) ).

thf(249,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ! [E: $i] :
          ( ( E @ is_Arr859726945e_indi )
         => ( ( D @ ( E @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
           => ( ( E @ ( B @ hAPP_A340536322t_bool ) )
              = ( E @ ( C @ hAPP_A340536322t_bool ) ) ) ) )
     => ( ( A @ ( D @ pi_Arr1801471756t_bool ) @ ( B @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
      <=> ( A @ ( D @ pi_Arr1801471756t_bool ) @ ( C @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_581_Pi__cong) ).

thf(1676,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ! [E: $i] :
          ( ( E @ is_Arr859726945e_indi )
         => ( ( D @ ( E @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
           => ( ( E @ ( B @ hAPP_A340536322t_bool ) )
              = ( E @ ( C @ hAPP_A340536322t_bool ) ) ) ) )
     => ( ( ( A @ ( D @ pi_Arr1801471756t_bool ) @ ( C @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
         => ( A @ ( D @ pi_Arr1801471756t_bool ) @ ( B @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) )
        & ( ( A @ ( D @ pi_Arr1801471756t_bool ) @ ( B @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
         => ( A @ ( D @ pi_Arr1801471756t_bool ) @ ( C @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(624,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_boo1746012499t_bool ) @ ( B @ ( member1258284266t_bool @ hAPP_f840347317l_bool ) @ hAPP_f937100551l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_b805997823l_bool ) @ ( A @ ( B @ hAPP_b763490121t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_PiE) ).

thf(3207,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_boo1746012499t_bool ) @ ( B @ ( member1258284266t_bool @ hAPP_f840347317l_bool ) @ hAPP_f937100551l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_b805997823l_bool ) @ ( A @ ( B @ hAPP_b763490121t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(700,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] : ( C @ ( B @ hAPP_nat_nat ) @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( B @ ( ord_less_eq_nat @ cOMBB_800536526ol_nat @ hAPP_f618557131t_bool ) @ ( cOMBC_nat_nat_bool @ hAPP_f229349961t_bool ) @ hAPP_n1699378549t_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_609_finite__less__ub) ).

thf(3514,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] : ( C @ ( B @ hAPP_nat_nat ) @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A @ ( B @ ( ord_less_eq_nat @ cOMBB_800536526ol_nat @ hAPP_f618557131t_bool ) @ ( cOMBC_nat_nat_bool @ hAPP_f229349961t_bool ) @ hAPP_n1699378549t_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).

thf(756,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_order__less__trans) ).

thf(3778,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).

thf(118,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun20916972t_bool )
     => ( B @ ( A @ pi_Pro1873779901t_bool ) @ is_fun1420103068l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_FuncSet_OPi_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oa) ).

thf(1238,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun20916972t_bool )
     => ( B @ ( A @ pi_Pro1873779901t_bool ) @ is_fun1420103068l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(354,axiom,
    ( ( top_to207207712i_bool @ ( h @ image_837079859di_nat ) )
    = ( top_to207207712i_bool @ finite354462354e_indi @ ( zero_zero_nat @ ord_at4362885an_nat @ hAPP_n1699378549t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_696_surjh) ).

thf(2015,plain,
    ( ( top_to207207712i_bool @ ( h @ image_837079859di_nat ) )
    = ( top_to207207712i_bool @ finite354462354e_indi @ ( zero_zero_nat @ ord_at4362885an_nat @ hAPP_n1699378549t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(639,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_522_psubset__trans) ).

thf(3286,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(310,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/sandbox2/benchmark/theBenchmark.p',fact_314_order__le__neq__trans) ).

thf(1883,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)],[310]) ).

thf(635,axiom,
    d @ is_Arr723427730le_alt,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_d____) ).

thf(3271,plain,
    d @ is_Arr723427730le_alt,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(634,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_xt1_I6_J) ).

thf(3269,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(859,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_1918246033t_bool @ hAPP_f633903640l_bool ) @ ( C @ pi_fun1555365306t_bool ) @ ( B @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
     => ( ( C @ ( B @ inj_on1962565012t_bool @ hAPP_f147218624l_bool ) @ hBOOL )
       => ( ( C @ ( cOMBK_761999167t_bool @ hAPP_f23348649l_bool ) @ ( D @ pi_fun328162388t_bool ) @ ( A @ ( member363954533t_bool @ hAPP_f1980578603l_bool ) @ hAPP_f1363425282l_bool ) @ hBOOL )
         => ( ( D @ ( A @ inj_on735362094t_bool @ hAPP_f560517119l_bool ) @ hBOOL )
           => ( ( C @ ( finite1323840035t_bool @ hAPP_f147218624l_bool ) @ hBOOL )
             => ( ( D @ ( finite274731772t_bool @ hAPP_f560517119l_bool ) @ hBOOL )
               => ( ( C @ finite1524925796t_bool )
                  = ( D @ finite945540987t_bool ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_600_card__bij) ).

thf(4140,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_1918246033t_bool @ hAPP_f633903640l_bool ) @ ( C @ pi_fun1555365306t_bool ) @ ( B @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
     => ( ( C @ ( B @ inj_on1962565012t_bool @ hAPP_f147218624l_bool ) @ hBOOL )
       => ( ( C @ ( cOMBK_761999167t_bool @ hAPP_f23348649l_bool ) @ ( D @ pi_fun328162388t_bool ) @ ( A @ ( member363954533t_bool @ hAPP_f1980578603l_bool ) @ hAPP_f1363425282l_bool ) @ hBOOL )
         => ( ( D @ ( A @ inj_on735362094t_bool @ hAPP_f560517119l_bool ) @ hBOOL )
           => ( ( C @ ( finite1323840035t_bool @ hAPP_f147218624l_bool ) @ hBOOL )
             => ( ( D @ ( finite274731772t_bool @ hAPP_f560517119l_bool ) @ hBOOL )
               => ( ( C @ finite1524925796t_bool )
                  = ( D @ finite945540987t_bool ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).

thf(156,axiom,
    ( arrow_583275979e_Prof
    = ( arrow_912654623le_Lin @ ( cOMBK_350223551e_indi @ hAPP_f1639180358l_bool ) @ ( top_to207207712i_bool @ pi_Arr1801471756t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_375_Prof__def) ).

thf(1365,plain,
    ( arrow_583275979e_Prof
    = ( arrow_912654623le_Lin @ ( cOMBK_350223551e_indi @ hAPP_f1639180358l_bool ) @ ( top_to207207712i_bool @ pi_Arr1801471756t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(322,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/sandbox2/benchmark/theBenchmark.p',fact_653_less__SucE) ).

thf(1920,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)],[322]) ).

thf(620,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_order__less__not__sym) ).

thf(3198,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(712,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( arrow_1549387998ctator @ hAPP_f783549695i_bool ) @ hAPP_A416869060i_bool ) @ hBOOL )
    <=> ! [C: $i] :
          ( ( arrow_583275979e_Prof @ ( C @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
         => ( ( C @ ( A @ hAPP_f1817389232t_bool ) )
            = ( B @ ( C @ hAPP_A340536322t_bool ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_380_dictator__def) ).

thf(3556,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i] :
            ( ( arrow_583275979e_Prof @ ( C @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
           => ( ( C @ ( A @ hAPP_f1817389232t_bool ) )
              = ( B @ ( C @ hAPP_A340536322t_bool ) ) ) )
       => ( B @ ( A @ ( arrow_1549387998ctator @ hAPP_f783549695i_bool ) @ hAPP_A416869060i_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( arrow_1549387998ctator @ hAPP_f783549695i_bool ) @ hAPP_A416869060i_bool ) @ hBOOL )
       => ! [C: $i] :
            ( ( arrow_583275979e_Prof @ ( C @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
           => ( ( C @ ( A @ hAPP_f1817389232t_bool ) )
              = ( B @ ( C @ hAPP_A340536322t_bool ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).

thf(312,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P667392034l_bool ) @ is_fun701126715l_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__fun_Itc__Arrow____Order) ).

thf(1888,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P667392034l_bool ) @ is_fun701126715l_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(707,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1482529602l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_486_in__mono) ).

thf(3546,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1482529602l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).

thf(280,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/sandbox2/benchmark/theBenchmark.p',fact_561_le__add1) ).

thf(1787,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)],[280]) ).

thf(435,axiom,
    ! [A: $i] : ( top_to207207712i_bool @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_412_subset__UNIV) ).

thf(2344,plain,
    ! [A: $i] : ( top_to207207712i_bool @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(166,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun701126715l_bool )
     => ( B @ ( A @ hAPP_f147218624l_bool ) @ is_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_014) ).

thf(1392,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun701126715l_bool )
     => ( B @ ( A @ hAPP_f147218624l_bool ) @ is_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(269,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/sandbox2/benchmark/theBenchmark.p',fact_620_add__is__0) ).

thf(1740,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)],[269]) ).

thf(223,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_nat_nat_bool @ hAPP_f229349961t_bool ) @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) )
      = ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U) ).

thf(1573,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_nat_nat_bool @ hAPP_f229349961t_bool ) @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) )
      = ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(638,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ is_Arr859726945e_indi )
        & ( A @ is_Arr859726945e_indi ) )
     => ( ( D @ ( C @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( A != B )
         => ( ( D @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
           => ( ( D @ ( B @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
             => ( ( A @ ( C @ hAPP_A1895296483di_nat ) )
               != ( B @ ( C @ hAPP_A1895296483di_nat ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_367_inj__on__contraD) ).

thf(3282,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ is_Arr859726945e_indi )
        & ( A @ is_Arr859726945e_indi ) )
     => ( ( D @ ( C @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( A != B )
         => ( ( D @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
           => ( ( D @ ( B @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
             => ( ( A @ ( C @ hAPP_A1895296483di_nat ) )
               != ( B @ ( C @ hAPP_A1895296483di_nat ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(176,axiom,
    ! [A: $i] :
      ( ( one_one_nat = A )
    <=> ( A = one_one_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_421_one__reorient) ).

thf(1423,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)],[176]) ).

thf(431,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( A @ ( B @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_472_set__rev__mp) ).

thf(2332,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( A @ ( B @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(647,axiom,
    ! [A: $i] :
      ( ( A @ is_fun701126715l_bool )
     => ( ( A @ ( top_to935749874l_bool @ ( ord_le1482529602l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
      <=> ( A = top_to935749874l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_top__unique) ).

thf(3314,plain,
    ! [A: $i] :
      ( ( A @ is_fun701126715l_bool )
     => ( ( ( A = top_to935749874l_bool )
         => ( A @ ( top_to935749874l_bool @ ( ord_le1482529602l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) )
        & ( ( A @ ( top_to935749874l_bool @ ( ord_le1482529602l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
         => ( A = top_to935749874l_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).

thf(528,axiom,
    ! [A: $i] : ( top_to846262053l_bool @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_UNIV__I) ).

thf(2820,plain,
    ! [A: $i] : ( top_to846262053l_bool @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(538,axiom,
    ! [A: $i] :
      ( ( A @ is_fun292781289l_bool )
     => ( ( A @ ( top_to1849101472l_bool @ ( ord_le2143686384l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
       => ( A = top_to1849101472l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_358_top__le) ).

thf(2872,plain,
    ! [A: $i] :
      ( ( A @ is_fun292781289l_bool )
     => ( ( A @ ( top_to1849101472l_bool @ ( ord_le2143686384l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
       => ( A = top_to1849101472l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(333,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/sandbox2/benchmark/theBenchmark.p',fact_568_mono__nat__linear__lb) ).

thf(1951,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)],[333]) ).

thf(792,axiom,
    ! [A: $i] : ( top_to207207712i_bool @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_UNIV__I) ).

thf(3894,plain,
    ! [A: $i] : ( top_to207207712i_bool @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).

thf(289,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/sandbox2/benchmark/theBenchmark.p',fact_419_add__left__cancel) ).

thf(1819,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)],[289]) ).

thf(873,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_442_subsetD) ).

thf(4187,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).

thf(4,axiom,
    ( top_to207207712i_bool
    = ( fTrue @ ( cOMBK_1391252605e_indi @ hAPP_b2116075462i_bool ) @ collec279390863e_indi ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_UNIV__def) ).

thf(889,plain,
    ( top_to207207712i_bool
    = ( fTrue @ ( cOMBK_1391252605e_indi @ hAPP_b2116075462i_bool ) @ collec279390863e_indi ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(66,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f740740988l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__fun_Itc__Arrow____O) ).

thf(1079,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f740740988l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(50,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/sandbox2/benchmark/theBenchmark.p',fact_333_order__le__less__trans) ).

thf(1027,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)],[50]) ).

thf(405,axiom,
    ! [A: $i] :
      ~ ( A @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_order__less__irrefl) ).

thf(2213,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(741,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( C @ ( D @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_P1122857141l_bool ) @ ( D @ ( A @ hAPP_P1813625415t_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_Pro1873779901t_bool ) @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_583_Pi__I_H) ).

thf(3727,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( C @ ( D @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_P1122857141l_bool ) @ ( D @ ( A @ hAPP_P1813625415t_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_Pro1873779901t_bool ) @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).

thf(129,axiom,
    lab @ is_fun20916972t_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_Lab____) ).

thf(1281,plain,
    lab @ is_fun20916972t_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(734,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( A @ ( C @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_ord__eq__less__trans) ).

thf(3647,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( A @ ( C @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).

thf(382,axiom,
    ! [A: $i] :
      ( ( A @ is_fun1420103068l_bool )
     => ( ( A != top_to846262053l_bool )
      <=> ( top_to846262053l_bool @ ( A @ ( ord_le1260664009l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_less__top) ).

thf(2112,plain,
    ! [A: $i] :
      ( ( A @ is_fun1420103068l_bool )
     => ( ( ( top_to846262053l_bool @ ( A @ ( ord_le1260664009l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
         => ( A != top_to846262053l_bool ) )
        & ( ( A != top_to846262053l_bool )
         => ( top_to846262053l_bool @ ( A @ ( ord_le1260664009l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(44,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun20916972t_bool )
     => ( ( B @ ( A @ ( fTrue @ ( if_fun1158274329t_bool @ hAPP_b910261233t_bool ) @ hAPP_f1000663785t_bool ) @ hAPP_f137597973t_bool ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqm) ).

thf(1012,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun20916972t_bool )
     => ( ( B @ ( A @ ( fTrue @ ( if_fun1158274329t_bool @ hAPP_b910261233t_bool ) @ hAPP_f1000663785t_bool ) @ hAPP_f137597973t_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(828,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( B = A )
       => ( C @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_xt1_I2_J) ).

thf(4027,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( B = A )
       => ( C @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).

thf(742,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( cOMBK_1673635960le_alt @ hAPP_f719005683l_bool ) @ ( B @ pi_Pro1873779901t_bool ) @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
     => ( ( B @ ( A @ inj_on398823523t_bool @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ( ( C @ ( finite_finite_bool @ hAPP_f387058535l_bool ) @ hBOOL )
         => ( C @ finite_card_bool @ ( B @ finite1044330389le_alt @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_588_card__inj) ).

thf(3731,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( cOMBK_1673635960le_alt @ hAPP_f719005683l_bool ) @ ( B @ pi_Pro1873779901t_bool ) @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
     => ( ( B @ ( A @ inj_on398823523t_bool @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ( ( C @ ( finite_finite_bool @ hAPP_f387058535l_bool ) @ hBOOL )
         => ( C @ finite_card_bool @ ( B @ finite1044330389le_alt @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).

thf(230,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/sandbox2/benchmark/theBenchmark.p',fact_269_linorder__le__less__linear) ).

thf(1592,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)],[230]) ).

thf(379,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Arr1064242500le_alt ) @ ( B @ ( member219620739le_alt @ hAPP_f1234917389l_bool ) @ hAPP_f1291635206l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_A340536322t_bool ) @ ( A @ ( B @ hAPP_A503573454le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_PiE) ).

thf(2100,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Arr1064242500le_alt ) @ ( B @ ( member219620739le_alt @ hAPP_f1234917389l_bool ) @ hAPP_f1291635206l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_A340536322t_bool ) @ ( A @ ( B @ hAPP_A503573454le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(34,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/sandbox2/benchmark/theBenchmark.p',fact_534_nat__add__commute) ).

thf(980,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)],[34]) ).

thf(506,axiom,
    ! [A: $i] : ( top_to1257323279t_bool @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_top__greatest) ).

thf(2694,plain,
    ! [A: $i] : ( top_to1257323279t_bool @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(808,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro1873779901t_bool ) @ ( B @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P1122857141l_bool ) @ ( A @ ( B @ hAPP_P1813625415t_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_PiE) ).

thf(3963,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro1873779901t_bool ) @ ( B @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P1122857141l_bool ) @ ( A @ ( B @ hAPP_P1813625415t_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).

thf(308,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/sandbox2/benchmark/theBenchmark.p',fact_338_xt1_I8_J) ).

thf(1878,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)],[308]) ).

thf(89,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun1084921220e_indi )
     => ( B @ ( A @ hAPP_n619554777e_indi ) @ is_Arr859726945e_indi ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oi) ).

thf(1138,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun1084921220e_indi )
     => ( B @ ( A @ hAPP_n619554777e_indi ) @ is_Arr859726945e_indi ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(593,axiom,
    ! [A: $i] : ( top_to1647826457l_bool @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_iso__tuple__UNIV__I) ).

thf(3078,plain,
    ! [A: $i] : ( top_to1647826457l_bool @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(272,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/sandbox2/benchmark/theBenchmark.p',fact_622_le__0__eq) ).

thf(1755,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)],[272]) ).

thf(588,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_462_subset__trans) ).

thf(3060,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(153,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_2133163426l_bool @ hAPP_f1458726223t_bool ) @ hAPP_f427533077t_bool ) @ hAPP_P1676879539t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Product____Type__Ounit_000tc__fun_Itc__Product____Ty) ).

thf(1350,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_2133163426l_bool @ hAPP_f1458726223t_bool ) @ hAPP_f427533077t_bool ) @ hAPP_P1676879539t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(328,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ finite_card_nat @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ord_at4362885an_nat @ hAPP_n1699378549t_bool ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( A
        = ( A @ finite_card_nat @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ord_at4362885an_nat @ hAPP_n1699378549t_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_699_subset__card__intvl__is__intvl) ).

thf(1936,plain,
    ! [A: $i,B: $i] :
      ( ( A @ finite_card_nat @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ord_at4362885an_nat @ hAPP_n1699378549t_bool ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( A
        = ( A @ finite_card_nat @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ord_at4362885an_nat @ hAPP_n1699378549t_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(69,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/sandbox2/benchmark/theBenchmark.p',fact_689_Suc__le__D) ).

thf(1089,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)],[69]) ).

thf(758,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
    <=> ( ~ ( A @ ( B @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
        & ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_less__le__not__le) ).

thf(3782,plain,
    ! [A: $i,B: $i] :
      ( ( ( ~ ( A @ ( B @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( ~ ( A @ ( B @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).

thf(212,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun20916972t_bool )
     => ( B @ ( A @ hAPP_f137597973t_bool ) @ is_fun20916972t_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___038) ).

thf(1541,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun20916972t_bool )
     => ( B @ ( A @ hAPP_f137597973t_bool ) @ is_fun20916972t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(393,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
    <=> ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
        & ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_491_set__eq__subset) ).

thf(2157,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(91,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/sandbox2/benchmark/theBenchmark.p',fact_664_less__iff__Suc__add) ).

thf(1143,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)],[91]) ).

thf(126,axiom,
    ( top_top_fun_nat_bool
    = ( fTrue @ ( cOMBK_bool_nat @ hAPP_b1013836512t_bool ) @ collect_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_UNIV__def) ).

thf(1270,plain,
    ( top_top_fun_nat_bool
    = ( fTrue @ ( cOMBK_bool_nat @ hAPP_b1013836512t_bool ) @ collect_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(607,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
    <=> ( ( A != B )
        & ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_446_psubset__eq) ).

thf(3122,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A != B )
          & ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( ( A != B )
          & ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(46,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P288224245l_bool ) @ is_fun1420103068l_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__fun_Itc__prod_Itc__Arro) ).

thf(1017,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P288224245l_bool ) @ is_fun1420103068l_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(504,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
    <=> ( A @ ( B @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_mem__def) ).

thf(2685,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ hAPP_nat_bool ) @ hBOOL )
       => ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A @ ( B @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(565,axiom,
    ! [A: $i] :
      ( ( A @ is_fun701126715l_bool )
     => ( ( A != top_to935749874l_bool )
      <=> ( top_to935749874l_bool @ ( A @ ( ord_le194694222l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_less__top) ).

thf(2973,plain,
    ! [A: $i] :
      ( ( A @ is_fun701126715l_bool )
     => ( ( ( top_to935749874l_bool @ ( A @ ( ord_le194694222l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
         => ( A != top_to935749874l_bool ) )
        & ( ( A != top_to935749874l_bool )
         => ( top_to935749874l_bool @ ( A @ ( ord_le194694222l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(83,axiom,
    arrow_912654623le_Lin @ is_fun1420103068l_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Arrow__Order__Mirabelle__wylsunqmtb_OLin) ).

thf(1121,plain,
    arrow_912654623le_Lin @ is_fun1420103068l_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(661,axiom,
    ! [A: $i] :
      ( ( A @ is_fun20916972t_bool )
     => ( ( A @ ( top_to1773227171t_bool @ ( ord_le64728819t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ( A = top_to1773227171t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_360_top__le) ).

thf(3381,plain,
    ! [A: $i] :
      ( ( A @ is_fun20916972t_bool )
     => ( ( A @ ( top_to1773227171t_bool @ ( ord_le64728819t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ( A = top_to1773227171t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).

thf(61,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_474_set__rev__mp) ).

thf(1064,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(72,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/sandbox2/benchmark/theBenchmark.p',fact_635_le__SucI) ).

thf(1096,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)],[72]) ).

thf(473,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_fun1555365306t_bool ) @ ( B @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_f1895971544l_bool ) @ ( A @ ( B @ hAPP_f1817389232t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_374_Pi__mem) ).

thf(2509,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_fun1555365306t_bool ) @ ( B @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_f1895971544l_bool ) @ ( A @ ( B @ hAPP_f1817389232t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(248,axiom,
    ! [A: $i] :
      ( zero_zero_nat
     != ( A @ ( suc @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_677_nat_Osimps_I2_J) ).

thf(1672,plain,
    ! [A: $i] :
      ( zero_zero_nat
     != ( A @ ( suc @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(730,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_513_psubsetD) ).

thf(3632,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).

thf(845,axiom,
    ! [A: $i] : ( top_top_fun_nat_bool @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_top__greatest) ).

thf(4095,plain,
    ! [A: $i] : ( top_top_fun_nat_bool @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).

thf(623,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_order__less__imp__le) ).

thf(3205,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

thf(883,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( C @ ( D @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
         => ( B @ ( D @ ( A @ hAPP_P1813625415t_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) )
     => ( B @ ( cOMBK_1673635960le_alt @ hAPP_f719005683l_bool ) @ ( C @ pi_Pro1873779901t_bool ) @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_576_funcsetI) ).

thf(4219,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( C @ ( D @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
         => ( B @ ( D @ ( A @ hAPP_P1813625415t_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) )
     => ( B @ ( cOMBK_1673635960le_alt @ hAPP_f719005683l_bool ) @ ( C @ pi_Pro1873779901t_bool ) @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).

thf(200,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/sandbox2/benchmark/theBenchmark.p',fact_328_xt1_I7_J) ).

thf(1493,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)],[200]) ).

thf(836,axiom,
    ! [A: $i] :
      ( ( A @ is_fun20916972t_bool )
     => ( ( A @ ( top_to1773227171t_bool @ ( ord_le64728819t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
      <=> ( A = top_to1773227171t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_top__unique) ).

thf(4049,plain,
    ! [A: $i] :
      ( ( A @ is_fun20916972t_bool )
     => ( ( ( A = top_to1773227171t_bool )
         => ( A @ ( top_to1773227171t_bool @ ( ord_le64728819t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
        & ( ( A @ ( top_to1773227171t_bool @ ( ord_le64728819t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
         => ( A = top_to1773227171t_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).

thf(338,axiom,
    top_top_bool @ is_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__HOL__Obool) ).

thf(1964,plain,
    top_top_bool @ is_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(484,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ is_Arr723427730le_alt )
        & ( B @ is_Arr723427730le_alt )
        & ( A @ is_Arr723427730le_alt ) )
     => ( ( D @ ( C @ ( arrow_163947511_mkbot @ hAPP_f102394819t_bool ) @ hAPP_A1014090479t_bool ) @ ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
      <=> ( ( ( A != D )
           => ( C @ ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
          & ( ( A = D )
           => ( A != B ) )
          & ( B != D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_in__mkbot) ).

thf(2561,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ is_Arr723427730le_alt )
        & ( B @ is_Arr723427730le_alt )
        & ( A @ is_Arr723427730le_alt ) )
     => ( ( ( ( ( A != D )
             => ( C @ ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
            & ( ( A = D )
             => ( A != B ) )
            & ( B != D ) )
         => ( D @ ( C @ ( arrow_163947511_mkbot @ hAPP_f102394819t_bool ) @ hAPP_A1014090479t_bool ) @ ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
        & ( ( D @ ( C @ ( arrow_163947511_mkbot @ hAPP_f102394819t_bool ) @ hAPP_A1014090479t_bool ) @ ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
         => ( ( ( A != D )
             => ( C @ ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
            & ( ( A = D )
             => ( A != B ) )
            & ( B != D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(455,axiom,
    ! [A: $i] : ( top_to1257323279t_bool @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_UNIV__I) ).

thf(2419,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)],[455]) ).

thf(437,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_532_less__not__refl3) ).

thf(2349,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)],[437]) ).

thf(94,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1965705105l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__prod_It) ).

thf(1160,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1965705105l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(540,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/sandbox2/benchmark/theBenchmark.p',fact_397_injI) ).

thf(2877,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)],[540]) ).

thf(597,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_nat_Product_unit ) @ ( B @ ( member1024687843t_unit @ hAPP_f1598887207l_bool ) @ hAPP_f537623936l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_n454528608t_bool ) @ ( A @ ( B @ hAPP_n633340360t_unit ) @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_PiE) ).

thf(3094,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_nat_Product_unit ) @ ( B @ ( member1024687843t_unit @ hAPP_f1598887207l_bool ) @ hAPP_f537623936l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_n454528608t_bool ) @ ( A @ ( B @ hAPP_n633340360t_unit ) @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(867,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_order__less__asym) ).

thf(4167,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).

thf(367,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun20916972t_bool )
     => ( ( B @ ( A @ ( fFalse @ ( if_fun1158274329t_bool @ hAPP_b910261233t_bool ) @ hAPP_f1000663785t_bool ) @ hAPP_f137597973t_bool ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqm) ).

thf(2053,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun20916972t_bool )
     => ( ( B @ ( A @ ( fFalse @ ( if_fun1158274329t_bool @ hAPP_b910261233t_bool ) @ hAPP_f1000663785t_bool ) @ hAPP_f137597973t_bool ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(295,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun1420103068l_bool )
     => ( ( B @ ( A @ ( cOMBK_350223551e_indi @ hAPP_f1639180358l_bool ) @ hAPP_A659996934l_bool ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe) ).

thf(1842,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun1420103068l_bool )
     => ( ( B @ ( A @ ( cOMBK_350223551e_indi @ hAPP_f1639180358l_bool ) @ hAPP_A659996934l_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(875,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( C @ is_fun20916972t_bool )
         => ( ( B @ ( C @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
           => ( A @ ( C @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) )
     => ( A @ ( B @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_508_subsetI) ).

thf(4191,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( C @ is_fun20916972t_bool )
         => ( ( B @ ( C @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
           => ( A @ ( C @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) )
     => ( A @ ( B @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).

thf(227,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/sandbox2/benchmark/theBenchmark.p',fact_566_add__le__mono1) ).

thf(1584,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)],[227]) ).

thf(282,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/sandbox2/benchmark/theBenchmark.p',fact_287_linorder__antisym__conv1) ).

thf(1791,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)],[282]) ).

thf(675,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/sandbox2/benchmark/theBenchmark.p',fact_232_xt1_I6_J) ).

thf(3428,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)],[675]) ).

thf(481,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/sandbox2/benchmark/theBenchmark.p',fact_250_xt1_I3_J) ).

thf(2551,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)],[481]) ).

thf(45,axiom,
    top_to1773227171t_bool @ is_fun20916972t_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__prod_Itc__Arrow____Order____Mir) ).

thf(1016,plain,
    top_to1773227171t_bool @ is_fun20916972t_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(870,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_521_psubset__trans) ).

thf(4180,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).

thf(53,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_226598744l_bool @ hAPP_f1722879237t_bool ) @ hAPP_f800510211t_bool ) @ hAPP_nat_bool ) )
      = ( B @ ( C @ ( A @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).

thf(1039,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_226598744l_bool @ hAPP_f1722879237t_bool ) @ hAPP_f800510211t_bool ) @ hAPP_nat_bool ) )
      = ( B @ ( C @ ( A @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(466,axiom,
    ! [A: $i] :
      ( ( A @ is_fun292781289l_bool )
     => ( ( A != top_to1849101472l_bool )
      <=> ( top_to1849101472l_bool @ ( A @ ( ord_le1141238780l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_less__top) ).

thf(2450,plain,
    ! [A: $i] :
      ( ( A @ is_fun292781289l_bool )
     => ( ( ( top_to1849101472l_bool @ ( A @ ( ord_le1141238780l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
         => ( A != top_to1849101472l_bool ) )
        & ( ( A != top_to1849101472l_bool )
         => ( top_to1849101472l_bool @ ( A @ ( ord_le1141238780l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(133,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1570138413i_bool ) @ is_fun2015243113i_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__008) ).

thf(1297,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1570138413i_bool ) @ is_fun2015243113i_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(186,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_Arr859726945e_indi )
     => ( B @ ( A @ hAPP_A955165183l_bool ) @ is_fun292781289l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It_002) ).

thf(1451,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_Arr859726945e_indi )
     => ( B @ ( A @ hAPP_A955165183l_bool ) @ is_fun292781289l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(188,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f866114756l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__Arrow__) ).

thf(1456,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f866114756l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(840,axiom,
    ! [A: $i] : ( top_top_fun_nat_bool @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_iso__tuple__UNIV__I) ).

thf(4068,plain,
    ! [A: $i] : ( top_top_fun_nat_bool @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).

thf(246,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ hAPP_A1948275303t_bool ) )
      = ( C @ ( B @ hAPP_A1895296483di_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__043) ).

thf(1668,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ hAPP_A1948275303t_bool ) )
      = ( C @ ( B @ hAPP_A1895296483di_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(326,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/sandbox2/benchmark/theBenchmark.p',fact_396_add__le__less__mono) ).

thf(1932,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)],[326]) ).

thf(771,axiom,
    ! [A: $i,B: $i] :
      ( ( arrow_912654623le_Lin @ ( B @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
     => ( arrow_912654623le_Lin @ ( A @ ( B @ ( arrow_163947511_mkbot @ hAPP_f102394819t_bool ) @ hAPP_A1014090479t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_mkbot__Lin) ).

thf(3819,plain,
    ! [A: $i,B: $i] :
      ( ( arrow_912654623le_Lin @ ( B @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
     => ( arrow_912654623le_Lin @ ( A @ ( B @ ( arrow_163947511_mkbot @ hAPP_f102394819t_bool ) @ hAPP_A1014090479t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).

thf(262,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_441_subsetD) ).

thf(1720,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(884,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun20916972t_bool )
        & ( A @ is_fun1420103068l_bool ) )
     => ( B @ ( A @ hAPP_f1733357041l_bool ) @ is_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___033) ).

thf(4223,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun20916972t_bool )
        & ( A @ is_fun1420103068l_bool ) )
     => ( B @ ( A @ hAPP_f1733357041l_bool ) @ is_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).

thf(563,axiom,
    ! [A: $i] :
      ~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_order__less__irrefl) ).

thf(2968,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(425,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( C @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_xt1_I1_J) ).

thf(2285,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( C @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(80,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ hAPP_A85603248t_bool ) )
      = ( C @ ( B @ hAPP_A340536322t_bool ) @ ( A @ hAPP_f102394819t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy) ).

thf(1114,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ hAPP_A85603248t_bool ) )
      = ( C @ ( B @ hAPP_A340536322t_bool ) @ ( A @ hAPP_f102394819t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(485,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
      | ( A != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Nat__Onat_T) ).

thf(2581,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)],[485]) ).

thf(59,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_1894996001t_bool @ hAPP_f1975142533t_bool ) @ hAPP_f590186314t_bool ) @ hAPP_A340536322t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A1906804694t_bool ) @ hAPP_f137597973t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_049) ).

thf(1060,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_1894996001t_bool @ hAPP_f1975142533t_bool ) @ hAPP_f590186314t_bool ) @ hAPP_A340536322t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A1906804694t_bool ) @ hAPP_f137597973t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(706,axiom,
    ~ ! [A: $i] :
        ( ( top_to207207712i_bool @ finite354462354e_indi @ ( 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_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ ( cOMBC_1373788917t_bool @ hAPP_f1283354413t_bool ) @ hAPP_f1898540574t_bool ) @ ( cOMBC_1894996001t_bool @ hAPP_f1975142533t_bool ) @ hAPP_f590186314t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( a @ ( b @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
         => ~ ( lba @ ( lab @ ( one_one_nat @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( h @ ( ord_less_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ ( cOMBC_1373788917t_bool @ hAPP_f1283354413t_bool ) @ hAPP_f1898540574t_bool ) @ ( cOMBC_1894996001t_bool @ hAPP_f1975142533t_bool ) @ hAPP_f590186314t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( b @ ( a @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_) ).

thf(3540,plain,
    ~ ! [A: $i] :
        ( ( top_to207207712i_bool @ finite354462354e_indi @ ( 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_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ ( cOMBC_1373788917t_bool @ hAPP_f1283354413t_bool ) @ hAPP_f1898540574t_bool ) @ ( cOMBC_1894996001t_bool @ hAPP_f1975142533t_bool ) @ hAPP_f590186314t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( a @ ( b @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
         => ~ ( lba @ ( lab @ ( one_one_nat @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( h @ ( ord_less_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ ( cOMBC_1373788917t_bool @ hAPP_f1283354413t_bool ) @ hAPP_f1898540574t_bool ) @ ( cOMBC_1894996001t_bool @ hAPP_f1975142533t_bool ) @ hAPP_f590186314t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( b @ ( a @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).

thf(470,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( member1704306684t_bool @ ( cOMBC_344067350l_bool @ hAPP_f1692576003l_bool ) @ hAPP_f574392641l_bool ) @ ( A @ ( member1704306684t_bool @ ( cOMBC_344067350l_bool @ hAPP_f1692576003l_bool ) @ hAPP_f574392641l_bool ) @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
    <=> ( B @ ( A @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_497_pred__subset__eq) ).

thf(2497,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
       => ( B @ ( member1704306684t_bool @ ( cOMBC_344067350l_bool @ hAPP_f1692576003l_bool ) @ hAPP_f574392641l_bool ) @ ( A @ ( member1704306684t_bool @ ( cOMBC_344067350l_bool @ hAPP_f1692576003l_bool ) @ hAPP_f574392641l_bool ) @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) )
      & ( ( B @ ( member1704306684t_bool @ ( cOMBC_344067350l_bool @ hAPP_f1692576003l_bool ) @ hAPP_f574392641l_bool ) @ ( A @ ( member1704306684t_bool @ ( cOMBC_344067350l_bool @ hAPP_f1692576003l_bool ) @ hAPP_f574392641l_bool ) @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(40,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/sandbox2/benchmark/theBenchmark.p',fact_416_add__imp__eq) ).

thf(1002,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)],[40]) ).

thf(298,axiom,
    top_to207207712i_bool @ is_fun2015243113i_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Arrow____Order____Mirabelle____) ).

thf(1852,plain,
    top_to207207712i_bool @ is_fun2015243113i_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(750,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le64728819t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ( A @ ( B @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_478_set__rev__mp) ).

thf(3760,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le64728819t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ( A @ ( B @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).

thf(533,axiom,
    n @ ( h @ ( top_to207207712i_bool @ hilber951314860di_nat ) @ hAPP_n619554777e_indi ) @ ( p @ hAPP_A340536322t_bool ) @ ( d @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0) ).

thf(2862,plain,
    n @ ( h @ ( top_to207207712i_bool @ hilber951314860di_nat ) @ hAPP_n619554777e_indi ) @ ( p @ hAPP_A340536322t_bool ) @ ( d @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(591,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( B @ ( C @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_order__less__imp__triv) ).

thf(3074,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( B @ ( C @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(574,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_453_psubset__imp__subset) ).

thf(3005,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(419,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( A @ ( B @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_414_subset__inj__on) ).

thf(2272,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( A @ ( B @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(656,axiom,
    ! [A: $i] : ( top_to1849101472l_bool @ ( A @ ( ord_le2143686384l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_top__greatest) ).

thf(3364,plain,
    ! [A: $i] : ( top_to1849101472l_bool @ ( A @ ( ord_le2143686384l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).

thf(389,axiom,
    ! [A: $i] :
      ( ( A @ ( top_to1849101472l_bool @ hAPP_f446648900l_bool ) @ hBOOL )
    <=> ( top_top_bool @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_top__apply) ).

thf(2140,plain,
    ! [A: $i] :
      ( ( ( top_top_bool @ hBOOL )
       => ( A @ ( top_to1849101472l_bool @ hAPP_f446648900l_bool ) @ hBOOL ) )
      & ( ( A @ ( top_to1849101472l_bool @ hAPP_f446648900l_bool ) @ hBOOL )
       => ( top_top_bool @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(518,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( B = A )
       => ( C @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_xt1_I2_J) ).

thf(2756,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( B = A )
       => ( C @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(627,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro269694131t_unit ) @ ( B @ ( member1226631410t_unit @ hAPP_f785487437l_bool ) @ hAPP_f557371893l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P822772139t_bool ) @ ( A @ ( B @ hAPP_P992343101t_unit ) @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_PiE) ).

thf(3215,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro269694131t_unit ) @ ( B @ ( member1226631410t_unit @ hAPP_f785487437l_bool ) @ hAPP_f557371893l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P822772139t_bool ) @ ( A @ ( B @ hAPP_P992343101t_unit ) @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(209,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/sandbox2/benchmark/theBenchmark.p',fact_637_Suc__leD) ).

thf(1525,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)],[209]) ).

thf(748,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_xt1_I8_J) ).

thf(3755,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).

thf(763,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_order__less__imp__not__less) ).

thf(3802,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).

thf(403,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ is_Arr723427730le_alt )
        & ( C @ is_Arr723427730le_alt )
        & ( B @ is_Arr723427730le_alt )
        & ( A @ is_Arr723427730le_alt ) )
     => ( ( ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) )
          = ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) ) )
       => ~ ( ( A = C )
           => ( B != D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_Pair__inject) ).

thf(2203,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ is_Arr723427730le_alt )
        & ( C @ is_Arr723427730le_alt )
        & ( B @ is_Arr723427730le_alt )
        & ( A @ is_Arr723427730le_alt ) )
     => ( ( ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) )
          = ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) ) )
       => ~ ( ( A = C )
           => ( B != D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(119,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1021828400l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel) ).

thf(1241,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1021828400l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(253,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/sandbox2/benchmark/theBenchmark.p',fact_665_less__add__Suc2) ).

thf(1695,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)],[253]) ).

thf(541,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
    <=> ( ( A = B )
        | ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_order__le__less) ).

thf(2883,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A = B )
          | ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( ( A = B )
          | ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(64,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1597773170l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__fun_Itc__fun_Itc) ).

thf(1071,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1597773170l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(105,axiom,
    ! [A: $i] : ( A @ ( suc @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_630_zero__less__Suc) ).

thf(1185,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)],[105]) ).

thf(265,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/sandbox2/benchmark/theBenchmark.p',fact_426_add__right__mono) ).

thf(1732,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)],[265]) ).

thf(545,axiom,
    ! [A: $i] :
      ~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_530_less__irrefl__nat) ).

thf(2909,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(178,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun20916972t_bool )
     => ( B @ ( A @ hAPP_f649586561t_bool ) @ is_fun1568535512t_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___035) ).

thf(1434,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun20916972t_bool )
     => ( B @ ( A @ hAPP_f649586561t_bool ) @ is_fun1568535512t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(301,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
         => ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
     => ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_610_bounded__nat__set__is__finite) ).

thf(1857,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
         => ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
     => ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(872,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( B @ ( zero_zero_nat @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( ord_less_nat @ ( cOMBC_nat_nat_bool @ hAPP_f229349961t_bool ) @ hAPP_n1699378549t_bool ) @ ( B @ ( suc @ ( member_nat @ cOMBB_1146692694ol_nat @ hAPP_f66927821l_bool ) @ ( cOMBC_226598744l_bool @ hAPP_f1722879237t_bool ) @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat @ hAPP_f1146629647l_bool ) @ cOMBS_nat_bool_bool ) @ collect_nat @ finite_card_nat )
        = ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ ( cOMBC_nat_nat_bool @ hAPP_f229349961t_bool ) @ hAPP_n1699378549t_bool ) @ ( B @ ( member_nat @ ( cOMBC_226598744l_bool @ hAPP_f1722879237t_bool ) @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat @ hAPP_f1146629647l_bool ) @ cOMBS_nat_bool_bool ) @ collect_nat @ finite_card_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_683_card__less__Suc2) ).

thf(4184,plain,
    ! [A: $i,B: $i] :
      ( ~ ( B @ ( zero_zero_nat @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( ord_less_nat @ ( cOMBC_nat_nat_bool @ hAPP_f229349961t_bool ) @ hAPP_n1699378549t_bool ) @ ( B @ ( suc @ ( member_nat @ cOMBB_1146692694ol_nat @ hAPP_f66927821l_bool ) @ ( cOMBC_226598744l_bool @ hAPP_f1722879237t_bool ) @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat @ hAPP_f1146629647l_bool ) @ cOMBS_nat_bool_bool ) @ collect_nat @ finite_card_nat )
        = ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ ( cOMBC_nat_nat_bool @ hAPP_f229349961t_bool ) @ hAPP_n1699378549t_bool ) @ ( B @ ( member_nat @ ( cOMBC_226598744l_bool @ hAPP_f1722879237t_bool ) @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat @ hAPP_f1146629647l_bool ) @ cOMBS_nat_bool_bool ) @ collect_nat @ finite_card_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).

thf(776,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_515_psubsetD) ).

thf(3834,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).

thf(141,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f2043811403e_indi ) @ is_Arr859726945e_indi ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_016) ).

thf(1318,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f2043811403e_indi ) @ is_Arr859726945e_indi ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(296,axiom,
    ! [A: $i] :
      ( ( A != zero_zero_nat )
     => ~ ! [B: $i] :
            ( A
           != ( B @ ( suc @ hAPP_nat_nat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_693_nat_Oexhaust) ).

thf(1846,plain,
    ! [A: $i] :
      ( ( A != zero_zero_nat )
     => ~ ! [B: $i] :
            ( A
           != ( B @ ( suc @ hAPP_nat_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(56,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1384787615l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_028) ).

thf(1054,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1384787615l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(561,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_order__less__trans) ).

thf(2963,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(648,axiom,
    fTrue @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).

thf(3321,plain,
    fTrue @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).

thf(106,axiom,
    ! [A: $i] :
      ( ( A @ is_bool )
     => ( ( A = fFalse )
        | ( A = fTrue ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).

thf(1187,plain,
    ! [A: $i] :
      ( ( A @ is_bool )
     => ( ( A = fFalse )
        | ( A = fTrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(462,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_order__less__imp__not__less) ).

thf(2440,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(49,axiom,
    top_to1849101472l_bool @ is_fun292781289l_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Orde) ).

thf(1026,plain,
    top_to1849101472l_bool @ is_fun292781289l_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(698,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( C @ ( D @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_f1895971544l_bool ) @ ( D @ ( A @ hAPP_f1817389232t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_fun1555365306t_bool ) @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_585_Pi__I_H) ).

thf(3508,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( C @ ( D @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_f1895971544l_bool ) @ ( D @ ( A @ hAPP_f1817389232t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_fun1555365306t_bool ) @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).

thf(97,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/sandbox2/benchmark/theBenchmark.p',fact_659_Suc__leI) ).

thf(1167,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)],[97]) ).

thf(498,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( arrow_912654623le_Lin @ ( C @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
     => ( ( C @ ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( B @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_Lin__irrefl) ).

thf(2645,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( arrow_912654623le_Lin @ ( C @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
     => ( ( C @ ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( B @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(673,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( B @ ( C @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
         => ( A @ ( C @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) )
     => ( A @ ( B @ ( ord_le1482529602l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_510_subsetI) ).

thf(3422,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( B @ ( C @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
         => ( A @ ( C @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) )
     => ( A @ ( B @ ( ord_le1482529602l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).

thf(571,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/sandbox2/benchmark/theBenchmark.p',fact_107_xt1_I2_J) ).

thf(2995,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)],[571]) ).

thf(820,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/sandbox2/benchmark/theBenchmark.p',fact_247_ord__le__eq__trans) ).

thf(4004,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)],[820]) ).

thf(738,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
    <=> ! [C: $i] :
          ( ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
         => ! [D: $i] :
              ( ( B @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
             => ( ( ( C @ ( A @ hAPP_nat_nat ) )
                  = ( D @ ( A @ hAPP_nat_nat ) ) )
               => ( C = D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_364_inj__on__def) ).

thf(3675,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i] :
            ( ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
           => ! [D: $i] :
                ( ( B @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
               => ( ( ( C @ ( A @ hAPP_nat_nat ) )
                    = ( D @ ( A @ hAPP_nat_nat ) ) )
                 => ( C = D ) ) ) )
       => ( B @ ( A @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
       => ! [C: $i] :
            ( ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
           => ! [D: $i] :
                ( ( B @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
               => ( ( ( C @ ( A @ hAPP_nat_nat ) )
                    = ( D @ ( A @ hAPP_nat_nat ) ) )
                 => ( C = D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).

thf(319,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Arr1801471756t_bool ) @ ( B @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_A659996934l_bool ) @ ( A @ ( B @ hAPP_A340536322t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_373_Pi__mem) ).

thf(1906,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Arr1801471756t_bool ) @ ( B @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_A659996934l_bool ) @ ( A @ ( B @ hAPP_A340536322t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(551,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( C @ ( D @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_P1122857141l_bool ) @ ( D @ ( A @ hAPP_P1813625415t_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_Pro1873779901t_bool ) @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_389_Pi__I) ).

thf(2936,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( C @ ( D @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
         => ( D @ ( B @ hAPP_P1122857141l_bool ) @ ( D @ ( A @ hAPP_P1813625415t_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) )
     => ( B @ ( C @ pi_Pro1873779901t_bool ) @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(737,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
    <=> ( ( ( A @ hBOOL )
        <=> ( B @ hBOOL ) )
        | ( B @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_order__le__less) ).

thf(3660,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( ( ( B @ hBOOL )
             => ( A @ hBOOL ) )
            & ( ( A @ hBOOL )
             => ( B @ hBOOL ) ) )
          | ( B @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
       => ( ( ( ( B @ hBOOL )
             => ( A @ hBOOL ) )
            & ( ( A @ hBOOL )
             => ( B @ hBOOL ) ) )
          | ( B @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).

thf(124,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/sandbox2/benchmark/theBenchmark.p',fact_667_one__is__add) ).

thf(1251,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)],[124]) ).

thf(397,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
    <=> ( ( A = B )
        | ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_449_subset__iff__psubset__eq) ).

thf(2176,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A = B )
          | ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( ( A = B )
          | ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(448,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ is_Arr723427730le_alt )
        & ( C @ is_Arr723427730le_alt )
        & ( B @ is_Arr723427730le_alt )
        & ( A @ is_Arr723427730le_alt ) )
     => ( ( ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) )
          = ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) ) )
      <=> ( ( B = D )
          & ( A = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_Pair__eq) ).

thf(2391,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ is_Arr723427730le_alt )
        & ( C @ is_Arr723427730le_alt )
        & ( B @ is_Arr723427730le_alt )
        & ( A @ is_Arr723427730le_alt ) )
     => ( ( ( ( B = D )
            & ( A = C ) )
         => ( ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) )
            = ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) ) ) )
        & ( ( ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) )
            = ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) ) )
         => ( ( B = D )
            & ( A = C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(790,axiom,
    ! [A: $i] : ( A @ ( top_to1257323279t_bool @ hAPP_P1676879539t_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_top1I) ).

thf(3890,plain,
    ! [A: $i] : ( A @ ( top_to1257323279t_bool @ hAPP_P1676879539t_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).

thf(604,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/sandbox2/benchmark/theBenchmark.p',fact_153_linorder__antisym__conv3) ).

thf(3111,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)],[604]) ).

thf(740,axiom,
    ! [A: $i] :
      ( ( ( ~ ( n @ ( A @ ( h @ hAPP_A1895296483di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( ( ( ( A @ ( h @ hAPP_A1895296483di_nat ) )
               != n )
             => ( e @ ( A @ ( p @ hAPP_A340536322t_bool ) @ ( arrow_163947511_mkbot @ hAPP_f102394819t_bool ) @ hAPP_A1014090479t_bool ) @ ( d @ ( e @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
            & ( ( ( A @ ( h @ hAPP_A1895296483di_nat ) )
                = n )
             => ( e @ ( c @ ( A @ ( p @ hAPP_A340536322t_bool ) @ ( arrow_1046586475_above @ hAPP_f684072049t_bool ) @ hAPP_A28770973t_bool ) @ hAPP_A1014090479t_bool ) @ ( d @ ( e @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) )
        & ( ( n @ ( A @ ( h @ hAPP_A1895296483di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( e @ ( A @ ( p @ hAPP_A340536322t_bool ) @ ( arrow_312654597_mktop @ hAPP_f102394819t_bool ) @ hAPP_A1014090479t_bool ) @ ( d @ ( e @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) )
    <=> ( ( ~ ( n @ ( A @ ( h @ hAPP_A1895296483di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( lba @ ( a @ ( b @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
        & ( ( n @ ( A @ ( h @ hAPP_A1895296483di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( lab @ ( a @ ( b @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk) ).

thf(3696,plain,
    ! [A: $i] :
      ( ( ( ( ~ ( n @ ( A @ ( h @ hAPP_A1895296483di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( lba @ ( a @ ( b @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
          & ( ( n @ ( A @ ( h @ hAPP_A1895296483di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( lab @ ( a @ ( b @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) )
       => ( ( ~ ( n @ ( A @ ( h @ hAPP_A1895296483di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( ( ( ( A @ ( h @ hAPP_A1895296483di_nat ) )
                 != n )
               => ( e @ ( A @ ( p @ hAPP_A340536322t_bool ) @ ( arrow_163947511_mkbot @ hAPP_f102394819t_bool ) @ hAPP_A1014090479t_bool ) @ ( d @ ( e @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
              & ( ( ( A @ ( h @ hAPP_A1895296483di_nat ) )
                  = n )
               => ( e @ ( c @ ( A @ ( p @ hAPP_A340536322t_bool ) @ ( arrow_1046586475_above @ hAPP_f684072049t_bool ) @ hAPP_A28770973t_bool ) @ hAPP_A1014090479t_bool ) @ ( d @ ( e @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) )
          & ( ( n @ ( A @ ( h @ hAPP_A1895296483di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( e @ ( A @ ( p @ hAPP_A340536322t_bool ) @ ( arrow_312654597_mktop @ hAPP_f102394819t_bool ) @ hAPP_A1014090479t_bool ) @ ( d @ ( e @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) )
      & ( ( ( ~ ( n @ ( A @ ( h @ hAPP_A1895296483di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( ( ( ( A @ ( h @ hAPP_A1895296483di_nat ) )
                 != n )
               => ( e @ ( A @ ( p @ hAPP_A340536322t_bool ) @ ( arrow_163947511_mkbot @ hAPP_f102394819t_bool ) @ hAPP_A1014090479t_bool ) @ ( d @ ( e @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
              & ( ( ( A @ ( h @ hAPP_A1895296483di_nat ) )
                  = n )
               => ( e @ ( c @ ( A @ ( p @ hAPP_A340536322t_bool ) @ ( arrow_1046586475_above @ hAPP_f684072049t_bool ) @ hAPP_A28770973t_bool ) @ hAPP_A1014090479t_bool ) @ ( d @ ( e @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) )
          & ( ( n @ ( A @ ( h @ hAPP_A1895296483di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( e @ ( A @ ( p @ hAPP_A340536322t_bool ) @ ( arrow_312654597_mktop @ hAPP_f102394819t_bool ) @ hAPP_A1014090479t_bool ) @ ( d @ ( e @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) )
       => ( ( ~ ( n @ ( A @ ( h @ hAPP_A1895296483di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( lba @ ( a @ ( b @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
          & ( ( n @ ( A @ ( h @ hAPP_A1895296483di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( lab @ ( a @ ( b @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).

thf(159,axiom,
    ! [A: $i] :
      ( ( A @ is_fun701126715l_bool )
     => ( A @ collec1567922785t_bool @ is_fun701126715l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oi) ).

thf(1374,plain,
    ! [A: $i] :
      ( ( A @ is_fun701126715l_bool )
     => ( A @ collec1567922785t_bool @ is_fun701126715l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(476,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( C = A )
       => ( A @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_ord__less__eq__trans) ).

thf(2524,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( C = A )
       => ( A @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(239,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/sandbox2/benchmark/theBenchmark.p',fact_661_Suc__le__eq) ).

thf(1631,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)],[239]) ).

thf(27,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_Arr859726945e_indi )
     => ( B @ ( A @ hAPP_A340536322t_bool ) @ is_fun20916972t_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It_004) ).

thf(965,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_Arr859726945e_indi )
     => ( B @ ( A @ hAPP_A340536322t_bool ) @ is_fun20916972t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(206,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( A @ ( C @ hAPP_nat_bool ) @ ( A @ ( B @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_le__funE) ).

thf(1510,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( A @ ( C @ hAPP_nat_bool ) @ ( A @ ( B @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(654,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun1568535512t_bool )
        & ( A @ is_fun1568535512t_bool ) )
     => ( ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( ( A != B )
         => ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_order__le__neq__trans) ).

thf(3358,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun1568535512t_bool )
        & ( A @ is_fun1568535512t_bool ) )
     => ( ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( ( A != B )
         => ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).

thf(785,axiom,
    ! [A: $i] :
      ~ ( A @ ( top_top_fun_nat_bool @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_not__top__less) ).

thf(3871,plain,
    ! [A: $i] :
      ~ ( A @ ( top_top_fun_nat_bool @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).

thf(361,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun2015243113i_bool )
     => ( ( B @ ( A @ ( cOMBK_1399131793t_bool @ hAPP_f1077635369i_bool ) @ hAPP_f431432850i_bool ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__) ).

thf(2033,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun2015243113i_bool )
     => ( ( B @ ( A @ ( cOMBK_1399131793t_bool @ hAPP_f1077635369i_bool ) @ hAPP_f431432850i_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(582,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_457_psubset__subset__trans) ).

thf(3042,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(486,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( ( ( A @ hBOOL )
        <=> ( B @ hBOOL ) )
        | ( B @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_order__le__imp__less__or__eq) ).

thf(2585,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( ( ( ( B @ hBOOL )
           => ( A @ hBOOL ) )
          & ( ( A @ hBOOL )
           => ( B @ hBOOL ) ) )
        | ( B @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(215,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/sandbox2/benchmark/theBenchmark.p',fact_660_le__imp__less__Suc) ).

thf(1548,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)],[215]) ).

thf(815,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_xt1_I5_J) ).

thf(3985,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).

thf(745,axiom,
    ! [A: $i] : ( top_to207207712i_bool @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_top__greatest) ).

thf(3738,plain,
    ! [A: $i] : ( top_to207207712i_bool @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).

thf(778,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( B = A )
       => ( C @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_xt1_I4_J) ).

thf(3839,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( B = A )
       => ( C @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).

thf(93,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
    <=> ! [C: $i] : ( C @ ( B @ hAPP_nat_bool ) @ ( C @ ( A @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_le__fun__def) ).

thf(1154,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i] : ( C @ ( B @ hAPP_nat_bool ) @ ( C @ ( A @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ! [C: $i] : ( C @ ( B @ hAPP_nat_bool ) @ ( C @ ( A @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(663,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/sandbox2/benchmark/theBenchmark.p',fact_115_xt1_I1_J) ).

thf(3387,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)],[663]) ).

thf(590,axiom,
    ( ( p @ ( f @ hAPP_f1817389232t_bool ) @ ( d @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
  <=> ( e @ ( p @ ( arrow_163947511_mkbot @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( e @ ( c @ ( p @ ( arrow_1046586475_above @ cOMBB_930893948e_indi @ hAPP_f1044120523t_bool ) @ ( cOMBC_1377016489t_bool @ hAPP_f114580065t_bool ) @ hAPP_A711952286t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( e @ ( p @ ( arrow_312654597_mktop @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( d @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_PW) ).

thf(3070,plain,
    ( ( ( e @ ( p @ ( arrow_163947511_mkbot @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( e @ ( c @ ( p @ ( arrow_1046586475_above @ cOMBB_930893948e_indi @ hAPP_f1044120523t_bool ) @ ( cOMBC_1377016489t_bool @ hAPP_f114580065t_bool ) @ hAPP_A711952286t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( e @ ( p @ ( arrow_312654597_mktop @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( d @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
     => ( p @ ( f @ hAPP_f1817389232t_bool ) @ ( d @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
    & ( ( p @ ( f @ hAPP_f1817389232t_bool ) @ ( d @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
     => ( e @ ( p @ ( arrow_163947511_mkbot @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( e @ ( c @ ( p @ ( arrow_1046586475_above @ cOMBB_930893948e_indi @ hAPP_f1044120523t_bool ) @ ( cOMBC_1377016489t_bool @ hAPP_f114580065t_bool ) @ hAPP_A711952286t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( e @ ( p @ ( arrow_312654597_mktop @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( d @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(42,axiom,
    ! [A: $i] :
      ( ( A @ ( zero_zero_nat @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_618_plus__nat_Oadd__0) ).

thf(1007,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)],[42]) ).

thf(321,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun20916972t_bool )
     => ( ( B @ ( A @ ( cOMBK_1685845624l_bool @ hAPP_f581841297t_bool ) @ hAPP_b763490121t_bool ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy) ).

thf(1916,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun20916972t_bool )
     => ( ( B @ ( A @ ( cOMBK_1685845624l_bool @ hAPP_f581841297t_bool ) @ hAPP_b763490121t_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(165,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_1377016489t_bool @ hAPP_f114580065t_bool ) @ hAPP_A711952286t_bool ) @ hAPP_A85603248t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A1202525278t_bool ) @ hAPP_A28770973t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_048) ).

thf(1389,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_1377016489t_bool @ hAPP_f114580065t_bool ) @ hAPP_A711952286t_bool ) @ hAPP_A85603248t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A1202525278t_bool ) @ hAPP_A28770973t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(768,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( A @ ( C @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_ord__eq__less__trans) ).

thf(3811,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( A @ ( C @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).

thf(85,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/sandbox2/benchmark/theBenchmark.p',fact_570_termination__basic__simps_I3_J) ).

thf(1125,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)],[85]) ).

thf(237,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/sandbox2/benchmark/theBenchmark.p',fact_644_add__Suc__right) ).

thf(1620,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)],[237]) ).

thf(271,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_1146692694ol_nat @ hAPP_f66927821l_bool ) @ hAPP_n215258509l_bool ) )
      = ( C @ ( B @ hAPP_nat_nat ) @ ( A @ hAPP_n215258509l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HO) ).

thf(1752,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_1146692694ol_nat @ hAPP_f66927821l_bool ) @ hAPP_n215258509l_bool ) )
      = ( C @ ( B @ hAPP_nat_nat ) @ ( A @ hAPP_n215258509l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(325,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/sandbox2/benchmark/theBenchmark.p',fact_687_Suc__eq__plus1__left) ).

thf(1929,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)],[325]) ).

thf(475,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
    <=> ( ( A != B )
        & ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_order__less__le) ).

thf(2514,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A != B )
          & ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( ( A != B )
          & ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(794,axiom,
    ! [A: $i] : ( top_to846262053l_bool @ ( A @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_top__greatest) ).

thf(3900,plain,
    ! [A: $i] : ( top_to846262053l_bool @ ( A @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).

thf(256,axiom,
    ( top_to935749874l_bool
    = ( fTrue @ ( cOMBK_776847951t_bool @ hAPP_b1461182872l_bool ) @ collec1567922785t_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_UNIV__def) ).

thf(1701,plain,
    ( top_to935749874l_bool
    = ( fTrue @ ( cOMBK_776847951t_bool @ hAPP_b1461182872l_bool ) @ collec1567922785t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(339,axiom,
    ! [A: $i] :
      ( ( A != zero_zero_nat )
    <=> ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_616_neq0__conv) ).

thf(1965,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)],[339]) ).

thf(834,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( C @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_xt1_I3_J) ).

thf(4041,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( C @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).

thf(861,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( ( ( C @ hBOOL )
        <=> ( A @ hBOOL ) )
       => ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_ord__le__eq__trans) ).

thf(4144,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( ( ( ( A @ hBOOL )
           => ( C @ hBOOL ) )
          & ( ( C @ hBOOL )
           => ( A @ hBOOL ) ) )
       => ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).

thf(659,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_order__antisym__conv) ).

thf(3372,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( ( B = A )
         => ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
        & ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).

thf(410,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro1208494515le_alt ) @ ( B @ ( member485283698le_alt @ hAPP_f2011903565l_bool ) @ hAPP_f1117143157l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P401722323t_bool ) @ ( A @ ( B @ hAPP_P1931143485le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_PiE) ).

thf(2225,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro1208494515le_alt ) @ ( B @ ( member485283698le_alt @ hAPP_f2011903565l_bool ) @ hAPP_f1117143157l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P401722323t_bool ) @ ( A @ ( B @ hAPP_P1931143485le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(696,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/sandbox2/benchmark/theBenchmark.p',fact_540_nat__le__linear) ).

thf(3504,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)],[696]) ).

thf(636,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ is_Arr723427730le_alt )
        & ( B @ is_Arr723427730le_alt ) )
     => ( ( B != C )
       => ( ( arrow_912654623le_Lin @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
         => ( arrow_912654623le_Lin @ ( C @ ( B @ ( A @ arrow_207701375_below ) ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_544_below__Lin) ).

thf(3272,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ is_Arr723427730le_alt )
        & ( B @ is_Arr723427730le_alt ) )
     => ( ( B != C )
       => ( ( arrow_912654623le_Lin @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
         => ( arrow_912654623le_Lin @ ( C @ ( B @ ( A @ arrow_207701375_below ) ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(855,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Product_unit_nat ) @ ( B @ ( member87760213it_nat @ hAPP_f1950626059l_bool ) @ hAPP_f339859954l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P32877782t_bool ) @ ( A @ ( B @ hAPP_P426034740it_nat ) @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_PiE) ).

thf(4122,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Product_unit_nat ) @ ( B @ ( member87760213it_nat @ hAPP_f1950626059l_bool ) @ hAPP_f339859954l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P32877782t_bool ) @ ( A @ ( B @ hAPP_P426034740it_nat ) @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).

thf(25,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/sandbox2/benchmark/theBenchmark.p',fact_691_Suc__lessE) ).

thf(958,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)],[25]) ).

thf(171,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/sandbox2/benchmark/theBenchmark.p',fact_417_add__left__imp__eq) ).

thf(1403,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)],[171]) ).

thf(630,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_order__eq__refl) ).

thf(3223,plain,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(203,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_bool )
     => ( B @ ( A @ hAPP_b1096750261t_bool ) @ is_fun1568535512t_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Ob) ).

thf(1503,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_bool )
     => ( B @ ( A @ hAPP_b1096750261t_bool ) @ is_fun1568535512t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(754,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( ( A @ ( B @ hAPP_nat_nat ) @ ( B @ ( C @ hilber195283148at_nat ) @ hAPP_nat_nat ) )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_385_inv__into__f__f) ).

thf(3773,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( ( A @ ( B @ hAPP_nat_nat ) @ ( B @ ( C @ hilber195283148at_nat ) @ hAPP_nat_nat ) )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).

thf(359,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] : ( C @ ( B @ hAPP_nat_bool ) @ ( C @ ( A @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_436_le__funI) ).

thf(2029,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] : ( C @ ( B @ hAPP_nat_bool ) @ ( C @ ( A @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(138,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/sandbox2/benchmark/theBenchmark.p',fact_424_add__mono) ).

thf(1312,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)],[138]) ).

thf(735,axiom,
    ! [A: $i] : ( top_to846262053l_bool @ ( A @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_406_subset__UNIV) ).

thf(3651,plain,
    ! [A: $i] : ( top_to846262053l_bool @ ( A @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).

thf(869,axiom,
    ! [A: $i,B: $i] :
      ( ( arrow_912654623le_Lin @ ( cOMBK_1918246033t_bool @ hAPP_f633903640l_bool ) @ ( arrow_583275979e_Prof @ pi_fun1555365306t_bool ) @ ( B @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
     => ( ! [C: $i] :
            ( ( arrow_583275979e_Prof @ ( C @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
           => ! [D: $i,E: $i] :
                ( ( ( E @ is_Arr723427730le_alt )
                  & ( D @ is_Arr723427730le_alt ) )
               => ( ( D != E )
                 => ( ( A @ ( C @ hAPP_A340536322t_bool ) @ ( E @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                   => ( C @ ( B @ hAPP_f1817389232t_bool ) @ ( E @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) ) )
       => ( A @ ( B @ ( arrow_1549387998ctator @ hAPP_f783549695i_bool ) @ hAPP_A416869060i_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_dictatorI) ).

thf(4171,plain,
    ! [A: $i,B: $i] :
      ( ( arrow_912654623le_Lin @ ( cOMBK_1918246033t_bool @ hAPP_f633903640l_bool ) @ ( arrow_583275979e_Prof @ pi_fun1555365306t_bool ) @ ( B @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
     => ( ! [C: $i] :
            ( ( arrow_583275979e_Prof @ ( C @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
           => ! [D: $i,E: $i] :
                ( ( ( E @ is_Arr723427730le_alt )
                  & ( D @ is_Arr723427730le_alt ) )
               => ( ( D != E )
                 => ( ( A @ ( C @ hAPP_A340536322t_bool ) @ ( E @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                   => ( C @ ( B @ hAPP_f1817389232t_bool ) @ ( E @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) ) )
       => ( A @ ( B @ ( arrow_1549387998ctator @ hAPP_f783549695i_bool ) @ hAPP_A416869060i_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).

thf(651,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun1568535512t_bool )
        & ( A @ is_fun1568535512t_bool ) )
     => ( ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
      <=> ( ( A = B )
          | ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_order__le__less) ).

thf(3340,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun1568535512t_bool )
        & ( A @ is_fun1568535512t_bool ) )
     => ( ( ( ( A = B )
            | ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) )
         => ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) )
        & ( ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
         => ( ( A = B )
            | ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).

thf(146,axiom,
    ! [A: $i] :
      ( ( A != zero_zero_nat )
     => ? [B: $i] :
          ( A
          = ( B @ ( suc @ hAPP_nat_nat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_692_not0__implies__Suc) ).

thf(1332,plain,
    ! [A: $i] :
      ( ( A != zero_zero_nat )
     => ? [B: $i] :
          ( A
          = ( B @ ( suc @ hAPP_nat_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(463,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro1873779901t_bool ) @ ( B @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_P1122857141l_bool ) @ ( A @ ( B @ hAPP_P1813625415t_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_372_Pi__mem) ).

thf(2442,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro1873779901t_bool ) @ ( B @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ( A @ ( D @ hAPP_P1122857141l_bool ) @ ( A @ ( B @ hAPP_P1813625415t_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(511,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Arr604548589di_nat ) @ ( B @ ( member873781636di_nat @ hAPP_f758593513l_bool ) @ hAPP_f599997089l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_A1948275303t_bool ) @ ( A @ ( B @ hAPP_A1895296483di_nat ) @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_PiE) ).

thf(2706,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Arr604548589di_nat ) @ ( B @ ( member873781636di_nat @ hAPP_f758593513l_bool ) @ hAPP_f599997089l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_A1948275303t_bool ) @ ( A @ ( B @ hAPP_A1895296483di_nat ) @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(467,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/sandbox2/benchmark/theBenchmark.p',fact_169_mem__def) ).

thf(2457,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)],[467]) ).

thf(114,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/sandbox2/benchmark/theBenchmark.p',fact_563_nat__add__left__cancel__le) ).

thf(1224,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)],[114]) ).

thf(391,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( member_Product_unit @ ( cOMBC_2133163426l_bool @ hAPP_f1458726223t_bool ) @ hAPP_f427533077t_bool ) @ ( A @ ( member_Product_unit @ ( cOMBC_2133163426l_bool @ hAPP_f1458726223t_bool ) @ hAPP_f427533077t_bool ) @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
    <=> ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_494_pred__subset__eq) ).

thf(2148,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( B @ ( member_Product_unit @ ( cOMBC_2133163426l_bool @ hAPP_f1458726223t_bool ) @ hAPP_f427533077t_bool ) @ ( A @ ( member_Product_unit @ ( cOMBC_2133163426l_bool @ hAPP_f1458726223t_bool ) @ hAPP_f427533077t_bool ) @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) )
      & ( ( B @ ( member_Product_unit @ ( cOMBC_2133163426l_bool @ hAPP_f1458726223t_bool ) @ hAPP_f427533077t_bool ) @ ( A @ ( member_Product_unit @ ( cOMBC_2133163426l_bool @ hAPP_f1458726223t_bool ) @ hAPP_f427533077t_bool ) @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(605,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_460_subset__psubset__trans) ).

thf(3118,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(408,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_440_subsetD) ).

thf(2220,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(58,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f54304608l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).

thf(1058,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f54304608l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(77,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1426445843l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Nat__Onat_J_Mtc__HOL__Obool_J) ).

thf(1107,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1426445843l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(691,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
    <=> ( A @ ( B @ hAPP_P1813625415t_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_mem__def) ).

thf(3487,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ hAPP_P1813625415t_bool ) @ hBOOL )
       => ( B @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ( A @ ( B @ hAPP_P1813625415t_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).

thf(70,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_264525026l_bool @ hAPP_f651290349i_bool ) @ hAPP_f1282033109i_bool ) @ hAPP_A416869060i_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_044) ).

thf(1092,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_264525026l_bool @ hAPP_f651290349i_bool ) @ hAPP_f1282033109i_bool ) @ hAPP_A416869060i_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(775,axiom,
    ! [A: $i] : ( top_to1773227171t_bool @ ( A @ ( ord_le64728819t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_409_subset__UNIV) ).

thf(3832,plain,
    ! [A: $i] : ( top_to1773227171t_bool @ ( A @ ( ord_le64728819t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).

thf(274,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f937100551l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__prod_Itc__Arrow____) ).

thf(1765,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f937100551l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(725,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_nat_bool ) @ ( B @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_n1006566506l_bool ) @ ( A @ ( B @ hAPP_nat_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_PiE) ).

thf(3619,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_nat_bool ) @ ( B @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_n1006566506l_bool ) @ ( A @ ( B @ hAPP_nat_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).

thf(644,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2015243113i_bool )
        & ( A @ is_fun2015243113i_bool ) )
     => ( ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( A = B )
          | ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_order__le__imp__less__or__eq) ).

thf(3302,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2015243113i_bool )
        & ( A @ is_fun2015243113i_bool ) )
     => ( ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( A = B )
          | ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).

thf(714,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_fun623621634t_unit ) @ ( B @ ( member982489409t_unit @ hAPP_f1160956173l_bool ) @ hAPP_f1082951236l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_f1009478556t_bool ) @ ( A @ ( B @ hAPP_f754536332t_unit ) @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_PiE) ).

thf(3568,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_fun623621634t_unit ) @ ( B @ ( member982489409t_unit @ hAPP_f1160956173l_bool ) @ hAPP_f1082951236l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_f1009478556t_bool ) @ ( A @ ( B @ hAPP_f754536332t_unit ) @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).

thf(436,axiom,
    ! [A: $i,B: $i] :
      ( ( A != B )
     => ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_order__neq__le__trans) ).

thf(2346,plain,
    ! [A: $i,B: $i] :
      ( ( A != B )
     => ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(600,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_350223551e_indi @ hAPP_f1639180358l_bool ) @ ( C @ pi_Arr1801471756t_bool ) @ ( B @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
     => ( ( C @ ( B @ inj_on1507564774t_bool @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( C @ ( cOMBK_1399131793t_bool @ hAPP_f1077635369i_bool ) @ ( D @ pi_fun596906370e_indi ) @ ( A @ ( member1935624595e_indi @ hAPP_f2022872455l_bool ) @ hAPP_f1021828400l_bool ) @ hBOOL )
         => ( ( D @ ( A @ inj_on302999388e_indi @ hAPP_f560517119l_bool ) @ hBOOL )
           => ( ( C @ ( finite921964625e_indi @ hAPP_f160177134l_bool ) @ hBOOL )
             => ( ( D @ ( finite274731772t_bool @ hAPP_f560517119l_bool ) @ hBOOL )
               => ( ( C @ finite354462354e_indi )
                  = ( D @ finite945540987t_bool ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_599_card__bij) ).

thf(3101,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_350223551e_indi @ hAPP_f1639180358l_bool ) @ ( C @ pi_Arr1801471756t_bool ) @ ( B @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
     => ( ( C @ ( B @ inj_on1507564774t_bool @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( C @ ( cOMBK_1399131793t_bool @ hAPP_f1077635369i_bool ) @ ( D @ pi_fun596906370e_indi ) @ ( A @ ( member1935624595e_indi @ hAPP_f2022872455l_bool ) @ hAPP_f1021828400l_bool ) @ hBOOL )
         => ( ( D @ ( A @ inj_on302999388e_indi @ hAPP_f560517119l_bool ) @ hBOOL )
           => ( ( C @ ( finite921964625e_indi @ hAPP_f160177134l_bool ) @ hBOOL )
             => ( ( D @ ( finite274731772t_bool @ hAPP_f560517119l_bool ) @ hBOOL )
               => ( ( C @ finite354462354e_indi )
                  = ( D @ finite945540987t_bool ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(383,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_943734388l_bool @ hAPP_f372913425t_bool ) @ hAPP_f1068593625t_bool ) @ hAPP_A1120018583t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A433435097l_bool ) @ hAPP_f1733357041l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000t) ).

thf(2119,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_943734388l_bool @ hAPP_f372913425t_bool ) @ hAPP_f1068593625t_bool ) @ hAPP_A1120018583t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A433435097l_bool ) @ hAPP_f1733357041l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(130,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( D @ is_Arr859726945e_indi )
         => ( ( C @ ( D @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
           => ( D @ ( B @ hAPP_A659996934l_bool ) @ ( D @ ( A @ hAPP_A659996934l_bool ) @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) )
     => ( B @ ( C @ pi_Arr1801471756t_bool ) @ ( A @ ( C @ pi_Arr1801471756t_bool ) @ ( ord_le1482529602l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_502_Pi__mono) ).

thf(1282,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( D @ is_Arr859726945e_indi )
         => ( ( C @ ( D @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
           => ( D @ ( B @ hAPP_A659996934l_bool ) @ ( D @ ( A @ hAPP_A659996934l_bool ) @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) )
     => ( B @ ( C @ pi_Arr1801471756t_bool ) @ ( A @ ( C @ pi_Arr1801471756t_bool ) @ ( ord_le1482529602l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(769,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_bool_nat ) @ ( B @ ( member_fun_bool_nat @ hAPP_f144393719l_bool ) @ hAPP_f67777128l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_b1013836512t_bool ) @ ( A @ ( B @ hAPP_bool_nat ) @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_PiE) ).

thf(3815,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_bool_nat ) @ ( B @ ( member_fun_bool_nat @ hAPP_f144393719l_bool ) @ hAPP_f67777128l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_b1013836512t_bool ) @ ( A @ ( B @ hAPP_bool_nat ) @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).

thf(444,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le194694222l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_518_psubsetD) ).

thf(2383,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le194694222l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(286,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/sandbox2/benchmark/theBenchmark.p',fact_526_add__leD2) ).

thf(1806,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)],[286]) ).

thf(415,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
       => ( ( A @ hBOOL )
        <=> ( B @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_order__antisym) ).

thf(2246,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
       => ( ( ( B @ hBOOL )
           => ( A @ hBOOL ) )
          & ( ( A @ hBOOL )
           => ( B @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(263,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/sandbox2/benchmark/theBenchmark.p',fact_304_linorder__antisym__conv2) ).

thf(1722,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)],[263]) ).

thf(611,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL )
    <=> ! [C: $i] :
          ( ( C @ is_Arr859726945e_indi )
         => ( ( B @ ( C @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
           => ! [D: $i] :
                ( ( D @ is_Arr859726945e_indi )
               => ( ( B @ ( D @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
                 => ( ( ( C @ ( A @ hAPP_A1895296483di_nat ) )
                      = ( D @ ( A @ hAPP_A1895296483di_nat ) ) )
                   => ( C = D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_365_inj__on__def) ).

thf(3138,plain,
    ! [A: $i,B: $i] :
      ( ( ! [C: $i] :
            ( ( C @ is_Arr859726945e_indi )
           => ( ( B @ ( C @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
             => ! [D: $i] :
                  ( ( D @ is_Arr859726945e_indi )
                 => ( ( B @ ( D @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
                   => ( ( ( C @ ( A @ hAPP_A1895296483di_nat ) )
                        = ( D @ ( A @ hAPP_A1895296483di_nat ) ) )
                     => ( C = D ) ) ) ) ) )
       => ( B @ ( A @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL )
       => ! [C: $i] :
            ( ( C @ is_Arr859726945e_indi )
           => ( ( B @ ( C @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
             => ! [D: $i] :
                  ( ( D @ is_Arr859726945e_indi )
                 => ( ( B @ ( D @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
                   => ( ( ( C @ ( A @ hAPP_A1895296483di_nat ) )
                        = ( D @ ( A @ hAPP_A1895296483di_nat ) ) )
                     => ( C = D ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(84,axiom,
    ! [A: $i] :
      ~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_611_less__zeroE) ).

thf(1122,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)],[84]) ).

thf(662,axiom,
    ! [A: $i] :
      ~ ( A @ ( top_to846262053l_bool @ ( ord_le1260664009l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_not__top__less) ).

thf(3384,plain,
    ! [A: $i] :
      ~ ( A @ ( top_to846262053l_bool @ ( ord_le1260664009l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(478,axiom,
    ! [A: $i] :
      ( ( A @ ( top_top_fun_nat_bool @ hAPP_nat_bool ) @ hBOOL )
    <=> ( top_top_bool @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_top__apply) ).

thf(2538,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)],[478]) ).

thf(299,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/sandbox2/benchmark/theBenchmark.p',fact_298_leD) ).

thf(1853,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)],[299]) ).

thf(752,axiom,
    ! [A: $i] :
      ~ ( A @ ( top_to1257323279t_bool @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_not__top__less) ).

thf(3764,plain,
    ! [A: $i] :
      ~ ( A @ ( top_to1257323279t_bool @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).

thf(568,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_xt1_I7_J) ).

thf(2987,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(496,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_531_less__not__refl2) ).

thf(2637,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)],[496]) ).

thf(709,axiom,
    arrow_912654623le_Lin @ ( lba @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74__096Lba_A_058_ALin_096) ).

thf(3551,plain,
    arrow_912654623le_Lin @ ( lba @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).

thf(81,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/sandbox2/benchmark/theBenchmark.p',fact_621_add__eq__self__zero) ).

thf(1117,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)],[81]) ).

thf(229,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ hAPP_A725195434t_bool ) )
      = ( C @ ( B @ hAPP_A416869060i_bool ) @ ( A @ hAPP_b910261233t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow_) ).

thf(1589,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ hAPP_A725195434t_bool ) )
      = ( C @ ( B @ hAPP_A416869060i_bool ) @ ( A @ hAPP_b910261233t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(37,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun701126715l_bool )
     => ( B @ ( A @ hAPP_f189058133l_bool ) @ is_fun701126715l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_015) ).

thf(996,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun701126715l_bool )
     => ( B @ ( A @ hAPP_f189058133l_bool ) @ is_fun701126715l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(424,axiom,
    lab @ ( b @ ( a @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).

thf(2284,plain,
    lab @ ( b @ ( a @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(602,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le64728819t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_470_set__mp) ).

thf(3106,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le64728819t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(685,axiom,
    ! [A: $i,B: $i] : ( B @ ( ord_less_nat @ ( cOMBC_nat_nat_bool @ hAPP_f229349961t_bool ) @ hAPP_n1699378549t_bool ) @ ( A @ ( fconj @ cOMBB_1015721476ol_nat @ hAPP_f1146629647l_bool ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_606_finite__M__bounded__by__nat) ).

thf(3468,plain,
    ! [A: $i,B: $i] : ( B @ ( ord_less_nat @ ( cOMBC_nat_nat_bool @ hAPP_f229349961t_bool ) @ hAPP_n1699378549t_bool ) @ ( A @ ( fconj @ cOMBB_1015721476ol_nat @ hAPP_f1146629647l_bool ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).

thf(276,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/sandbox2/benchmark/theBenchmark.p',fact_547_not__add__less2) ).

thf(1771,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)],[276]) ).

thf(554,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_xt1_I7_J) ).

thf(2945,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(543,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A @ ( B @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_413_subset__inj__on) ).

thf(2896,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A @ ( B @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(251,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/sandbox2/benchmark/theBenchmark.p',fact_650_less__SucI) ).

thf(1690,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)],[251]) ).

thf(616,axiom,
    ! [A: $i] :
      ( ( A @ ( top_to207207712i_bool @ hAPP_A416869060i_bool ) @ hBOOL )
    <=> ( top_top_bool @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_top__apply) ).

thf(3182,plain,
    ! [A: $i] :
      ( ( ( top_top_bool @ hBOOL )
       => ( A @ ( top_to207207712i_bool @ hAPP_A416869060i_bool ) @ hBOOL ) )
      & ( ( A @ ( top_to207207712i_bool @ hAPP_A416869060i_bool ) @ hBOOL )
       => ( top_top_bool @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(160,axiom,
    top_to1257323279t_bool @ is_fun1568535512t_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL) ).

thf(1376,plain,
    top_to1257323279t_bool @ is_fun1568535512t_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(181,axiom,
    ! [A: $i] :
      ( ( zero_zero_nat @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_619_Nat_Oadd__0__right) ).

thf(1439,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)],[181]) ).

thf(850,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( A != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_order__less__imp__not__eq) ).

thf(4107,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).

thf(136,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/sandbox2/benchmark/theBenchmark.p',fact_685_less__imp__Suc__add) ).

thf(1307,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)],[136]) ).

thf(371,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/sandbox2/benchmark/theBenchmark.p',fact_537_nat__add__left__cancel) ).

thf(2065,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)],[371]) ).

thf(101,axiom,
    ! [A: $i] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
     != zero_zero_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_673_Suc__neq__Zero) ).

thf(1175,plain,
    ! [A: $i] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
     != zero_zero_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(682,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( A @ ( C @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_ord__eq__less__trans) ).

thf(3456,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( A @ ( C @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).

thf(490,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ in_rel1361124802le_alt ) ) @ hBOOL )
    <=> ( A @ ( C @ ( B @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_575_in__rel__def) ).

thf(2605,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( C @ ( B @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ( C @ ( B @ ( A @ in_rel1361124802le_alt ) ) @ hBOOL ) )
      & ( ( C @ ( B @ ( A @ in_rel1361124802le_alt ) ) @ hBOOL )
       => ( A @ ( C @ ( B @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(848,axiom,
    ! [A: $i] : ( top_to935749874l_bool @ ( A @ ( ord_le1482529602l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_408_subset__UNIV) ).

thf(4103,plain,
    ! [A: $i] : ( top_to935749874l_bool @ ( A @ ( ord_le1482529602l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).

thf(762,axiom,
    ! [A: $i] : ( top_to1849101472l_bool @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_iso__tuple__UNIV__I) ).

thf(3800,plain,
    ! [A: $i] : ( top_to1849101472l_bool @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).

thf(95,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/sandbox2/benchmark/theBenchmark.p',fact_573_termination__basic__simps_I1_J) ).

thf(1162,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)],[95]) ).

thf(618,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( C @ ( D @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
         => ( B @ ( D @ ( A @ hAPP_f1817389232t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) )
     => ( B @ ( cOMBK_1918246033t_bool @ hAPP_f633903640l_bool ) @ ( C @ pi_fun1555365306t_bool ) @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_578_funcsetI) ).

thf(3192,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( C @ ( D @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
         => ( B @ ( D @ ( A @ hAPP_f1817389232t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) )
     => ( B @ ( cOMBK_1918246033t_bool @ hAPP_f633903640l_bool ) @ ( C @ pi_fun1555365306t_bool ) @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

thf(11,axiom,
    ! [A: $i] :
      ~ ( A @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_631_Suc__n__not__le__n) ).

thf(915,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)],[11]) ).

thf(689,axiom,
    e @ ( p @ ( arrow_163947511_mkbot @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( e @ ( c @ ( p @ ( arrow_1046586475_above @ cOMBB_930893948e_indi @ hAPP_f1044120523t_bool ) @ ( cOMBC_1377016489t_bool @ hAPP_f114580065t_bool ) @ hAPP_A711952286t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( e @ ( p @ ( arrow_312654597_mktop @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( d @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/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(3483,plain,
    e @ ( p @ ( arrow_163947511_mkbot @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( e @ ( c @ ( p @ ( arrow_1046586475_above @ cOMBB_930893948e_indi @ hAPP_f1044120523t_bool ) @ ( cOMBC_1377016489t_bool @ hAPP_f114580065t_bool ) @ hAPP_A711952286t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( e @ ( p @ ( arrow_312654597_mktop @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( d @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).

thf(513,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1482529602l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
     => ( A @ ( B @ pi_fun1555365306t_bool ) @ ( A @ ( C @ pi_fun1555365306t_bool ) @ ( ord_le2143686384l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_404_Pi__anti__mono) ).

thf(2710,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1482529602l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
     => ( A @ ( B @ pi_fun1555365306t_bool ) @ ( A @ ( C @ pi_fun1555365306t_bool ) @ ( ord_le2143686384l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(79,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_nat_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__HOL__Obool) ).

thf(1112,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_nat_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(839,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_order__less__imp__not__eq2) ).

thf(4064,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)],[839]) ).

thf(346,axiom,
    a @ is_Arr723427730le_alt,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_a____) ).

thf(1993,plain,
    a @ is_Arr723427730le_alt,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(812,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ is_Arr859726945e_indi )
        & ( A @ is_Arr859726945e_indi ) )
     => ( ( top_to207207712i_bool @ ( C @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( ( A @ ( C @ hAPP_A1895296483di_nat ) )
            = ( B @ ( C @ hAPP_A1895296483di_nat ) ) )
         => ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_384_injD) ).

thf(3977,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ is_Arr859726945e_indi )
        & ( A @ is_Arr859726945e_indi ) )
     => ( ( top_to207207712i_bool @ ( C @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( ( A @ ( C @ hAPP_A1895296483di_nat ) )
            = ( B @ ( C @ hAPP_A1895296483di_nat ) ) )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).

thf(144,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/sandbox2/benchmark/theBenchmark.p',fact_694_zero__induct) ).

thf(1325,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)],[144]) ).

thf(51,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/sandbox2/benchmark/theBenchmark.p',fact_279_less__le__not__le) ).

thf(1029,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)],[51]) ).

thf(7,axiom,
    ! [A: $i] :
      ( zero_zero_nat
     != ( A @ ( suc @ hAPP_nat_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_674_Zero__neq__Suc) ).

thf(895,plain,
    ! [A: $i] :
      ( zero_zero_nat
     != ( A @ ( suc @ hAPP_nat_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(190,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/sandbox2/benchmark/theBenchmark.p',fact_549_trans__less__add1) ).

thf(1460,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)],[190]) ).

thf(426,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_fun568395771l_bool ) @ ( B @ ( member2021375116l_bool @ hAPP_f1171266041l_bool ) @ hAPP_f560261801l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_f812095627l_bool ) @ ( A @ ( B @ hAPP_f1733357041l_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_PiE) ).

thf(2289,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_fun568395771l_bool ) @ ( B @ ( member2021375116l_bool @ hAPP_f1171266041l_bool ) @ hAPP_f560261801l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_f812095627l_bool ) @ ( A @ ( B @ hAPP_f1733357041l_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(499,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
    <=> ( ~ ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
        & ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_399_less__fun__def) ).

thf(2647,plain,
    ! [A: $i,B: $i] :
      ( ( ( ~ ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( ~ ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(19,axiom,
    lba @ is_fun20916972t_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_Lba____) ).

thf(943,plain,
    lba @ is_fun20916972t_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(48,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_bool )
     => ( ( B @ ( A @ ( cOMBK_776847951t_bool @ hAPP_b1461182872l_bool ) @ hAPP_f1378099862l_bool ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabel) ).

thf(1022,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_bool )
     => ( ( B @ ( A @ ( cOMBK_776847951t_bool @ hAPP_b1461182872l_bool ) @ hAPP_f1378099862l_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(783,axiom,
    ! [A: $i] :
      ( ! [B: $i,C: $i] :
          ( ( ( C @ is_Arr859726945e_indi )
            & ( B @ is_Arr859726945e_indi ) )
         => ( ( ( B @ ( A @ hAPP_A1895296483di_nat ) )
              = ( C @ ( A @ hAPP_A1895296483di_nat ) ) )
           => ( B = C ) ) )
     => ( top_to207207712i_bool @ ( A @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_398_injI) ).

thf(3861,plain,
    ! [A: $i] :
      ( ! [B: $i,C: $i] :
          ( ( ( C @ is_Arr859726945e_indi )
            & ( B @ is_Arr859726945e_indi ) )
         => ( ( ( B @ ( A @ hAPP_A1895296483di_nat ) )
              = ( C @ ( A @ hAPP_A1895296483di_nat ) ) )
           => ( B = C ) ) )
     => ( top_to207207712i_bool @ ( A @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).

thf(530,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_order__less__asym_H) ).

thf(2842,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(16,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/sandbox2/benchmark/theBenchmark.p',fact_627_less__imp__add__positive) ).

thf(932,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)],[16]) ).

thf(99,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f2016919811l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_013) ).

thf(1171,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f2016919811l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(168,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f882250837l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls) ).

thf(1396,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f882250837l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(195,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_bool )
     => ( B @ ( A @ hAPP_b2116075462i_bool ) @ is_fun2015243113i_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabelle____wyls) ).

thf(1474,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_bool )
     => ( B @ ( A @ hAPP_b2116075462i_bool ) @ is_fun2015243113i_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(376,axiom,
    ! [A: $i] : ( A @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_order__refl) ).

thf(2086,plain,
    ! [A: $i] : ( A @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(242,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_bool )
     => ( ( B @ ( A @ ( cOMBK_790042732t_unit @ hAPP_b1096750261t_bool ) @ hAPP_P1676879539t_bool ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Product____Type__Ounit_U) ).

thf(1643,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_bool )
     => ( ( B @ ( A @ ( cOMBK_790042732t_unit @ hAPP_b1096750261t_bool ) @ hAPP_P1676879539t_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(765,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_order__less__imp__le) ).

thf(3806,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).

thf(441,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_455_psubset__subset__trans) ).

thf(2369,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(357,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/sandbox2/benchmark/theBenchmark.p',fact_625_ex__least__nat__less) ).

thf(2022,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)],[357]) ).

thf(876,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( B != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_order__less__imp__not__eq2) ).

thf(4196,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( B != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).

thf(536,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( A @ ( B @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_473_set__rev__mp) ).

thf(2867,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( A @ ( B @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(35,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/sandbox2/benchmark/theBenchmark.p',fact_274_order__less__le) ).

thf(983,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)],[35]) ).

thf(373,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/sandbox2/benchmark/theBenchmark.p',fact_647_Suc__less__eq) ).

thf(2075,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)],[373]) ).

thf(231,axiom,
    ! [A: $i] :
      ( ( A @ is_fun2015243113i_bool )
     => ( ( A @ collec279390863e_indi )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_Collect__def) ).

thf(1594,plain,
    ! [A: $i] :
      ( ( A @ is_fun2015243113i_bool )
     => ( ( A @ collec279390863e_indi )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(255,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f67777128l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__Nat__Onat_J_Mtc__HOL__Obool_) ).

thf(1699,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f67777128l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(729,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_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ ( cOMBC_1373788917t_bool @ hAPP_f1283354413t_bool ) @ hAPP_f1898540574t_bool ) @ ( cOMBC_1894996001t_bool @ hAPP_f1975142533t_bool ) @ hAPP_f590186314t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( b @ ( a @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_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_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ ( cOMBC_1373788917t_bool @ hAPP_f1283354413t_bool ) @ hAPP_f1898540574t_bool ) @ ( cOMBC_1894996001t_bool @ hAPP_f1975142533t_bool ) @ hAPP_f590186314t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( a @ ( b @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
      & ( top_to207207712i_bool @ finite354462354e_indi @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I) ).

thf(3627,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_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ ( cOMBC_1373788917t_bool @ hAPP_f1283354413t_bool ) @ hAPP_f1898540574t_bool ) @ ( cOMBC_1894996001t_bool @ hAPP_f1975142533t_bool ) @ hAPP_f590186314t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( b @ ( a @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_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_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ ( cOMBC_1373788917t_bool @ hAPP_f1283354413t_bool ) @ hAPP_f1898540574t_bool ) @ ( cOMBC_1894996001t_bool @ hAPP_f1975142533t_bool ) @ hAPP_f590186314t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( a @ ( b @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
      & ( top_to207207712i_bool @ finite354462354e_indi @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).

thf(395,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/sandbox2/benchmark/theBenchmark.p',fact_91_linorder__cases) ).

thf(2171,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)],[395]) ).

thf(366,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/sandbox2/benchmark/theBenchmark.p',fact_629_Suc__mono) ).

thf(2051,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)],[366]) ).

thf(521,axiom,
    ~ ! [A: $i] :
        ( ( A @ is_fun20916972t_bool )
       => ( ( A @ ( a @ ( b @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
         => ~ ( arrow_912654623le_Lin @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_) ).

thf(2765,plain,
    ~ ! [A: $i] :
        ( ( A @ is_fun20916972t_bool )
       => ( ( A @ ( a @ ( b @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
         => ~ ( arrow_912654623le_Lin @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(55,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/sandbox2/benchmark/theBenchmark.p',fact_284_order__le__less) ).

thf(1044,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)],[55]) ).

thf(121,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f2053170815l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__prod_Itc__Arrow____Order____) ).

thf(1245,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f2053170815l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(62,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/sandbox2/benchmark/theBenchmark.p',fact_553_less__add__eq__less) ).

thf(1066,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)],[62]) ).

thf(183,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_800536526ol_nat @ hAPP_f618557131t_bool ) @ hAPP_n1699378549t_bool ) )
      = ( C @ ( B @ hAPP_nat_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).

thf(1445,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_800536526ol_nat @ hAPP_f618557131t_bool ) @ hAPP_n1699378549t_bool ) )
      = ( C @ ( B @ hAPP_nat_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(414,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_520_psubset__trans) ).

thf(2244,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(39,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P1305865168l_bool ) @ is_fun292781289l_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Product____Type__Ounit_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow) ).

thf(1000,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P1305865168l_bool ) @ is_fun292781289l_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(699,axiom,
    ! [A: $i] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_order__refl) ).

thf(3512,plain,
    ! [A: $i] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).

thf(75,axiom,
    ! [A: $i] :
      ( ( A @ ( ord_less_nat @ ( cOMBC_nat_nat_bool @ hAPP_f229349961t_bool ) @ hAPP_n1699378549t_bool ) @ collect_nat @ finite_card_nat )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_604_card__Collect__less__nat) ).

thf(1102,plain,
    ! [A: $i] :
      ( ( A @ ( ord_less_nat @ ( cOMBC_nat_nat_bool @ hAPP_f229349961t_bool ) @ hAPP_n1699378549t_bool ) @ collect_nat @ finite_card_nat )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(572,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_bool )
     => ( ( B @ ( A @ ( cOMBK_715978704t_bool @ hAPP_b805997823l_bool ) @ hAPP_f1733357041l_bool ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order_) ).

thf(2999,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_bool )
     => ( ( B @ ( A @ ( cOMBK_715978704t_bool @ hAPP_b805997823l_bool ) @ hAPP_f1733357041l_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(652,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_761999167t_bool @ hAPP_f23348649l_bool ) @ ( C @ pi_fun328162388t_bool ) @ ( B @ ( member363954533t_bool @ hAPP_f1980578603l_bool ) @ hAPP_f1363425282l_bool ) @ hBOOL )
     => ( ( C @ ( B @ inj_on735362094t_bool @ hAPP_f560517119l_bool ) @ hBOOL )
       => ( ( C @ ( cOMBK_1918246033t_bool @ hAPP_f633903640l_bool ) @ ( D @ pi_fun1555365306t_bool ) @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
         => ( ( D @ ( A @ inj_on1962565012t_bool @ hAPP_f147218624l_bool ) @ hBOOL )
           => ( ( C @ ( finite274731772t_bool @ hAPP_f560517119l_bool ) @ hBOOL )
             => ( ( D @ ( finite1323840035t_bool @ hAPP_f147218624l_bool ) @ hBOOL )
               => ( ( C @ finite945540987t_bool )
                  = ( D @ finite1524925796t_bool ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_597_card__bij) ).

thf(3348,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_761999167t_bool @ hAPP_f23348649l_bool ) @ ( C @ pi_fun328162388t_bool ) @ ( B @ ( member363954533t_bool @ hAPP_f1980578603l_bool ) @ hAPP_f1363425282l_bool ) @ hBOOL )
     => ( ( C @ ( B @ inj_on735362094t_bool @ hAPP_f560517119l_bool ) @ hBOOL )
       => ( ( C @ ( cOMBK_1918246033t_bool @ hAPP_f633903640l_bool ) @ ( D @ pi_fun1555365306t_bool ) @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
         => ( ( D @ ( A @ inj_on1962565012t_bool @ hAPP_f147218624l_bool ) @ hBOOL )
           => ( ( C @ ( finite274731772t_bool @ hAPP_f560517119l_bool ) @ hBOOL )
             => ( ( D @ ( finite1323840035t_bool @ hAPP_f147218624l_bool ) @ hBOOL )
               => ( ( C @ finite945540987t_bool )
                  = ( D @ finite1524925796t_bool ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).

thf(787,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( C @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_xt1_I1_J) ).

thf(3876,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( C @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).

thf(14,axiom,
    ! [A: $i] :
      ( ( A @ ( cOMBI_nat @ hAPP_nat_nat ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBI_1_1_COMBI_000tc__Nat__Onat_U) ).

thf(922,plain,
    ! [A: $i] :
      ( ( A @ ( cOMBI_nat @ hAPP_nat_nat ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(881,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( cOMBK_1918246033t_bool @ hAPP_f633903640l_bool ) @ ( B @ pi_fun1555365306t_bool ) @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
     => ( ( B @ ( A @ inj_on1962565012t_bool @ hAPP_f147218624l_bool ) @ hBOOL )
       => ( ( C @ ( finite274731772t_bool @ hAPP_f560517119l_bool ) @ hBOOL )
         => ( C @ finite945540987t_bool @ ( B @ finite1524925796t_bool @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_590_card__inj) ).

thf(4209,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( cOMBK_1918246033t_bool @ hAPP_f633903640l_bool ) @ ( B @ pi_fun1555365306t_bool ) @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
     => ( ( B @ ( A @ inj_on1962565012t_bool @ hAPP_f147218624l_bool ) @ hBOOL )
       => ( ( C @ ( finite274731772t_bool @ hAPP_f560517119l_bool ) @ hBOOL )
         => ( C @ finite945540987t_bool @ ( B @ finite1524925796t_bool @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).

thf(567,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/sandbox2/benchmark/theBenchmark.p',fact_392_inj__imp__inv__eq) ).

thf(2984,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)],[567]) ).

thf(340,axiom,
    a != b,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75__096a_A_126_061_Ab_096) ).

thf(1973,plain,
    a != b,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(576,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun1568535512t_bool )
        & ( A @ is_fun1568535512t_bool ) )
     => ( ( A != B )
       => ( ( A @ ( B @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
         => ( A @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_xt1_I12_J) ).

thf(3009,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun1568535512t_bool )
        & ( A @ is_fun1568535512t_bool ) )
     => ( ( A != B )
       => ( ( A @ ( B @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
         => ( A @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(332,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_1722249314l_bool @ hAPP_f1500902601l_bool ) @ hAPP_f189058133l_bool ) @ hAPP_f1378099862l_bool ) )
      = ( B @ ( C @ ( A @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__) ).

thf(1948,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_1722249314l_bool @ hAPP_f1500902601l_bool ) @ hAPP_f189058133l_bool ) @ hAPP_f1378099862l_bool ) )
      = ( B @ ( C @ ( A @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(557,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( ~ ( ( A @ hBOOL )
          <=> ( B @ hBOOL ) )
       => ( B @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_order__le__neq__trans) ).

thf(2952,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( ~ ( ( ( B @ hBOOL )
             => ( A @ hBOOL ) )
            & ( ( A @ hBOOL )
             => ( B @ hBOOL ) ) )
       => ( B @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(306,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun701126715l_bool )
     => ( B @ ( A @ pi_fun1555365306t_bool ) @ is_fun292781289l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_FuncSet_OPi_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oin) ).

thf(1873,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun701126715l_bool )
     => ( B @ ( A @ pi_fun1555365306t_bool ) @ is_fun292781289l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(804,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ is_Arr723427730le_alt )
        & ( B @ is_Arr723427730le_alt )
        & ( A @ is_Arr723427730le_alt ) )
     => ( ( D @ ( C @ ( arrow_312654597_mktop @ hAPP_f102394819t_bool ) @ hAPP_A1014090479t_bool ) @ ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
      <=> ( ( ( B != D )
           => ( C @ ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
          & ( ( B = D )
           => ( A != B ) )
          & ( A != D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_in__mktop) ).

thf(3936,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ is_Arr723427730le_alt )
        & ( B @ is_Arr723427730le_alt )
        & ( A @ is_Arr723427730le_alt ) )
     => ( ( ( ( ( B != D )
             => ( C @ ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
            & ( ( B = D )
             => ( A != B ) )
            & ( A != D ) )
         => ( D @ ( C @ ( arrow_312654597_mktop @ hAPP_f102394819t_bool ) @ hAPP_A1014090479t_bool ) @ ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
        & ( ( D @ ( C @ ( arrow_312654597_mktop @ hAPP_f102394819t_bool ) @ hAPP_A1014090479t_bool ) @ ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
         => ( ( ( B != D )
             => ( C @ ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
            & ( ( B = D )
             => ( A != B ) )
            & ( A != D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).

thf(108,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/sandbox2/benchmark/theBenchmark.p',fact_624_add__gr__0) ).

thf(1203,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)],[108]) ).

thf(193,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f742658307l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell) ).

thf(1467,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f742658307l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(666,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( member_nat @ ( cOMBC_226598744l_bool @ hAPP_f1722879237t_bool ) @ hAPP_f800510211t_bool ) @ ( A @ ( member_nat @ ( cOMBC_226598744l_bool @ hAPP_f1722879237t_bool ) @ hAPP_f800510211t_bool ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
    <=> ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_496_pred__subset__eq) ).

thf(3395,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( B @ ( member_nat @ ( cOMBC_226598744l_bool @ hAPP_f1722879237t_bool ) @ hAPP_f800510211t_bool ) @ ( A @ ( member_nat @ ( cOMBC_226598744l_bool @ hAPP_f1722879237t_bool ) @ hAPP_f800510211t_bool ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
      & ( ( B @ ( member_nat @ ( cOMBC_226598744l_bool @ hAPP_f1722879237t_bool ) @ hAPP_f800510211t_bool ) @ ( A @ ( member_nat @ ( cOMBC_226598744l_bool @ hAPP_f1722879237t_bool ) @ hAPP_f800510211t_bool ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).

thf(362,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( D @ is_Arr859726945e_indi )
         => ( ( C @ ( D @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
           => ( D @ ( B @ hAPP_A659996934l_bool ) @ ( D @ ( A @ hAPP_A340536322t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) )
     => ( B @ ( C @ pi_Arr1801471756t_bool ) @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_584_Pi__I_H) ).

thf(2037,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( D @ is_Arr859726945e_indi )
         => ( ( C @ ( D @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
           => ( D @ ( B @ hAPP_A659996934l_bool ) @ ( D @ ( A @ hAPP_A340536322t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) )
     => ( B @ ( C @ pi_Arr1801471756t_bool ) @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(385,axiom,
    ! [A: $i] : ( top_to935749874l_bool @ ( A @ ( ord_le1482529602l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_top__greatest) ).

thf(2124,plain,
    ! [A: $i] : ( top_to935749874l_bool @ ( A @ ( ord_le1482529602l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(344,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/sandbox2/benchmark/theBenchmark.p',fact_285_leI) ).

thf(1990,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)],[344]) ).

thf(642,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun1568535512t_bool )
        & ( A @ is_fun1568535512t_bool ) )
     => ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
      <=> ( ( A != B )
          & ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_order__less__le) ).

thf(3292,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun1568535512t_bool )
        & ( A @ is_fun1568535512t_bool ) )
     => ( ( ( ( A != B )
            & ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) )
         => ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) )
        & ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
         => ( ( A != B )
            & ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).

thf(678,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( cOMBK_350223551e_indi @ hAPP_f1639180358l_bool ) @ ( B @ pi_Arr1801471756t_bool ) @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
     => ( ( B @ ( A @ inj_on1507564774t_bool @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( C @ ( finite274731772t_bool @ hAPP_f560517119l_bool ) @ hBOOL )
         => ( C @ finite945540987t_bool @ ( B @ finite354462354e_indi @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_589_card__inj) ).

thf(3444,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( cOMBK_350223551e_indi @ hAPP_f1639180358l_bool ) @ ( B @ pi_Arr1801471756t_bool ) @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
     => ( ( B @ ( A @ inj_on1507564774t_bool @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( C @ ( finite274731772t_bool @ hAPP_f560517119l_bool ) @ hBOOL )
         => ( C @ finite945540987t_bool @ ( B @ finite354462354e_indi @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).

thf(412,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_order__le__less__trans) ).

thf(2239,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(527,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun1084921220e_indi )
     => ( ( top_to207207712i_bool @ ( B @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ! [C: $i] :
              ( ( C @ ( A @ hAPP_n619554777e_indi ) @ ( B @ hAPP_A1895296483di_nat ) )
              = C )
         => ( ( B @ ( top_to207207712i_bool @ hilber951314860di_nat ) )
            = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_393_inj__imp__inv__eq) ).

thf(2816,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun1084921220e_indi )
     => ( ( top_to207207712i_bool @ ( B @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ! [C: $i] :
              ( ( C @ ( A @ hAPP_n619554777e_indi ) @ ( B @ hAPP_A1895296483di_nat ) )
              = C )
         => ( ( B @ ( top_to207207712i_bool @ hilber951314860di_nat ) )
            = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(547,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ is_Arr859726945e_indi )
        & ( A @ is_Arr859726945e_indi ) )
     => ( ( D @ ( C @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( ( A @ ( C @ hAPP_A1895296483di_nat ) )
            = ( B @ ( C @ hAPP_A1895296483di_nat ) ) )
         => ( ( D @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
           => ( ( D @ ( B @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
             => ( A = B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_371_inj__onD) ).

thf(2914,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( B @ is_Arr859726945e_indi )
        & ( A @ is_Arr859726945e_indi ) )
     => ( ( D @ ( C @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( ( A @ ( C @ hAPP_A1895296483di_nat ) )
            = ( B @ ( C @ hAPP_A1895296483di_nat ) ) )
         => ( ( D @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
           => ( ( D @ ( B @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
             => ( A = B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(580,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
         => ( ( B @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
           => ( ( ( C @ ( A @ hAPP_nat_nat ) )
                = ( D @ ( A @ hAPP_nat_nat ) ) )
             => ( C = D ) ) ) )
     => ( B @ ( A @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_591_inj__onI) ).

thf(3031,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
         => ( ( B @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
           => ( ( ( C @ ( A @ hAPP_nat_nat ) )
                = ( D @ ( A @ hAPP_nat_nat ) ) )
             => ( C = D ) ) ) )
     => ( B @ ( A @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(857,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ hBOOL )
      | ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).

thf(4136,plain,
    ! [A: $i,B: $i] :
      ( ( B @ hBOOL )
      | ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).

thf(492,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_464_set__mp) ).

thf(2614,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(717,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
    <=> ( A @ ( B @ hAPP_f1733357041l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_mem__def) ).

thf(3576,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ( B @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
       => ( A @ ( B @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).

thf(20,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun1420103068l_bool )
     => ( B @ ( A @ hAPP_f560517119l_bool ) @ is_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl_030) ).

thf(944,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun1420103068l_bool )
     => ( B @ ( A @ hAPP_f560517119l_bool ) @ is_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(813,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_order__trans) ).

thf(3981,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).

thf(471,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( C @ is_bool )
         => ( ( B @ ( C @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
           => ( A @ ( C @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) )
     => ( A @ ( B @ ( ord_le742797417l_bool @ hAPP_f612708895l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_504_subsetI) ).

thf(2503,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( C @ is_bool )
         => ( ( B @ ( C @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
           => ( A @ ( C @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) )
     => ( A @ ( B @ ( ord_le742797417l_bool @ hAPP_f612708895l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(67,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/sandbox2/benchmark/theBenchmark.p',fact_632_not__less__eq__eq) ).

thf(1081,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)],[67]) ).

thf(811,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_xt1_I10_J) ).

thf(3975,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).

thf(18,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun20916972t_bool )
     => ( ( B @ ( A @ ( cOMBK_776703103e_indi @ hAPP_f590186314t_bool ) @ hAPP_A340536322t_bool ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy_045) ).

thf(939,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun20916972t_bool )
     => ( ( B @ ( A @ ( cOMBK_776703103e_indi @ hAPP_f590186314t_bool ) @ hAPP_A340536322t_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(800,axiom,
    ! [A: $i] : ( A @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_492_subset__refl) ).

thf(3921,plain,
    ! [A: $i] : ( A @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).

thf(418,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( E @ is_Arr723427730le_alt )
        & ( D @ is_Arr723427730le_alt )
        & ( C @ is_Arr723427730le_alt ) )
     => ( ( D != E )
       => ( ( E != C )
         => ( ( D != C )
           => ( ( arrow_583275979e_Prof @ ( B @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
             => ( ( arrow_583275979e_Prof @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
               => ( ! [F: $i] :
                      ( ( F @ is_Arr859726945e_indi )
                     => ( ( F @ ( B @ hAPP_A340536322t_bool ) @ ( E @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                      <=> ( F @ ( A @ hAPP_A340536322t_bool ) @ ( C @ ( E @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) )
                 => ( ( B @ ( f @ hAPP_f1817389232t_bool ) @ ( E @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                  <=> ( A @ ( f @ hAPP_f1817389232t_bool ) @ ( C @ ( E @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8__C4_C) ).

thf(2256,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( ( E @ is_Arr723427730le_alt )
        & ( D @ is_Arr723427730le_alt )
        & ( C @ is_Arr723427730le_alt ) )
     => ( ( D != E )
       => ( ( E != C )
         => ( ( D != C )
           => ( ( arrow_583275979e_Prof @ ( B @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
             => ( ( arrow_583275979e_Prof @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
               => ( ! [F: $i] :
                      ( ( F @ is_Arr859726945e_indi )
                     => ( ( ( F @ ( A @ hAPP_A340536322t_bool ) @ ( C @ ( E @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                         => ( F @ ( B @ hAPP_A340536322t_bool ) @ ( E @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
                        & ( ( F @ ( B @ hAPP_A340536322t_bool ) @ ( E @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                         => ( F @ ( A @ hAPP_A340536322t_bool ) @ ( C @ ( E @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) )
                 => ( ( ( A @ ( f @ hAPP_f1817389232t_bool ) @ ( C @ ( E @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                     => ( B @ ( f @ hAPP_f1817389232t_bool ) @ ( E @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
                    & ( ( B @ ( f @ hAPP_f1817389232t_bool ) @ ( E @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                     => ( A @ ( f @ hAPP_f1817389232t_bool ) @ ( C @ ( E @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(852,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_fun187048122l_bool ) @ ( B @ ( member48503289l_bool @ hAPP_f2087408397l_bool ) @ hAPP_f750478076l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_f721327224l_bool ) @ ( A @ ( B @ hAPP_f446648900l_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_PiE) ).

thf(4113,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_fun187048122l_bool ) @ ( B @ ( member48503289l_bool @ hAPP_f2087408397l_bool ) @ hAPP_f750478076l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_f721327224l_bool ) @ ( A @ ( B @ hAPP_f446648900l_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).

thf(816,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le64728819t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
     => ( A @ ( B @ pi_Pro1873779901t_bool ) @ ( A @ ( C @ pi_Pro1873779901t_bool ) @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_402_Pi__anti__mono) ).

thf(3988,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le64728819t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
     => ( A @ ( B @ pi_Pro1873779901t_bool ) @ ( A @ ( C @ pi_Pro1873779901t_bool ) @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).

thf(214,axiom,
    top_to846262053l_bool @ is_fun1420103068l_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Ord) ).

thf(1547,plain,
    top_to846262053l_bool @ is_fun1420103068l_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(534,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Arr656802323t_bool ) @ ( B @ ( member104322770t_bool @ hAPP_f1836999501l_bool ) @ hAPP_f1898839893l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_A701636433l_bool ) @ ( A @ ( B @ hAPP_A739031709t_bool ) @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_PiE) ).

thf(2863,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Arr656802323t_bool ) @ ( B @ ( member104322770t_bool @ hAPP_f1836999501l_bool ) @ hAPP_f1898839893l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_A701636433l_bool ) @ ( A @ ( B @ hAPP_A739031709t_bool ) @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(831,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro1114473858t_bool ) @ ( B @ ( member1044213697t_bool @ hAPP_f813426957l_bool ) @ hAPP_f866114756l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P667392034l_bool ) @ ( A @ ( B @ hAPP_P1245388556t_bool ) @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_PiE) ).

thf(4035,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro1114473858t_bool ) @ ( B @ ( member1044213697t_bool @ hAPP_f813426957l_bool ) @ hAPP_f866114756l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P667392034l_bool ) @ ( A @ ( B @ hAPP_P1245388556t_bool ) @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).

thf(170,axiom,
    ! [A: $i] :
      ( ( A @ collect_nat )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_Collect__def) ).

thf(1400,plain,
    ! [A: $i] :
      ( ( A @ collect_nat )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(30,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/sandbox2/benchmark/theBenchmark.p',fact_551_add__less__mono1) ).

thf(971,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)],[30]) ).

thf(243,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/sandbox2/benchmark/theBenchmark.p',fact_557_less__imp__le__nat) ).

thf(1647,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)],[243]) ).

thf(625,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le742797417l_bool @ hAPP_f612708895l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ( A @ ( B @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_471_set__rev__mp) ).

thf(3209,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le742797417l_bool @ hAPP_f612708895l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ( A @ ( B @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(211,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/sandbox2/benchmark/theBenchmark.p',fact_633_le__Suc__eq) ).

thf(1531,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)],[211]) ).

thf(73,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_Arr859726945e_indi )
     => ( B @ ( A @ hAPP_A701636433l_bool ) @ is_fun701126715l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It) ).

thf(1098,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_Arr859726945e_indi )
     => ( B @ ( A @ hAPP_A701636433l_bool ) @ is_fun701126715l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(36,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_441619036t_bool @ hAPP_f775987425t_bool ) @ hAPP_f1840820673t_bool ) @ hAPP_A1781286015t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A64811457t_bool ) @ hAPP_f1068593625t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000t_047) ).

thf(993,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_441619036t_bool @ hAPP_f775987425t_bool ) @ hAPP_f1840820673t_bool ) @ hAPP_A1781286015t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A64811457t_bool ) @ hAPP_f1068593625t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(835,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( B != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_order__less__imp__not__eq2) ).

thf(4045,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( B != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).

thf(553,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2015243113i_bool )
        & ( A @ is_fun2015243113i_bool ) )
     => ( ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( A != B )
         => ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_order__le__neq__trans) ).

thf(2942,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2015243113i_bool )
        & ( A @ is_fun2015243113i_bool ) )
     => ( ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( A != B )
         => ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(283,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1363425282l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_029) ).

thf(1798,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1363425282l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(664,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_482_in__mono) ).

thf(3391,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(400,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1260664009l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_516_psubsetD) ).

thf(2192,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1260664009l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(3,axiom,
    ( top_to1257323279t_bool
    = ( fTrue @ ( cOMBK_790042732t_unit @ hAPP_b1096750261t_bool ) @ collect_Product_unit ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_UNIV__def) ).

thf(887,plain,
    ( top_to1257323279t_bool
    = ( fTrue @ ( cOMBK_790042732t_unit @ hAPP_b1096750261t_bool ) @ collect_Product_unit ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(220,axiom,
    ! [A: $i] :
      ( ( A @ is_fun1568535512t_bool )
     => ( A @ collect_Product_unit @ is_fun1568535512t_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000tc__Product____Type__Ounit) ).

thf(1566,plain,
    ! [A: $i] :
      ( ( A @ is_fun1568535512t_bool )
     => ( A @ collect_Product_unit @ is_fun1568535512t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(796,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ hBOOL )
      <=> ( B @ hBOOL ) )
     => ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_xt1_I3_J) ).

thf(3904,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( B @ hBOOL )
         => ( C @ hBOOL ) )
        & ( ( C @ hBOOL )
         => ( B @ hBOOL ) ) )
     => ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).

thf(23,axiom,
    ( top_to846262053l_bool
    = ( fTrue @ ( cOMBK_715978704t_bool @ hAPP_b805997823l_bool ) @ collec612883262t_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_UNIV__def) ).

thf(954,plain,
    ( top_to846262053l_bool
    = ( fTrue @ ( cOMBK_715978704t_bool @ hAPP_b805997823l_bool ) @ collec612883262t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(684,axiom,
    ! [A: $i] :
      ( ( A @ ( top_to935749874l_bool @ hAPP_f1378099862l_bool ) @ hBOOL )
    <=> ( top_top_bool @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_top__apply) ).

thf(3462,plain,
    ! [A: $i] :
      ( ( ( top_top_bool @ hBOOL )
       => ( A @ ( top_to935749874l_bool @ hAPP_f1378099862l_bool ) @ hBOOL ) )
      & ( ( A @ ( top_to935749874l_bool @ hAPP_f1378099862l_bool ) @ hBOOL )
       => ( top_top_bool @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).

thf(877,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_order__le__less__trans) ).

thf(4200,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).

thf(452,axiom,
    ! [A: $i] : ( A @ ( top_top_fun_nat_bool @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_top1I) ).

thf(2407,plain,
    ! [A: $i] : ( A @ ( top_top_fun_nat_bool @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(446,axiom,
    ! [A: $i] :
      ~ ( A @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_order__less__irrefl) ).

thf(2386,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(723,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_order__eq__refl) ).

thf(3608,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)],[723]) ).

thf(115,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/sandbox2/benchmark/theBenchmark.p',fact_318_xt1_I11_J) ).

thf(1230,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)],[115]) ).

thf(260,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/sandbox2/benchmark/theBenchmark.p',fact_560_le__add2) ).

thf(1716,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)],[260]) ).

thf(240,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f339859954l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__Nat__Onat_J_Mtc_) ).

thf(1637,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f339859954l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(711,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1482529602l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_444_subsetD) ).

thf(3554,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1482529602l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).

thf(317,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_Arr723427730le_alt )
     => ( B @ ( A @ hAPP_A1120018583t_bool ) @ is_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_000tc__HOL__Ob) ).

thf(1901,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_Arr723427730le_alt )
     => ( B @ ( A @ hAPP_A1120018583t_bool ) @ is_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(364,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( D @ is_Arr859726945e_indi )
         => ( ( C @ ( D @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
           => ( B @ ( D @ ( A @ hAPP_A340536322t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) )
     => ( B @ ( cOMBK_350223551e_indi @ hAPP_f1639180358l_bool ) @ ( C @ pi_Arr1801471756t_bool ) @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_577_funcsetI) ).

thf(2044,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ! [D: $i] :
          ( ( D @ is_Arr859726945e_indi )
         => ( ( C @ ( D @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
           => ( B @ ( D @ ( A @ hAPP_A340536322t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) )
     => ( B @ ( cOMBK_350223551e_indi @ hAPP_f1639180358l_bool ) @ ( C @ pi_Arr1801471756t_bool ) @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(112,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( A @ ( C @ hAPP_nat_bool ) @ ( A @ ( B @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_le__funD) ).

thf(1220,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( A @ ( C @ hAPP_nat_bool ) @ ( A @ ( B @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(10,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/sandbox2/benchmark/theBenchmark.p',fact_669_gr0__conv__Suc) ).

thf(907,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)],[10]) ).

thf(259,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/sandbox2/benchmark/theBenchmark.p',fact_684_inc__induct) ).

thf(1711,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)],[259]) ).

thf(594,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_less__imp__neq) ).

thf(3080,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)],[594]) ).

thf(517,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ! [E: $i] :
          ( ( D @ ( E @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
         => ( ( E @ ( C @ hAPP_P1813625415t_bool ) @ hBOOL )
          <=> ( E @ ( B @ hAPP_P1813625415t_bool ) @ hBOOL ) ) )
     => ( ( A @ ( D @ pi_Pro1873779901t_bool ) @ ( C @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
      <=> ( A @ ( D @ pi_Pro1873779901t_bool ) @ ( B @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_580_Pi__cong) ).

thf(2747,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ! [E: $i] :
          ( ( D @ ( E @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
         => ( ( ( E @ ( B @ hAPP_P1813625415t_bool ) @ hBOOL )
             => ( E @ ( C @ hAPP_P1813625415t_bool ) @ hBOOL ) )
            & ( ( E @ ( C @ hAPP_P1813625415t_bool ) @ hBOOL )
             => ( E @ ( B @ hAPP_P1813625415t_bool ) @ hBOOL ) ) ) )
     => ( ( ( A @ ( D @ pi_Pro1873779901t_bool ) @ ( B @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
         => ( A @ ( D @ pi_Pro1873779901t_bool ) @ ( C @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) )
        & ( ( A @ ( D @ pi_Pro1873779901t_bool ) @ ( C @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
         => ( A @ ( D @ pi_Pro1873779901t_bool ) @ ( B @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(645,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_1673635960le_alt @ hAPP_f719005683l_bool ) @ ( C @ pi_Pro1873779901t_bool ) @ ( B @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
     => ( ( C @ ( B @ inj_on398823523t_bool @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ( ( C @ ( cOMBK_1685845624l_bool @ hAPP_f581841297t_bool ) @ ( D @ pi_boo1542163389le_alt ) @ ( A @ ( member300433020le_alt @ hAPP_f452450509l_bool ) @ hAPP_f2053170815l_bool ) @ hBOOL )
         => ( ( D @ ( A @ inj_on67207011le_alt @ hAPP_f387058535l_bool ) @ hBOOL )
           => ( ( C @ ( finite955821396le_alt @ hAPP_f1733357041l_bool ) @ hBOOL )
             => ( ( D @ ( finite_finite_bool @ hAPP_f387058535l_bool ) @ hBOOL )
               => ( ( C @ finite1044330389le_alt )
                  = ( D @ finite_card_bool ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_598_card__bij) ).

thf(3305,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_1673635960le_alt @ hAPP_f719005683l_bool ) @ ( C @ pi_Pro1873779901t_bool ) @ ( B @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
     => ( ( C @ ( B @ inj_on398823523t_bool @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ( ( C @ ( cOMBK_1685845624l_bool @ hAPP_f581841297t_bool ) @ ( D @ pi_boo1542163389le_alt ) @ ( A @ ( member300433020le_alt @ hAPP_f452450509l_bool ) @ hAPP_f2053170815l_bool ) @ hBOOL )
         => ( ( D @ ( A @ inj_on67207011le_alt @ hAPP_f387058535l_bool ) @ hBOOL )
           => ( ( C @ ( finite955821396le_alt @ hAPP_f1733357041l_bool ) @ hBOOL )
             => ( ( D @ ( finite_finite_bool @ hAPP_f387058535l_bool ) @ hBOOL )
               => ( ( C @ finite1044330389le_alt )
                  = ( D @ finite_card_bool ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(177,axiom,
    ! [A: $i] :
      ( ( A @ is_fun292781289l_bool )
     => ( A @ collec1517527055t_bool @ is_fun292781289l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsu) ).

thf(1432,plain,
    ! [A: $i] :
      ( ( A @ is_fun292781289l_bool )
     => ( A @ collec1517527055t_bool @ is_fun292781289l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(421,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( ( B @ hBOOL )
        <=> ( A @ hBOOL ) )
     => ( ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_order__neq__le__trans) ).

thf(2276,plain,
    ! [A: $i,B: $i] :
      ( ~ ( ( ( A @ hBOOL )
           => ( B @ hBOOL ) )
          & ( ( B @ hBOOL )
           => ( A @ hBOOL ) ) )
     => ( ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(342,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/sandbox2/benchmark/theBenchmark.p',fact_423_add__le__imp__le__right) ).

thf(1980,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)],[342]) ).

thf(140,axiom,
    arrow_1486210539le_alt @ undefi1471133025le_alt @ is_Arr723427730le_alt,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt) ).

thf(1317,plain,
    arrow_1486210539le_alt @ undefi1471133025le_alt @ is_Arr723427730le_alt,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(291,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f537623936l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Product____Type__Ounit_J_Mtc_) ).

thf(1830,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f537623936l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(273,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( C @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_490_rev__predicate1D) ).

thf(1763,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ hAPP_nat_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( C @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(509,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/sandbox2/benchmark/theBenchmark.p',fact_187_inv__f__f) ).

thf(2701,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)],[509]) ).

thf(489,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
    <=> ( A @ ( B @ hAPP_f1378099862l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_mem__def) ).

thf(2599,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ hAPP_f1378099862l_bool ) @ hBOOL )
       => ( B @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
       => ( A @ ( B @ hAPP_f1378099862l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(727,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/sandbox2/benchmark/theBenchmark.p',fact_123_xt1_I9_J) ).

thf(3623,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)],[727]) ).

thf(669,axiom,
    ! [A: $i] : ( arrow_583275979e_Prof @ ( lba @ ( lab @ ( A @ ( h @ ( ord_less_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ ( cOMBC_1373788917t_bool @ hAPP_f1283354413t_bool ) @ hAPP_f1898540574t_bool ) @ ( cOMBC_1894996001t_bool @ hAPP_f1975142533t_bool ) @ hAPP_f590186314t_bool ) @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_PiProf) ).

thf(3412,plain,
    ! [A: $i] : ( arrow_583275979e_Prof @ ( lba @ ( lab @ ( A @ ( h @ ( ord_less_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ ( cOMBC_1373788917t_bool @ hAPP_f1283354413t_bool ) @ hAPP_f1898540574t_bool ) @ ( cOMBC_1894996001t_bool @ hAPP_f1975142533t_bool ) @ hAPP_f590186314t_bool ) @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).

thf(87,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/sandbox2/benchmark/theBenchmark.p',fact_574_termination__basic__simps_I5_J) ).

thf(1130,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)],[87]) ).

thf(225,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/sandbox2/benchmark/theBenchmark.p',fact_536_nat__add__assoc) ).

thf(1579,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)],[225]) ).

thf(268,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f599997089l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O) ).

thf(1738,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f599997089l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(111,axiom,
    ! [A: $i] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_623_less__eq__nat_Osimps_I1_J) ).

thf(1218,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)],[111]) ).

thf(368,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( suc @ hAPP_nat_nat ) )
        = ( B @ ( suc @ hAPP_nat_nat ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_638_Suc__inject) ).

thf(2056,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)],[368]) ).

thf(327,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun1420103068l_bool )
     => ( B @ ( A @ hAPP_f574392641l_bool ) @ is_fun1420103068l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl_031) ).

thf(1934,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun1420103068l_bool )
     => ( B @ ( A @ hAPP_f574392641l_bool ) @ is_fun1420103068l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(213,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_bool )
     => ( ( B @ ( A @ ( cOMBK_1391252605e_indi @ hAPP_b2116075462i_bool ) @ hAPP_A416869060i_bool ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Arrow____Order____Mirabelle____wyl) ).

thf(1543,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_bool )
     => ( ( B @ ( A @ ( cOMBK_1391252605e_indi @ hAPP_b2116075462i_bool ) @ hAPP_A416869060i_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(774,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_420816290l_bool @ hAPP_f1152614183t_bool ) @ hAPP_f137597973t_bool ) @ hAPP_P1813625415t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb_) ).

thf(3829,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_420816290l_bool @ hAPP_f1152614183t_bool ) @ hAPP_f137597973t_bool ) @ hAPP_P1813625415t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).

thf(692,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_452_psubset__imp__subset) ).

thf(3493,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).

thf(860,axiom,
    e @ ( p @ ( arrow_163947511_mkbot @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( e @ ( c @ ( p @ ( arrow_1046586475_above @ cOMBB_930893948e_indi @ hAPP_f1044120523t_bool ) @ ( cOMBC_1377016489t_bool @ hAPP_f114580065t_bool ) @ hAPP_A711952286t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( e @ ( p @ ( arrow_312654597_mktop @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( d @ ( e @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/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(4143,plain,
    e @ ( p @ ( arrow_163947511_mkbot @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( e @ ( c @ ( p @ ( arrow_1046586475_above @ cOMBB_930893948e_indi @ hAPP_f1044120523t_bool ) @ ( cOMBC_1377016489t_bool @ hAPP_f114580065t_bool ) @ hAPP_A711952286t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( e @ ( p @ ( arrow_312654597_mktop @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( d @ ( e @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).

thf(579,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
    <=> ( ~ ( A @ ( B @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
        & ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_400_less__fun__def) ).

thf(3024,plain,
    ! [A: $i,B: $i] :
      ( ( ( ~ ( A @ ( B @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( ~ ( A @ ( B @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(556,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ hBOOL )
      | ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).

thf(2949,plain,
    ! [A: $i,B: $i] :
      ( ( A @ hBOOL )
      | ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(885,axiom,
    ! [A: $i] :
      ( ( A @ ( p @ hAPP_A340536322t_bool ) @ ( d @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
    <=> ( ( ~ ( n @ ( A @ ( h @ hAPP_A1895296483di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( ( ( ( A @ ( h @ hAPP_A1895296483di_nat ) )
               != n )
             => ( e @ ( A @ ( p @ hAPP_A340536322t_bool ) @ ( arrow_163947511_mkbot @ hAPP_f102394819t_bool ) @ hAPP_A1014090479t_bool ) @ ( d @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
            & ( ( ( A @ ( h @ hAPP_A1895296483di_nat ) )
                = n )
             => ( e @ ( c @ ( A @ ( p @ hAPP_A340536322t_bool ) @ ( arrow_1046586475_above @ hAPP_f684072049t_bool ) @ hAPP_A28770973t_bool ) @ hAPP_A1014090479t_bool ) @ ( d @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) )
        & ( ( n @ ( A @ ( h @ hAPP_A1895296483di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
         => ( e @ ( A @ ( p @ hAPP_A340536322t_bool ) @ ( arrow_312654597_mktop @ hAPP_f102394819t_bool ) @ hAPP_A1014090479t_bool ) @ ( d @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J) ).

thf(4225,plain,
    ! [A: $i] :
      ( ( ( ( ~ ( n @ ( A @ ( h @ hAPP_A1895296483di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( ( ( ( A @ ( h @ hAPP_A1895296483di_nat ) )
                 != n )
               => ( e @ ( A @ ( p @ hAPP_A340536322t_bool ) @ ( arrow_163947511_mkbot @ hAPP_f102394819t_bool ) @ hAPP_A1014090479t_bool ) @ ( d @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
              & ( ( ( A @ ( h @ hAPP_A1895296483di_nat ) )
                  = n )
               => ( e @ ( c @ ( A @ ( p @ hAPP_A340536322t_bool ) @ ( arrow_1046586475_above @ hAPP_f684072049t_bool ) @ hAPP_A28770973t_bool ) @ hAPP_A1014090479t_bool ) @ ( d @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) )
          & ( ( n @ ( A @ ( h @ hAPP_A1895296483di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( e @ ( A @ ( p @ hAPP_A340536322t_bool ) @ ( arrow_312654597_mktop @ hAPP_f102394819t_bool ) @ hAPP_A1014090479t_bool ) @ ( d @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) )
       => ( A @ ( p @ hAPP_A340536322t_bool ) @ ( d @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
      & ( ( A @ ( p @ hAPP_A340536322t_bool ) @ ( d @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ( ( ~ ( n @ ( A @ ( h @ hAPP_A1895296483di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( ( ( ( A @ ( h @ hAPP_A1895296483di_nat ) )
                 != n )
               => ( e @ ( A @ ( p @ hAPP_A340536322t_bool ) @ ( arrow_163947511_mkbot @ hAPP_f102394819t_bool ) @ hAPP_A1014090479t_bool ) @ ( d @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
              & ( ( ( A @ ( h @ hAPP_A1895296483di_nat ) )
                  = n )
               => ( e @ ( c @ ( A @ ( p @ hAPP_A340536322t_bool ) @ ( arrow_1046586475_above @ hAPP_f684072049t_bool ) @ hAPP_A28770973t_bool ) @ hAPP_A1014090479t_bool ) @ ( d @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) )
          & ( ( n @ ( A @ ( h @ hAPP_A1895296483di_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
           => ( e @ ( A @ ( p @ hAPP_A340536322t_bool ) @ ( arrow_312654597_mktop @ hAPP_f102394819t_bool ) @ hAPP_A1014090479t_bool ) @ ( d @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).

thf(807,axiom,
    ! [A: $i] : ( top_to207207712i_bool @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_iso__tuple__UNIV__I) ).

thf(3961,plain,
    ! [A: $i] : ( top_to207207712i_bool @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).

thf(657,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_fun596906370e_indi ) @ ( B @ ( member1935624595e_indi @ hAPP_f2022872455l_bool ) @ hAPP_f1021828400l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_f431432850i_bool ) @ ( A @ ( B @ hAPP_f1283454584e_indi ) @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_PiE) ).

thf(3366,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_fun596906370e_indi ) @ ( B @ ( member1935624595e_indi @ hAPP_f2022872455l_bool ) @ hAPP_f1021828400l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_f431432850i_bool ) @ ( A @ ( B @ hAPP_f1283454584e_indi ) @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).

thf(851,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_xt1_I7_J) ).

thf(4111,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).

thf(640,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le2143686384l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_485_in__mono) ).

thf(3288,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le2143686384l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(90,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/sandbox2/benchmark/theBenchmark.p',fact_564_trans__le__add1) ).

thf(1141,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)],[90]) ).

thf(458,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_order__less__asym) ).

thf(2426,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(154,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/sandbox2/benchmark/theBenchmark.p',fact_425_add__left__mono) ).

thf(1353,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)],[154]) ).

thf(334,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/sandbox2/benchmark/theBenchmark.p',fact_571_termination__basic__simps_I4_J) ).

thf(1955,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)],[334]) ).

thf(878,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/sandbox2/benchmark/theBenchmark.p',fact_463_set__mp) ).

thf(4202,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)],[878]) ).

thf(33,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( B @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( C @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_479_predicate1D) ).

thf(978,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( B @ hAPP_nat_bool ) @ hBOOL )
       => ( A @ ( C @ hAPP_nat_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(474,axiom,
    ! [A: $i] :
      ~ ( A @ ( top_to1849101472l_bool @ ( ord_le1141238780l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_not__top__less) ).

thf(2511,plain,
    ! [A: $i] :
      ~ ( A @ ( top_to1849101472l_bool @ ( ord_le1141238780l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(127,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P957402556i_bool ) @ is_fun2015243113i_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__040) ).

thf(1272,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P957402556i_bool ) @ is_fun2015243113i_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(798,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
       => ( ( B @ hBOOL )
        <=> ( A @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_xt1_I5_J) ).

thf(3914,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
       => ( ( ( A @ hBOOL )
           => ( B @ hBOOL ) )
          & ( ( B @ hBOOL )
           => ( A @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).

thf(575,axiom,
    ! [A: $i] : ( top_to1773227171t_bool @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_iso__tuple__UNIV__I) ).

thf(3007,plain,
    ! [A: $i] : ( top_to1773227171t_bool @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(862,axiom,
    lba @ ( a @ ( b @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).

thf(4150,plain,
    lba @ ( a @ ( b @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).

thf(519,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_465_set__mp) ).

thf(2760,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(681,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( ~ ( ( B @ hBOOL )
          <=> ( A @ hBOOL ) )
       => ( B @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_xt1_I11_J) ).

thf(3452,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( ~ ( ( ( A @ hBOOL )
             => ( B @ hBOOL ) )
            & ( ( B @ hBOOL )
             => ( A @ hBOOL ) ) )
       => ( B @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).

thf(749,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( B != A )
       => ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_xt1_I11_J) ).

thf(3757,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( B != A )
       => ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).

thf(103,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_1373788917t_bool @ hAPP_f1283354413t_bool ) @ hAPP_f1898540574t_bool ) @ hAPP_A1906804694t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A725195434t_bool ) @ hAPP_f1000663785t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_052) ).

thf(1180,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_1373788917t_bool @ hAPP_f1283354413t_bool ) @ hAPP_f1898540574t_bool ) @ hAPP_A1906804694t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A725195434t_bool ) @ hAPP_f1000663785t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(507,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le2113500159t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_519_psubsetD) ).

thf(2696,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le2113500159t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(866,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_514_psubsetD) ).

thf(4165,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).

thf(559,axiom,
    arrow_912654623le_Lin @ ( lab @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73__096Lab_A_058_ALin_096) ).

thf(2960,plain,
    arrow_912654623le_Lin @ ( lab @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(293,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/sandbox2/benchmark/theBenchmark.p',fact_690_lessE) ).

thf(1834,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)],[293]) ).

thf(705,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ is_Arr723427730le_alt )
        & ( A @ is_Arr723427730le_alt ) )
     => ( ( arrow_912654623le_Lin @ ( C @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
       => ( ( A != B )
         => ( ~ ( C @ ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
          <=> ( C @ ( A @ ( B @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_notin__Lin__iff) ).

thf(3533,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ is_Arr723427730le_alt )
        & ( A @ is_Arr723427730le_alt ) )
     => ( ( arrow_912654623le_Lin @ ( C @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
       => ( ( A != B )
         => ( ( ( C @ ( A @ ( B @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
             => ~ ( C @ ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
            & ( ~ ( C @ ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
             => ( C @ ( A @ ( B @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).

thf(173,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( C @ is_Arr859726945e_indi )
         => ( ( B @ ( C @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
           => ( A @ ( C @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) )
     => ( A @ ( B @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_506_subsetI) ).

thf(1412,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( C @ is_Arr859726945e_indi )
         => ( ( B @ ( C @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
           => ( A @ ( C @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) )
     => ( A @ ( B @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(184,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f750478076l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_025) ).

thf(1448,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f750478076l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(266,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/sandbox2/benchmark/theBenchmark.p',fact_657_Suc__le__lessD) ).

thf(1734,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)],[266]) ).

thf(535,axiom,
    ! [A: $i] : ( top_to935749874l_bool @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_iso__tuple__UNIV__I) ).

thf(2865,plain,
    ! [A: $i] : ( top_to935749874l_bool @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(539,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_439_subsetD) ).

thf(2875,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(175,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_bool )
     => ( B @ ( A @ hAPP_bool_bool ) @ is_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) ).

thf(1421,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_bool )
     => ( B @ ( A @ hAPP_bool_bool ) @ is_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(353,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/sandbox2/benchmark/theBenchmark.p',fact_567_add__le__mono) ).

thf(2013,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)],[353]) ).

thf(858,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_fun1555365306t_bool ) @ ( B @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_f1895971544l_bool ) @ ( A @ ( B @ hAPP_f1817389232t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_PiE) ).

thf(4138,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_fun1555365306t_bool ) @ ( B @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_f1895971544l_bool ) @ ( A @ ( B @ hAPP_f1817389232t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).

thf(244,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun1568535512t_bool )
     => ( B @ ( A @ hAPP_f427533077t_bool ) @ is_fun1568535512t_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_000tc__fun_I) ).

thf(1649,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun1568535512t_bool )
     => ( B @ ( A @ hAPP_f427533077t_bool ) @ is_fun1568535512t_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(667,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( ( D @ is_Arr859726945e_indi )
            & ( C @ is_Arr859726945e_indi ) )
         => ( ( B @ ( C @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
           => ( ( B @ ( D @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
             => ( ( ( C @ ( A @ hAPP_A1895296483di_nat ) )
                  = ( D @ ( A @ hAPP_A1895296483di_nat ) ) )
               => ( C = D ) ) ) ) )
     => ( B @ ( A @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_592_inj__onI) ).

thf(3401,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i,D: $i] :
          ( ( ( D @ is_Arr859726945e_indi )
            & ( C @ is_Arr859726945e_indi ) )
         => ( ( B @ ( C @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
           => ( ( B @ ( D @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
             => ( ( ( C @ ( A @ hAPP_A1895296483di_nat ) )
                  = ( D @ ( A @ hAPP_A1895296483di_nat ) ) )
               => ( C = D ) ) ) ) )
     => ( B @ ( A @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).

thf(377,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( member161528657e_indi @ ( cOMBC_264525026l_bool @ hAPP_f651290349i_bool ) @ hAPP_f1282033109i_bool ) @ ( A @ ( member161528657e_indi @ ( cOMBC_264525026l_bool @ hAPP_f651290349i_bool ) @ hAPP_f1282033109i_bool ) @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
    <=> ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_495_pred__subset__eq) ).

thf(2088,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( B @ ( member161528657e_indi @ ( cOMBC_264525026l_bool @ hAPP_f651290349i_bool ) @ hAPP_f1282033109i_bool ) @ ( A @ ( member161528657e_indi @ ( cOMBC_264525026l_bool @ hAPP_f651290349i_bool ) @ hAPP_f1282033109i_bool ) @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) )
      & ( ( B @ ( member161528657e_indi @ ( cOMBC_264525026l_bool @ hAPP_f651290349i_bool ) @ hAPP_f1282033109i_bool ) @ ( A @ ( member161528657e_indi @ ( cOMBC_264525026l_bool @ hAPP_f651290349i_bool ) @ hAPP_f1282033109i_bool ) @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(719,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2015243113i_bool )
        & ( A @ is_fun2015243113i_bool ) )
     => ( ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
      <=> ( ( A = B )
          | ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_order__le__less) ).

thf(3589,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2015243113i_bool )
        & ( A @ is_fun2015243113i_bool ) )
     => ( ( ( ( A = B )
            | ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) )
         => ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) )
        & ( ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
         => ( ( A = B )
            | ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).

thf(596,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_xt1_I10_J) ).

thf(3092,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(32,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f966397426l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_026) ).

thf(976,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f966397426l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(786,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_1918246033t_bool @ hAPP_f633903640l_bool ) @ ( C @ pi_fun1555365306t_bool ) @ ( B @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_f1817389232t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_379_funcset__mem) ).

thf(3874,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( cOMBK_1918246033t_bool @ hAPP_f633903640l_bool ) @ ( C @ pi_fun1555365306t_bool ) @ ( B @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
       => ( D @ ( A @ ( B @ hAPP_f1817389232t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).

thf(617,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ is_Arr859726945e_indi )
     => ( ( C @ ( B @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( C @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
         => ( ( A @ ( B @ hAPP_A1895296483di_nat ) @ ( B @ ( C @ hilber951314860di_nat ) @ hAPP_n619554777e_indi ) )
            = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_386_inv__into__f__f) ).

thf(3188,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ is_Arr859726945e_indi )
     => ( ( C @ ( B @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( C @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
         => ( ( A @ ( B @ hAPP_A1895296483di_nat ) @ ( B @ ( C @ hilber951314860di_nat ) @ hAPP_n619554777e_indi ) )
            = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(708,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( zero_zero_nat @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( ord_less_nat @ ( cOMBC_nat_nat_bool @ hAPP_f229349961t_bool ) @ hAPP_n1699378549t_bool ) @ ( B @ ( suc @ ( member_nat @ cOMBB_1146692694ol_nat @ hAPP_f66927821l_bool ) @ ( cOMBC_226598744l_bool @ hAPP_f1722879237t_bool ) @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat @ hAPP_f1146629647l_bool ) @ cOMBS_nat_bool_bool ) @ collect_nat @ finite_card_nat @ ( suc @ hAPP_nat_nat ) )
        = ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ ( cOMBC_nat_nat_bool @ hAPP_f229349961t_bool ) @ hAPP_n1699378549t_bool ) @ ( B @ ( member_nat @ ( cOMBC_226598744l_bool @ hAPP_f1722879237t_bool ) @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat @ hAPP_f1146629647l_bool ) @ cOMBS_nat_bool_bool ) @ collect_nat @ finite_card_nat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_681_card__less__Suc) ).

thf(3548,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( zero_zero_nat @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( ord_less_nat @ ( cOMBC_nat_nat_bool @ hAPP_f229349961t_bool ) @ hAPP_n1699378549t_bool ) @ ( B @ ( suc @ ( member_nat @ cOMBB_1146692694ol_nat @ hAPP_f66927821l_bool ) @ ( cOMBC_226598744l_bool @ hAPP_f1722879237t_bool ) @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat @ hAPP_f1146629647l_bool ) @ cOMBS_nat_bool_bool ) @ collect_nat @ finite_card_nat @ ( suc @ hAPP_nat_nat ) )
        = ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ ( cOMBC_nat_nat_bool @ hAPP_f229349961t_bool ) @ hAPP_n1699378549t_bool ) @ ( B @ ( member_nat @ ( cOMBC_226598744l_bool @ hAPP_f1722879237t_bool ) @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat @ hAPP_f1146629647l_bool ) @ cOMBS_nat_bool_bool ) @ collect_nat @ finite_card_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).

thf(401,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
    <=> ( ~ ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
        & ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_less__le__not__le) ).

thf(2194,plain,
    ! [A: $i,B: $i] :
      ( ( ( ~ ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
       => ( ~ ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(491,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
      | ~ ( B @ ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Nat__Onat_T) ).

thf(2611,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)],[491]) ).

thf(803,axiom,
    ! [A: $i] :
      ( ( A @ ( top_top_fun_nat_bool @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
    <=> ( A = top_top_fun_nat_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_top__unique) ).

thf(3928,plain,
    ! [A: $i] :
      ( ( ( A = top_top_fun_nat_bool )
       => ( A @ ( top_top_fun_nat_bool @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
      & ( ( A @ ( top_top_fun_nat_bool @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A = top_top_fun_nat_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).

thf(279,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/sandbox2/benchmark/theBenchmark.p',fact_267_linorder__not__less) ).

thf(1781,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)],[279]) ).

thf(5,axiom,
    fFalse @ is_bool,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_fFalse) ).

thf(891,plain,
    fFalse @ is_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(404,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( ( B @ hBOOL )
        <=> ( A @ hBOOL ) )
     => ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_xt1_I12_J) ).

thf(2209,plain,
    ! [A: $i,B: $i] :
      ( ~ ( ( ( A @ hBOOL )
           => ( B @ hBOOL ) )
          & ( ( B @ hBOOL )
           => ( A @ hBOOL ) ) )
     => ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(728,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_order__less__not__sym) ).

thf(3625,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).

thf(843,axiom,
    arrow_912654623le_Lin @ ( cOMBK_1918246033t_bool @ hAPP_f633903640l_bool ) @ ( arrow_583275979e_Prof @ pi_fun1555365306t_bool ) @ ( f @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_assms_I1_J) ).

thf(4078,plain,
    arrow_912654623le_Lin @ ( cOMBK_1918246033t_bool @ hAPP_f633903640l_bool ) @ ( arrow_583275979e_Prof @ pi_fun1555365306t_bool ) @ ( f @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).

thf(381,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro1925515229t_bool ) @ ( B @ ( member928589940t_bool @ hAPP_f177302985l_bool ) @ hAPP_f1965705105l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P288224245l_bool ) @ ( A @ ( B @ hAPP_P401722323t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_PiE) ).

thf(2110,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Pro1925515229t_bool ) @ ( B @ ( member928589940t_bool @ hAPP_f177302985l_bool ) @ hAPP_f1965705105l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_P288224245l_bool ) @ ( A @ ( B @ hAPP_P401722323t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(43,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/sandbox2/benchmark/theBenchmark.p',fact_525_add__leD1) ).

thf(1010,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)],[43]) ).

thf(434,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/sandbox2/benchmark/theBenchmark.p',fact_480_in__mono) ).

thf(2342,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)],[434]) ).

thf(587,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( B @ ( C @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
         => ( A @ ( C @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
     => ( A @ ( B @ ( ord_le64728819t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_511_subsetI) ).

thf(3056,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( B @ ( C @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
         => ( A @ ( C @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
     => ( A @ ( B @ ( ord_le64728819t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(187,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( cOMBK_1662914336e_indi @ hAPP_f1393414918t_bool ) @ hAPP_A1948275303t_bool ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Arrow___) ).

thf(1453,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( cOMBK_1662914336e_indi @ hAPP_f1393414918t_bool ) @ hAPP_A1948275303t_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(304,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/sandbox2/benchmark/theBenchmark.p',fact_626_ex__least__nat__le) ).

thf(1866,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)],[304]) ).

thf(501,axiom,
    ! [A: $i] : ( top_to1257323279t_bool @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_411_subset__UNIV) ).

thf(2658,plain,
    ! [A: $i] : ( top_to1257323279t_bool @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(348,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P822772139t_bool ) @ is_fun1568535512t_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__041) ).

thf(1998,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P822772139t_bool ) @ is_fun1568535512t_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(761,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_order__antisym) ).

thf(3797,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).

thf(164,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/sandbox2/benchmark/theBenchmark.p',fact_695_nat__induct) ).

thf(1385,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)],[164]) ).

thf(26,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/sandbox2/benchmark/theBenchmark.p',fact_394_less__add__one) ).

thf(963,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)],[26]) ).

thf(318,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/sandbox2/benchmark/theBenchmark.p',fact_686_gr0__implies__Suc) ).

thf(1903,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)],[318]) ).

thf(198,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/sandbox2/benchmark/theBenchmark.p',fact_559_less__or__eq__imp__le) ).

thf(1481,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)],[198]) ).

thf(21,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/sandbox2/benchmark/theBenchmark.p',fact_435_add__less__cancel__right) ).

thf(946,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)],[21]) ).

thf(564,axiom,
    ! [A: $i] : ( top_to1849101472l_bool @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_UNIV__I) ).

thf(2971,plain,
    ! [A: $i] : ( top_to1849101472l_bool @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(757,axiom,
    ! [A: $i] : ( top_to1647826457l_bool @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_UNIV__I) ).

thf(3780,plain,
    ! [A: $i] : ( top_to1647826457l_bool @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).

thf(217,axiom,
    ! [A: $i] :
      ~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_615_less__nat__zero__code) ).

thf(1558,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)],[217]) ).

thf(396,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/sandbox2/benchmark/theBenchmark.p',fact_127_order__less__asym_H) ).

thf(2174,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)],[396]) ).

thf(447,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_xt1_I8_J) ).

thf(2389,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(196,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/sandbox2/benchmark/theBenchmark.p',fact_292_order__neq__le__trans) ).

thf(1476,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)],[196]) ).

thf(149,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/sandbox2/benchmark/theBenchmark.p',fact_303_order__less__imp__le) ).

thf(1341,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)],[149]) ).

thf(690,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun1568535512t_bool )
        & ( A @ is_fun1568535512t_bool ) )
     => ( ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( ( A = B )
          | ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_order__le__imp__less__or__eq) ).

thf(3484,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun1568535512t_bool )
        & ( A @ is_fun1568535512t_bool ) )
     => ( ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( ( A = B )
          | ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).

thf(759,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( B @ ( C @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
         => ( A @ ( C @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) )
     => ( A @ ( B @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_505_subsetI) ).

thf(3789,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( B @ ( C @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
         => ( A @ ( C @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) )
     => ( A @ ( B @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).

thf(532,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( D @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( ( D @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
         => ( ( ( B @ ( C @ hAPP_nat_nat ) )
              = ( A @ ( C @ hAPP_nat_nat ) ) )
          <=> ( B = A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_368_inj__on__iff) ).

thf(2855,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( D @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( ( D @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
         => ( ( ( B = A )
             => ( ( B @ ( C @ hAPP_nat_nat ) )
                = ( A @ ( C @ hAPP_nat_nat ) ) ) )
            & ( ( ( B @ ( C @ hAPP_nat_nat ) )
                = ( A @ ( C @ hAPP_nat_nat ) ) )
             => ( B = A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(241,axiom,
    ! [A: $i] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
     != A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_640_Suc__n__not__n) ).

thf(1639,plain,
    ! [A: $i] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
     != A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(525,axiom,
    ! [A: $i] :
      ~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_527_less__not__refl) ).

thf(2811,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(601,axiom,
    ! [A: $i] : ( top_to1773227171t_bool @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_UNIV__I) ).

thf(3104,plain,
    ! [A: $i] : ( top_to1773227171t_bool @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(695,axiom,
    ! [A: $i] :
      ( ( A @ is_fun2015243113i_bool )
     => ( ( A @ ( top_to207207712i_bool @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( A = top_to207207712i_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_363_top__le) ).

thf(3501,plain,
    ! [A: $i] :
      ( ( A @ is_fun2015243113i_bool )
     => ( ( A @ ( top_to207207712i_bool @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( A = top_to207207712i_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).

thf(573,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/sandbox2/benchmark/theBenchmark.p',fact_238_order__trans) ).

thf(3003,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)],[573]) ).

thf(822,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( member1619170513t_bool @ ( cOMBC_1528317666l_bool @ hAPP_f863441901l_bool ) @ hAPP_f1028172757l_bool ) @ ( A @ ( member1619170513t_bool @ ( cOMBC_1528317666l_bool @ hAPP_f863441901l_bool ) @ hAPP_f1028172757l_bool ) @ ( ord_le2143686384l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
    <=> ( B @ ( A @ ( ord_le2143686384l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_498_pred__subset__eq) ).

thf(4010,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ ( ord_le2143686384l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
       => ( B @ ( member1619170513t_bool @ ( cOMBC_1528317666l_bool @ hAPP_f863441901l_bool ) @ hAPP_f1028172757l_bool ) @ ( A @ ( member1619170513t_bool @ ( cOMBC_1528317666l_bool @ hAPP_f863441901l_bool ) @ hAPP_f1028172757l_bool ) @ ( ord_le2143686384l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) )
      & ( ( B @ ( member1619170513t_bool @ ( cOMBC_1528317666l_bool @ hAPP_f863441901l_bool ) @ hAPP_f1028172757l_bool ) @ ( A @ ( member1619170513t_bool @ ( cOMBC_1528317666l_bool @ hAPP_f863441901l_bool ) @ hAPP_f1028172757l_bool ) @ ( ord_le2143686384l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le2143686384l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).

thf(701,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_Arr723427730le_alt )
        & ( A @ is_Arr723427730le_alt ) )
     => ( ( A != B )
       => ? [C: $i] :
            ( ( C @ ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
            & ( arrow_912654623le_Lin @ ( C @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
            & ( C @ is_fun20916972t_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_complete__Lin) ).

thf(3516,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_Arr723427730le_alt )
        & ( A @ is_Arr723427730le_alt ) )
     => ( ( A != B )
       => ? [C: $i] :
            ( ( C @ ( B @ ( A @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
            & ( arrow_912654623le_Lin @ ( C @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
            & ( C @ is_fun20916972t_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).

thf(610,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_484_in__mono) ).

thf(3136,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1079191765l_bool @ hAPP_f1700034367l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(658,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( A != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_less__imp__neq) ).

thf(3368,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).

thf(558,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/sandbox2/benchmark/theBenchmark.p',fact_185_inv__f__eq) ).

thf(2956,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)],[558]) ).

thf(374,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/sandbox2/benchmark/theBenchmark.p',fact_550_trans__less__add2) ).

thf(2081,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)],[374]) ).

thf(546,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_xt1_I8_J) ).

thf(2912,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(633,axiom,
    ! [A: $i] :
      ( ( arrow_912654623le_Lin @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
     => ( arrow_583275979e_Prof @ ( A @ ( cOMBK_776703103e_indi @ hAPP_f590186314t_bool ) @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_const__Lin__Prof) ).

thf(3267,plain,
    ! [A: $i] :
      ( ( arrow_912654623le_Lin @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
     => ( arrow_583275979e_Prof @ ( A @ ( cOMBK_776703103e_indi @ hAPP_f590186314t_bool ) @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).

thf(793,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/sandbox2/benchmark/theBenchmark.p',fact_111_ord__less__eq__trans) ).

thf(3896,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)],[793]) ).

thf(704,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( A != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_less__imp__neq) ).

thf(3529,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).

thf(440,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/sandbox2/benchmark/theBenchmark.p',fact_256_order__antisym__conv) ).

thf(2362,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)],[440]) ).

thf(760,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( C = A )
       => ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_ord__le__eq__trans) ).

thf(3793,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( C = A )
       => ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).

thf(653,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/sandbox2/benchmark/theBenchmark.p',fact_381_inj__eq) ).

thf(3351,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)],[653]) ).

thf(8,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/sandbox2/benchmark/theBenchmark.p',fact_634_Suc__le__mono) ).

thf(899,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)],[8]) ).

thf(733,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/sandbox2/benchmark/theBenchmark.p',fact_229_linorder__le__cases) ).

thf(3645,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)],[733]) ).

thf(871,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Arr742795713t_bool ) @ ( B @ ( member689634176t_bool @ hAPP_f1063991245l_bool ) @ hAPP_f2016919811l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_A955165183l_bool ) @ ( A @ ( B @ hAPP_A1433148491t_bool ) @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_PiE) ).

thf(4182,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_Arr742795713t_bool ) @ ( B @ ( member689634176t_bool @ hAPP_f1063991245l_bool ) @ hAPP_f2016919811l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_A955165183l_bool ) @ ( A @ ( B @ hAPP_A1433148491t_bool ) @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member161528657e_indi @ hAPP_A45661955l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).

thf(302,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_483_in__mono) ).

thf(1861,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(676,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2015243113i_bool )
        & ( A @ is_fun2015243113i_bool ) )
     => ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
      <=> ( ( A != B )
          & ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_448_psubset__eq) ).

thf(3430,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2015243113i_bool )
        & ( A @ is_fun2015243113i_bool ) )
     => ( ( ( ( A != B )
            & ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) )
         => ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) )
        & ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
         => ( ( A != B )
            & ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).

thf(278,axiom,
    ! [A: $i] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
     != zero_zero_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_676_Suc__not__Zero) ).

thf(1777,plain,
    ! [A: $i] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
     != zero_zero_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(469,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun1568535512t_bool )
        & ( A @ is_fun1568535512t_bool ) )
     => ( ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( ( B != A )
         => ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_xt1_I11_J) ).

thf(2494,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun1568535512t_bool )
        & ( A @ is_fun1568535512t_bool ) )
     => ( ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( ( B != A )
         => ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(182,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/sandbox2/benchmark/theBenchmark.p',fact_688_Suc__eq__plus1) ).

thf(1442,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)],[182]) ).

thf(347,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun1420103068l_bool )
     => ( ( B @ ( A @ ( cOMBK_1918246033t_bool @ hAPP_f633903640l_bool ) @ hAPP_f1895971544l_bool ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabe_050) ).

thf(1994,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun1420103068l_bool )
     => ( ( B @ ( A @ ( cOMBK_1918246033t_bool @ hAPP_f633903640l_bool ) @ hAPP_f1895971544l_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(710,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_boo679625100t_bool ) @ ( B @ ( member1024929995t_bool @ hAPP_f1518101645l_bool ) @ hAPP_f620747982l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_b1461182872l_bool ) @ ( A @ ( B @ hAPP_b821377302t_bool ) @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_PiE) ).

thf(3552,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_boo679625100t_bool ) @ ( B @ ( member1024929995t_bool @ hAPP_f1518101645l_bool ) @ hAPP_f620747982l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_b1461182872l_bool ) @ ( A @ ( B @ hAPP_b821377302t_bool ) @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).

thf(672,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/sandbox2/benchmark/theBenchmark.p',fact_131_order__less__imp__triv) ).

thf(3420,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)],[672]) ).

thf(456,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_711698847le_alt @ hAPP_f1656652505l_bool ) @ hAPP_A433435097l_bool ) )
      = ( C @ ( B @ hAPP_A1561816353le_alt ) @ ( A @ hAPP_P1151433609l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb_) ).

thf(2421,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_711698847le_alt @ hAPP_f1656652505l_bool ) @ hAPP_A433435097l_bool ) )
      = ( C @ ( B @ hAPP_A1561816353le_alt ) @ ( A @ hAPP_P1151433609l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(407,axiom,
    ~ ( lba @ ( b @ ( a @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78__096_Ia_M_Ab_J_A_126_058_ALba_096) ).

thf(2218,plain,
    ~ ( lba @ ( b @ ( a @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(380,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun1568535512t_bool )
        & ( A @ is_fun1568535512t_bool ) )
     => ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
      <=> ( ( A != B )
          & ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_447_psubset__eq) ).

thf(2102,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun1568535512t_bool )
        & ( A @ is_fun1568535512t_bool ) )
     => ( ( ( ( A != B )
            & ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) )
         => ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) )
        & ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
         => ( ( A != B )
            & ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(335,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/sandbox2/benchmark/theBenchmark.p',fact_558_le__neq__implies__less) ).

thf(1957,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)],[335]) ).

thf(28,axiom,
    ( ( top_to1257323279t_bool @ finite1949902593t_unit )
    = one_one_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_603_card__UNIV__unit) ).

thf(967,plain,
    ( ( top_to1257323279t_bool @ finite1949902593t_unit )
    = one_one_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(743,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_458_subset__psubset__trans) ).

thf(3733,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).

thf(791,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( B @ ( C @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( A @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_order__less__imp__triv) ).

thf(3892,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( B @ ( C @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( A @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).

thf(162,axiom,
    ! [A: $i] :
      ( ( A != zero_zero_nat )
     => ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_613_gr0I) ).

thf(1380,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)],[162]) ).

thf(307,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f212509069l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__) ).

thf(1876,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f212509069l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(210,axiom,
    ! [A: $i] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
     != zero_zero_nat ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_675_nat_Osimps_I3_J) ).

thf(1527,plain,
    ! [A: $i] :
      ( ( A @ ( suc @ hAPP_nat_nat ) )
     != zero_zero_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(739,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ hBOOL )
      <=> ( A @ hBOOL ) )
     => ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_order__eq__refl) ).

thf(3690,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A @ hBOOL )
         => ( B @ hBOOL ) )
        & ( ( B @ hBOOL )
         => ( A @ hBOOL ) ) )
     => ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).

thf(613,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ! [E: $i] :
          ( ( D @ ( E @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
         => ( ( E @ ( B @ hAPP_f1817389232t_bool ) )
            = ( E @ ( C @ hAPP_f1817389232t_bool ) ) ) )
     => ( ( A @ ( D @ pi_fun1555365306t_bool ) @ ( B @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
      <=> ( A @ ( D @ pi_fun1555365306t_bool ) @ ( C @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_582_Pi__cong) ).

thf(3164,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ! [E: $i] :
          ( ( D @ ( E @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
         => ( ( E @ ( B @ hAPP_f1817389232t_bool ) )
            = ( E @ ( C @ hAPP_f1817389232t_bool ) ) ) )
     => ( ( ( A @ ( D @ pi_fun1555365306t_bool ) @ ( C @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
         => ( A @ ( D @ pi_fun1555365306t_bool ) @ ( B @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) )
        & ( ( A @ ( D @ pi_fun1555365306t_bool ) @ ( B @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
         => ( A @ ( D @ pi_fun1555365306t_bool ) @ ( C @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(320,axiom,
    ! [A: $i] :
      ( ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
    <=> ? [B: $i] :
        ! [C: $i] :
          ( ( A @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
         => ( B @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_607_finite__nat__set__iff__bounded__le) ).

thf(1908,plain,
    ! [A: $i] :
      ( ( ? [B: $i] :
          ! [C: $i] :
            ( ( A @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
           => ( B @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
       => ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) )
      & ( ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
       => ? [B: $i] :
          ! [C: $i] :
            ( ( A @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
           => ( B @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(351,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/sandbox2/benchmark/theBenchmark.p',fact_670_less__Suc0) ).

thf(2003,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)],[351]) ).

thf(660,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_fun1012573681t_unit ) @ ( B @ ( member416763266t_unit @ hAPP_f715600357l_bool ) @ hAPP_f1384787615l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_f649586561t_bool ) @ ( A @ ( B @ hAPP_f1636264423t_unit ) @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_PiE) ).

thf(3379,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_fun1012573681t_unit ) @ ( B @ ( member416763266t_unit @ hAPP_f715600357l_bool ) @ hAPP_f1384787615l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_f649586561t_bool ) @ ( A @ ( B @ hAPP_f1636264423t_unit ) @ ( member_Product_unit @ hAPP_P607165281l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).

thf(833,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_xt1_I7_J) ).

thf(4039,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
       => ( C @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).

thf(152,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_Arr859726945e_indi )
     => ( B @ ( A @ hAPP_A659996934l_bool ) @ is_fun1420103068l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It_003) ).

thf(1348,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_Arr859726945e_indi )
     => ( B @ ( A @ hAPP_A659996934l_bool ) @ is_fun1420103068l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(207,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/sandbox2/benchmark/theBenchmark.p',fact_646_less__Suc__eq) ).

thf(1512,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)],[207]) ).

thf(277,axiom,
    ! [A: $i] :
      ( ( A @ is_bool )
     => ( ( A = fFalse )
        | ( A = fTrue ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqm) ).

thf(1774,plain,
    ! [A: $i] :
      ( ( A @ is_bool )
     => ( ( A = fFalse )
        | ( A = fTrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(445,axiom,
    arrow_583275979e_Prof @ ( p @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__096P_A_058_AProf_096) ).

thf(2385,plain,
    arrow_583275979e_Prof @ ( p @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(782,axiom,
    top_to207207712i_bool @ ( h @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_injh) ).

thf(3860,plain,
    top_to207207712i_bool @ ( h @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).

thf(608,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/sandbox2/benchmark/theBenchmark.p',fact_542_le__trans) ).

thf(3132,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)],[608]) ).

thf(123,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun2015243113i_bool )
     => ( B @ ( A @ hilber951314860di_nat ) @ is_fun1084921220e_indi ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Hilbert__Choice_Oinv__into_000tc__Arrow____Order____Mirabelle____wylsunqmt) ).

thf(1248,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun2015243113i_bool )
     => ( B @ ( A @ hilber951314860di_nat ) @ is_fun1084921220e_indi ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(622,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_fun1236347660l_bool ) @ ( B @ ( member1402889547l_bool @ hAPP_f1338606733l_bool ) @ hAPP_f1138659662l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_f591334822l_bool ) @ ( A @ ( B @ hAPP_f1378099862l_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_PiE) ).

thf(3203,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ pi_fun1236347660l_bool ) @ ( B @ ( member1402889547l_bool @ hAPP_f1338606733l_bool ) @ hAPP_f1138659662l_bool ) @ hBOOL )
     => ( ~ ( A @ ( D @ hAPP_f591334822l_bool ) @ ( A @ ( B @ hAPP_f1378099862l_bool ) @ ( member_bool @ hAPP_b1787118453l_bool ) @ hAPP_f387058535l_bool ) @ hBOOL )
       => ~ ( C @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(589,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2015243113i_bool )
        & ( A @ is_fun2015243113i_bool ) )
     => ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
      <=> ( ( A != B )
          & ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_order__less__le) ).

thf(3062,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2015243113i_bool )
        & ( A @ is_fun2015243113i_bool ) )
     => ( ( ( ( A != B )
            & ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) )
         => ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) )
        & ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
         => ( ( A != B )
            & ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(179,axiom,
    e @ is_Arr723427730le_alt,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_e____) ).

thf(1436,plain,
    e @ is_Arr723427730le_alt,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(805,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ is_Arr723427730le_alt )
        & ( B @ is_Arr723427730le_alt ) )
     => ( ( B != C )
       => ( ( arrow_912654623le_Lin @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
         => ( arrow_912654623le_Lin @ ( C @ ( B @ ( A @ ( arrow_1046586475_above @ hAPP_f684072049t_bool ) @ hAPP_A28770973t_bool ) @ hAPP_A1014090479t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_above__Lin) ).

thf(3956,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ is_Arr723427730le_alt )
        & ( B @ is_Arr723427730le_alt ) )
     => ( ( B != C )
       => ( ( arrow_912654623le_Lin @ ( A @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
         => ( arrow_912654623le_Lin @ ( C @ ( B @ ( A @ ( arrow_1046586475_above @ hAPP_f684072049t_bool ) @ hAPP_A28770973t_bool ) @ hAPP_A1014090479t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).

thf(650,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( F @ is_Arr723427730le_alt )
        & ( E @ is_Arr723427730le_alt )
        & ( D @ is_Arr723427730le_alt )
        & ( C @ is_Arr723427730le_alt ) )
     => ( ( E != F )
       => ( ( C != D )
         => ( ( arrow_583275979e_Prof @ ( B @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
           => ( ( arrow_583275979e_Prof @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
             => ( ! [G: $i] :
                    ( ( G @ is_Arr859726945e_indi )
                   => ( ( G @ ( B @ hAPP_A340536322t_bool ) @ ( F @ ( E @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                    <=> ( G @ ( A @ hAPP_A340536322t_bool ) @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) )
               => ( ( B @ ( f @ hAPP_f1817389232t_bool ) @ ( F @ ( E @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                <=> ( A @ ( f @ hAPP_f1817389232t_bool ) @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_pairwise__neutrality) ).

thf(3328,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( F @ is_Arr723427730le_alt )
        & ( E @ is_Arr723427730le_alt )
        & ( D @ is_Arr723427730le_alt )
        & ( C @ is_Arr723427730le_alt ) )
     => ( ( E != F )
       => ( ( C != D )
         => ( ( arrow_583275979e_Prof @ ( B @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
           => ( ( arrow_583275979e_Prof @ ( A @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
             => ( ! [G: $i] :
                    ( ( G @ is_Arr859726945e_indi )
                   => ( ( ( G @ ( A @ hAPP_A340536322t_bool ) @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                       => ( G @ ( B @ hAPP_A340536322t_bool ) @ ( F @ ( E @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
                      & ( ( G @ ( B @ hAPP_A340536322t_bool ) @ ( F @ ( E @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                       => ( G @ ( A @ hAPP_A340536322t_bool ) @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) )
               => ( ( ( A @ ( f @ hAPP_f1817389232t_bool ) @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                   => ( B @ ( f @ hAPP_f1817389232t_bool ) @ ( F @ ( E @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
                  & ( ( B @ ( f @ hAPP_f1817389232t_bool ) @ ( F @ ( E @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                   => ( A @ ( f @ hAPP_f1817389232t_bool ) @ ( D @ ( C @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).

thf(139,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/sandbox2/benchmark/theBenchmark.p',fact_679_less__eq__Suc__le__raw) ).

thf(1314,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)],[139]) ).

thf(201,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/sandbox2/benchmark/theBenchmark.p',fact_645_not__less__eq) ).

thf(1495,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)],[201]) ).

thf(432,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le2143686384l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_468_set__mp) ).

thf(2334,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le2143686384l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(398,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/sandbox2/benchmark/theBenchmark.p',fact_119_ord__eq__less__trans) ).

thf(2186,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)],[398]) ).

thf(764,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1482529602l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
       => ( A @ ( B @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_477_set__rev__mp) ).

thf(3804,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1482529602l_bool @ hAPP_f1547458257l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
       => ( A @ ( B @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).

thf(454,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_order__less__imp__le) ).

thf(2417,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(560,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/sandbox2/benchmark/theBenchmark.p',fact_103_order__less__trans) ).

thf(2961,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)],[560]) ).

thf(402,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( cOMBK_1662914336e_indi @ hAPP_f1393414918t_bool ) @ ( B @ pi_Arr604548589di_nat ) @ ( A @ ( member873781636di_nat @ hAPP_f758593513l_bool ) @ hAPP_f599997089l_bool ) @ hBOOL )
     => ( ( B @ ( A @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
         => ( C @ finite_card_nat @ ( B @ finite354462354e_indi @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_587_card__inj) ).

thf(2201,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( cOMBK_1662914336e_indi @ hAPP_f1393414918t_bool ) @ ( B @ pi_Arr604548589di_nat ) @ ( A @ ( member873781636di_nat @ hAPP_f758593513l_bool ) @ hAPP_f599997089l_bool ) @ hBOOL )
     => ( ( B @ ( A @ inj_on1331630279di_nat @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
         => ( C @ finite_card_nat @ ( B @ finite354462354e_indi @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(12,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun20916972t_bool )
     => ( B @ ( A @ hAPP_f1344932147l_bool ) @ is_fun1420103068l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___037) ).

thf(918,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun20916972t_bool )
     => ( B @ ( A @ hAPP_f1344932147l_bool ) @ is_fun1420103068l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(864,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_489_equalityD1) ).

thf(4157,plain,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).

thf(147,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/sandbox2/benchmark/theBenchmark.p',fact_297_xt1_I12_J) ).

thf(1335,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)],[147]) ).

thf(826,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/sandbox2/benchmark/theBenchmark.p',fact_143_order__less__imp__not__less) ).

thf(4024,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)],[826]) ).

thf(218,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ hAPP_A340536322t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A85603248t_bool ) @ hAPP_A1014090479t_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_046) ).

thf(1561,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ hAPP_A340536322t_bool ) )
      = ( B @ ( C @ ( A @ hAPP_A85603248t_bool ) @ hAPP_A1014090479t_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(510,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ ( plus_plus_nat @ ( cOMBC_nat_nat_nat @ hAPP_f416620757at_nat ) @ hAPP_nat_fun_nat_nat ) @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_545_inj__on__add__nat) ).

thf(2704,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ ( plus_plus_nat @ ( cOMBC_nat_nat_nat @ hAPP_f416620757at_nat ) @ hAPP_nat_fun_nat_nat ) @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(57,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f350403485e_indi ) @ is_Arr859726945e_indi ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__006) ).

thf(1056,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f350403485e_indi ) @ is_Arr859726945e_indi ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(281,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/sandbox2/benchmark/theBenchmark.p',fact_395_add__less__le__mono) ).

thf(1789,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)],[281]) ).

thf(515,axiom,
    ! [A: $i] :
      ( ( A @ ( arrow_885770895le_IIA @ hAPP_f446648900l_bool ) @ hBOOL )
    <=> ! [B: $i] :
          ( ( arrow_583275979e_Prof @ ( B @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
         => ! [C: $i] :
              ( ( arrow_583275979e_Prof @ ( C @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
             => ! [D: $i,E: $i] :
                  ( ( ( E @ is_Arr723427730le_alt )
                    & ( D @ is_Arr723427730le_alt ) )
                 => ( ! [F: $i] :
                        ( ( F @ is_Arr859726945e_indi )
                       => ( ( F @ ( B @ hAPP_A340536322t_bool ) @ ( E @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                        <=> ( F @ ( C @ hAPP_A340536322t_bool ) @ ( E @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) )
                   => ( ( B @ ( A @ hAPP_f1817389232t_bool ) @ ( E @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                    <=> ( C @ ( A @ hAPP_f1817389232t_bool ) @ ( E @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_IIA__def) ).

thf(2714,plain,
    ! [A: $i] :
      ( ( ! [B: $i] :
            ( ( arrow_583275979e_Prof @ ( B @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
           => ! [C: $i] :
                ( ( arrow_583275979e_Prof @ ( C @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
               => ! [D: $i,E: $i] :
                    ( ( ( E @ is_Arr723427730le_alt )
                      & ( D @ is_Arr723427730le_alt ) )
                   => ( ! [F: $i] :
                          ( ( F @ is_Arr859726945e_indi )
                         => ( ( ( F @ ( C @ hAPP_A340536322t_bool ) @ ( E @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                             => ( F @ ( B @ hAPP_A340536322t_bool ) @ ( E @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
                            & ( ( F @ ( B @ hAPP_A340536322t_bool ) @ ( E @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                             => ( F @ ( C @ hAPP_A340536322t_bool ) @ ( E @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) )
                     => ( ( ( C @ ( A @ hAPP_f1817389232t_bool ) @ ( E @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                         => ( B @ ( A @ hAPP_f1817389232t_bool ) @ ( E @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
                        & ( ( B @ ( A @ hAPP_f1817389232t_bool ) @ ( E @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                         => ( C @ ( A @ hAPP_f1817389232t_bool ) @ ( E @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) ) ) ) )
       => ( A @ ( arrow_885770895le_IIA @ hAPP_f446648900l_bool ) @ hBOOL ) )
      & ( ( A @ ( arrow_885770895le_IIA @ hAPP_f446648900l_bool ) @ hBOOL )
       => ! [B: $i] :
            ( ( arrow_583275979e_Prof @ ( B @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
           => ! [C: $i] :
                ( ( arrow_583275979e_Prof @ ( C @ ( member1265098019t_bool @ hAPP_f621397159l_bool ) @ hAPP_f147218624l_bool ) @ hBOOL )
               => ! [D: $i,E: $i] :
                    ( ( ( E @ is_Arr723427730le_alt )
                      & ( D @ is_Arr723427730le_alt ) )
                   => ( ! [F: $i] :
                          ( ( F @ is_Arr859726945e_indi )
                         => ( ( ( F @ ( C @ hAPP_A340536322t_bool ) @ ( E @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                             => ( F @ ( B @ hAPP_A340536322t_bool ) @ ( E @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
                            & ( ( F @ ( B @ hAPP_A340536322t_bool ) @ ( E @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                             => ( F @ ( C @ hAPP_A340536322t_bool ) @ ( E @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) )
                     => ( ( ( C @ ( A @ hAPP_f1817389232t_bool ) @ ( E @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                         => ( B @ ( A @ hAPP_f1817389232t_bool ) @ ( E @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
                        & ( ( B @ ( A @ hAPP_f1817389232t_bool ) @ ( E @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
                         => ( C @ ( A @ hAPP_f1817389232t_bool ) @ ( E @ ( D @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(619,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P1151433609l_bool ) @ is_fun1420103068l_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__042) ).

thf(3196,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_P1151433609l_bool ) @ is_fun1420103068l_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(674,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ ord_at4362885an_nat @ hAPP_n1699378549t_bool ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_697_finite__atLeastLessThan) ).

thf(3426,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ ord_at4362885an_nat @ hAPP_n1699378549t_bool ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).

thf(697,axiom,
    ! [A: $i,B: $i] :
      ( ( arrow_912654623le_Lin @ ( B @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
     => ( arrow_912654623le_Lin @ ( A @ ( B @ ( arrow_312654597_mktop @ hAPP_f102394819t_bool ) @ hAPP_A1014090479t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_mktop__Lin) ).

thf(3506,plain,
    ! [A: $i,B: $i] :
      ( ( arrow_912654623le_Lin @ ( B @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL )
     => ( arrow_912654623le_Lin @ ( A @ ( B @ ( arrow_312654597_mktop @ hAPP_f102394819t_bool ) @ hAPP_A1014090479t_bool ) @ ( member1704306684t_bool @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).

thf(779,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le64728819t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_445_subsetD) ).

thf(3843,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le64728819t_bool @ hAPP_f1344932147l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).

thf(151,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun292781289l_bool )
     => ( B @ ( A @ hAPP_f1028172757l_bool ) @ is_fun292781289l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_024) ).

thf(1346,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun292781289l_bool )
     => ( B @ ( A @ hAPP_f1028172757l_bool ) @ is_fun292781289l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(370,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_bool )
     => ( B @ ( A @ hAPP_b805997823l_bool ) @ is_fun1420103068l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order__) ).

thf(2063,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_bool )
     => ( B @ ( A @ hAPP_b805997823l_bool ) @ is_fun1420103068l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(236,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/sandbox2/benchmark/theBenchmark.p',fact_555_nat__less__le) ).

thf(1610,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)],[236]) ).

thf(1,conjecture,
    p @ ( f @ hAPP_f1817389232t_bool ) @ ( d @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ( p @ ( f @ hAPP_f1817389232t_bool ) @ ( d @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(886,plain,
    ~ ( p @ ( f @ hAPP_f1817389232t_bool ) @ ( d @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(480,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_order__less__not__sym) ).

thf(2549,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(438,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
    <=> ( ~ ( A @ ( B @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
        & ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_401_less__fun__def) ).

thf(2353,plain,
    ! [A: $i,B: $i] :
      ( ( ( ~ ( A @ ( B @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ~ ( A @ ( B @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(290,axiom,
    ! [A: $i] :
      ( ( top_to846262053l_bool @ ( cOMBK_1918246033t_bool @ hAPP_f633903640l_bool ) @ ( A @ pi_fun1555365306t_bool ) )
      = top_to1849101472l_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_Pi__UNIV) ).

thf(1827,plain,
    ! [A: $i] :
      ( ( top_to846262053l_bool @ ( cOMBK_1918246033t_bool @ hAPP_f633903640l_bool ) @ ( A @ pi_fun1555365306t_bool ) )
      = top_to1849101472l_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(125,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_Arr859726945e_indi )
        & ( A @ is_fun2015243113i_bool ) )
     => ( B @ ( A @ hAPP_A416869060i_bool ) @ is_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__HOL__O) ).

thf(1268,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_Arr859726945e_indi )
        & ( A @ is_fun2015243113i_bool ) )
     => ( B @ ( A @ hAPP_A416869060i_bool ) @ is_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(789,axiom,
    ( ( e @ ( p @ ( arrow_163947511_mkbot @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( e @ ( c @ ( p @ ( arrow_1046586475_above @ cOMBB_930893948e_indi @ hAPP_f1044120523t_bool ) @ ( cOMBC_1377016489t_bool @ hAPP_f114580065t_bool ) @ hAPP_A711952286t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( e @ ( p @ ( arrow_312654597_mktop @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( d @ ( e @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
  <=> ( lba @ ( lab @ ( n @ ( h @ ( ord_less_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ ( cOMBC_1373788917t_bool @ hAPP_f1283354413t_bool ) @ hAPP_f1898540574t_bool ) @ ( cOMBC_1894996001t_bool @ hAPP_f1975142533t_bool ) @ hAPP_f590186314t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( a @ ( b @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/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(3886,plain,
    ( ( ( lba @ ( lab @ ( n @ ( h @ ( ord_less_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ ( cOMBC_1373788917t_bool @ hAPP_f1283354413t_bool ) @ hAPP_f1898540574t_bool ) @ ( cOMBC_1894996001t_bool @ hAPP_f1975142533t_bool ) @ hAPP_f590186314t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( a @ ( b @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
     => ( e @ ( p @ ( arrow_163947511_mkbot @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( e @ ( c @ ( p @ ( arrow_1046586475_above @ cOMBB_930893948e_indi @ hAPP_f1044120523t_bool ) @ ( cOMBC_1377016489t_bool @ hAPP_f114580065t_bool ) @ hAPP_A711952286t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( e @ ( p @ ( arrow_312654597_mktop @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( d @ ( e @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
    & ( ( e @ ( p @ ( arrow_163947511_mkbot @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( e @ ( c @ ( p @ ( arrow_1046586475_above @ cOMBB_930893948e_indi @ hAPP_f1044120523t_bool ) @ ( cOMBC_1377016489t_bool @ hAPP_f114580065t_bool ) @ hAPP_A711952286t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( e @ ( p @ ( arrow_312654597_mktop @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( d @ ( e @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
     => ( lba @ ( lab @ ( n @ ( h @ ( ord_less_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ ( cOMBC_1373788917t_bool @ hAPP_f1283354413t_bool ) @ hAPP_f1898540574t_bool ) @ ( cOMBC_1894996001t_bool @ hAPP_f1975142533t_bool ) @ hAPP_f590186314t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( a @ ( b @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).

thf(134,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/sandbox2/benchmark/theBenchmark.p',fact_662_less__Suc__eq__le) ).

thf(1299,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)],[134]) ).

thf(592,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/sandbox2/benchmark/theBenchmark.p',fact_438_subsetD) ).

thf(3076,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)],[592]) ).

thf(82,axiom,
    b @ is_Arr723427730le_alt,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_b____) ).

thf(1120,plain,
    b @ is_Arr723427730le_alt,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(388,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le2143686384l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_443_subsetD) ).

thf(2138,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le2143686384l_bool @ hAPP_f1216491309l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1619170513t_bool @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(117,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/sandbox2/benchmark/theBenchmark.p',fact_572_termination__basic__simps_I2_J) ).

thf(1236,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)],[117]) ).

thf(413,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_344067350l_bool @ hAPP_f1692576003l_bool ) @ hAPP_f574392641l_bool ) @ hAPP_f1733357041l_bool ) )
      = ( B @ ( C @ ( A @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wy) ).

thf(2241,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_344067350l_bool @ hAPP_f1692576003l_bool ) @ hAPP_f574392641l_bool ) @ hAPP_f1733357041l_bool ) )
      = ( B @ ( C @ ( A @ hAPP_f1332197581l_bool ) @ hAPP_f560517119l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(544,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/sandbox2/benchmark/theBenchmark.p',fact_156_linorder__neq__iff) ).

thf(2898,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)],[544]) ).

thf(715,axiom,
    ! [A: $i] :
      ( ( A @ ( top_top_bool @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( ( A @ hBOOL )
      <=> ( top_top_bool @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_356_top__le) ).

thf(3570,plain,
    ! [A: $i] :
      ( ( A @ ( top_top_bool @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
     => ( ( ( top_top_bool @ hBOOL )
         => ( A @ hBOOL ) )
        & ( ( A @ hBOOL )
         => ( top_top_bool @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).

thf(668,axiom,
    c @ is_Arr723427730le_alt,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_c____) ).

thf(3411,plain,
    c @ is_Arr723427730le_alt,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).

thf(226,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun292781289l_bool )
     => ( B @ ( A @ hAPP_f322109294l_bool ) @ is_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyls_023) ).

thf(1582,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun292781289l_bool )
     => ( B @ ( A @ hAPP_f322109294l_bool ) @ is_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(784,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_order__less__imp__le) ).

thf(3869,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
     => ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).

thf(47,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBS_nat_bool_bool ) @ hAPP_nat_bool ) )
      = ( C @ ( B @ hAPP_nat_bool ) @ ( C @ ( A @ hAPP_n1006566506l_bool ) @ hAPP_bool_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U) ).

thf(1019,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBS_nat_bool_bool ) @ hAPP_nat_bool ) )
      = ( C @ ( B @ hAPP_nat_bool ) @ ( C @ ( A @ hAPP_n1006566506l_bool ) @ hAPP_bool_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(341,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( B != zero_zero_nat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_614_gr__implies__not0) ).

thf(1976,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)],[341]) ).

thf(216,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/sandbox2/benchmark/theBenchmark.p',fact_562_le__iff__add) ).

thf(1550,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)],[216]) ).

thf(770,axiom,
    ! [A: $i] : ( A @ ( suc @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_672_inj__Suc) ).

thf(3817,plain,
    ! [A: $i] : ( A @ ( suc @ inj_on_nat_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).

thf(809,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun1568535512t_bool )
        & ( A @ is_fun1568535512t_bool ) )
     => ( ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
      <=> ( ( A = B )
          | ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_450_subset__iff__psubset__eq) ).

thf(3965,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun1568535512t_bool )
        & ( A @ is_fun1568535512t_bool ) )
     => ( ( ( ( A = B )
            | ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) )
         => ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) )
        & ( ( B @ ( A @ ( ord_le1874503007t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL )
         => ( ( A = B )
            | ( B @ ( A @ ( ord_le1976645739t_bool @ hAPP_f272527115l_bool ) @ hAPP_f2028818269l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).

thf(323,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/sandbox2/benchmark/theBenchmark.p',fact_429_add__less__imp__less__left) ).

thf(1923,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)],[323]) ).

thf(578,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( A != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_less__imp__neq) ).

thf(3020,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(880,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/sandbox2/benchmark/theBenchmark.p',fact_152_linorder__neqE) ).

thf(4206,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)],[880]) ).

thf(324,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun701126715l_bool )
     => ( ( B @ ( A @ ( cOMBK_761999167t_bool @ hAPP_f23348649l_bool ) @ hAPP_f1332130404l_bool ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyl) ).

thf(1925,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun701126715l_bool )
     => ( ( B @ ( A @ ( cOMBK_761999167t_bool @ hAPP_f23348649l_bool ) @ hAPP_f1332130404l_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(232,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/sandbox2/benchmark/theBenchmark.p',fact_415_add__right__imp__eq) ).

thf(1597,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)],[232]) ).

thf(746,axiom,
    ~ ( top_top_fun_nat_bool @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_605_infinite__UNIV__nat) ).

thf(3740,plain,
    ~ ( top_top_fun_nat_bool @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).

thf(309,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_1528317666l_bool @ hAPP_f863441901l_bool ) @ hAPP_f1028172757l_bool ) @ hAPP_f446648900l_bool ) )
      = ( B @ ( C @ ( A @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyl) ).

thf(1880,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ ( cOMBC_1528317666l_bool @ hAPP_f863441901l_bool ) @ hAPP_f1028172757l_bool ) @ hAPP_f446648900l_bool ) )
      = ( B @ ( C @ ( A @ hAPP_f881677315l_bool ) @ hAPP_f322109294l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(204,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1898839893l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_012) ).

thf(1505,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1898839893l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(799,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2015243113i_bool )
        & ( A @ is_fun2015243113i_bool ) )
     => ( ( A != B )
       => ( ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
         => ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_order__neq__le__trans) ).

thf(3918,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2015243113i_bool )
        & ( A @ is_fun2015243113i_bool ) )
     => ( ( A != B )
       => ( ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
         => ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).

thf(235,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_bool )
     => ( ( B @ ( A @ ( cOMBK_bool_nat @ hAPP_b1013836512t_bool ) @ hAPP_nat_bool ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U) ).

thf(1606,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_bool )
     => ( ( B @ ( A @ ( cOMBK_bool_nat @ hAPP_b1013836512t_bool ) @ hAPP_nat_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(503,axiom,
    ! [A: $i] :
      ( ~ ( ( A @ hBOOL )
        <=> ( top_top_bool @ hBOOL ) )
    <=> ( top_top_bool @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_less__top) ).

thf(2672,plain,
    ! [A: $i] :
      ( ( ( top_top_bool @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
       => ~ ( ( ( top_top_bool @ hBOOL )
             => ( A @ hBOOL ) )
            & ( ( A @ hBOOL )
             => ( top_top_bool @ hBOOL ) ) ) )
      & ( ~ ( ( ( top_top_bool @ hBOOL )
             => ( A @ hBOOL ) )
            & ( ( A @ hBOOL )
             => ( top_top_bool @ hBOOL ) ) )
       => ( top_top_bool @ ( A @ ( ord_less_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(142,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun20916972t_bool )
     => ( B @ ( A @ hAPP_f431432850i_bool ) @ is_fun2015243113i_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___034) ).

thf(1320,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun20916972t_bool )
     => ( B @ ( A @ hAPP_f431432850i_bool ) @ is_fun2015243113i_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(337,axiom,
    ! [A: $i] : ( A @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_628_lessI) ).

thf(1962,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)],[337]) ).

thf(802,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
     => ( A != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_order__less__imp__not__eq) ).

thf(3924,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)],[802]) ).

thf(331,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/sandbox2/benchmark/theBenchmark.p',fact_651_Suc__lessI) ).

thf(1945,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)],[331]) ).

thf(598,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_order__less__imp__not__less) ).

thf(3096,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(865,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( C @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_xt1_I1_J) ).

thf(4161,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B = C )
     => ( ( C @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
       => ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).

thf(369,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_bool )
     => ( ( B @ ( A @ ( cOMBK_1733734784le_alt @ hAPP_b763490121t_bool ) @ hAPP_P1813625415t_bool ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__prod_Itc__Arrow____Order____Mirabe) ).

thf(2059,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_bool )
     => ( ( B @ ( A @ ( cOMBK_1733734784le_alt @ hAPP_b763490121t_bool ) @ hAPP_P1813625415t_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(874,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/sandbox2/benchmark/theBenchmark.p',fact_147_order__less__not__sym) ).

thf(4189,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)],[874]) ).

thf(63,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f817344902l_bool ) @ is_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl) ).

thf(1069,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f817344902l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(566,axiom,
    ( ( e @ ( p @ ( arrow_163947511_mkbot @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( e @ ( c @ ( p @ ( arrow_1046586475_above @ cOMBB_930893948e_indi @ hAPP_f1044120523t_bool ) @ ( cOMBC_1377016489t_bool @ hAPP_f114580065t_bool ) @ hAPP_A711952286t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( e @ ( p @ ( arrow_312654597_mktop @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( e @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
  <=> ( lba @ ( lab @ ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( h @ ( ord_less_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ ( cOMBC_1373788917t_bool @ hAPP_f1283354413t_bool ) @ hAPP_f1898540574t_bool ) @ ( cOMBC_1894996001t_bool @ hAPP_f1975142533t_bool ) @ hAPP_f590186314t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( b @ ( a @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Am) ).

thf(2980,plain,
    ( ( ( lba @ ( lab @ ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( h @ ( ord_less_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ ( cOMBC_1373788917t_bool @ hAPP_f1283354413t_bool ) @ hAPP_f1898540574t_bool ) @ ( cOMBC_1894996001t_bool @ hAPP_f1975142533t_bool ) @ hAPP_f590186314t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( b @ ( a @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
     => ( e @ ( p @ ( arrow_163947511_mkbot @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( e @ ( c @ ( p @ ( arrow_1046586475_above @ cOMBB_930893948e_indi @ hAPP_f1044120523t_bool ) @ ( cOMBC_1377016489t_bool @ hAPP_f114580065t_bool ) @ hAPP_A711952286t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( e @ ( p @ ( arrow_312654597_mktop @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( e @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) )
    & ( ( e @ ( p @ ( arrow_163947511_mkbot @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( e @ ( c @ ( p @ ( arrow_1046586475_above @ cOMBB_930893948e_indi @ hAPP_f1044120523t_bool ) @ ( cOMBC_1377016489t_bool @ hAPP_f114580065t_bool ) @ hAPP_A711952286t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( e @ ( p @ ( arrow_312654597_mktop @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( e @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL )
     => ( lba @ ( lab @ ( one_one_nat @ ( n @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( h @ ( ord_less_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ ( cOMBC_1373788917t_bool @ hAPP_f1283354413t_bool ) @ hAPP_f1898540574t_bool ) @ ( cOMBC_1894996001t_bool @ hAPP_f1975142533t_bool ) @ hAPP_f590186314t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( b @ ( a @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(819,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/sandbox2/benchmark/theBenchmark.p',fact_265_linorder__linear) ).

thf(4002,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)],[819]) ).

thf(631,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( B = A )
       => ( C @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_xt1_I2_J) ).

thf(3227,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
     => ( ( B = A )
       => ( C @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(157,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/sandbox2/benchmark/theBenchmark.p',fact_268_linorder__not__le) ).

thf(1367,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)],[157]) ).

thf(461,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_order__less__asym) ).

thf(2438,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
     => ~ ( A @ ( B @ ( ord_le382113706t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(428,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/sandbox2/benchmark/theBenchmark.p',fact_263_order__eq__iff) ).

thf(2297,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)],[428]) ).

thf(837,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/sandbox2/benchmark/theBenchmark.p',fact_170_mem__def) ).

thf(4056,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)],[837]) ).

thf(732,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2015243113i_bool )
        & ( A @ is_fun2015243113i_bool ) )
     => ( ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
      <=> ( ( A = B )
          | ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_451_subset__iff__psubset__eq) ).

thf(3637,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2015243113i_bool )
        & ( A @ is_fun2015243113i_bool ) )
     => ( ( ( ( A = B )
            | ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) )
         => ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) )
        & ( ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
         => ( ( A = B )
            | ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).

thf(570,axiom,
    ! [A: $i] : ( A @ ( top_to1849101472l_bool @ hAPP_f446648900l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_top1I) ).

thf(2993,plain,
    ! [A: $i] : ( A @ ( top_to1849101472l_bool @ hAPP_f446648900l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(621,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2015243113i_bool )
        & ( A @ is_fun2015243113i_bool ) )
     => ( ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( B != A )
         => ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_xt1_I11_J) ).

thf(3200,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun2015243113i_bool )
        & ( A @ is_fun2015243113i_bool ) )
     => ( ( B @ ( A @ ( ord_le1028202352i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL )
       => ( ( B != A )
         => ( B @ ( A @ ( ord_le1791992956i_bool @ hAPP_f563440173l_bool ) @ hAPP_f160177134l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(174,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/sandbox2/benchmark/theBenchmark.p',fact_524_add__leE) ).

thf(1417,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)],[174]) ).

thf(522,axiom,
    e @ ( p @ ( arrow_163947511_mkbot @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( e @ ( c @ ( p @ ( arrow_1046586475_above @ cOMBB_930893948e_indi @ hAPP_f1044120523t_bool ) @ ( cOMBC_1377016489t_bool @ hAPP_f114580065t_bool ) @ hAPP_A711952286t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( e @ ( p @ ( arrow_312654597_mktop @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( e @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL,
    file('/export/starexec/sandbox2/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(2771,plain,
    e @ ( p @ ( arrow_163947511_mkbot @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( e @ ( c @ ( p @ ( arrow_1046586475_above @ cOMBB_930893948e_indi @ hAPP_f1044120523t_bool ) @ ( cOMBC_1377016489t_bool @ hAPP_f114580065t_bool ) @ hAPP_A711952286t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( fequal_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( e @ ( p @ ( arrow_312654597_mktop @ cOMBB_640263118e_indi @ hAPP_f2027600413t_bool ) @ ( cOMBC_325526267t_bool @ hAPP_f832306437t_bool ) @ hAPP_A630236912t_bool ) @ ( n @ ( h @ ( ord_less_nat @ cOMBB_552200224e_indi @ hAPP_f1882280879t_bool ) @ ( cOMBC_70761414t_bool @ hAPP_f595617317i_bool ) @ hAPP_n1600508401i_bool ) @ ( if_fun1158274329t_bool @ cOMBB_810329756e_indi @ hAPP_f1931036015t_bool ) @ cOMBS_995062533t_bool ) @ cOMBS_178315313t_bool ) @ ( f @ hAPP_f1817389232t_bool ) @ ( e @ ( c @ ( produc1456060119le_alt @ hAPP_A1171966089le_alt ) @ hAPP_A1561816353le_alt ) @ ( member720722004le_alt @ hAPP_P1151433609l_bool ) @ hAPP_f1733357041l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(4262,plain,
    $false,
    inference(e,[status(thm)],[892,1322,1718,2094,1469,4169,1105,1840,1850,1982,2559,2544,1179,3566,1295,1036,2822,1586,1501,2744,1190,3053,4101,2336,2031,4062,1767,4022,1729,2463,1899,2280,3172,1686,2250,1855,1750,1005,3040,3910,3108,3012,2282,3498,1692,1305,1437,1211,3990,4037,2309,2940,1406,2622,3858,2808,1522,3762,1808,3417,3460,2947,1939,3959,3098,1073,1173,4105,3217,1671,3120,1310,4097,2918,2448,2712,1233,2042,2146,1458,4026,3044,1164,2316,3446,3414,3481,1063,2844,1507,1222,2360,1095,3634,2432,4079,2020,973,3809,2400,2405,2869,3836,2216,1243,1127,2227,1576,3308,4124,1803,3880,2136,1703,1623,3597,2654,1709,2814,3275,2698,3046,3495,2274,3776,3845,1832,1992,2126,1287,3221,4070,4151,1871,3574,2708,3821,1330,2444,3612,3653,1462,1132,2691,1800,4119,1892,1890,1479,3470,2989,3180,3231,1100,4008,2169,2403,1087,1247,2049,969,2373,1398,3084,3902,1568,2222,3322,3524,2027,1373,4115,2616,1465,4072,1811,1450,4018,3393,1109,2893,3527,3473,3983,3438,2122,3621,2925,3973,1151,937,2291,1383,2254,3300,3923,1960,2555,3290,1183,2073,2017,905,2508,1169,1377,1215,956,1886,3808,1943,2965,1600,1697,4211,1564,2762,4033,2618,1896,2190,2424,2371,1394,2772,3157,3361,2002,998,3606,3211,2154,1863,1651,2011,3582,920,3450,925,1338,3995,2641,2660,2000,1604,2922,3767,3054,2083,4031,1736,1274,2409,3603,2596,1355,1487,3742,4204,3134,2528,2589,3735,3827,2428,1343,4016,1042,952,1570,1676,3207,3514,3778,1238,2015,3286,1883,3271,3269,4140,1365,1920,3198,3556,1888,3546,1787,2344,1392,1740,1573,3282,1423,2332,3314,2820,2872,1951,3894,1819,4187,889,1079,1027,2213,3727,1281,3647,2112,1012,4027,3731,1592,2100,980,2694,3963,1878,1138,3078,1755,3060,1350,1936,1089,3782,1541,2157,1143,1270,3122,1017,2685,2973,1121,3381,1064,1096,2509,1672,3632,4095,3205,4219,1493,4049,1964,2561,2419,2349,1160,2877,3094,4167,2053,1842,4191,1584,1791,3428,2551,1016,4180,1039,2450,1297,1451,1456,4068,1668,1932,3819,1720,4223,2968,2285,1114,2581,1060,3540,2497,1002,1852,3760,2862,3074,3005,2272,3364,2140,2756,3215,1525,3755,3802,2203,1241,1695,2883,1071,1185,1732,2909,1434,1857,4184,3834,1318,1846,1054,2963,3321,1187,2440,1026,3508,1167,2645,3422,2995,4004,3675,1906,2936,3660,1251,2176,2391,3890,3111,3696,1374,2524,1631,965,1510,3358,3871,2033,3042,2585,1548,3985,3738,3839,1154,3387,3070,1007,1916,1389,3811,1125,1620,1752,1929,2514,3900,1701,1965,4041,4144,3372,2225,3504,3272,4122,958,1403,3223,1503,3773,2029,1312,3651,4171,3340,1332,2442,2706,2457,1224,2148,3118,2220,1058,1107,3487,1092,3832,1765,3619,3302,3568,2346,3101,2119,1282,3815,2383,1806,2246,1722,3138,1122,3384,2538,1853,3764,2987,2637,3551,1117,1589,996,2284,3106,3468,1771,2945,2896,1690,3182,1376,1439,4107,1307,2065,1175,3456,2605,4103,3800,1162,3192,915,3483,2710,1112,4064,1993,3977,1325,1029,895,1460,2289,2647,943,1022,3861,2842,932,1171,1396,1474,2086,1643,3806,2369,2022,4196,2867,983,2075,1594,1699,3627,2171,2051,2765,1044,1245,1066,1445,2244,1000,3512,1102,2999,3348,3876,922,4209,2984,1973,3009,1948,2952,1873,3936,1203,1467,3395,2037,2124,1990,3292,3444,2239,2816,2914,3031,4136,2614,3576,944,3981,2503,1081,3975,939,3921,2256,4113,3988,1547,2863,4035,1400,971,1647,3209,1531,1098,993,4045,2942,1798,3391,2192,887,1566,3904,954,3462,4200,2407,2386,3608,1230,1716,1637,3554,1901,2044,1220,907,1711,3080,2747,3305,1432,2276,1980,1317,1830,1763,2701,2599,3623,3412,1130,1579,1738,1218,2056,1934,1543,3829,3493,4143,3024,2949,4225,3961,3366,4111,3288,1141,2426,1353,1955,4202,978,2511,1272,3914,3007,4150,2760,3452,3757,1180,2696,4165,2960,1834,3533,1412,1448,1734,2865,2875,1421,2013,4138,1649,3401,2088,3589,3092,976,3874,3188,3548,2194,2611,3928,1781,891,2209,3625,4078,2110,1010,2342,3056,1453,1866,2658,1998,3797,1385,963,1903,1481,946,2971,3780,1558,2174,2389,1476,1341,3484,3789,2855,1639,2811,3104,3501,3003,4010,3516,3136,3368,2956,2081,2912,3267,3896,3529,2362,3793,3351,899,3645,4182,1861,3430,1777,2494,1442,1994,3552,3420,2421,2218,2102,1957,967,3733,3892,1380,1876,1527,3690,3164,1908,2003,3379,4039,1348,1512,1774,2385,3860,3132,1248,3203,3062,1436,3956,3328,1314,1495,2334,2186,3804,2417,2961,2201,918,4157,1335,4024,1561,2704,1056,1789,2714,3196,3426,3506,3843,1346,2063,1610,886,2549,2353,1827,1268,3886,1299,3076,1120,2138,1236,2241,2898,3570,3411,1582,3869,1019,1976,1550,3817,3965,1923,3020,4206,1925,1597,3740,1880,1505,3918,1606,2672,1320,1962,3924,1945,3096,4161,2059,4189,1069,2980,4002,3227,1367,2438,2297,4056,3637,2993,3200,1417,2771]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SCT171+2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.08  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/10.51  % Computer : n002.cluster.edu
% 0.15/10.51  % Model    : x86_64 x86_64
% 0.15/10.51  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/10.51  % Memory   : 8046.5625MB
% 0.15/10.51  % OS       : Linux 6.8.0-71-generic
% 0.15/10.51  % CPULimit : 300
% 0.15/10.51  % WCLimit  : 300
% 0.15/10.51  % DateTime : Sat Sep 26 06:40:49 UTC 2026
% 0.15/10.51  % CPUTime  : 
% 0.15/10.51  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.90/11.11  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 2.30/11.54  % [INFO] 	 Parsing done (425ms). 
% 2.30/11.56  % [INFO] 	 Running in sequential loop mode. 
% 3.42/11.94  % [INFO] 	 eprover registered as external prover. 
% 3.42/11.95  % [INFO] 	 Scanning for conjecture ... 
% 4.34/12.21  % [INFO] 	 Found a conjecture (or negated_conjecture) and 884 axioms. Running axiom selection ... 
% 6.01/12.63  % [INFO] 	 Axiom selection finished. Selected 883 axioms (removed 1 axioms). 
% 7.45/13.11  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 7.86/13.15  % [INFO] 	 Type checking passed. 
% 7.86/13.15  % [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 ... 
% 31.93/19.14  % External prover 'e' found a proof!
% 31.93/19.14  % [INFO] 	 Killing All external provers ... 
% 31.93/19.15  % Time passed: 8486ms (effective reasoning time: 7582ms)
% 31.93/19.15  % 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)>
% 31.93/19.16  % Axioms used in derivation (883): help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__043, fact_266_le__fun__def, fact_25_top1I, fact_523_in__below, fact_337_xt1_I8_J, fact_82__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_, fact_222_Pi__UNIV, fact_132_order__less__imp__not__eq2, fact_509_subsetI, fact_566_add__le__mono1, fact_60_not__top__less, fact_679_less__eq__Suc__le__raw, fact_130_order__less__imp__triv, fact_395_add__less__le__mono, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell, fact_667_one__is__add, fact_556_le__eq__less__or__eq, fact_74__096Lba_A_058_ALin_096, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__prod_Itc__Arrow_, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Product____Type__Ounit_Mtc__Nat__Onat_J_Mtc_, fact_180_pred__equals__eq2, fact_493_pred__subset__eq, fact_572_termination__basic__simps_I2_J, help_If_3_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqm, help_If_1_1_If_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqm, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__O_015, fact_673_Suc__neq__Zero, gsy_c_FuncSet_OPi_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc_, fact_490_rev__predicate1D, fact_339_xt1_I8_J, fact_184_inv__f__eq, gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__039, help_COMBK_1_1_COMBK_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Arrow___, gsy_c_Arrow__Order__Mirabelle__wylsunqmtb_OLin, fact_158_order__less__irrefl, gsy_c_hAPP_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obool, fact_67_less__top, fact_264_order__eq__iff, fact_602_finite__Collect__le__nat, fact_144_order__less__not__sym, fact_98_xt1_I10_J, fact_684_inc__induct, fact_336_xt1_I8_J, gsy_v_Lab____, fact_84_n_I2_J, fact_283_order__le__less, fact_175_mem__def, fact_494_pred__subset__eq, fact_275_less__le__not__le, fact_215_PiE, fact_218_PiE, fact_357_top__le, fact_663_less__eq__Suc__le, fact_400_less__fun__def, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Arrow____Order____Mirabelle__, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Arrow____Order____Mirabell_025, gsy_c_Hilbert__Choice_Oinv__into_000tc__Arrow____Order____Mirabelle____wylsunqmt, fact_448_psubset__eq, fact_199_PiE, help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__Nat__Onat_U, fact_616_neq0__conv, fact_133_order__less__imp__not__eq2, fact_166_UNIV__def, gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__041, fact_111_ord__less__eq__trans, fact_346_top__greatest, fact_95_order__less__asym, fact_626_ex__least__nat__le, fact_397_injI, gsy_c_hAPP_000tc__fun_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_Mtc__009, gsy_c_hAPP_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb__Oalt_Mtc__042, gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__fun_Itc__fun_Itc__Arrow____Orde, fact_689_Suc__le__D, fact_544_below__Lin, help_fconj_3_1_U, fact_52_top__apply, help_COMBS_1_1_COMBS_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000, fact_64_less__top, fact_245_xt1_I4_J, fact_622_le__0__eq, fact_646_less__Suc__eq, fact_422_add__le__imp__le__left, fact_376_inj__on__id2, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U, fact_385_inv__into__f__f, fact_471_set__rev__mp, fact_299_order__less__imp__le, help_fequal_2_1_fequal_000tc__Nat__Onat_T, fact_541_eq__imp__le, fact_358_top__le, fact_128_order__less__imp__triv, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___036, fact_76__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096, fact_440_subsetD, fact_126_order__less__asym_H, fact_488_equalityD2, fact_101_order__less__trans, fact_235_xt1_I5_J, fact_578_funcsetI, fact_643_add__Suc, gsy_c_hAPP_000tc__fun_Itc__Product____Type__Ounit_Mtc__HOL__Obool_J_000tc__fun_I, fact_323_order__less__le__trans, gsy_c_Orderings_Otop__class_Otop_000tc__fun_Itc__Arrow____Order____Mirabelle____, fact_284_order__le__less, fact_540_nat__le__linear, fact_442_subsetD, fact_210_PiE, help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Arrow____Order____Mirabelle____wyl, fact_224_order__refl, fact_160_order__less__irrefl, fact_474_set__rev__mp, fact_522_psubset__trans, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyl_031, fact_318_xt1_I11_J, fact_276_less__le__not__le, fact_156_linorder__neq__iff, fact_388_inv__into__f__eq, gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It, fact_499_pred__subset__eq, fact_404_Pi__anti__mono, fact_214_PiE, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Arrow____Order____Mirabel, fact_304_linorder__antisym__conv2, fact_255_order__antisym__conv, fact_30_top1I, fact_225_order__refl, fact_585_Pi__I_H, fact_6__C2_C, fact_405_pred__subset__eq2, fact_559_less__or__eq__imp__le, fact_461_equalityE, fact_444_subsetD, fact_306_order__le__imp__less__or__eq, fact_492_subset__refl, fact_648_not__less__less__Suc__eq, fact_624_add__gr__0, fact_94_order__less__asym, fact_421_one__reorient, fact_300_order__less__imp__le, fact_403_Pi__anti__mono, fact_464_set__mp, fact_319_xt1_I11_J, fact_61_not__top__less, fact_47_iso__tuple__UNIV__I, fact_528_nat__neq__iff, fact_50_top__apply, fact_22_Pair__eq, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order____Mirabel_027, gsy_c_Finite__Set_Ofinite_000tc__prod_Itc__Arrow____Order____Mirabelle____wylsun, help_COMBC_1_1_COMBC_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000_049, fact_0_assms_I3_J, fact_644_add__Suc__right, fact_79__096_Ib_M_Aa_J_A_126_058_ALab_096, fact_354_top__unique, fact_209_PiE, fact_169_mem__def, fact_412_subset__UNIV, fact_413_subset__inj__on, fact_447_psubset__eq, gsy_v_b____, fact_420_ab__semigroup__add__class_Oadd__ac_I1_J, fact_535_nat__add__left__commute, fact_653_less__SucE, gsy_c_hAPP_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wylsunqmtb___033, fact_664_less__iff__Suc__add, fact_591_inj__onI, fact_120_xt1_I9_J, fact_551_add__less__mono1, fact_603_card__UNIV__unit, gsy_v_Lba____, fact_277_less__le__not__le, fact_428_add__le__cancel__right, help_fTrue_1_1_T, fact_293_xt1_I12_J, fact_470_set__mp, fact_693_nat_Oexhaust, fact_201_PiE, fact_118_ord__eq__less__trans, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__HOL__Obool_Mtc__fun_Itc__prod_Itc__Arrow____, fact_41_iso__tuple__UNIV__I, gsy_c_Set_OCollect_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabelle____wyls, fact_239_order__trans, fact_137_order__less__imp__not__eq, fact_558_le__neq__implies__less, fact_309_order__le__imp__less__or__eq, fact_670_less__Suc0, fact_243_xt1_I4_J, fact_650_less__SucI, fact_529_linorder__neqE__nat, fact_415_add__right__imp__eq, gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__prod_Itc__Arrow____Order__, fact_452_psubset__imp__subset, gsy_c_hAPP_000tc__Arrow____Order____Mirabelle____wylsunqmtb__Oindi_000tc__fun_It_004, fact_512_psubsetD, fact_476_set__rev__mp, fact_504_subsetI, 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_3__096P_A_058_AProf_096, gsy_c_fFalse, fact_191_PiE, fact_345_top__greatest, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__Product____Type__Ounit_J_Mtc_, fact_666_less__add__Suc1, fact_676_Suc__not__Zero, fact_613_gr0I, fact_416_add__imp__eq, fact_135_order__less__imp__not__eq2, fact_100_order__less__trans, fact_517_psubsetD, gsy_c_fTrue, fact_145_order__less__not__sym, fact_355_top__unique, fact_545_inj__on__add__nat, fact_454_psubset__imp__subset, fact_29_top1I, gsy_c_hAPP_000tc__HOL__Obool_000tc__fun_Itc__prod_Itc__Arrow____Order____Mirabel, fact_593_inj__on__cong, fact_263_order__eq__iff, fact_419_add__left__cancel, 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% 31.93/19.16  % No. of inferences in proof: 1770
% 31.93/19.16  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 8486 ms resp. 7582 ms w/o parsing
% 35.09/19.81  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 35.09/19.82  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------